Dr Xavier Gellynck

Dr Bianka Kühne

Executive Summary Final Report

The NetGrow project was a 4-year European FP7 project (May 1, 2010to April 30, 2014). It aimed at enhancing the innovativeness of food small and medium sized enterprises (SMEs) through improved management of network learning and strategic network behaviour. The project combined scientific research with developing network learning tools of practical use to food SMEs, network organisations and policy makers. The project bundled the capacities of universities, research institutions and SMEs organizations from 9 different countries, i.e. Belgium, Ireland, Netherlands, Hungary, Sweden, Denmark, Italy, France and Germany. This project combined research actions at two levels: 1) the focal company level, investigating how a food SMEs' attitudes and preferences towards networks determine its individual network behaviour in order to achieve its business objectives; and 2) the network level, investigating the functioning of the network as a whole and its effect on innovation and economic growth and how network stakeholders can make the network perform better. Based on this research, the project's main findings and conclusions are: 1) There is no network-that-fits-all due to the very diverse innovation and network preferences and needs of food SMEs. Hence, food SMEs and network managers need to set their focus carefully according to the firm's characteristics, experiences and innovation focus in order to achieve a good match of SMEs' needs and demands and the network's offer. 2) Measuring network performance is not straightforward and requires a holistic approach considering both the network and the firm level, because the determinants of performance at these levels can be different (e.g. network diversity has a positive influence on the food SME's firm performance, but not on the performance of the network). Furthermore different stakeholders (e.g. policymakers, network managers, SMEs) have different perspectives on network performance. For certain stakeholders, only a few indicators are needed, while for others (i.e. the policy-makers) many are needed ('they need the bigger picture'). In the end, all research results were combined with insights from innovation and technology management, chain and network science, organizational and communication theory, and useful tools existing in other technology fields resulting in the NetGrow Network Learning Toolbox, which is available for download and usage on www.netgrow.eu/toolbox (i-depot, registration no. 054415). The toolbox was tested and validated by about 960 food SMEs, network managers, policy makers and researchers. Specific information and training was also provided to more than 3800 food SMEs and other relevant stakeholders all over Europe. NetGrow's specific results were disseminated and can still be consulted on www.netgrow.eu, the six newsletters (http://www.netgrow.eu/index.php?hova=17), and by joining the consortium on LinkedIn: http://www.linkedin.com/groups/NetGrow-7429625. Towards the research community, more than 85 scientific papers as well as reports and books were produced. Most of these publications are also useful and interesting for food SMEs, industry associations, network managers and policy makers. In particular, we contributed to open-access special issues on NetGrow of two journals: a) International Journal on Food System Dynamics -Special Issue on Networks and Innovation (Vol. 3, Issue 3) and b) Journal of Chain and Network Science -Special NetGrow Issue (Vol. 14, Issue 2). Finally, a Food Industry Report was prepared at the end of the project, entitled "Open Innovation in the Food Industry: An Evidence Based Guide" and is also available on http://www.netgrow.eu/_doc/Industry_report.pdf The impact of the NetGrow project's findings reach from a greater availability of usable know-how regarding European SME networks and the factors determining success in SMEs for all relevant stakeholders to the development of business tools to enable SMEs to assess their own network needs, interests, and preferences for to allow organizational change and strategic management leading to competitive and sustainable business networks, support the emergence of dynamic and sustainable SME networks capable of promoting and sustaining innovation in the food sector, and finally to support long-term KBBE strategies in the European Research Area (ERA). Furthermore, the project's result should create sustainable growth and further employment by food SMEs and enable policy makers to tailor their strategies in the fields of agriculture and food, competition, enterprise, regional policy, and research and innovation at regional, national and European level. Through the high level of engagement of relevant stakeholders during the project a strong platform for the adoption of the toolbox is provided.

Summary description of project context and objectives

The NetGrow project was a 4-year European FP7 project which started on May 1, 2010 and finished on April 30, 2014. It aimed at enhancing the innovativeness of food SMEs through improved management of network learning and strategic network behaviour. The project combined scientific research with developing network learning tools of practical use to food SMEs, network organisations and policy makers. The project bundled the capacities of universities, research institutions and SMEs organizations from 9 different countries, i.e. Belgium, Ireland, Netherlands, Hungary, Sweden, Denmark, Italy, France and Germany.

PROJECT CONTEXT Strategic network learning is of crucial importance for innovation, and hence for company competitiveness and growth, as it enables the company to expand its resource base and to absorb new trends and technologies. In the food sector, which is characterized by 99% of SMEs, it is observed that companies often fail in establishing a strategic and efficient network; a network which is defined as a set of actors connected by a set of repeated interaction through formal and/or informal ties. The actors are firms (competitors, suppliers, customers, auxiliary businesses etc.), individuals (boundary spanners etc.) knowledge centres (universities and research centres etc.) and other actors (network organizations, governments, specialinterest groups, industry organizations etc.). The ties are relationships between the actors; they may be formal (contractual, institutionalized etc.) or informal (social, trust-based etc.).

The project followed four main ideas set at the beginning of the project:

A. Network learning contributes to innovation, economic growth, employment and sustainable competitive advantage

As products become increasingly modular and knowledge is distributed across organizations and increasingly specialised, innovation has become highly dependent on interaction in networks, both on the local and regional level as on the global stage. Innovation involves exploring new trajectories and anticipating new trends and technologies which requires stocks of knowledge and experience not solely found in-house (Gellynck et al., 2007;Gemunden et al., 1996;Kaufmann and Todtling, 2001). Network relations exist in several forms and in this project a broad definition of the network was used. Our definition of networking encompasses both networking with competitors, suppliers, knowledge centres and with a variety of actors through formal and informal linkages. The NetGrow project generated a profound insight into the relationship between the design of networks and their contribution to innovation in SMEs and sustainable competitive advantage with a particular interest in the interaction between SMEs themselves and also between SMEs and multinational companies (MNCs).

B. Fostering network learning by food SMEs

Obviously, network intensity differs between domains of the economy. Our focus on food SMEs is underpinned by following arguments: The food industry is fundamental to the EU's competitiveness, being the world's largest exporter and importer of food products. On the other hand, the food sector is characterized by a low rate of innovation coupled with a high new product failure rate after market introduction (Stewart-Knox and Mitchell, 2003). In food SMEs, particular barriers are experienced due to their smaller resource base, having an impact on their network behaviour and the effectiveness of network learning (Aragon-Sanchez and Sanchez-Marin, 2005;Asheim et al., 2001). However, it should also be acknowledged that the population of food SMEs is a diverse group ranging from highly to non-dynamic companies. Although this project's main focus was on food SMEs, strongly linked activities in the Knowledge-Based Bio-Economy (KBBE) also deserved attention.

C. Success in network learning depends upon network behaviour and underlying preferences, attitudes and skills

There is convincing evidence that particular groups of companies lack the skills and competences to benefit from networks and network support (Pittaway et al., 2004;Vermeire and Gellynck, 2007). While many companies are aware of the value of networking, they face difficulties when it comes to identifying and exploiting the opportunities present. One part of the explanation lies in the efficiency and effectiveness of policy interventions. The other part of the explanation lies in the attitude of companies towards public network support and networking in general. As such, the NetGrow project developed scientifically underpinned business tools aimed at helping companies to improve their network effectiveness through organisational change and strategic management.

D. Policy strategies for simulating networking

It are not solely successful networks that increase the innovation capacity and performance of the participating companies and their environment, but also the institutional context is a factor in the creation of networks as it embeds knowledge and allows for knowledge creation by enhancing interaction between the available physical and human resources (Malmberg and Maskell, 2006). Characteristic to innovation policies is the emphasis on cooperation between policy domains and disciplines. A particular interest was hence paid to regional policy on the one hand and to EU policy on the other. The research of the NetGrow project delivered efficient policy instruments to EU and regional policy makers, which will help to enhance the creation of dynamic, sustainable and competitive networks in the short term and therefore provide assistance to food SMEs to contribute to economic growth, employment and sustainable development.

CONCEPTS

The four main ideas presented above shaped the foundations of this project, which are synthesized in the conceptual framework presented in figure 1:

In our project, network learning was defined as the exchange of resources between food SMEs and a variety of relevant network actors, vital for developing innovation and hence sustainable economic growth. These exchange relationships can be both formal and informal and are usually a combination of both. To analyse this, two approaches to network learning were combined, in order to address the two perspectives envisaged: the SMEs' perspective on the network and the policy maker's and network organization's perspective on the network of as a whole:  On the left side, the focal company approach, taking the perspective of SMEs using the network to exchange resources in order to develop innovations and increase profit.  On the right side, the network approach, taking the perspective of the network as a whole, with the aim of improving performance in fostering innovation in the food sector as a whole. This distinction reflects the two major different perspectives, stakes and instruments with respect to network learning.

Following these main ideas and concepts, the NetGrow project formulated an answer to the following question: How can networks, by enhancing strategic network behaviour of food SMEs on the one hand and by assessing network performance at the network level on the other, become more innovative and perform better? The response can be found in the NetGrow Toolbox (www.netgrow.eu/toolbox, i-depot, registration no. 054415).

PROJECT OBJECTIVES

The overall objective of the NetGrow project was to enhance network learning leading to increased innovation, economic growth and sustainable competitive advantage for food SMEs. Instrumental for achieving this is usable know-how about network learning, the attitude of food SMEs in different EU member states and the functioning and performance of different types of networks.

The following specific objectives of the project have been addressed and achieved:

 To organise and safeguard the methodological integration between the WPs  To understand the success factors and barriers of network learning, its antecedents and contribution to innovation & economic growth and sustainable competitive advantage  To understand attributes of networks and their respective attribute levels which contribute to effective network learning by SMEs (focal company approach)  To define the optimal design of networks based on segmentation of food SMEs reflecting their preferences for networking (focal company approach)  To develop a prototype tool for measuring the learning performance of networks in the food sector (network approach)  To test the assessment tool, to fine-tune it and to make a first identification of low and high performing networks (network approach)  To effectively enhance the capacity of food SMEs, formal network organization and policy makers in managing their network strategically  To communicate the project findings and network learning toolbox to food SMEs, formal network organizations and policy makers  To coordinate and manage the project from an administrative, technical and strategic point of view

Description of the main S&T results/foregrounds

To improve innovation, economic growth and sustainable competitive advantage in European food SMEs, the NetGrow project combined scientific research at company and network level by investigating the drivers and barriers for network learning and strategic networking behaviour, which are crucial skills required to support innovation.

Within the NetGrow project, scientific research has been conducted in seven work packages (WP) with each WP depending to a certain extend on the input of the preceding one. WP2 formed the basis for all following WPs, WP3 and 4 focused on the company approach, and WP5 and 6 focused on the network approach. All results were then combined in WP7 where the NetGrow Network Learning Toolbox was developed. WP1, 8, and 9 were horizontal work packages, assuring scientific and project-administrative management as well as dissemination.

WP2 investigated the success factors and bottlenecks of network learning in formal, informal and global networks through a case study approach with 28 networks. These case studies conducted were compiled in a book entitled "Mapping formal networks and identifying their role for innovation in EU Food SMEs", which is available on http://www.netgrow.eu/_doc/wp2_d2_1book.pdf.

Focal company level: First, in WP3, the 5 most relevant attributes and levels were identified based on an extensive literature review on SMEs' innovation and network preferences as well as relevant network attributes and their levels. These were then validated and adapted based on brainstorm sessions and Delphi rounds with experts and stakeholders from the food industry. Subsequently, the top 3 identified relevant attributes and levels were considered as the starting point for developing a quantitative web-survey in WP4. The survey was sent to 8175 food SMEs in six countries i.e. Belgium, France, Hungary, Ireland, Italy and Sweden between October 2012 and April 2013. About one third of the food SMEs responded to the web survey, but only 231 responses could be used for the choice-based experiment due to the fact that not all food SMEs filled in the questionnaire completely (i.e. a 3% response rate of eligible questionnaires). The data were analyzed and a report on network preferences (D4.3b) was prepared based on preliminary results. The data analysis turned out to be more difficult than expected due to non-linear relationships and interlinkages between the network attributes and firm characteristics. Further analyses of the choice-based experiment data were performed which constituted the basis for an academic paper in an A1 international, peer-reviewed journal (D4.3a). This scientific paper includes an extensive literature review on network attributes and firm's networking behavior. The results show that in general food SMEs prefer networks with supply chain members, confidential information sharing and where they get support in building their network of partners for innovation. However, when taking firm characteristics and innovation focus into account the preferences change. Food SMEs with collaborative experience prefer networks with research institutions and where they get support to develop innovation (e.g. market information, pilot facilities, etc.). Food SMEs with a focus on market innovation prefer networks with open information sharing and where they get support on how to manage their network of partners for innovation.

Network level:

In WP5 a prototype tool for measuring network performance at network level was developed. The indicators were first indicated through an extensive literature review and subsequently validated at discussion sessions with experts and stakeholders from the food sector (network managers, funding agencies and researchers). The outcome was a list of indicators suitable for measuring network performance at network level. In WP6, the inputs from WP5 were used to develop three questionnaires: Questionnaire 1a (Q1a) was administered to the network manager and Questionnaire 1b (Q1b) was administered to the network members (food SMEs) in form of an online questionnaire. This approach was selected to ensure the collection of accurate, high quality data relating to a specific network whilst minimising respondent fatigue. The second questionnaire (Q2) was a semi-structured questionnaire and adopted a means-end chain approach. The data were collected in six countries (Belgium, Ireland, The Netherlands, Hungary, Denmark, and Germany). First, in October 2012, Q1a was administered to the network managers (D6.2). These network managers subsequently sent the adapted online questionnaire (Q1b) to their members between January and June 2013. Obtaining a sufficient response rate of members per network was challenging (despite modifying the questionnaire following piloting, sending reminders etc. via the network manager) and meant that project partners undertook exhaustive activities (personal contact, attending industry events, etc.) to increase the response rate. However to facilitate the data cleaning and subsequently data analysis process, data collection ceased in June 2013. Data collection was also undertaken within this period for Q2 with food SMEs, network managers, policy makers and other stakeholders of the food industry. To ensure adequate investigation of four aspects of network performance without excessively overburdening respondents 3 partners (UGent, FV and IFAU) addressed the consequences of 2 dimensions of network performance (knowledge sharing and relationship quality) and 3 other partners (TEAG, DEB and UBO) addressed the consequences of 2 further dimensions of network performance (goal attainment and collaboration) (D6.3). Data analysis for Q1a+b was undertaken by using SPSS and AMOS. Data analysis on Q2 was undertaken using Laddermap. Based on the preliminary results of Q1a+b and Q2 and additional sources of documentation, D6.4 was prepared discussing the evolution of the input-output-outcome model (arising from WP5) in coherence with the findings in WP6. After further data analysis a report on high/low performance and associated determinants and consequences (D6.5a) and an academic paper (D6.5b.) were prepared.

In general the results of WP6 indicate that food SMEs' participation in network activities and social interactions within the network are most strongly linked to network performance: just receiving newsletters or other kind of "passive" information is not sufficient to achieve good network performance. Hence, initiatives and tools should focus on promoting participation in network activities (network managers should request feedback from their members in terms of satisfaction, whether the network fulfils their needs, etc.), foster social mechanisms (i.e. culture of shared goals/values/etc.), and assist participant-governed networks to manage their external relations. Furthermore, the network manager's capabilities matter for network performance and because measuring network performance is not straightforward, instead a holistic approach needs to be followed. Different stakeholders (e.g. policy-makers, network managers, SMEs) have different perspectives on what network performance means for them. For certain stakeholders, only a few indicators are needed, while for others (i.e. the policy-makers) many may be needed ('they need the bigger picture'). In conclusion, in the holistic approach both the firm and network level of performance should be considered as the determinants of performance at these levels may be different (e.g. network diversity has a positive influence on the food SMEs' firm performance, but not on the performance of the network).

The overarching WP7 developed a network learning toolbox based on the outcomes of WP 2, 3, 4, 5 and 6. The first draft of the business implications of the research outcomes from these WPs was discussed and refined among the project partners. Additional inputs from WP4 and WP6 were further used to refine the business implications. This was combined with insights from innovation and technology management, chain and network science, organizational theory and communication theory with insight in the food sector and useful tools existing in other technology fields to produce the NetGrow Network Learning Toolbox (D7.1a). Based on the business implications the framework of the network toolbox was distilled. Subsequently field experts (food SMEs, network managers, public actors, etc.) were consulted through in-depth interviews in all countries in order to verify that the framework of the toolbox is in business language. Based on the confrontation, refinements and adaptations a prototype toolbox was developed (D7.1b). In the following stage a training method (D7.2) was developed to market-test the prototype toolbox. The market-testing was done in four regional food networks in The Netherlands, Belgium, Italy, and Hungary following a two-stage testing. In a first workshop, the toolbox was explained to the participants (food SMEs and innovation network stakeholders), who were then asked to provide feedback on their first impression and to apply the toolbox in the time between the first and second workshop. The insights and feedback were used to improve the toolbox prototype and resulted in the toolbox prototype B that was presented in the second stakeholder workshop, where the toolbox and its improvements received further evaluation and suggestions for improvement. The result of this is D7.3 Draft publication 'Description of the network learning toolbox', which was edited into a book and web format in WP8.

At the overall project level, WP1 (methodological integration), WP8 (dissemination) and WP9 (project management) carefully monitored the scientific and project-administrative management as well as the progress of dissemination in the form of newsletters, other promotional material, and scientific publications (see project website). Furthermore, specific efforts were conducted to produce and disseminate a report targeting policy makers (D8.2a -4 issues, see website).

The main outcome of this project is the NetGrow Toolbox (developed in WP7 and 8) which is available on www.netgrow.eu/toolbox (i-depot, registration no. 054415). The final NetGrow Toolbox was presented at the NetGrow Network Learning Day on April 10, 2014 in Brussels, Belgium to 65 participants from food industry, innovation networks, policy and research. A public report is also available at our project's website.

The NetGrow toolbox consists of a set of nine tools (guidelines, questionnaires, recommendations), including links to the NetGrow website. Target groups are food SMEs (including food producers, and manufacturers of technology, equipment and services for the food industry), network managers and policy makers.

The NetGrow Toolbox Book consists of 32 full coloured pages and contains 9 tools:

1. Why networks work? 2. Find your network.

3. Identify your needs. 4. Define Innovation Process Steps. 5. Evaluate your network. 6. Match your needs with the services/activities of your network. 7. How to develop, build and maintain a well-performing network? 8. Customer satisfaction. 9. Recommendations for policy makers.

Why this toolbox

It is observed that SMEs in the food sector often face difficulties in establishing a strategic and efficient network. The NetGrow project focuses on the kind of formal networks typically used by food SMEs that consist of a wide variety of actors such as competitors, suppliers, knowledge centres and a variety of other actors through formal and informal linkages. The NetGrow toolbox has been developed based on the identified business implications of the research carried out in work packages 2-6 of the NetGrow project as well as the feedback from experts and by a two-stage testing by food SMEs, network managers and policy makers of the toolbox. Every NetGrow Partner has contributed with observations, knowledge, experience and advice.

For whom & How to use this toolbox

The NetGrow Network Learning Toolbox is made for food SMEs (not only food producers, but also manufacturers of technology, equipment and services for the food industry), Network managers and policy makers. Food SMEs and Network managers can benefit directly from the use of the toolbox through the embedded tools. Also, policy makers can benefit from the toolbox through the feedback from networks and SMEs on network learning. This will provide policy makers with better insight into where and how networks and food SMEs can be better supported for innovation.

The toolbox is presented as a recipe book which can be consulted to find inspiration and the "right" recipe for the user's personal network capabilities. The toolbox is in particular tailored for SMEs and Network organizations in the food sector. The NetGrow Toolbox book is supported by a website that contains all tools that are available in the NetGrow Toolbox Book as downloadable pdf. Furthermore the website offers additional information material, secondary literature and links to informative websites that relate to the content of the toolbox. The website gives also access to a database of innovation networks in Europe with relevance for the food sector. The aim of this database is to support SMEs in their decision making process before joining a network and to provide a better understanding about the different types of network and the services /activities that networks are offering. Managers of food networks can provide their network details, their offered activities and services to the database for profiling and policy makers will gain a better understanding of the variety of networks needed to serve the variety of needs of food SMEs.

A total of 1500 hardcopy books "NetGrow Toolbox -Tools for open innovation in the food industry" were printed and can be ordered via Karen Hamann, IFAU, www.ifau.dk (ISBN: 9789081609395) or any other partner of the NetGrow consortium (see below for contact details).

3 The potential impact and the main dissemination activities and exploitation of results

POTENTIAL IMPACT

Five main areas of impacts were identified in the beginning of the NetGrow project:

1) Greater availability of usable know-how regarding European SMEs networks Within NetGrow, know-how was created through state-of-the-art scientific research and subsequently made available by structuring and transforming the created know-how according to the dissemination plan to European SMEs, associations, policy makers and scientists. The final result is the NetGrow toolbox available on www.netgrow.eu/toolbox (i-depot, registration no. 054415), which was market-tested and received good feedback from about 960 food SMEs associations, network managers and policy makers. Furthermore, a Food Industry Report was prepared at the end of the project, entitled "Open Innovation in the Food Industry: An Evidence Based Guide" and is also available on http://www.netgrow.eu/_doc/Industry_report.pdf 2) Develop business tools to enable SMEs to assess their own network needs, interests and preferences and to allow organisational change and strategic management leading to competitive and sustainable business networks The research conducted in WP3 and WP4 focused on the food SMEs' perspective in order to assess the food SMEs' network preferences. The results formed the basis for three tools within the NetGrow Toolbox: "Find your network", "Identify your needs", and "Match your needs to the services/activities of your network".

3) Support the emergence of dynamic and sustainable SMEs networks capable of promoting and sustaining innovation in the food sector

The main impact of the NetGrow activities refer to stimulating the strategic networking behaviour of food SMEs, network organizations and policy makers and in developing these networks. Thereby the complexity of these networks is taken into account (WP5 and 6) and consequently specific actions are proposed and targeted for the different network actors in the network learning toolbox. The according tools in the NG Toolbox for food SMEs and network managers are as follows: "Evaluate your network", "Create excellent networks", and "Customer satisfaction".

4) Provide information and advice to policymakers and regulatory bodies regarding the factors determining success in SMEs

The research activities in NetGrow also aimed at increasing the policy maker's understanding of food SMEs in relation to their network preferences, behaviour and needs. A third and fourth issue of "relevant results to policy makers" (D8.2) was produced based on the findings of WP3, 4, 5, 6, and 7. These reports are available on www.netgrow.eu -publications. Furthermore, the NetGrow Toolbox contributes to the implementation of the EU innovation policy in particular to the ambition of stimulating cooperation between public and private stakeholders.

5) Support long-term KBBE strategies in the European Research Area (ERA)

Since the network concept is inherent to all KBBE policies for the intensive exchange of knowledge and resources between sectors and stakeholders, the final results of the NetGrow project support the long-term KBBE strategies in the ERA by providing clear indications on how to enhance strategic network behaviour and learning, and efficient network management in order to improving the innovation capacity of European food SMEs.

SOCIETAL IMPLICATIONS

The NetGrow project engaged with societal actors beyond the research community, such as governments, public bodies, policy makers, network managers, food SMEs and other industry stakeholders. Through communication, dissemination and encouraging the usage of the project's results, the consortium aimed to enhance the strategic network behaviour of food SMEs and consequently their innovation capacity, and at improving the network's offer towards more successful innovation and better performance for their members. In the long-term improving the innovative capacity of food SMEs should create sustainable growth and hence further employment. Furthermore, the generated project results should enable policy makers to tailor their strategies in particular in the fields of agriculture and food, competition, enterprise, regional policy, and research and innovation at regional, national and European level. This high level of engagement provides a strong platform for the adoption of the toolbox.

MAIN DISSEMINATION ACTIVITIES AND EXPLOITATION OF RESULTS

The NetGrow consortium has developed 2 main electronic media tools to facilitate the dissemination of the scientific outputs from NetGrow, which are the NetGrow project website and the NetGrow newsletter.

At the end of the project, the NetGrow website had 3327 visitors (56.9% new visitors, 43.1% returning visitors in the last 18 months of the project). Most of the visitors to the website come from the Netherlands (22.06%), Ireland (12.77%), Hungary (11.27%), Italy (10.37%) and Belgium (10.04%). However, the website has also attracted visitors from France, Sweden, Germany, Denmark, United States, Spain, United Kingdom, India, Brazil, Japan, Thailand, Ukraine and Romania (See Figure 2 below). To complement the NetGrow website, a specific web page1 was created for the NetGrow Network Learning Day Event which took place on April 10, 2014 in Brussels, Belgium. FV, as leaders of WP8, also created and manages the LinkedIn page2 for the NetGrow Group. In additions to the NetGrow website and NetGrow's social media a database search engine was included into the website where registered users can search for different kinds of learning and innovation networks within the NetGrow Toolbox area.

The 'flagship' mode of communication to relevant stakeholders has been the NetGrow Newsletter. Six issues of the NetGrow Newsletter were published, made available on the NetGrow website (http://www.netgrow.eu/index.php?hova=17), and disseminated to over 198 subscribers via e-mail. The NetGrow Newsletter has maintained the interest of its readership based on the proportion of newsletter emails opened and specific articles clicked upon. Thirty-seven per cent of subscribers (in the last 18 months of the project as against 40% in middle 18 months of the project) browse the newsletters that arrive in their inbox, of which the same proportion as per the middle period (46%) click to read specific contributor articles. The NetGrow consortium also supported the EC's efforts in publishing the NetGrow Results in Brief "Sustainable growth for food firms through networking" (http://cordis.europa.eu/result/brief/rcn/11520_en.html).

In order to promote the NetGrow Toolbox to the target audience of our project, i.e. food SMEs, network managers, and policy makers, the consortium organized a Network Learning Day on April 10, 2014 in Brussels, Belgium. Additionally, in particular focused on food SMEs, specific sessions were organized in the nine participating countries between January and May 2014 reaching more than 3800 food SMEs and other relevant stakeholders, to introduce them to the background and usefulness of the NetGrow Toolbox.

With regards to dissemination towards the research community, more than 85 scientific papers as well as reports and books were produced for scientific conferences and academic journals. Most of these publications are also useful and interesting for food SMEs, industry associations, network managers and policy makers. In particular, the consortium contributed to open-access special issues on NetGrow of two journals: a) International Journal on Food System Dynamics -Special Issue on Networks and Innovation (Vol. 3, Issue 3. URL: http://centmapress.ilb.uni-bonn.de/ojs/index.php/fsd/issue/view/15) b) Journal of Chain and Network Science -Special NetGrow Issue (Vol. 14, Issue 2. URL: http://wageningenacademic.metapress.com/content/k76rx2v84856/?p=1dff27de5ee446bc95e0933 168bab7d0&pi=0#.U7KxiEDuaId, guest editor: Loic Sauvee)

At the end of the project a Food Industry Report was prepared, entitled "Open Innovation in the Food Industry: An Evidence Based Guide" (http://www.netgrow.eu/_doc/Industry_report.pdf).

Figure 2 :

 2 Figure 2: Location of visitors to the NetGrow Website

Conceptual Framework of the NetGrow Project

	Focal company approach		Network approach
			Network Learning	Network
	Food SME s Network preference	Network behaviour	Exchange of resources through formal/ relationships informal	Food companies (SMEs and MNEs) Policy makers Scientists Civil Society Organizations KBBE companies	Success factors
	Strategic management	Innovation	Network performance	Policy strategies (KBBE)
	tools
		Economic growth and sustainable
			competitive advantage
	Figure 1:

https://dl.dropboxusercontent.com/u/383026/netgrow/index.html

http://www.linkedin.com/groups/NetGrow-7429625/about

Food Valley NL F. Fortuin, R. Kleijwegt, R. Klefoth Frances.fortuin@foodv alley.nl IFAU K. Hamann karen@ifau.dk Institut Polytechnique LaSalle Beauvais L. Sauvee, Z. Abdirahman loic.sauvee@lasallebeauvais.fr Skane Food Innovation Network M. Nilsson, C. Sia Ljungström Magnus.Nilsson@fek.lu .se Teagasc -the Agriculture and Food Development Authority M. Henchion, D. Sorenson Maeve.Henchion@teag asc.ie University of Bologna D. Viaggi, M. Raggi, F. Minarelli, R. Ghelfi, R. Fanfani, P. Chatzinikolaou davide.viaggi@unibo.it University of Bonn G. Schiefer, J. Deiters, E. Heuß schiefer@uni-bonn.de University of Debrecen J. Felfoldi, K. Kovács jfelfoldi@agr.unideb.hu

The address of the project public website

The project website has been designed at the beginning of the project to offer a platform for communicating the results and achievements of the project to food SMEs, associations, network managers, policy makers, and the wider public. Up to 24 months after the end of the project, the website will continuously be updated and inform about the further results linked to the project. This website is located at a domain specifically registered for the project: www.netgrow.eu

List of all beneficiaries and Coordinator contact details

The NetGrow Consortium:

Partner logo Partner name Person name Main contact address

Ghent University X. Gellynck, B. Kühne, V. Lefebvre Xavier.Gellynck@UGen t.be


Sureshk Gad

Antonio Osorio-Cordero

Rogelio Lozano

Ruben A Garrido

S K Gadi

A Osorio

Delayed system •

Keywords:

This paper presents a stability analysis of the interaction between a human and a linear mov-ing Force Augmenting Device (FAD). The analysis employs a mathematical model of the human arm, the FAD and their interaction. As a depart from past works, this article presents a stability analysis considering time-delays in the human model. A key ingredient in the analysis is the use of the Rekasius substitution for replacing the time-delay terms. It is proved that the human machine interaction is stable when the human model has no delays. When delays are considered in the human model, the analysis provides an upper bound for the time-delays preserving a stable interaction. Numerical simulations allow to assess the human-FAD interaction. An experiment is performed with a laboratory prototype, where a human operator lifts a load. It is observed that the human machine interaction is stable and the human opera-tor is able to move the load to a desired position by experiencing very little effort.

Introduction

Recently, there has been a lot of interest in developing exoskeletons and force augmenting devices [START_REF] Guizzo | The rise of the body bots [robotic exoskeletons[END_REF], i.e. mechanical systems that are worn by humans in such a way as to increase their force. There exist many possible applications for these devices; for instance, in industries where it is commonly required to move heavy loads. This task is mostly done by machines, which are usually controlled by humans who do not necessarily feel the force exerted on the load. This may lead to unsafe operations in confined spaces with obstacles. Exoskeletons and force augmenting devices (FAD) represent a possible solution to this problem [START_REF] Kim | Development of the heavy load transferring task oriented exoskeleton adapted by lower extremity using qausi-active joints[END_REF]. Indeed a FAD amplifies the human strength and allows the operator handling heavy loads but still feeling the effort performed to move a load [START_REF] Snyder | A novel material handling system[END_REF].

There are many papers in the literature dealing with human-machine interaction [START_REF]Hardiman 1 prototype project[END_REF][START_REF] Kazerooni | Human machine interaction via the transfer of power and information signals[END_REF][START_REF] Kazerooni | Human-robot interaction via the transfer of power and information signals[END_REF][START_REF] Lee | Power assist control for leg with hal-3 based on virtual torque and impedance adjustment[END_REF][START_REF] Yamamoto | Development of power assisting suit for assisting nurse labor[END_REF][START_REF] Kazerooni | The Berkeley lower extremity exoskeleton[END_REF][START_REF] Kong | Control of exoskeletons inspired by fictitious gain in human model[END_REF], however the stability of the proposed control algorithms has not been thoroughly studied. In order to study the stability of the human machine interaction we need to introduce a model for the human behaviour. There are several possible models for the human operator [START_REF] Merton | Speculations on the servo-control of movement[END_REF][START_REF] Mcintyre | Servo hypotheses for the biological control of movement[END_REF][START_REF] Schweighofer | Role of the cerebellum in reaching movements in humans. i. distributed inverse dynamics control[END_REF][START_REF] Schweighofer | Role of the cerebellum in reaching movements in humans. ii. a neural model of the intermediate cerebellum[END_REF][START_REF] Oshima | Robotic analyses of output force distribution developed by human limbs[END_REF] and we have selected the model proposed in [START_REF] Mcintyre | Servo hypotheses for the biological control of movement[END_REF] because it takes into account the delays present in the human reflexes.

In this paper we present a simple controller for the FAD and a stability proof of its interaction with a human operator. We first study the stability of the interaction considering no delays in the human model. The closed loop system is of 4 th order and the proof of the stability is carried out using the Routh-Hurwitz stability criterion. Furthermore, we have also studied the stability considering delays in the human model. An upper bound for the delays has been found such that the stability is preserved. The human-FAD interaction is illustrated through numerical simulations.

The paper is organized as follows: The next section introduces a model of the FAD, a model of a human operator and the control algorithm proposed in [START_REF] Gadi | Stability analysis and experiments for a force augmenting device[END_REF][START_REF] Gadi | Stability analysis for a force augmenting device considering delays in the human model[END_REF] for the FAD. This is followed by a section providing the stability proof for the system ignoring delays in the human model. Subsequently, the stability is studied considering that both delays in the human model are equal. In the next section a stability analysis is performed assuming that both delays in the human model are independent. Simulation and experimental results support the results obtained. Concluding remarks are given in the final section.

Mathematical Model

The force augmenting device (FAD) considered in this paper is shown in Figs. 1a and b depicts its block diagram. This figure also shows the interaction between a human operator and the FAD. The FAD has a moving block of 24 kg connected to a ball-screw mechanism, and acts as the load to be lifted by the human operator. The ball-screw mechanism is driven by a DC servo motor. Force and position sensors are attached to the FAD to capture the force exerted by the human on the moving block and to measure its position respectively. The total force exerted on the moving block (F ) can be decomposed as

F (t) = F A (t) + F e (t) -W (1)
where F A is the force exerted by the motor on the moving block, F e is the force exerted by the human on the moving block, W = Mg is the weight of the moving block, M is the mass of the moving block, g is the acceleration due to gravity and t is the time. Considering zero initial conditions, the dynamics of the moving block can be written as

y e (s) F (s) = 1 Ms 2 + K f s (2)
where y e is the position of the moving block, K f is the viscous friction coefficient of the FAD and s is the Laplace transform complex variable. The human model used for describing the human operator arm is based on a servo hypothesis proposed in [START_REF] Mcintyre | Servo hypotheses for the biological control of movement[END_REF], where the spinal cord actuates the muscles of the musculoskeletal system by processing the signals received from the brain, and the position and velocity feedback signals produced by the sensory organs of the musculoskeletal system. The position reached by the human arm is not exactly equal to the position commanded by the spinal cord due to the arm inertia, so the command given by the spinal cord to the musculoskeletal system is termed as the virtual position [START_REF] Mcintyre | Servo hypotheses for the biological control of movement[END_REF][START_REF] Latash | Reconstruction of shifting elbow joint compliant characteristics during fast and slow movements[END_REF]. The human brain generates a desired trajectory along which the arm must move; based on the desired trajectory the brain computes a signal and sends it to the spinal cord [START_REF] Schweighofer | Role of the cerebellum in reaching movements in humans. i. distributed inverse dynamics control[END_REF], which is the virtual desired position [START_REF] Mcintyre | Servo hypotheses for the biological control of movement[END_REF]. The musculoskeletal system is modeled as a second order linear transfer function.

1 s 1 Js B + K + G p G v + + + d 2 d 1 + E -1 l a l a y h θ h _ θ vd . θ vd _ _ _ _ θ v _ _ F e F h
The human arm can be modeled as a second order linear dynamic system [START_REF] Mcintyre | Servo hypotheses for the biological control of movement[END_REF][START_REF] Schweighofer | Role of the cerebellum in reaching movements in humans. i. distributed inverse dynamics control[END_REF]. The torque produced at the joint is a function of the actual arm position and its velocity and the desired arm position and velocity. The authors of [START_REF] Mcintyre | Servo hypotheses for the biological control of movement[END_REF] presented a mathematical model for this torque. This model is an improved version based on the virtual trajectory control hypothesis. This model was experimentally validated by the authors of [START_REF] Mcintyre | Servo hypotheses for the biological control of movement[END_REF][START_REF] Schweighofer | Role of the cerebellum in reaching movements in humans. i. distributed inverse dynamics control[END_REF] at various velocities. It is observed that this model is valid up to a velocity around 0.32 m s 1 . Figure 1b shows the dynamics of the musculoskeletal system, which can by modeled as:

τ h (s) = J θh (s) + B θh (s) + K(θ h (s) -θ v (s)) (3)
where τ h is the external torque acting on the human joint, θ h is the human arm position, θ v is the output of the spinal cords reflex action, J is the human arm moment of inertia, B is the viscous friction in the human arm movement and K is the muscle stiffness.

The term θ v represents the virtual arm position. In a human being, the sensory feedback received by the spinal cord is delayed. This delay makes the stability issue challenging. The following equation represents the spinal cord reflex action:

θ v (s) = θ vd (s) + G p (θ vd (s) -θ h (s)e -sd 1 ) +sG v (θ vd (s) -θ h (s)e -sd 2 ) (4)
where θ vd is the virtual desired position, G p and G v are the control parameters of the spinal chord, d 1 is 0.15 0.16 0.17 the delay in the position reflex feedback and d 2 is the delay in the velocity reflex feedback.

The force exerted by the human arm F e on the moving block can be expressed as

F e (t) = -F h (t) = (y h (t) -y e (t))E (5) y h (t) = θ h (t)l a (6)
where F h is the force exerted by the moving block on the human arm, E is the physical compliance of the human flesh, y h is the human arm displacement at the end of the arm and l a is human arm length. The torque exerted by the moving block on the human arm, τ h , can be given as τ h (t) = F h (t)l a = (y e (t)y h (t))El a [START_REF] Lee | Power assist control for leg with hal-3 based on virtual torque and impedance adjustment[END_REF] The following control algorithm [START_REF] Gadi | Stability analysis and experiments for a force augmenting device[END_REF] is applied to the FAD: [START_REF] Yamamoto | Development of power assisting suit for assisting nurse labor[END_REF] where K A is the augmenting factor that amplifies the force exerted by the human operator, K d is the derivative gain and K p is the proportional gain.

F A (t) = (K A -1)F e (t) -K d ẏe (t) -K p y e (t)
Since the input terms W , y vd and sy vd do not affect the stability, these terms can be neglected for the stability study. The characteristic equation for the closed loop system can be written as

P (s) = C 4 s 4 + C 3 s 3 + C 2 s 2 + C 1 s + C 0 ( 9
)
where

C 4 = J M ( 10
)
C 3 = M(B + G v Ke -sd 2 ) + J (K d + K f ) ( 11
)
C 2 = M(El 2 a + K(G p e -sd 1 + 1)) +(K d + K f )(B + G v Ke -sd 2 ) +J (K p + EK A ) ( 12
)
C 1 = (B + G v Ke -sd 2 )(K p + EK A ) +(K d + K f )(El 2 a + K(G p e -sd 1 + 1)) (13) C 0 = (K p + EK A )(El 2 a + K(G p e -sd 1 + 1)) -E 2 K A l 2 a (14)
In the following section we will study the stability of the above polynomial.

Stability Analysis When the Delays are Zero

Considering that d 1 = d 2 = 0, Eq. 9 can be rewritten as

P (s) = A 4 s 4 + A 3 s 3 + A 2 s 2 + A 1 s + A 0 ( 15
A 4 = J M ( 16
)
A 3 = M(B + G v K) + J (K d + K f ) ( 17
)
A 2 = M(El 2 a + K(G p + 1)) +(K d + K f )(B + G v K) +J (K p + EK A ) ( 18
)
A 1 = (B + G v K)(K p + EK A ) +(K d + K f )(El 2 a + K(G p + 1)) ( 19
)
A 0 = EK p l 2 a + (G p + 1)KK p +E(G p + 1)KK A ( 20
)
As per the Routh-Hurwitz stability criterion, the closed loop system is stable if and only if

A 0 > 0; A 1 > 0; A 2 > 0; A 3 > 0; A 4 > 0; A 5 > 0 (21) b 1 := A 3 A 2 -A 4 A 1 A 3 > 0 (22) c 1 := b 1 A 1 -A 3 A 0 b 1 > 0 ( 23
)
The above conditions are indeed satisfied for all the positive values of the involved parameters [START_REF] Gadi | Modelado y control de un dispositivo de aumento de fuerza[END_REF]. In the succeeding sections, a numerical example is introduced to study the stability considering the delays.

Stability Considering Identical Delays

Assume that both delays are the same, i.e.

e -sd = 1 -T s 1 + T s T ∈ , d ∈ + (24)
which is defined when s = jω, ω ∈ . Unlike Pad approximation, this is an exact substitution. This substitution allows to replace the exponential transcendental term associated to the time-delay (i.e. e -sd ) by a rational expression of the variables s and T . It is observed that using this substitution leads to less conservative stability results than the approach employing Lyapunov-Krasovskii functionals [START_REF] Ebenbauer | Stability analysis for timedelay systems using rekasius's substitution and sum of squares[END_REF]. We are using this fact to identify the exact point at which the system goes from stable to unstable. As opposed to other techniques, the values obtained with this approach are accurate. The relation between d , T and ω can be given as [START_REF] Olgac | The direct method for stability analysis of time delayed LTI systems[END_REF][START_REF] Rekasius | A stability test for systems with delays[END_REF]

d = 2 ω arctan (T ω) + lπ l = -∞, ... -1, 0, 1, ..., ∞ (25)
where for a fixed ω each T maps to infinitely many values of d. Substituting (24) into (9), we get

P (s) = B 5 s 5 + B 4 s 4 + B 3 s 3 + B 2 s 2 + B 1 s + B 0 ( 26
)
where

B 5 = J MT (27) B 4 = J M + BMT + J (K d + K f )T -G v KMT (28) B 3 = EMT l 2 a + BM + J (K d + K f ) +G v KM + B(K d + K f )T + J K p T + KMT +EJ K A T -G v K(K d + K f )T -G p KMT (29) B 2 = B(K d + K f ) + J K p + KM + EJ K A +G v K(K d + K f ) + G p KM + BK p T +K(K d + K f )T + EMl 2 a +E(K d + K f )T l 2 a + BEK A T -G p K(K d + K f )T -G v KK p T -EG v KK A T (30) B 1 = BK p + K(K d + K f ) + BEK A +G p K(K d + K f ) + G v KK p + KK p T +E(K d + K f )l 2 a +EK p T l 2 a + EG v KK A + EKK A T -G p KK p T -EG p KK A T (31) B 0 = EK p l 2 a + KK p + EKK A + G p KK p EG p KK A ( 32
)
The estimated values for the laboratory setup shown in Fig. 1a are M = 23.4 kg and K f = 0 N m -1 . The authors in [START_REF] Mcintyre | Servo hypotheses for the biological control of movement[END_REF] use the following parameters for a human arm: flesh is given in [START_REF] Pataky | Viscoelastic response of the finger pad to incremental tangential displacements[END_REF]. Taking l a = 0.35 m and the control parameters K A = 125, K d = 65 kg s -1 and K p = 45 kg s -2 . Substituting these values in P (s), Eq. 26 is rewritten as Since the system is stable when the delays are zero, all the poles are in the left hand side of the complex plane. New poles are introduced from the left hand side of the complex plane as a consequence of the presence of delays [START_REF] Michiels | Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach[END_REF]. The position of the poles in the complex plane as a function of the delay is continuous [START_REF] Michiels | Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach[END_REF][START_REF] Neimark | D-subdivisions and spaces of quasipolynomials[END_REF]. As the delays increase, the poles move towards the right hand side of the plane and finally cross the jω axis. The substitution ( 24) is valid at the moment when the poles are on the imaginary axis just before crossing it.

J = 0.1 N m rad -1 s -1 , B = 0.89 N m rad -1 s -1 , K = 4 N m rad -1 , G p = 2 and G v = 0.
P (s) = 2.
A Routh array can be constructed for Eq. 33 as As per the Routh-Hurwitz stability criterion, when the poles are on the imaginary axis, a row of the Routh array becomes zero and its previous row is called the auxiliary polynomial. The auxiliary polynomial gives the location of the poles on the imaginary axis. Solving B 11 = 0 and considering only real values for T , the solution is T = 2.44372 or T = 0.11131. The auxiliary polynomial (P A ) is given by the next expression

s
P A = B 21 s 2 + 1.
d| l=-1 = -2.9817
The smallest positive delay at which the poles cross the imaginary axis for the first time is called the critical delay (d c ). The critical delay for this system occurs for the values l = 0, d = d c = 0.1599. Repeating the above calculations for the different values of K A , we can obtain the critical delay corresponding to each value of K A . Figure 2 shows the change in the critical delay as a function of the augmenting factor K A .

Stability Considering Independent Delays

In this section let us consider different delays d 1 and d 2 . A Rekasius substitution similar to Eq. 24 for the two time-delays is

e -sd 1 = 1 -T 1 s 1 + T 1 s T 1 ∈ , d 1 ∈ + (35) e -sd 2 = 1 -T 2 s 1 + T 2 s T 2 ∈ , d 2 ∈ + (36)
and the relation between T 1 , ω 1 , and d 1 and T 2 , ω 2 , and d 2 is given by

d 1 = 2 ω arctan (T 1 ω) + lπ l = -∞, ... -1, 0, 1, ..., ∞ (37)
d 2 = 2 ω arctan (T 2 ω) + lπ l = -∞, ... -1, 0, 1, ..., ∞ (38)
Substituting ( 35) and (36) into ( 9), we get a characteristic polynomial of order six. Using the values for the parameters B, E, G p , G v , J , K, K A , K d , K f , K p , l a , M given in the previous section, the following polynomial is obtained. Giving T 1 a numerical value in Eq. 39, results in P (s) depending only on T 2 , giving a similar situation to Eq. 33. The computation for solving T given in the previous section can be used to obtain T 2 , therefore the critical delays corresponding to T 1 and T 2 can be computed using (37) and (38).

P (s) = T 1 T 2 s 6 + (T 1 + T 2 -0.
Varying T 1 in the region [0.001 10] and solving for T 2 critical delays for d 1 and d 2 are obtained, see Fig. 3a. Also, varying K A from 50 to 200, results in Fig. 3b which shows the critical delays of d 1 and d 2 as a function of K A .

Simulation Results

A simulation has been performed on the system shown in Fig. 1a using MATLAB Simulink. A Runge-Kutta solver of 4 th order with a step size of 1 ms is used for the numerical simulation. Simulation is performed with the system parameters given in the previous sections and K A is taken as 125. Let p = (d 1 , d 2 ) be any point on Fig. 3a representing delays. Simulation is performed at p 0 = (0.1599, 0.1599), p 1 = (0, 0.15), p 2 = (0.1, 0.15), p 3 = (0.2, 0.15), p 4 = (0.6, 0.15), p 5 = (0.7, 0.15), p 6 = (0.6, 0.05), p 7 = (0.6, 0.35), p 8 = (0.6, 0.375). The simulation results are shown in Fig. 4.

Another simulation was performed to simulate the interaction between the human and the FAD at a high value of the force augmenting factor i.e. K A = 100 × 10 3 , and considering d 1 = d = 2 = 40 ms. It has been observed from the simulations that the interaction is unstable for the values G p = 2 and G v = 1.11. However, it is observed that the interaction goes from the unstable region to the stable region just by changing the values of the constants internal to the human body, i.e. changing the value of G v to 0.3. These results are shown in Fig. 5. Hence, through the simulations, it is also possible to verify that the human's learning capability helps stabilizing the interaction.

Experimental Results

The prototype designed at the laboratory uses a computer with Windows XP operating system, which runs MATLAB-SIMULINK along with the WinCon software. This setup allows performing a real time experiment with the FAD. We have used a sampling time of 1 ms. The control parameters used for the experiments are K A = 125, K d = 65 kg s -1 and K p = 45 kg s -2 . Figure 6a andb show the experimental results. It can be noted from Fig. 6b that the human operator is experiencing a load of ≈ 2 N ≈ 204 g while lifting a mass of 24 kg.

The prototype at our laboratory remains stable for very high values of the gains. We have tried to reach the instability region by increasing the value of K A but we have not succeeded to render it unstable. The following reasons may be a possible explanation for this behavior. 1. The delays in the human subject's reflex path are very small as compared to the critical delays of the system. 2. The torque produced by the electric motor driving the ball-screw mechanism saturates for high values of K A , and such a non-linearity stabilizes the system.

Conclusion

In this paper we have analysed the stability of the interaction of a human and a FAD. We have considered a general human operator model proposed in [START_REF] Mcintyre | Servo hypotheses for the biological control of movement[END_REF].

We have proved the stability in the case of zero delays using the Routh-Hurwitz criterion. When the human model includes time-delays, we have also found an upper bound for the delays such that the stability is preserved.

It should be pointed out that the actual delays presented by any healthy human being are about four times smaller than the upper bound found for the delays in this study, beyond which instability will occur in the system. For this reason from a practical point of view, it can be considered that the scheme presented is robust enough to delays.

The numerical simulations presented show that if the delays are maintained below the upper bound found, the system is stable.

A real time experiment was conducted in a prototype. It was observed that the human machine interaction is stable and it is also observed that the damping introduced is sufficient enough to maintain the system without any oscillation. It is also observed that the operator is actually exerting a small fraction of the total force needed to lift the weight.

In this paper the stiffness and the viscosity parameters of the human arm have been considered constant. The stability analysis proves that the closed loop will remain stable for any positive values of these two coefficients. In the future we aim at improving the performance of the control strategy in the presence of variations of the stiffness and the viscosity parameters which may occur when changing the user.

  Block diagram of the human-FAD interaction

Fig. 1

 1 Fig. 1 Human operating a force augmenting device

Fig. 2

 2 Fig. 2 Critical delay d c at 50 ≤ K A ≤ 200 in equal delay case (i.e. d 1 = D 2 )

Fig. 3 Fig. 4

 34 Fig. 3 Critical delay for d 1 and d 2

d 1 =

 1 d 2 = d. The substitution proposed by Rekasius is[START_REF] Olgac | The direct method for stability analysis of time delayed LTI systems[END_REF][START_REF] Rekasius | A stability test for systems with delays[END_REF]

Fig. 5

 5 Fig. 5 Simulation results showing the effect of G v in the stability of the human FAD interaction

3 × 10 5 T s 5 +( 2 . 3 × 10 5 - 7 . 5 × 10 4 T )s 4 +( 1 . 4 × 3 +( 1 . 5 × 10 9 - 2 . 9 × 10 9 T )s 2 +( 2 . 5 ×

 31052357544143159299225 10 9 T + 5.5 × 10 6 )s 10 10 -4.6 × 10 10 T )s +1.4 × 10 11(33)

Fig. 6

 6 Fig. 6 Experimental result

  Output of the spinal cords reflex action τ h External torque acting on the human joint B Viscous friction in the human arm movement d 1 Delay in the position reflex feedback d 2 Delay in the velocity reflex feedback E Physical compliance of the human flesh F Total force exerted on the moving block F A Force exerted by the motor on the moving block F e Force exerted by the human on the moving block F h Force exerted by the moving block on the human arm g Acceleration due to gravity G p Control parameter of the spinal chord G v Control parameter of the spinal chord J Human arm moment of inertia Position of the moving block y h Human arm displacement at the end of the arm

	2 Nomenclature θ h Human arm position θ vd Virtual desired position θ v K Muscle stiffness K A Force augmenting gain K d Derivative gain K f Viscous friction coefficient of FAD K p Proportional gain l a Human arm length M Mass of the moving block s Laplace transform complex variable t Time W Weight of the moving block y e

  3T 1 T 2 )s 5 +(23.7T 1 -0.3T 2 + 6 × 10 3 T 1 T 2 + 1)s 4 + (6 × 10 3 T 1 +6 × 10 3 T 2 -1 × 10 4 T 1 T 2 + 23.7)s 3 +(1.1 × 10 5 T 1 -1.2 × 10 4 T 2 -2 × 10 5 T 1 T 2 + 6.2 × 10 3 )s 2 +(6 × 10 5 T 2 -2 × 10 5 T 1 + 1.1 × 10 5 )s

	+6 × 10 5	(39)

Acknowledgments Work carried out in the UMI LAFMIA at CINVESTAV, Mexico in the framework of the Labex MS2T, funded by the French Government, through the National Agency for Research (Reference ANR-11-IDEX-0004-02). The authors would like to thank Gerardo Castro, and Jess Meza, for their help in implementing the electrical setup and Roberto Lagunes for his help in building the mechanical setup. Also, the authors are thankful to the reviewers for their valuable suggestions to improve the paper.


A T Espinoza-Fraire

Yangquan Chen

• A Dzul

• R Lozano

• R Juarez

Keywords: Adaptive control, Adjustment mechanism, Sliding mode control, PD controller

This paper presents an adaptive PD control law by using a modified MIT rule. The adaptation of the controller gains is based on the adjustment mechanism of the MIT rule by the gradient method with three types of sliding-mode control, i.e., first order sliding-mode control, second order sliding-mode (2SM), and high order sliding-mode control (HOSM). The proposed adjustment mechanism with the PD controller have been designed for the altitude movement, directional and lateral dynamics of a fixed-wing miniture aerial autonomous vehicle (MAV). Several simulations have been carried out in order to analyze the response of the modified MIT rule.

Introduction

In control theory, there exist several dynamic systems possessing constant uncertain parameters or parameters varying slowly [START_REF] Slotine | Applied Nonlinear Control[END_REF]. For example, when we develop an MAV (Mini Aerial Vehicle), we can add or remove sensors or batteries, then we modify the weight and consequently the inertia parameters. In the same way, when an MAV flies in bad weather, it is exposed to changes in the air density which are usually considered as a constant value. In order to solve the aforementioned problems, several control laws could be designed. One of such options is the use of an adaptive controller [START_REF] Cook | Flight Dynamics Principles[END_REF] allowing the MAV performs a stable flight under such conditions. The adaptive control has been applied in areas as the robot manipulators, airplanes, rockets, chemical process, electronic systems, ships, bioengineering and other applications [START_REF] Slotine | Applied Nonlinear Control[END_REF][START_REF] Åström | Adaptive Control, 2nd edn[END_REF].

Exist a lot of literature about adaptive control, but in this work we are going focus in works related to the MIT rule, thus, as in [START_REF] Jain | Design of a model reference adaptive controller using modified MIT rule for a second order system[END_REF], where it has been applied the MIT rule based on model reference adaptive control (MRAC) for the regulation of a second order system; the contribution of [START_REF] Jain | Design of a model reference adaptive controller using modified MIT rule for a second order system[END_REF] is the modification of the MIT rule with the objective to obtain a major amplitude of reference desired, due to the MIT rule tends to be unstable with large reference values, and this is one of the inconvenient in work with the MIT rule and even more, is sensitive to big numerical changes in the adaptation gain, that is, even with decimal changes in this gain, the system tends to be unstable. In [START_REF] Jain | Design of a model reference adaptive controller using modified MIT rule for a second order system[END_REF] only show an example to make one gain adaptable of the control law, and the other gain of the control law proposed is not adaptable (constant value).

Also, [START_REF] George | Model reference control of binary distillation column composition using MIT adaptive mechanism[END_REF] the MIT rule has been applied to a distillation process, considering a linearized model, in addition to applying an adaptive feedback control for two parameters of the controller, and by considering as reference a unitary Fixed-Wing MAV Adaptive PD Control Based on a Modified MIT Rule with Sliding-Mode Control step signal. In [START_REF] Kumer | Model reference adaptive control of a spherical tank[END_REF], they have presented a comparison of the MIT rule with the gradient method and by the Lyapunov method. In [START_REF] Kumer | Model reference adaptive control of a spherical tank[END_REF] has been designed a control law for tracking and regulation for an aspheric tank with selecting a small reference for the input, and they have not presented a modification to the MIT rule.

By other hand, [START_REF] Hakan | A model reference adaptive controller performance of an aircraft roll attitude control system[END_REF] applied a Model Reference Adaptive Controller (MRAC) based on the MIT rule in the roll angle for a very large four engine passenger jet aircraft, the authors of [START_REF] Hakan | A model reference adaptive controller performance of an aircraft roll attitude control system[END_REF] mentioned a very important point about the adaptation gain, that is, based on the simulation results obtained with MatLab software, with high values on the adaptation gain it is obtained a fast response on the system but with larger overshoots, and with low values of gamma the system response is slow with small overshoot. The interval of this gain is from 1 to 5 Beyond this interval the system performance is not satisfactory.

In [START_REF] Ghaffar | Model reference adaptive control and LQR control for quadrotor with parametric uncertainties, world academy of science[END_REF] a MRAC with a LQR has been applied to stabilize a quadrotor with parametric uncertainties, this union was proposed because the authors of [START_REF] Ghaffar | Model reference adaptive control and LQR control for quadrotor with parametric uncertainties, world academy of science[END_REF] mentioned that the adaptive control is a method for ensuring the stability of the quadrotor, but the adaptive control working alone is not ideal because fast adaptation can lead to undesirable oscillations and instability. The work presented in [START_REF] Zhou | Design of attitude control system for UAV based on feedback linearization and adaptive control[END_REF] is shown a design based on feedback linearization and adaptive control (MRAC), the controller has been applied to control the attitude of fixed-wing UAV, the control laws is applied for decoupling dynamics which defines the UAV, that are, pitch, yaw and roll angles, respectively. In [START_REF] Zhou | Design of attitude control system for UAV based on feedback linearization and adaptive control[END_REF] used the same reference for the three angles and even realized a linearization of the decoupling model.

The works mentioned at the top have shown results using the Matlab software (simulation results).

In summary in this work, we have applied the MIT rule with the sliding modes theory, the objective of this union is to obtain a robust adjustment mechanism in presence of wind gusts to change the gains of a PD controller. The union of the MIT rule with the sliding mode theory implies a first order sliding mode, and due to that with this union is presented the chattering effect, we have added a second order sliding mode in order to reduce this effect, and finally we have appreciated than the chattering effect is presented still with two sliding modes, so we have added a high order sliding mode in order to reduced the effect chattering in the design of the adaptive control. Thus, the adaptive controller obtained, is applied in order to lead the altitude movement, yaw and roll angles to a desired values.

With the union mentioned before (MIT rule with sliding mode theory), we have obtained a lower sensitivity in the adaptive gain, and it is possible to vary the reference required with different desired values, unlike the aforementioned works. Furthermore, we have proposed a different definition of the adjustment mechanism based on the MIT rule with sign function and with signsign functions than the presented in [START_REF] Slotine | Applied Nonlinear Control[END_REF][START_REF] Åström | Adaptive Control, 2nd edn[END_REF]. We also added a disturbance which acts on the process input [START_REF] Åström | Adaptive Control, 2nd edn[END_REF], with the objective of test the robustness of the adjustment mechanism for the adaptive PD controller in presence of not modeled disturbances in the fixed-wing MAV. Such disturbances are small wind gusts, but are unknown and random.

The paper is organized as follows: Section 2 shows the equations that define the dynamical model of the MAV; in Section 3, it is presented the control law design for the fixedwing MAV dynamics. In Section 4, is shown the simulation results and an analysis of the error signals and the efforts of the control inputs, Section 5 presents the conclusions of this work.

Airplane Model

In order to obtain the model equations, by omitting any flexible structure of the MAV, the fixed-wing MAV can then considered as a rigid body. Also, we do not consider the curvature of the earth, it is considered just as a plane because we assume that the fixed-wing MAV will only fly short distances. With the previous considerations, we obtain the model by applying the Newton's laws of motion. It should be mentioned that the model presented in this work represents a pure motion pitch to achieve the desired altitude, and the same concept of pure motion is applied to the yaw and roll angles.

Longitudinal Dynamics

The used dynamical model to control the altitude of the MAV is given by [START_REF] Brian | Aircraft Control and Simulation[END_REF]:

θ = q (1) q = ρSV c2 4I yy C m q q + ρV 2 S c 2I yy C m δe δ e (2) ḣ = V sin(θ) ( 3
)
where V is the magnitude of the airplane speed (for the simulations presented in this work is considered as constant), θ denotes the pitch angle. q is the pitch angular rate with respect to the y-axis of the aircraft body, h defines the airplane altitude and δ e represents the elevator deviation [START_REF] Brian | Aircraft Control and Simulation[END_REF]. We can see these variables in the in Fig. 1.

Directional-Lateral Dynamic

The lateral dynamics generates the roll motion and, at the same time, induces a yaw motion (and vice versa), then a natural coupling exists between the rotations about the roll and yaw axes [START_REF] Mclean | Automatic Flight Control Systems[END_REF]. In our case, to solve it, we have considered a decoupling of the yaw and roll angles [START_REF] Cook | Flight Dynamics Principles[END_REF]. Thus, each angle can be controlled independently. Generally, the effects of the engine thrust are also ignored [START_REF] Mclean | Automatic Flight Control Systems[END_REF].

In the Fig. 2, the yaw angle (directional dynamics) is represented, which can be described by the following equations:

ψ = r (4) ṙ = ρV Sb 2 4I zz C n r r + ρV 2 Sb 2I zz C n δr δ r ( 5
)
where ψ represents the yaw angle and r denotes the yaw rate with respect to the center of gravity of the MAV. δ r is the rudder deflection. The following equations describe the dynamics for the roll angle (lateral dynamics):

φ = p (6) ṗ = ρV Sb 2 4I xx C l p p + ρV 2 Sb 2I xx C l δa δ a ( 7
)
where p denotes the roll rate, φ describes the roll angle, and δ a represents the deviation of the ailerons. In the Fig. 3 are shown the variables of the roll motion. In Fig. 4 is shows a Solidworks model designed to calculate the moments of inertia.

Remark 1 It should be mentioned that the mathematical model defined in this work, only represents the Euler angles and the angular rates, due to that with this approximation in the mathematical model has been obtained a good performance in real-time flight tests (see [START_REF] Espinoza Fraire | Design and implementation of fixed-wing MAV controllers[END_REF][START_REF] Parada | Performance analysis of nonlinear observers applied to the fixed-wing unmanned aerial vehicles flight under decoupled-reduced model[END_REF], and [START_REF] Espinoza-Fraire | Real-time implementation and flight tests using linear and nonlinear controllers for a fixed-wing miniature aerial vehicle (MAV)[END_REF]).

And the control design presented in this work needs the knowledge of only such physical variables.

Remark 2

The parameters of the wingspan, fuselage, etc, of the aeromodelling model T-28 Trojan, were provided by the manufacturer (http://www.horizonhobby.com/), see Table 1.

Remark 3

The validation of the model has been proved with the design of the backstepping controller presented in [START_REF] Espinoza Fraire | Design and implementation of fixed-wing MAV controllers[END_REF] and with the design of nonlinear observers presented on [START_REF] Parada | Performance analysis of nonlinear observers applied to the fixed-wing unmanned aerial vehicles flight under decoupled-reduced model[END_REF], that is, the backstepping controller needs the complete knowledge of the model for its design process and the same situation can be consider for the design of the nonlinear observers (see [START_REF] Parada | Performance analysis of nonlinear observers applied to the fixed-wing unmanned aerial vehicles flight under decoupled-reduced model[END_REF]), otherwise it is not possible to obtain a stable flight with the fixed-wing MAV, namely, it is not possible to achieve the control objective. Therefore, in this sense, we can prove the validity of the aerodynamic model.

Change of Variables of the Directional-Lateral Aerodynamic Model

In order to design the adaptive control law, we have conducted a change in the variables notation for the altitude, directional and lateral dynamics; this is due to the fact that the dynamics are similar. Then, the directional dynamics is represented in the new variables by: with l := θ, ψ, φ for the pitch, roll and yaw angles, respectively. The definition of the acronym l is with the objective of known or differentiate which dynamic model is been used in the control law. u l defines the control input, that is, u θ := δ e , u ψ := δ r and u φ := δ a . The same subindex are going to use in the description of the adaptive control presented in the Section 3.

ẋ1l = x 2l (8) ẋ2l = C 1l x 2l + C 2l u l (9)

Design of the Adaptive Control

We have designed a PD control law with adaptive gains, thus, the adaptive part of the controller is given by the proportional and the derivative gains. These gains are defined as kpla and kvla respectively. The methodology to design the adaptive control is based on the MRAS, in order to design the adjustment mechanism by the MIT rule based on the gradient method with sliding-mode theory, that is, we have modified the MIT rule based on the gradient method by inserting the theory of first order sliding-mode, second order (2-SM) and high order sliding-mode (HOSM), with the purpose of obtaining a robust adjustment mechanism for the adaptive control law and to stabilize the system in presence of unknown perturbations (wind gusts), and trying to reduce the chattering effect. The block diagram representing the MRAS proposed is shown in Fig. 5, where the Plant is the aerodynamic model which represents the fixed-wing MAV, and the block called as Model represents the model-reference. Consider the Eqs. 8-9, The adaptive control is given by: u l = kpla e l + kvla ėl [START_REF] Brian | Aircraft Control and Simulation[END_REF] where kpla and kvla are called as the position and velocity gains, respectively, thus, these are the adaptive gains. The error of the directional and lateral dynamics has been defined as e l = x d 1lx 1l . The gains of the PD control have implicit a subscript to indicate the algorithm that has been applied as adjustment mechanism, a = a 1 , a 2 , a 3 , a 4 where a 1 corresponds to the MIT rule, a 2 corresponds to the MIT rule with sliding-mode (MIT-SM), a 3 uses the MIT rule with 2-sliding-mode (MIT-2SM), and finally a 4 represents the MIT rule with high order sliding mode (MIT-HOSM). Therefore, for the design of the MIT rule, it is introduced an error given by: e l m = x 1l mx 1l [START_REF] Mclean | Automatic Flight Control Systems[END_REF] where x 1l m is the output from the reference model. We have followed the methodology that has been presented in [START_REF] Åström | Adaptive Control, 2nd edn[END_REF] for the MIT rule, taking this into account, the aerodynamic model has been transformed into the representation of a transference function in order to develop the derivatives of sensitivity; these have been obtained by computing partial derivatives with respect to the controller parameters kpla and kvla . Thus, the closed-loop transfer function with the adaptive PD controller has been defined as:

x 1l = kpl C 2l s 2 + (C 2l kvl -C 1l )s + C 2l kpl x d 1l (12)
and the model of reference has been defined as:

x 1lm = ω 2 n s 2 + 2ζ ω n s + ω 2 n x d 1l ( 13
)
where ζ = 3.17 and ω = 3.16. Consider ( 11)-( 13) and calculate the partial derivatives with respect to kpla and kvla , then it is obtained:

∂e l m ∂ kpl = C 2l s 2 + (C 2l kvl -C 1l )s + C 2l kpl x 1l -x d 1l ( 14
)
∂e l m ∂ kvl = C 2l s s 2 + (C 2l kvl -C 1l )s + C 2l kpl x 1l -x d 1l ( 15
)
Generally, the expressions ( 14) and ( 15) cannot be used due to the unknown parameters kpla and kvla . Thus, an optimum case has been assumed, it is defined as:

s 2 + (C 1l + C 2l kvl )s + C 2l kpl = s 2 + 2ζ ω n s + ω 2 n (16)
thus, after these approximations, we have obtained the differential equations of the adaptive PD controller.

kpla 1 = -γ 1l 1 s 2 + 2ζ ω n s + ω 2 n x 1l -x d 1l e l m ( 17
)
kvla 1 = -γ 2l s s 2 + 2ζ ω n s + ω 2 n x 1l -x d 1l e l m ( 18
)
Now, it is proposed an MIT rule with second order sliding-mode; this approach is different than the defined in [START_REF] Åström | Adaptive Control, 2nd edn[END_REF], and then, it is defined a sliding-mode surface as s 1l = ẋ1lmx 2l + k 1l e l m (we search to increase the stability to the adjustment mechanism), where k 1l > 0. Then, the differential equations of the adaptive controller, with the methodology by sliding-mode, are given by:

kpla 2 = -γ 1l 1 s 2 + 2ζ ω n s + ω 2 n x 1l -x d 1l (β p1l sign(s 1l )) (19) kvla 2 = -γ 2l s s 2 + 2ζ ω n s + ω 2 n x 1l -x d 1l (β v1l sign(s 1l )) (20)
where the gains are β p1l , β v1l > 0. Due to the chattering effect of the first order sliding-mode, let us design an adjustment mechanism with a second order slidingmode. These second order sliding-mode includes a robust differentiator of first order [START_REF] Levant | Robust exact differentition via sliding mode technique[END_REF]. This differentiator is defined by:

ẋ0 = v 0 = -λ 0 |x 0 -s 1l | 1/2 sign(x 0 -s 1l ) + x 1 ẋ1 = -λ 1 sign(x 1 -v 0 )
where x 0 and x 1 are real-time estimations of s 1l and ṡ1l , respectively. The values of λ 1 , λ 2 are constants and positives. Thus, the differential equations of the adaptive PD controller with a second order sliding-mode are defined by:

kpla 3 = -γ 1l 1 s 2 + 2ζ ω n s + ω 2 n x 1l -x d 1l ×(β p1l sign(s 1l ) + β p2l sign(ṡ 1l )) ( 21
)
kvla 3 = -γ 2l s s 2 + 2ζ ω n s + ω 2 n x 1l -x d 1l ×(β v1l sign(s 1l ) + β v2l sign(ṡ 1l )) ( 22
)
where the gains are β p1l , β p2l , β v1l , β v2l > 0. In order to reduce or eliminated the chattering effect in the second order sliding-mode, we have designed an adjustment mechanism with HOSM. To design the adjustment mechanism, it is necessary a robust differentiator of second order [START_REF] Levant | Robust exact differentition via sliding mode technique[END_REF], which is given by:

ẋ0 = v 0 = -λ 0 |x 0 -s 1l | 2/3 sign(x 0 -s 1l ) + x 1 ẋ1 = v 1 = -λ 1 |x 1 -v 0 | 1/2 sign(x 1 -v 0 ) + x 2 ẋ2 = -λ 2 sign |x 2 -v 1 |
where x 0 , x 1 and x 2 are real-time estimations of s 1l , ṡ1l and s1l . The values of λ 0 , λ 1 and λ 2 are defined as positive constants. Finally, the differential equations of the adaptive PD controller with HOSM are defined by:

kpla 4 = -γ 1l 1 s 2 + 2ζ ω n s + ω 2 n x 1l -x d 1l ×(α pl [s 1l + 2(|ṡ 1l | 3 + |s 1l | 2 ) 1/6 × sign(ṡ 1l + |s 1l | 2/3 sign(s 1l ))]) (23) kvla 4 = -γ 2l s s 2 + 2ζ ω n s + ω 2 n x 1l -x d 1l ×(α vl [s 1l + 2(|ṡ 1l | 3 + |s 1l | 2 ) 1/6 × sign(ṡ 1l + |s 1l | 2/3 sign(s 1l ))]) ( 24
)
where the gains are α pl , α vl > 0.

Simulation Results

In this work we are going to use the L 2norm to describe the results obtained with the different adaptive mechanism based on the MIT rule with the sliding mode theory. Such L 2norm is applied to the error between the model reference and the aerodynamic model that describe the fixed-wing MAV, and even the same norm is applied to know the control effort. Then, the L 2norm for the error is defined as

L 2 [e l m ] = 1 T -t 0 T t 0 e l 2 dt
(25) And the L 2norm to know the control effort of the adaptive law with the different adaptive mechanisms, the L 2norm is given as

L 2 [δ s ] = 1 T -t 0 T t 0 δ s 2 dt (26)

Altitude Movement

In the Fig. 6 is shown the results obtain with the different adaptive mechanism designed to obtain an adaptive PD controller. In this altitude simulation, we have set different desired altitude, such altitude or control objectives are 10, 15 and 20 meters. It is appreciates at the first desired altitude (10 meters) the adaptive controller achieves the desired altitude of critically damped form, and after that, the other altitudes achieves in a soft signal due to the desired altitude signal, see the Fig. 6.

The smaller error obtained in altitude is with the adjustment mechanism based on MIT-SM, this is 7.39, 10.77 and 10.71% smaller than the adjustment mechanism based on MIT, MIT-2SM and MIT-HOSM respectively.

The control signals generated by the PD adaptive with the different adjustment mechanism are presented in the Fig. 7.

Then, the control effort of the adaptive mechanism based on MIT-HOSM is 86, 90, and 99% smaller than the generated by the adjustment mechanism based on MIT, MIT-SM, and MIT-HOSM, respectively (see Table 2).

By other hand, the mechanism which presented a bigger error in altitude was the MIT-2SM in altitude, that is, the MIT-2SM is bigger than the adjustment mechanism based on MIT, MIT-SM and MIT-HOSM, that is, 4.23, 14.33 and 0.06%, respectively. Also, the control effort generated by the adjustment mechanism based on MIT-SM is bigger than the presented by the adjustment mechanism based on MIT, MIT-2SM and MIT-HOSM, that is, 28.57, 98.57 and 98.57%, respectively (see Table 2).

In the Fig. 8 is presented the minimization of the cost function with the different adaptive mechanism, and is proved in the figure that J (θ) → 0. In the Fig. 9 is presented the performance of the adaptive proportional gain kp and in the Fig. 10 is appreciated the performance of the adaptive derivative gain kv in altitude movement for the different adaptive mechanism.

The response of the sliding manifold for the adjustment mechanism based on sliding mode theory for the adaptive PD controller in altitude are presented in the Fig. 11 for the adaptive proportional gain and in the Fig. 12 is for the adaptive derivative gain.

Yaw Movement

In the Fig. 13 is shown the results obtained with the PD adaptive controller with the different adjustment mechanism. In this figure the objective of control is achieve three different values for the yaw angle, such values are 5 2). In the Fig. 14 is presented the control response of the adaptive PD controller with the different adjustment mechanism.

The adjustment mechanism based on MIT-HOSM presented a bigger error in the yaw angle, that is, 93.83, 92.98 and 79.70% than the MIT, MIT-SM and MIT-2SM respectively. Even more, the control effort generated by the PD adaptive control with the adjustment mechanism based on MIT-HOSM is bigger than the adjustment mechanism based on MIT, MIT-SM, and MIT-2SM, that is, 93.66, 94.76, and 82.57%, respectively, see the Table 2.

In the Fig. 15 is presented the result of the minimization of the cost function for the yaw angle, it is appreciated that J (ψ) → 0. In the Fig. 16 is shown the performance of the adaptive proportional gain kp , and in the Fig. 17 is appreciated the performance of the adaptive derivative gain kv in yaw angle for the different adjustment mechanism.

The response of the sliding manifold for the adjustment mechanism based on sliding mode theory for the adaptive PD controller in the yaw angle are presented in the Fig. 18 for the adaptive proportional gain and in the Fig. 19 is for the adaptive derivative gain.

Roll Movement

In the Fig. 20, is presented the response of the adaptive PD controller with the different adjustment mechanism. In this figure the references of roll angle to archive by the adaptive PD controller are 5 • , 25 • , and 40 • . Then, It is appreciated that the error presented by the MIT adjustment mechanism is 16.04, 66.84 and 92.99% smaller than the adjustment mechanism based on MIT-SM, MIT-2SM, and MIT-HOSM, respectively. Also, the control effort of the adaptive PD controller with the adjustment mechanism based on MIT-SM is 3.17, 67.60 and 94.76% smaller than the adjustment mechanism based on MIT, MIT-2SM and MIT-HOSM respectively, see the Table 2 and Fig. 21.

The adjustment mechanism based on the MIT-HOSM rule, the error in roll angle is 92.99, 91.65, and 78.88% bigger than the adjustment mechanism based on MIT, MIT-SM, and MIT-2SM, respectively. Even more, the adjustment based on the MIT-HOSM, it is 94.59, 94.76, and 83.84 bigger than the adjustment mechanism based on MIT, MIT-SM, and MIT-2SM, respectively (see the Table 2). The minimization of the cost function in the roll angle is presented in the Fig. it is appreciated that J (φ) → 0. Also, in the Fig. 23 is shown the performance of the adaptive proportional gain kp , and in the Fig. 24 is appreciated the performance of the adaptive derivative gain kv in roll angle for the different adjustment mechanism.

The response of the sliding manifold for the adjustment mechanism based on sliding mode theory for the adaptive PD controller in the roll angle are presented in the Fig. 25 for the adaptive proportional gain, the Fig. 26 is for the adaptive derivative gain. YangQuan Chen received his Ph.D. degree in advanced control and instrumentation from Nanyang Technological University, Singapore, in 1998. Dr. Chen was on the Faculty of Electrical and Computer Engineering at Utah State University before he joined the School of Engineering, University of California, Merced in 2012 where he teaches mechatronics for juniors and fractional order mechanics for graduates. His research interests include mechatronics for sustainability, cognitive process control and hybrid lighting control, multi-UAV based cooperative multi-spectral personal remote sensing and applications, applied fractional calculus in controls, signal processing and energy informatics; distributed measurement and distributed control of distributed parameter systems using mobile actuator and sensor networks. R. Juarez, works as university professor in the Facultad de Contaduría y Administración, FCA, Torreon Coahuila campus, of the Universidad Autónoma de Coahuila, UAdeC. He obtained his diploma on Physics and Mathematics in the Escuela Superior deFísica and Matemáticas (ESFM) in the Instituto Politecnico Nacional (IPN). He obtained the Master's and Ph degree both in sciences with speciality in ControlTheory in the Centro de Investigación y de Estudios Avanzados del InstitutoPolitécnico Nacional (CINVESTAV-IPN) in Mexico city. He has written somes cientific publications on scientific journals and conferences. His research is directed to the investigation of mathematical models supported by ICTs to generate business development and management; the management of knowledge and transmission of technology to vulnerable groups supported in the innovation; the generation and transfer of scientific and technological innovation supported on sustainability; optimal control, non-linear control, robust control, hybrid systems, switched, implicit and with delays, applied in the area of economy, administration and finance; game theory, intelligent control, stochastic control and control of unmanned aerial vehicles (UAV); the development of computational algorithms for the modeling, optimization and control of economic and financial systems: Econometrics; and the modeling of physical systems and economic.

Fig. 1

 1 Fig. 1 Pure pitching motion

Fig. 2

 2 Fig. 2 Pure yawing motion

Fig. 3

 3 Fig. 3 Pure rolling motion

Fig. 4

 4 Fig. 4 SolidWorks software model

Fig. 5

 5 Fig. 5 Block diagram of the MRAS

Fig. 6

 6 Fig.[START_REF] Kumer | Model reference adaptive control of a spherical tank[END_REF] Adaptive PD controller response in altitude movement (with disturbances)

Fig. 7

 7 Fig. 7 Control signal of the Adaptive PD controller in altitude (with disturbances)

Fig. 8 Fig. 9 Fig. 11 Fig. 12 Fig. 14 Fig. 15

 8911121415 Fig. 8 Minimization of the cost function in altitude (with disturbances)

Fig. 19 Fig. 21 Fig. 25 Fig. 26

 19212526 Fig. 19 Response of the manifold in the adaptive derivative gain in yaw angle movement (with disturbances)

A.

  Dzul was born in Gómez Palacio, México, on April 30, 1971. He received the B.S. degree in electronic engineering and the M.S. degree in electrical engineering, both from Instituto Tecnológico de La Laguna, México, in 1993 and 1997, respectively, and the Ph.D. degree in automatic control from Université de Technologie de Compiègne, France, in 2002. Dr. Dzul has been a research professor with the Electrical and Electronic Engineering Department at Instituto Tecnológico de La Laguna since 2003. His current research interests are in the areas of nonlinear dynamics and control, and real-time control with applications to aerial vehicles. R. Lozano received the master of science degree in electrical engineering from Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City, Mexico, in 1977, and the Ph.D. degree in automatic control from the Laboratoire d'Automatique de Grenoble, Grenoble, France, in 1981. From 1981 to 1989, he was with the Department of Electrical Engineering, CINVESTAV. He was the Head of the Section of Automatic Control from 1985 to 1987. He has held visiting positions at the University of Newcastle, Callaghan, NSW, Australia, from 1983 to 1984, the NASA Langley Research Center, Hampton, VA, USA, from 1987 to 1988, and the Laboratoire d'Automatique de Grenoble, from 1989 to 1990. Since 1990, he has been the CNRS Research Director with the University of Technology of Compiègne, Compiègne, France, where he was the Head of the Laboratory Heudiasyc UMR 6599 CNRS-UTC, Compiègne, France, from 1995 to 2007. His current research interests include adaptive control of linear, nonlinear systems, robot manipulators, passive systems, teleoperation, unmanned aerial vehicles, and autonomous underwater vehicles. Dr. Lozano was an Associate Editor of the Automatica from 1987 to 2000 and he has beenan Associate Editor of the International Journal of Adaptive Control and Signal Processing since 1993.

Table 1

 1

	Fixed-wing MAV
	parameters	Name

Table 2 L

 2 [START_REF] Cook | Flight Dynamics Principles[END_REF] norm for the error and the control effort

	Altitude movement
	Adaptive mechanism	L 2 [e hm ]	L 2 [u θ ]
	MIT	0.1583	0.0050
	MIT-SM	0.1466	0.0070
	MIT-2SM	0.1653	1.7873×10 -4
	MIT-HOSM	0.1652	1.7872×10 -4
	Yaw angle
	Adaptive mechanism	L 2 [e ψm ]	L 2 [u ψ ]
	MIT	0.0760	0.0132
	MIT-SM	0.0865	0.0109
	MIT-2SM	0.2501	0.0363
	MIT-HOSM	1.2323	0.2083
	Roll angle
	Adaptive mechanism	L 2 [e φm ]	L 2 [u φ ]
	MIT	0.1964	0.1272
	MIT-SM	0.1892	0.1177
	MIT-2SM	0.1768	0.3523
	MIT-HOSM	0.0780	2.6101

HEUDIASYC Laboratory, Université de Technologie de Compiègne, Compiègne, Oise 60200, France

Facultad de Contaduría y Administración, Universidad Autonoma de Cohauila, Torreon, Coahuila, México

Acknowledgements

This work was partially supported by funds of the Faculty of Engineering, Science and Architecture UJED, and the TecNM projects.

Conclusions

In this work has been proposed an adjustment mechanism based on the union of the MIT rule using the gradient method with the sliding mode theory, this adjustment mechanism was development to obtain an adaptive PD controller. Thus, with the adjustment mechanism based on the MIT rule with high order sliding mode (MIT-HOSM) was possible reduce the chattering effect and even the unknown perturbation is reduced significantly in the altitude movement and in the roll angle. Also, for yaw angle was possible some reduction in the chattering effect by the use of the MIT rule with high order sliding mode (MIT-HOSM). Then, with the use of the adjustment mechanism based on in the MIT rule with the gradient method is not possible reduced the unknown perturbation and in consequence is not possible achieve an stable or equilibrate flight. The adjustment mechanism based on the MIT rule with first order sliding mode (MIT-SM) presented the undesired chattering effect, but with the MIT with second order sliding mode (MIT-2SM) was possible attenuate in a better way in the altitude movement. By other hand, for the yaw and roll angles exist some reduction but not enough to reduce the chattering and the unknown perturbation with the MIT with second order sliding mode (MIT-2SM). Thus, designing an adjustment mechanism based on the union of the MIT rule by the gradient method with the high order sliding mode is possible design a robust adjustment mechanism for a adaptive PD controller in order to attenuate the chattering effect and reduce the perturbations (wind gusts) which affect the performance of a fixed-wing miniature unmanned aerial vehicle.