THE "SOCIAL" IN THE INSTITUTIONALISATION OF LOCAL CULTURAL POLICIES IN FRANCE AND GERMANY

First published in French as "Le "social" dans l"institutionnalisation des politiques culturelles locales en France et en Allemagne". Translated and reproduced by permission.

Vincent Dubois and Pascale Laborier

Can one produce an international comparison of cultural policies, and if so, how? These are our initial questions. The possibility of a comparative approach appears as a particular problem in France, where the thesis positing the very existence of cultural policiesamalgamated with the existence of a ministry for cultureas nationally specific enjoys a broad consensus, thereby depriving any comparative analysis of an object. Whether it is celebrated or denounced, i the "French exception" is scarcely questioned. Furthermore, the "French model" has become the object of an export drive, as is shown by the occupation by agents from the Ministry of Culture of positions in international institutions (Unesco, the Council of Europe), the recent organisation of the "Malraux colloquia" whose vocation is the diffusion of this "unique model" across the world, and even the references in other countries to this supposed "model". ii Against this flat refusal of any comparative approach, seeing no foreign cases for comparison, one can setnotably in the framework of specialised international organisations the juxtaposition of national monograph studies that presuppose a common identity for objects presented as equivalent. This was the case, for example, with the programme of studies launched by Unesco in the 1970s and 1980s, which gave rise to the publication of some sixty brochures on "cultural policies". The more recent programme for the evaluation of national cultural policies developed by the Council of Europe also puts side by side situations whose homogeneity, to say the least, is not an a priori given (from Sweden at the end of the 1980s to the institutional addresses PECO ten years later). The seemingly intractable question of the standardisation of indicators for evaluation is, moreover, itself a good indication of the problematic character of such homogenisation (see [START_REF] Gray | Comparing cultural policy: a reformulation[END_REF].

Absolute national specificities on the one hand, indiscriminate generalisations on the other hand: for opposite reasons, these two postures divert attention from what could constitute a true comparison. To move beyond this impasse, a comparative approach must not, as it seems to us, focus on "things" conceived as the distinct manifestations of a common essence (cultural policies in France and Germany), but rather on processes, namely the construction of the categories of public intervention in cultural matters. iii The object of comparison then becomes the way in which domains of action are divided up; the aggregation of objects and practices of intervention which are thereby brought together and conceptualised conjointly; the production of principles bringing elements to cohere that in other times and places would be considered separately. In other words, the point of this article is not so much to compare the conduct of cultural policies whose form might be seen as identical from one country to another, but rather, precisely, to confront in the two cases under consideration the work that gave these policies their form, and through which the policies were presented and given meaning.

Let us initially recall the principal characteristics of this policy-forming process. In France, the Ministry of Cultural Affairs, created in 1959, established itself by marking itself off from neighbouring categories of public intervention, such as popular education, leisure, or later sociocultural animation. This process of institutionalisation through differentiation can be seen equally at the level of local authorities, who gradually equipped themselves with specifically cultural administrative structures, separating these from larger groupingsdepartments for sports and fine arts, animation, youth, etc.which previously had been able to integrate the elements constituting local action for culture. French cultural policies, whether local or national, thus assumed their identity through a work of classification that emancipated them from more general categories (such as, notably, sociocultural animation). Kulturpolitik in the Federal Republic of Germany, developed at the level of the regions and municipalities, brings together not simply the cultural sector in the narrow sense of the fine arts and cultural institutions, but sometimes also education, even if the institutionalisation of cultural policies took place here, as in France, through a differenciation with regard to other sectors of intervention.

In order to account for these differenciated processes of categorisation and formation, we have chosen to focus on what, both in France and Germany, has been and continues to be problematic: the insertion of the public treatment of culture in a social context. For it is here that comes into play, among other things, the question of the definition of the type of culture for which intervention is appropriate (legitimate, popular, subversive…) (see [START_REF] Passeron | Figures et contestation de la culture[END_REF]. Equally, it is here that come into play the principles giving legitimacy to those agents that intervene: the social competence of the animateur, the political vision of the engaged artist, or the technical expertise of the cultural manager. It is in the formation and questioning of such loose and intermediary categories ("socioculturel" in French, "Soziokultur" in German) that we can observe most clearly the moves to cross and mark frontiers constituting that work of categorisation we wish to study.

In the 1960s and 1970s, new forms of public treatment of culture were invented, characterized by a strong anchoring in local areas, the involvement of activists, and a deliberate distancing of legitimate culture. This was sociocultural animation in France, and Soziokultur in the FRG. The agents and points of reference associated with these movements, although playing a not inconsiderable role in the formation of public intervention in culture at a local level, were generally sidelined as this policy developed. New agents, laying claim to cultural expertise and referring to a body of professional knowledge, organised, especially from the mid-1980s onwards, the relegation of these "pioneers", brought down to the rank of amateurs or activists, full of good will but with only limited professional competence. Some of the themes characterising those older forms of policy have nevertheless resurfaced over recent years. It is by laying claim to a new type of expertise, this time linked to their knowledge of the "terrain" and to the "cultural" management of the social and urban crises, that the professionals of local cultural policies have been reoccupying problematics against which they had previously constructed their identities and established their positions.

What were the conditions for the invention, in France and Germany in the 1960s and 1970s, of forms of treatment of culture structured around explicitly "social" objectives? What position do these forms occupy in the development of public intervention in culture at a local level? Finally, what are the logics presiding over the relegation and then the partial rediscovery of these modes of intervention? It is around these questions that we would like to provide some elements of comparison between the French and German cases. Besides confronting different modes of categorisation of local public policy in different places and times, reviewing these transformations will enable us also to shed light on the different forms of expertise in play at a local level: from the disparagement of expertise in the name of activism and proximity to the social "terrain", to the moves laying claim to a professionalism associated with the constitution at a national level of a body of "cultural mediators", to, finally, the invention of new types of know-how and professional positions at the interface between the social and the cultural, tied to an "expert" understandingi.e. mediated by technical procedures and specialised forms of knowledgeof the local terrain.

SOCIOCULTURAL, SOZIOKULTUR: SOCIAL MOBILISATIONS AND CULTURAL INNOVATIONS

Following the manifold local initiatives of the 1960s, and after the processes of mobilisation issuing from the contestatory movements of the end of the decade, new kinds of relation to culture were invented both in France and the Federal Republic of Germany, locally situated and detached from the "dominant" culture. Sociocultural animation in France and Soziokultur in Germany enabled in different ways the diverse networks of associations and activists to form coherent groupings, followed by the institutionalisation of a new category of public intervention.

In both countries, suburban districts and urban areas in general, at different times and following different rhythms from case to case, often constituted the sites of powerful social mobilisations around cultural issues. In the 1960s and 1970s, the most visible form of these was the mobilisation and investment of the middle classes in the communitarian and civic utopias of sociocultural animation. iv This localised production of cultural life was strongly marked by the local and social identities it symbolised. Suburban cultural action was thus inextricably enmeshed in the general sphere of social relations.

The social insertion of cultural policies nevertheless took place in different manners in the two countries. The social effects of cultural action oscillate between "integration and subversion" [START_REF] Gaudibert | Action culturelle, intégration et/ou subversion[END_REF], and one might schematically associate developments in France with the first term of this opposition, while developments in Germany can be considered as coming closer to the second term.

Social integration through local cultural action

In France, the task of inserting cultural policies into social contexts fell to the constellation of post-war popular education groups (such as People and Culture or the Federation of Houses for Youth and Culture). v It was also carried out with the support of local politicians, notably but not exclusively from the Left. Thus 1960 saw the creation in France of the National Federation of Local Cultural Centres (FNCCC -Fédération nationale des centres culturels communaux), which defended an alternative model of cultural action to that propounded by the new Ministry for Cultural Affairs. The local politicians and animateurs affiliated to the FNCCC advocated a cultural policy closely related to local associations and looking to promote forms of local sociability (collective outings, amateur practices…) that were supposed to organise around the municipality a stronger sense of social cohesion. Their "experience of the local terrain" was put forward to counter the "theory" of ministerial experts denounced as "gurus" and "technocrats" (see [START_REF] Dubois | Pour la culture ou contre l"Etat? La FNCCC et l"institutionnalisation des politiques culturelles au début des années soixante[END_REF][START_REF] Urfalino | L"échec d"une contre-politique culturelle[END_REF].

Communist local politicians participated in this type of mobilisation, but did not bring with them the discourses of revolution or working-class autonomy, since these had been officially abandoned by the Central Committee meeting at Argenteuil in 1966 (see [START_REF] Lambert | Politiques locales et enjeux culturels: les clochers d'une querelle[END_REF]. Certains elements of the "New Left" were also present in these processes of mobilisation, without for all that bringing with them any kind of cultural radicalism. Overall, while "the social functions of culture", to use the typical vocabulary of the time, were constituted as a suitable issue for politicisation, they were hardly conceptualised with reference to the supposedly "subversive" virtues of artistic creation. More stress was placed instead on intermediary and not exclusively artistic forms of culture (festivals, carnivals, extracurricular acitivities…) whose promotion was envisaged as a "soft" way of managing social problems: the improvement of the urban environment, efforts to make the new urban estates more human, etc.

A more radical politicisation: Soziokultur in the Federal Republic of Germany This politicisation takes on a more subversive aspect in the Federal Republic of Germany, where the promoters of Soziokultur at the end of the 1960s base their work more than French animateurs on politically committed forms of art (see [START_REF] Laborier | Politiques locales et enjeux culturels: les clochers d'une querelle[END_REF]. It originates in the radical denunciation of traditional cultural institutions by activists of a socalled "alternative" culture, coming both from small extreme-left groupings and also from the new social movements. Intellectuals and politically committed artists, such as Peter Weiss or Josef Beuys, became the heralds of this culture of "resistance". The culture promoted by this "critical" new left and the social movements included initiatives undertaken in urban districts to bring art out of the museums, as well as avant-garde artistic expression as a whole. To some extent, the sociocultural programmes also pursued the goal of rehabilitating and respecting the cultural practices of certain "minorities", whether understood in "ethnic", sexual, social or religious terms. The aesthetisication of everyday life was thus based on a "multicultural" approach.

Soziokultur was thus originally fostered by the "alternative" elements of the new left. Their challenge to the legitimacy of the State attracted a myriad of movements with a sociocultural vocation, forming so many composite intermediaries that would over the 1980s inflect the content of cultural policies under socialist municipal councils, by successfully claiming subsidies for their community projects.

THE INSTITUTIONALISATION OF NEW CATEGORIES OF ACTION

These processes of mobilisation were to a large extent, in France as in Germany, at the origin of the development of local cultural policies, in particular in suburban districts. In fact, they were followed by a twofold movement, professionalising and dividing up a sector progressively specified as "cultural", to the extent that its designation gradually shed the prefix "socio". This transition from multiform mobilisations evolving out of given circumstances to more compartmentalised local policies inscribed in established institutions and positions was not self-evident. For how are activist engagements converted into professional positions? How does one maintain a role of social intermediary while at the same time developing a cultural specialisation? The transformation was all the more problematic since, as well as their professional conversion, it also led to the relegation of agents and discourses that had promoted the very development of these policies.

Contradictions generated by a process of institutionalisation

The distinctive attribute of the anti-institutional movements, whose promoters campaigned for a break with preestablished categories, was to be brought up finally against a choice between disappearing and giving up on their original project. They could disappear when the initial activist engagement lost impetus; or they could give up on their initial principles when these groups became institutionalised, when wide-ranging forms of intervention became just one compartmentalised sector of activity, and when personal engagement gave way to professional positioning. From the 1970s in France, the development of the "sociocultural" sector was accompanied by a form of renunciation; in the Federal Republic of Germany, this was less pronounced and, above all, occured only later.

Firstly, community-based forms of mobilisation were progressively municipalised. The themes of "citizen participation" and "improved cohabitation" developed in France thanks to the fostering of cultural programs in "pioneering" cities from the middle of the 1960s onwards (notably in Grenoble and Rennes), and then very extensively after the muncipal elections of 1971 and 1977, which brought left-wing non-communist activists into municipal councils.

In the Federal Republic of Germany, politicians and intellectuals close to the German Socialist Party (SPD) or left-wing trades union organisations very rapidly set in motion, albeit in a euphemistic manner, the dynamic of institutionalisation, in groups for consultation and evaluation such as the Council of German Cities (Deutscher Städtetag) or the Society for Cultural Policy (Kulturpolitische Gesellschaft). Emphasis was placed largely on intermediary forms of culture, the improvement of the "living environment" and on the "humanisation" of new urban estates, as in France, as well as on defending more generally a "culture of daily life" for all.

The institutionalisation of socioculture in socialist regional governments or municipal authorities, as in the city of Frankfurt or the city-states of Berlin, Bremen and Hamburg, turned this policy into an object of competition between the SPD and the Greens. However, this competition was subsequently displaced once the programmes of conservative regional and federal governments at the end of the 1980s took socioculture into account. Certainly, this integration constituted a new opportunity for sociocultural animation, but at the same time it unhooked this animation from its activist networks as it based itself above all on criteria of professional competence.

The initiative for the creation in the FRG of alternative sites of culture came in over a third of cases from citizens" movements and in over half of the cases from individuals; administrative bodies seem to have occupied a marginal role in the organisation of socioculture (5.5%) and to have left all the initiative in this domain to "civil society" (see Hussmann"s survey, 1992). Nevertheless, once they had been set up, these district and local centres generally found themselves under the authority of municipal councils as far as the supervision of installations and the permanent employment of social workers were concerned.

Secondly, on the basis of these once activist and subsequently municipal practices, a new sector of intervention was constituted and recognised through the setting up of sites where it could be formalised, public forums constituted by the different specialists and practitioners involved. It was in this way that, despite conflicting representations of their cultural objectives, the different agents of cultural policy managed to establish a compromise through the construction of a common language.

The harmonisation and diffusion of this new model of public action were developed principally in the FRG through the framework of the Council of German Cities, a national pressure group representing municipal councils before the regional and federal governments. Its new strategic orientations of 1973 and the institutional launch of socioculture were the achievements of a group of critical intellectuals from the SPD (or close to this party) engaged in the implementation of municipal policies. In France, several bodies played a similar role: the Socialist Party"s Culture Office created in 1974, groupings of elected politicians (the FNCC and FNESR), federations issuing from the popular education movement (Léo-Lagrange Clubs, Houses for Youth and Culture, etc.), or again the sites for the training of animateurs (the CFNA, INJEP, and ADRAC…) as well as reviews (Cahiers de l'animation, Pour, Silex…). vi This transition from informal practices to municipal policies therefore brought with it a professionalisation of sociocultural activities. The transition from volunteers to salaried workers in these domains resulted in France, and to a lesser extent in the FRG, in a professionalisation of work previously carried out by activists and its transformation into specific types of activity paving the way for new kinds of professional logic. The processes of institutionalisation and professionalisation of cultural action were marked at the end of the 1970s, as much in France as in the FRG, by the intervention of new categories of agents in the social treatment of culture, who progressively took the place of the representatives of the community and activist networks. Once public action took over from voluntary action, and once the latter tended to be converted into professional specialisation, the management of issues became a technical matter requiring their conceptualisation in formal terms by experts thereby becoming effectively a delocalized form of management. This transition from voluntary worker to professional, from human qualities (the ability to relate to people, "charisma", etc.) to technical skills is described as an experience of being torn between two poles in the abundant literature on the "profession of animateur", which stresses more or less critically the difficulties of reconciling a politically based (in the broad sense of the term) personal engagement and the attributes required by the specialist seeking professional recognition. vii

Institutionalisation and relegation

The institutionalisation of a sociocultural sector did thus not take place without contradictions. Furthermore, whereas the voluntary activism characterising the sociocultural constellation helped local cultural policies to emerge, the institutionalisation of these policies and their "cultural" specification, the specialisation of the structures and of the agents implementing them led to a sidelining of the agents and discourses of the "sociocultural" domain, which had become the residue of a henceforth illegitimate inheritance.

The specification of cultural policies detached from the adjacent sectors of animation or leisure, autonomous with regard to the social networks that contributed to their emergence, and equipped with specific rules and norms, led to a considerable transformation of the position they occupied in the space of local society.

The process of professionalisation which characterised them meant that, over the course of their development, a whole series of social agents were sidelined (amateurs, voluntary workers, community activists, trade unionists, social workers, even politicians) who previously could have taken part in discussions. The principle of cultural delegation was thereby transformed: the agents authorised to speak of culture in the name of the social group were no longer those who through their voluntary commitment or political acitivity had been assigned representative functions, but rather those who could boast of a specialised competence, guaranteed by the fact that they belonged to the world of the professionals.

It is therefore understandable that local cultural policies, after a period of intense politicisation, might appear as depoliticised: those who were defining them had managed to win their autonomy with regard to elected politicians, but also with regard to politically constituted networks of support (politically partisan networks, or the post-1968 movement in France, for example).

It is equally understandable that this process was accompanied by a process of "delocalisation". Agents engaged in cultural matters had previously been predisposed by the position they occupied to invest in and valorize local matters (elected politicians "close to the people" and more generally on the political left, community activists issuing from the middle classes). This state of affairs was succeeded by the invention of professional positions, whose success implied the sidelining of both local attachments and also references to heteronomous discourses (political ideologies, and principles inherited from other social spaces, such as that of social work). The tendency that has often been observed for municipal cultural policies to become standardized is one of the indicators of this delocalisation -itself induced by the growing importance of norms defined in a nationally constituted professional milieu for the elaboration of these policies.

Finally, it is understandable that all this has been accompanied by what one could call the "de-socialisation" of local cultural policies. These policies had originally been constituted partly on the basis of collective mobilisations and around "social" objectives; they tended over the 1980s and 1990s to become a matter for "specialists" who proclaimed their political and social neutrality by invoking cultural excellence, and who were predisposed to assert specifically cultural objectives (the democratisation of culture, aid for contemporary creation, etc.) to the detriment of more "social" objectives that were left to the specialists of the sector for social action.

THE REINVENTION OF A "SOCIAL" ROLE

While over the 1980s, references to the social aspects of cultural animation were progressively eclipsed by other logics and agents (those of cultivated culture, the field of the media, economic interests, etc.), it seems that we have been seeing increasingly over recent years the reemergence of properly social objectives for the public treatment of culture. viii This reemergence has been particularly strong in France in working-class suburban zones, and in the Federal Republic of Germany in the context of unification, where the integration of the East German population raises likewise the problem of the "social" integration of certain marginalised social categories.

In France, since the end of the 1980s, this reemergence has given rise, for example, to the invention of new and diverse cultural and institutional forms, such as the public commissioning of contemporary works of art designed to "restructure urban space" and to "revitalise the democratic debate"; the setting up of writing workshops for young people experiencing difficulties; cultural support and legitmation for practices deemed specific to suburban areas, such as rap or graffiti; the sometimes very "cultural" tone of regeneration projects developed in the framework of urban policy (contracts issuing from the urban social development unit (DSQ) and from the unit for the social development of urban districts (DSQ)), etc. In the former East Germany, it is a question more generally of valorising initiative, the "apprenticeship" of individual autonomy and freedom of expression, and thus of implanting and transferring a tried and tested form of democratic culture (see Laborier, 1996a). Here, the federal public funds attributed to socioculture in the new regions partially take up again the explicit principles of the first institutions from the years 1975 to 1979, assigning themselves as objectives the intitiation of people into the social forms of political work and democratic culture, and the development of a culture of resistance against "fascist forces". Nevertheless, it is no longer a question in this context of mixing together different age-groups, social origins or nationalities, but rather of integrating German populations into the West German model. This reemergence of references to the social context in local cultural action only appears to represent a return. For this "return to the social context" assumes different forms to those prevalent over the first period, due to the presence of new types of agents, who are the bearers of different types of discourse and logic. It follows principally two paths that are contradictory as far as the "cultural theory" underpinning them is concerned (cf. [START_REF] Passeron | Figures et contestation de la culture[END_REF], but which are often mixed up in practice. The first path forms part of the movement aiming at the "cultural rehabilitation" of socially disadvantaged populations, developed especially over the period of the second Lang administration (1988)(1989)(1990)(1991)(1992)(1993). This cultural labelling consists in an ethnographic and/or aesthetic treatment (i.e., in both cases, conforming to the criteria of professional expertise) of practices that are external to the universe of consecrated culture, and indeed socially stigmatized. ix The second path of the "return to the social context" consists in the intervention of professional and recognised artists in "difficult zones". The case of public art has already been evoked, and one could add the funding of artists in residence in working-class districts, or again the staging of performances by theatre directors or choreographers in partnership with the local population. These practices can sometimes seem very close to two formerly prevalent and symmetrically opposed orientations. However, at least in rhetorical terms, they aspire to distinguish themselves from these, denying their proximity to classical cultural proselytism by stressing how they organise the capacity of the relevant social groups to voice their concerns in a cultural perspective, and denying their proximity to old-style sociocultural animation by stressing the reference to "creation" and the intervention of professional artists.

The reaffirmation of the necessary "social" anchoring of cultural policies (i.e. their mobilisation in the treatment of social problems) is thus not an identical repetition of the practices of the 1960s and 1970s which, after their relegation, have thereby been in part "recycled", x and hence partially integrated into the invention of new forms. This recycling is indeed partial: in France especially, sociocultural animation continues to act largely as a foil, even -and perhaps especially -for those cultural professionals who have invested most in "social" issues.

What, then, are the principal logics governing this "return to the social context" in local cultural policies? We would like to propose two hypotheses here, which by no means exclude others. The first hypothesis concerns the link between this "return to the social context" and the budget constraints weighing on cultural policies, which appear to exert opposite effects in the two countries. In the FRG, after a period of relative consensus, it is budgetary pressure that has brought Soziokultur back on the agenda, and it is denounced again as representing a bad use of public funds and is thus designated as a prime sector for cuts in the culture budgets. The reduction of sums allocated to culture seems to point more in the direction of a "social" reclassification of cultural expenditure. It is all as if, since the argmument of "cultural democratisation" now appears dated and the budgets are under threat, new types of "investments in appearance" xi had to be agreed that could provide justifications for funding in line with the political priorities proclaimed both locally and nationally of the "struggle against social exclusion" and the "reduction of social division". One should not fall prey to the cynical view that activities are simply being "dressed up" in social terms for selfserving ends, for the current conditions are no doubt likewise ripe for reactivating the belief among cultural professionals in the re-socialising virtues of their activities. Nevertheless, it is conceivable that many projects of so-called social "requalification" through culture (in the sense of rehabilitation) correspond also to a recategorisation in "social" terms of cultural interventions translated into and reproblematised through the perspective of the "struggle against social exclusion" and the restoration of the "social bond".

The second hypothesis concerns inverse movements between local and national levels in the two countries. In the FRG, Soziokultur, initially invented in a period of intense politicisation thanks to the emergence of the Greens as a political force, and then relayed by left-wing municipal councils, was by the end of the 1980s and the beginning of the 1990s accepted even by conservatives as a legitimate component of cultural policy. Thanks to reunification, the assertion of the necessary social anchoring of cultural policies would finally become part of a national discourse. In France, one sees in some ways a movement in the opposite direction. The process of professionalisation evoked above, and with it the relegation of the "sociocultural" domain, are largely the product of national policies initiated at the beginning of the 1980s. The same is the case for the "return to the social context" that takes place locally, not through some kind of revenge on the part of 1970s activists and animateurs, but to a great extent in conformity with the norms of the national model of professionalised cultural policies.

***

The attribution of social objectives -in the sens of social policies -to the public financing of culture is thus also a function of the relations between the different levels of public intervention -the local and the national levels in France, and the municipalities, regions and federal State in Germany. The differences between these sets of relations in the two countries helps explain the differences between the forms assumed by the "return to the social context". This rediscovery also goes beyond the national framework; it has become, so it seems, a norm at the European level.

Germany and France are not the only countries in Europe to have witnessed such an evolution. In Italy, public investment in culture has often been presented as useful in the struggle against unemployment, and in Ireland or Great Britain, it has been integrated partially into programmes of so-called social cohesion. As was the case in the 1970s around the notion of sociocultural animation in cities, an international institution such as the Council of Europe tends today to highlight in its programmes and meetings the need for a cultural dimension in projects of social integration, particularly in disadvantaged urban areas. The "struggle against social exclusion" is a topic for debate and the exchange of experiences among the networks of cultural professionals. xii Finally, the attribution of social policy objectives to the public financing of culture takes place especially at the level of the European Community, for several reasons. Firstly, the relative weakness up until now of European Union programmes for culture has led to funding for cultural projects to be sought via programmes with a "social" dimension (such as PHARE, or URBAN) and, consequently, to the "social" recategorization of these projects. Secondly, the resistance of representatives of several member States -in particular Great Britain -to the assertion of a European Union role in the cultural domain has made it necessary to resort to other than specifically cultural arguments to legimate the development of interventions in this domain. These have included arguments based on the promotion of European identity, support for development of the tourist industry and thus of the economy as a whole, or equally the notion of a "social cohesion" strengthened through culture.

Translated by Jeremy Ahearne recherche. Essais en l'honneur de Raymonde Moulin, Paris: La Documentation française.

i See e.g. [START_REF] Rigaud | Culture et pouvoirs publics sous la Cinquième République[END_REF]. For an overview of these debates, see [START_REF] Dubois | Politiques culturelles et politiques médiatiques[END_REF].

ii This was the case notably in Italy during the debates over 1995 and 1996 concerning the establishment of a "French-style" Ministry of Culture (see [START_REF] Monsaingeon | Un ministère pour la culture? L"Italie entre traumatisme, tutelle et tentation[END_REF]. The reference to the French case was also present when the regional government of Baden-Württemberg wanted in 1990 to unify responsibilities that were "dispersed" among five ministries under the authority of a grand regional ministry for culture (see [START_REF] Pongy | Politiques culturelles et régions en Europe[END_REF]. The reference to the "French model" was also present to a lesser degree during the debates associated with the creation of a British Department of National Heritage in 1992, and subsequently with the creation of a Department for Culture, Media and Sport in 1997. iii This comparative sketch is based on studies which originally had no directly comparative aim (see Dubois, 1994 and[START_REF] Dubois | La politique culturelle. Genèse d'une catégorie d'intervention publique[END_REF]Laborier, 1996). These empirical studies allowed us to adopt together a comparative perspective that looks to pay heed to the salutary warning and the propositions recently put forward by D. [START_REF] Gaxie | Remarques sur le comparatisme, le franco-centrisme et quelques autres sujets topiques[END_REF] iv See e.g. [START_REF] Pinçon | Classes moyennes, enjeux culturels et trajectoires sociales[END_REF][START_REF] Saez | Vers un mode d"être "culturel local[END_REF][START_REF] Simonot | Les couches moyennes au pouvoir: le cas de Louviers[END_REF][START_REF] Schulze | Die Erlebnisgesellschaft. Kultursoziologie der Gegenwart[END_REF] For a sociological analysis of the mobilisations through associations characterizing these "middle classes" in the cultural domain, see Balme, 1987. v vii See e.g. Besnard, 1980; Ion, 1982; Moulinier, 1980; Poujol, 1978; Simonot, 1974; Liebald, 1992; Hussmann and Steinert, 1990. viii For a partial survey of cultural projects structured around the "struggle against social exclusion" in France, see e.g. "La culture pour s"en sortir", Télérama, hors série, January 1996. One should add certain programmes of the Ministry of Culture, notably after 1995, such as those targetting 22 "difficult" suburban districts. See "L"an II des projets culturels de quartiers", Policultures: la lettre des politiques culturelles et artistiques, 15, April 1997; "Projets culturels de quartier: premier bilan", Lettre d'information du ministère de la Culture, 2, 29 janvier 1997. ix For a case-study, see Dubois, 1994a. x The expression is from Lascoumes, 1994. xi Investissements de forme -see Thévenot, 1986. xii One might cite, for example, the network of European suburbs, that has been based around the Laiterie in Strasbourg, and that is designed to valorise the cultural experiences of working-class districts; or, more punctualy, the meeting on 21-22 October 1996 at La Villette of representatives from 16 cultural institutions in different countries, who came together to debate the responses of cultural spaces to problems associated with unemployment, poverty and delinquency (see Bedarida, 1996).

  [Translator"s note: on post-war popular education groups, see Brian Rigby, Popular Culture in Modern France, London, Routledge, 1991, pp. 39-67] vi [Translator"s note: the FNCC stands for the National Federation of Communes for Culture; the FNESR for the National Federation of Socialist and Republican Politicians; the CFNA for the National Centre for the Training of Animateurs; the INJEP for the National Institute for Youth and Popular Education; and the ADRAC for *****************************************]


Anh-Lam Do

Olivier Sename

Luc Dugard

An LPV Control Approach for Semi-active Suspension Control with Actuator Constraints

This paper presents a new solution for the semiactive suspension control problem. First, a quarter vehicle model equipped with a semi-active damper is reformulated in the LPV framework using the nonlinear static semi-active damper model. This formulation allows to turn the control problem with dissipativity constraint into that with input saturation. Then the damper force saturation is taken into account in an original LPV fashion. This leads to the definition of a new LPV model with two parameters which is handled in a polytopic way. The H∞ control design for polytopic systems is then applied. The interest of the provided methodology is emphasized by simulations on a nonlinear vehicle model.

I. INTRODUCTION

Suspension systems play a key role in vehicles. A well designed suspension system may considerably improve not only the comfort (vibration insulation of the passengers against road irregularities) but also the road holding (the vehicle road contact). Today semi-active suspensions (like friction, Magneto-Rheological, Electro-Rheological suspension ...) are widely used in automobile industry because of some advantages: small weight and volume, low energy consumption (compared with active suspensions), low price, good performance... The control design problem for semi-active suspension systems has been tackled with many approaches during the last three decades. One of the first control methods to be applied in commercial vehicles is the Skyhook control [START_REF] Karnopp | Vibration control using semi-active force generators[END_REF]. In this linear-model based control design, the damping coefficient is adjusted continuously or switched between a maximum and a minimum value. Recently, the ADD (Acceleration Driven Damping) [START_REF] Savaresi | Identification of semiphysical and black-box models: the case of MR-dampers for vehicles control[END_REF] and the mixed Skyhook-ADD (SH-ADD) [START_REF] Savaresi | Mixed sky-hook and ADD: Approaching the filtering limits of a semi-active suspension[END_REF] algorithms, based on optimal control, have improved the Skyhook technique. Such controllers, however, can only provide a good comfort while neglecting the road holding. On the contrary, the ground-hook controller [START_REF] Valasek | Extended groundhook new concept of semi-active control of trucks suspension[END_REF], designed in a similar way to Skyhook controller, improves only the road holding. The vehicle performance can be improved by the hybrid control [START_REF] Gven | Semi active suspension control system development for a light commercial vehicle[END_REF] (combination of skyhook and ground-hook) and by the H ∞ control [START_REF] Sammier | Skyhook and H∞ control of active vehicle suspensions: some practical aspects[END_REF] since they improve both comfort and road holding.

The controllers above have been proved to enhance the performance of the vehicle. However, the nonlinear characteristic (the bi-viscous and the hysteretic behaviors of semiactive dampers) and especially the dissipativity constraint of a semi-active suspension are not taken into account in the The authors are with GIPSA-lab, Control Systems Dept, CNRS-Grenoble INP, ENSE3, BP 46, F-38402 St Martin d'Hères cedex, France {anh-lam.do, olivier.sename, luc.dugard}@gipsa-lab.grenoble-inp.fr design strategy. Then a clipped strategy is used to keep the dissipative behavior of the damper, without any performance guarantee [START_REF] Karnopp | Active damping in road vehicle suspension systems[END_REF], [START_REF] Sammier | Skyhook and H∞ control of active vehicle suspensions: some practical aspects[END_REF]. In [START_REF] Poussot-Vassal | New semi-active suspension control strategy through LPV technique[END_REF], an LPV approach is proposed in order to satisfy the dissipativity constraint. A scheduling parameter is indeed defined as the difference between the real controlled damper force and the required one given by the controller. The performance objectives are satisfied but the dissipativity constraint is not theoretically fulfilled. Moreover, no damper model is used in the synthesis (only the external forces are taken into account).

The main contribution of the present paper is to propose a new control design method for semi-active suspension which can reach the performance objectives while satisfying the dissipativity constraint. The methodology is based on a nonlinear static model of the semi-active damper, as in [START_REF] Guo | Dynamic modeling of magnetorheological damper behaviors[END_REF]. Hence the bi-viscous and hysteretic behaviors of the damper are taken into account. Then, the nonlinear system associated with the quarter vehicle model is reformulated in the LPV framework. The problem of dissipativity is then brought into the problem of input saturation. To solve the input saturation problem, a new design method is proposed that allows integrating the saturation actuator in the initial system to create a new LPV system. The LPV controller is then synthesized using the well-known results given in [START_REF] Apkarian | A convex characterization of gain scheduled H∞ controllers[END_REF] and [START_REF] Scherer | Multiobjective outputfeedback control via LMI optimization[END_REF]. The advantage of this method is that the control input always meets the saturation constraint and hence the dissipativity constraint is fulfilled.

This paper is organized as follows. In Section II, the LPV model for the quarter car with MR damper is developed. Then, a new solution for the problem of dissipativity constraint is proposed in Section III. In Section IV, some outlines about the H ∞ control for polytopic systems are presented and a controller for semi-active suspension is designed. In Section V, the results obtained in simulations with a nonlinear quarter car model are discussed. Finally, some conclusions and perspectives are drawn in Section VI.

II. PROBLEM FORMULATION A. System description

Consider a simple model of quarter vehicle (see Fig. 1) made up of a sprung mass (m s ) and an unsprung mass (m us ). A spring with the stiffness coefficient k s and a semi-active damper connect these two masses. The wheel tire is modeled by a spring with the stiffness coefficient k t . In this model, z s (respectively z us ) is the vertical position of m s (respectively m us ) and z r is the road profile. It is assumed that the wheelroad contact is ensured. The dynamical equations of a quarter vehicle are governed by:

m s zs = -F spring -F mr m us zus = F spring + F mr -k t (z us -z r ) (1)
F spring = k s z def : spring force. z def = z s -z us : damper deflection (assumed to be measured or estimated). żdef = żs -żus : deflection velocity (can be directly computed from z def ).

In this paper, the behavior of the semi-active suspension is represented using the following nonlinear equation, as in [START_REF] Guo | Dynamic modeling of magnetorheological damper behaviors[END_REF]):

Fmr = a 2 żdef + v 0 x 0 z def + a 1 tanh a 3 żdef + v 0 x 0 z def (2)
where a 2 , a 3 , v 0 and x 0 are constant parameters and a 1 is varying according to the electrical current in coil (0 < a 1min ≤ a 1 ≤ a 1max ). This model allows fulfilling the dissipativity constraint of the semi-active damper.

In the following, in order to better emphasize the controllable property of the damper, a 1 will be denoted as the control input, and for simplicity, the damping and stiffness parameters are defined respectively by:

• c mr = a 2 : damper damping coefficient

• k mr = a 2 v0 x0 : damper stiffness coefficient
The quarter vehicle using in this paper is the "Renault Mégane Coupé" model (see [START_REF] Zin | A nonlinear vehicle bicycle model for suspension and handling control studies[END_REF]) whose specific parameters are:

m s = 315 kg, m us = 37.5 kg, k s = 29500 N/m, k t = 210000 N/m.
The damper model parameters have been chosen according to the MR damper in [START_REF] Nino-Juarez | Minimizing the frequency in a black box model of a mr damper[END_REF]:

a 2 = 1500 Ns/m, a 3 = 129 s/m, v 0 = 0.788x10 -3 m/s, x 0 = 1.195x10 -3 m, F 0 = 200 N .

B. LPV model formulation

The nonlinear model ( 1)-( 2) is now rewritten in the LPV framework. Indeed, denoting:

ρ 1 = tanh a 3 żdef + v 0 x 0 z def (3)
the following state-space representation of the quarter-car model can be deduced as follows:

ẋs = A s x s + B s ρ 1 a 1 + B s1 w y = C s x s (4)
where

x s =(z s ,
-ks+kmr+kt mus -cmr mus     B s =     0 -1 ms 0 1 mus     , B s1 =     0 0 0 kt mus     , C s =     1 0 -1 0     T C.

Model reformulation

As explained above, the control signal a 1 must be positive (0 < a 1min ≤ a 1 ≤ a 1max ) so that the dissipativity constraint is satisfied. The positivity problem can be solved by defining u = a 1 -F 0 where F 0 is the mean value of a 1 (i.e F 0 = (a 1min + a 1max )/2). The positivity constraint of a 1 is recast as a saturation constraint on u (u can take values in [-F 0 ; +F 0 ] only). With this modification, the state-space representation of quarter vehicle is given as follows:

P : ẋs = (A s + B s2 ρ1 Cs2xs C s2 )x s + B s ρ 1 u + B s1 w y = C s x s (5)

III. TOWARD A CONTROL ORIENTED LPV MODEL ACCOUNTING FOR INPUT SATURATION

A. Ideal linear design

In (5) the control input matrix B s ρ 1 is parameter dependent, which is not consistent with the solution of the H ∞ design problem for polytopic systems [START_REF] Apkarian | A convex characterization of gain scheduled H∞ controllers[END_REF]. This problem can be easily solved by adding a strictly proper filter into Eq. ( 5) to make the controlled input matrix independent from the scheduling parameter (see [START_REF] Poussot-Vassal | Robust multivariable linear parameter varying automotive global chassis control[END_REF]):

F : ẋf u = A f B f C f 0 x f u c (6)
where A f , B f , C f are constant matrices. From Eq. ( 5) and Eq. ( 6) and denoting ρ 2 = ρ1 Cs2xs , the control oriented model is now represented by an LPV system with two scheduling parameters ρ 1 and ρ 2 (notice that ρ 1 and ρ 2 are not independent):

ẋ = A (ρ 1 , ρ 2 ) x + Bu c + B 1 w y = Cx (7)
where

x = x s T x f T T A (ρ 1 , ρ 2 ) = A s + ρ 2 B s2 C s2 ρ 1 B s C f 0 A f , B = 0 B f , B 1 = B s1 0 , C = C s 0 T ρ 1 = tanh(C s2 x s ) ∈ [-1; 1] ρ 2 = tanh(Cs2xs) Cs2xs ∈ [0; 1]
In this study, the LPV model ( 7) is used to design a polytopic (LPV) controller considering the convex set of bounded parameters (ρ 1 , ρ 2 ). However, such a controller may not ensure the closed-loop performances since the saturation constraint (i.e the dissipativity constraint) is not accounted for in the controller design. Some solutions for this problem have been proposed. For example, in [START_REF] Poussot-Vassal | New semi-active suspension control strategy through LPV technique[END_REF], a scheduling parameter is indeed defined as the difference between the real controlled damper force and the required one given by the controller. However the dissipativity constraint is not theoretically fulfilled. Another possible method is to add in the closed-loop system an AWBT (Anti Wind-up Bumpless Transfer) compensation (may be also of the form LPV) to minimize the adverse effects of the control input saturation on the closed-loop performance. In the next section, a simple method to solve the control problem with input saturation will be proposed.

B. A new solution for the problem of input saturation

First the system (7) (made up of a filter and a quarter vehicle) is augmented by adding a saturated actuator as in Fig. 2. where ----F P y u f u c u Fig. 2. Linear design with input saturation.

u = sat(u f ) =    F 0 if u f > F 0 u f if -F 0 ≤ u f ≤ F 0 -F 0 if u f < -F 0 (8)
To cope with a linear control design, the saturation function sat(u f ) is roughly approximated by a tangent hyperbolic function: F 0 tanh(

u f F0 ) or F 0 tanh( C f x f F0
). The state-space representation of the transfer function from u c to u is then:

F 1 : ẋf u = A f B f C f ρ 3 0 x f u c (9)
where

ρ 3 = tanh(α) α and α = C f x f F0
This leads to a slight modification of model [START_REF] Karnopp | Active damping in road vehicle suspension systems[END_REF] with new scheduling parameters ρ 1 * = ρ 1 ρ 3 and ρ 2 * = ρ 2 :

ẋ = A (ρ 1 * , ρ 2 * ) x + Bu c + B 1 w y = Cx (10)
Notice also that ρ * 1 and ρ * 2 are not independent. IV. CONTROLLER SYNTHESIS In order to improve the driving comfort (see [START_REF] Poussot-Vassal | New semi-active suspension control strategy through LPV technique[END_REF]), the frequency response of the vehicle body acceleration zs /z r must be kept small in the frequency range [0.5-10] Hz. For the road holding, the frequency responses of z us /z r must be small in [0-20] Hz. The frequency response of z def /z r should be small in [0-20] Hz to keep the damper deflection far from the structural limits. To make a controller satisfying these objectives, the H ∞ design method for LPV systems is used.

A. LPV systems and H ∞ controller

Definition 1: LPV generalized system. A dynamical LPV system can be described in the following form:

Σ(θ) :   ẋ z y   =   A(θ) B1(θ) B2(θ) C1(θ) D11(θ) D12(θ) C2(θ) D21(θ) D22(θ)     x w u   (11)
where x, w and u define the state, the exogenous and control input, respectively; z and y hold for the controlled output and system measure, respectively. θ(.) ∈ Θ is the set of varying parameters that describe a set of systems.

A ∈ R n×n , B 1 ∈ R n×nw , B 2 ∈ R n×nu , C 1 ∈ R nz×n , D 11 ∈ R nz×nw , D 12 ∈ R nz×nu , C 12 ∈ R ny×n , D 21 ∈ R ny×nw and D 22 ∈ R ny×nu are affine in θ. Definition 2: H ∞ LPV controller.
An LPV controller is defined by

K(θ) : ẋc u = A c (θ) B c (θ) C c (θ) D c (θ) x c y ( 12
)
where x c , y and u are the state, the input and output of the controller, respectively, of the controller associated to the system [START_REF] Scherer | Multiobjective outputfeedback control via LMI optimization[END_REF]. θ(.) ∈ Θ is the set of the varying parameters associated to the controller.

A c ∈ R n×n , B c ∈ R n×ny , C c ∈ R nu×n and D c ∈ R nu×ny .
The H ∞ control problem for the LVP system Σ(θ) consists in finding an LPV controller K(θ) such that the closedloop system is quadratically stable and that, for a given positive real γ, the L 2 -induced norm of the operator mapping w into z is bounded by γ for all possible trajectories of θ.

The LPV controller is obtained by solving an LMI problem. See the detail of this algorithm in [START_REF] Apkarian | A convex characterization of gain scheduled H∞ controllers[END_REF] and [START_REF] Scherer | Multiobjective outputfeedback control via LMI optimization[END_REF] or in the PhD thesis [START_REF] Poussot-Vassal | Robust multivariable linear parameter varying automotive global chassis control[END_REF]. For a polytopic set of parameters, the solution of the previous LMIs problem at each vertex of the polytope will give a controller. The convex combination of these controllers results in the global controller for LPV systems.

K(θ) = Co{ A c k B c k C c k D c k } (13)
where k = 1 : 2 i , i is the number of vertices of the polytope,

A c k B c k C c k D c k
is the controller corresponding to the k th vertex (see [START_REF] Poussot-Vassal | Robust multivariable linear parameter varying automotive global chassis control[END_REF] for more details).

B. Controller design for semi-active suspension

The considered control configuration is given in Fig. 4. With the performance objectives mentioned previously, the controlled output vector is z = (z s , z us ) T . The generalized system for the LPV controller synthesis is as follows: Note that F (s) = 50 s+50 is chosen with a sufficiently large bandwidth.

   ẋ = A (ρ 1 * , ρ 2 * ) x + Bu c + B 1 w z = C 1 (ρ 1 * , ρ 2 * ) x y = Cx (14) where x = x s x f T A (ρ 1 * , ρ 2 * ) = A s + ρ 2 * B s2 C s2 ρ 1 * B s C f 0 A f , B = 0 B f , B 1 = B s1 0 C 1 (ρ 1 * , ρ 2 * ) = C s1 ρ 1 * D s1 C f , C = C s 0 C s1 = -
D s1 = -1 ms 0 C s = 1 0 -1 0 zs z us W zs W zus z r u z def żdef ρ 1 * , ρ 2 * K(ρ 1 * , ρ 2 * ) P F z 1 z 2 - - - W zr - w 1 u f u c
To account for performance specifications, some weighting functions are added as usual in the H ∞ control approach. W zs and W zus have been chosen to emphasize frequencies up to 20 Hz and to reduce the peaks around 16 Hz for z us and z def .

W zs = s 2 +2ξ11Ω1s+Ω1 2 s 2 +2ξ12Ω1s+Ω1 2 , W zus = s 2 +2ξ21Ω2s+Ω2 2 s 2 +2ξ22Ω2s+Ω2 2 , W zr =3 × 10 -2 where Ω 1 = 2πf 1 with f 1 = 20 Hz, ξ 11 = 20, ξ 12 = 1, Ω 2 = 2πf 2 with f 2 = 11 Hz, ξ 21 = 20, ξ 22 = 1.
Due to the self-dependence between ρ 1 and ρ 2 , the set of parameters (ρ 1 * , ρ 2 * ) is not a polytope as seen in Fig. 3. In this preliminary study, ρ 1 * and ρ 2 * are considered as independent parameters and (ρ 1 * , ρ 2 * ) belongs to a larger polytope whose vertices are P 1 = (1, 1), P 2 = (-1, 1), P 3 = (-1, 0), P 4 = (1, 0). A controller for this LPV system is easily found by applying the H ∞ design method -polytopic approach presented above.

V. SIMULATION AND RESULTS

For the simulation, the spring force F spring is a nonlinear function of z def (see [START_REF] Zin | A nonlinear vehicle bicycle model for suspension and handling control studies[END_REF] for more details). In the following, the different cases are considered for the performance evaluation of the proposed methodology:

• Passive = Renault Mégane Car equipped with an optimized passive damper. • SH-ADD = Renault Mégane Car equipped with a semiactive damper whose damping coefficient is tuned by the SH-ADD strategy (see [START_REF] Savaresi | Mixed sky-hook and ADD: Approaching the filtering limits of a semi-active suspension[END_REF]). • H ∞ /LP V Control = Renault Mégane Car equipped with a semi-active damper controlled by the proposed methodology.

A. Frequency domain analysis

The criterion used for the evaluation is the power spectral density (PSD) measure of the frequency responses (z s /z r , z us /z r , z def /z r ) according to a sinusoidal road profile of magnitude z r = ±1.5cm whose frequency is varying (see [START_REF] Sammier | Skyhook and H∞ control of active vehicle suspensions: some practical aspects[END_REF]).

P SD f1→f2 (x) = f2 f1 x(f )df (15)
Let us recall that the performance objectives are as follows:

• Comfort: decrease the gain of zs /z r over [0.5-10] Hz.

• Road holding: decrease the gain of z us /z r over Hz. In Tab. I, the comparison of the PSD criteria is made w.r.t the passive case as follows:

I p = passive PSD -X PSD passive PSD (16)
where X stands either for SH-ADD or H ∞ /LP V control methods. Notice that I p > 0 means that there is an improvement w.r.t the passive case and I p < 0, a deterioration, in terms of performance.

As seen in Fig. 5-7 and Tab. I, the frequency response zs /z r (the comfort) in the H ∞ /LP V case is better than that in the passive case but worse than that in the case using the SH-ADD strategy (which is known to be comfort oriented). For the road holding, the frequency response z us /z r in the H ∞ /LP V case is better than that in both the passive and the SH-ADD cases. The peak value of the gain of z us /z r in the H ∞ /LP V case is sharply reduced comparing to those in both other cases. The suspension stroke (z def ) is also improved in the sense that it is much better than in the passive case and slightly better than in the SH-ADD case.

B. Time domain analysis

In the time domain simulation, z r is a uniformly distributed random signal with amplitude between [-2.0 cm ; 2.0 cm] and period of 0.5 s. The vehicle responses (z s , z s , z us , z def ) are compared between the different strategies and respectively given in Fig. 11121314. The proposed H ∞ /LP V methodology allows getting globally much better performances than the passive and SH-ADD suspensions, improving comfort and road holding. As shown in Fig. 8, the input force u provided by the semi-active controller is within the range [-200 N ; +200 N]. The damper force F mr then satisfies the dissipativity constraint thanks to the H ∞ /LP V methodology (see Fig. 9). Finally, the scheduling parameters ρ 1 * , ρ 2 * mostly vary for significant changes of z r to allow for controller adaptation.

VI. CONCLUSION

In this paper, a new method for semi-active suspension control was proposed. An LPV model for a quarter vehicle with a semi-active damper is formulated and an LPV controller is synthesized to improve the driving comfort and the road holding capability in the frequency range of interest respectively. The results in the frequency and time domains have shown that the performance objectives can be reached while satisfying the dissipativity constraint of the damper. In future works, to enhance the performance, the reduction of the conservatism in the controller design will be considered. The variation of the semi-active damper parameters (a 3 , v 0 , x 0 and specially a 2 ) will be taken into account to well adapt the controller to real applications.

Fig. 1 .

 1 Fig. 1. Model of quarter vehicle with a semi-active damper.

  żs , z us , żus ) T , w=z r , y=z s -z us measured output.

3 T

 3 where B s2 = 0; -F0 ms ; 0; F0 mus T , C s2 = a3v0 x0 ; a 3 ; -a3v0 x0 ; -a Note that the term c mr żdef +k mr z def +F 0 ρ 1 corresponds to a nominal MR damper force (u = 0).

Fig. 3 .

 3 Fig. 3. Set of (ρ 1 * , ρ 2 * ) (shade area + curved line) and set of (ρ 1 , ρ 2 ) (curved line).

Fig. 4 .

 4 Fig. 4. Block diagram for semi-active suspension control.

Fig. 5 .

 5 Fig. 5. Nonlinear frequency responses zs/zr.

Fig. 6 .

 6 Fig. 6. Nonlinear frequency responses zus/zr.

Fig. 7 .

 7 Fig. 7. Nonlinear frequency responses z def /zr.

Fig. 8 .

 8 Fig. 8. Control input u.

Fig. 9 .

 9 Fig. 9. MR damper force Fmr versus deflection velocity.

Fig. 10 .

 10 Fig. 10. Scheduling parameters ρ 1 * and ρ 2 * .

Fig. 11 .

 11 Fig. 11. Time reponses zs.

Fig. 12 .

 12 Fig. 12. Time reponses zs.

Fig. 13 .

 13 Fig. 13. Time reponses zus.

Fig. 14 .

 14 Fig. 14. Time reponses z def .

•

  Suspension stroke: limit the gain of z def /z r over [0-20] Hz.

			Ip : Performance improvement in %
	Signal	Passive PSD SH-ADD H∞/LP V
	zs/zr	234.7	50.6%	17.7%
	zus/zr	1.089	-1.6%	7.9%
	z def /zr	1.066	14.5%	16.2%


N Sadaka

J F Ponge

Climatic effects on soil trophic networks and the resulting humus profiles in holm oak (Quercus rotundifolia) forests in the High Atlas of Morocco as revealed by correspondence analysis

Multivariate methods have been widely used for revealing the structures of communities, and in this paper we explore one particular method, namely correspondence analysis (also called reciprocal averaging) for studying humus profiles by the 'method of small volumes'. The present study was done on humus profiles under holm oak (Quercus rotundifolia), an evergreen Mediterranean species, in the High Atlas of Morocco. Three sites (1500 m, 1700 m, 1900 m altitude) and two years (1999 and 2002) were compared. The humus form is Dysmull (mull with thick litter horizons), with variations in the thickness of OL (entire leaves), OF (fragmented leaves with faecal pellets) and A (hemorganic) horizons according to altitude and year. The dead leaves are rapidly incorporated into holorganic (earthworm, insect) and hemorganic (enchytraeid) animal faeces, which form the bulk of OF and A horizons. The S horizon (weathering parent rock) shows the greatest development of the root system.

Introduction

The analysis of topsoil horizons based on the identification of humus components created by biological activity (animal faeces, plant organs at different decomposition stages), called 'method of small volumes' [START_REF] Ponge | Étude écologique d'un humus forestier par l'observation d'un petit volume, premiers résultats. I. La couche L1 d'un moder sous pin sylvestre[END_REF][START_REF] Bernier | Humus form dynamics during the sylvogenetic cycle in a mountain spruce forest[END_REF], may help to throw light on foodwebs in the soil, and their changes under natural or human influences. Traits of the past and trends for the future may also be derived from the observation of successive horizons [START_REF] Bernier | Humus form dynamics during the sylvogenetic cycle in a mountain spruce forest[END_REF][START_REF] Gillet | Humus forms and metal pollution in soil[END_REF].

When several humus profiles, taken from different sites, have to be compared, our interest could be to find a synthetic description of the whole set of samples, beside the information given by individual profiles. The purpose of the present study was to apply a multivariate method to the description of a set of humus profiles, each taken in a given environmental condition, when the absence of replication prevents the use of statistical tests.

As an example, six humus profiles, each composed of a varying number of layers, have been compared in mountain holm oak forests (Quercus rotundifolia) from the Moroccan Atlas, where large differences are expected to occur according to altitude and time.

Given the efficiency of correspondence analysis (Greenacre, 1994) for disentangling complex relationships between living organisms and ecological factors in the absence of replication [START_REF] Ponge | Biocenoses of Collembola in Atlantic temperate grass-woodland ecosystems[END_REF][START_REF] Loranger | Does soil acidity explain altitudinal sequences in collembolan communities[END_REF], we postulated that this multivariate method could be applied to the analysis of the complex variation in humus profiles which result from changes in litter amount and climate effects on soil animal and microbial communities.

Compared with the leaves of deciduous oak, evergreen oak leaves decay slowly because they are tough and contain much lignin and tannin. Despite these features, which indicate recalcitrance of the litter towards microbial decomposition, [START_REF] Rapp | Cycle de la matière organique et des éléments minéraux dans quelques écosystèmes méditerranéens[END_REF] observed a rapid incorporation of dead leaves in humus, pointing to the importance of soil fauna as active comminuters and humifiers of the litter. Previous studies have shown that the white rot Marasmius quercophilus Pouzar was chiefly responsible for the strong loss of weight and the increase in nitrogen content observed when leaves of Q. rotundifolia become bleached (Sadaka-Laulan & Ponge, 2000a), and that this fungus, and the leaves it colonized, were highly attractive to saprophagous fauna (Sadaka-Laulan & Ponge, 2000b). Thus we may hypothesize that, although at first sight resistent to microbial degradation, holm oak litter decomposes through an active trophic network involving mutual relations between microbes and animals [START_REF] Lavelle | Interactions, hiérarchies et régulations dans le sol: à la recherche d'une nouvelle approche conceptuelle[END_REF][START_REF] Lavelle | Ecological challenges for soil science[END_REF].

Material and methods

Holm oak with sweet acorns (Quercus rotundifolia Lam.) is an evergreen Mediterranean tree common in western Mediterranean countries (Morocco, Algeria, Tunisia, Central Spain), mostly in mountains where it tolerates a dry and cold climate [START_REF] Achhal | A propos de la valeur bioclimatique et dynamique de quelques essences forestières au Maroc[END_REF][START_REF] Barbero | Le chêne vert en région méditerranéenne[END_REF]. It is characterized by persistent, spiny, sclerophyllous foliage. Litter falls throughout the year, mainly from April to June. The thickness of litter is determined by seasonal litter fall, decomposition rate, and biennial cycles of large and small amounts of litter input [START_REF] Rapp | Cycle de la matière organique et des éléments minéraux dans quelques écosystèmes méditerranéens[END_REF][START_REF] Poli | Produzione di littiera nella lecceta del M. Minardo (Etna) nel periodo Settembre 1970-Giugnio 1974[END_REF]Sadaka-Laulan & Ponge, 2000a).

Study sites

We made our study in 1999 and 2002 in a holm oak forest at Toufliht (on the northern slopes of the High Atlas, Morocco). The climate is sub-humid to semi-arid Mediterranean, with most precipitation from October to February and a long warm dry period from May to September (mean annual rainfall 840 mm; maximum summer temperature ca 30.5°C and minimum winter temperature ca 1°C). The parent rock is Triassic molasse comprising alternating beds of red clay, sandstone and conglomerate [START_REF] Beauchamp | Reconstitution d'un milieu de sédimentation dans les molasses rouges Triasiques du Haut Atlas[END_REF].

Three sites (SI, SII and SIII), where Q. rotundifolia is the dominant tree species (3-7 m height, 85-95 %cover), were chosen according to an altitudinal gradient from 1500 to 1900 m above sea level. At the site SI (1500 m, N-NE aspect), the shrub layer consisted of Juniperus oxycedrus L. and Cistus monspeliensis L. At SII (1700 m, N-NE aspect), the shrub layer consisted of J. oxycedrus, C. monspeliensis, Cistus salvifolius L. and Nerium oleander L. At SIII (1900 m, E-SE aspect), the evergreen oak was associated with J. oxycedrus, Pinus halepensis L., Cistus laurifolius L. and Chamaerops humilis L.

Despite variations in litter thickness, the humus form is always of the Dysmull type [START_REF] Brêthes | Classification of forest humus forms: a French proposal[END_REF], with a thick (> 1 cm) OF horizon and an A horizon with a microcrumb structure. The pH (in water) of the A horizon was 5.5-5.8. The A horizon overlaid a S horizon, made of weathered parent rock.

Sampling procedure

In 1999 and 2002, at each site, a humus block 25 cm² area and 8.5 to 11.5 cm depth was excavated by the method devised by [START_REF] Ponge | Étude écologique d'un humus forestier par l'observation d'un petit volume, premiers résultats. I. La couche L1 d'un moder sous pin sylvestre[END_REF]. It was cut with a sharp knife, with as little disturbance as possible, and the litter and soil surrounding it were gently excavated. Layers, about 0.5 to 2.5 cm thickness, were separated directly in the field from the top to the bottom of the profile on the basis of morphological differences visible to the nake eye, and immediately preserved in 95% ethyl alcohol (Table 1). Their thickness was noted beforehand. Biogenic structures present in the different layers were fixed and consolidated through precipitation of colloids by ethyl alcohol. Samples were classified into OL (entire leaves), OF (fragmented leaves with faecal pellets), A (hemorganic horizon) and S (mineral horizon), taking as a basis the classification of forest humus horizons by [START_REF] Brêthes | Classification of forest humus forms: a French proposal[END_REF]. When several layers were sampled in the same horizon (on the basis of visible differences) they were numbered according to their order from the top to the bottom of a given horizon, for example OL1, OL2, OF1, OF2... Thus A2 (Table 1) was not an A 2 horizon (eluvial horizon in past European classifications) but it was just the second layer sampled in the A horizon.

The fixed material was examined under a dissecting microscope (at x40 magnification), with a cross reticle in the eye piece. Each layer was transferred to a Petri dish filled with ethyl alcohol, then a 200-point grid was positioned over the studied material, and the points that covered each class of humus component were counted. Countings were summed for each class then transformed into volume percentages of the total solid matter (soil matrix). Classes were determined from litter and soil components according to their origin (plant, animal, microbial, mineral) and the stage of decomposition or mineral weathering. This method, devised by [START_REF] Ponge | Étude écologique d'un humus forestier par l'observation d'un petit volume, premiers résultats. I. La couche L1 d'un moder sous pin sylvestre[END_REF] and modified by [START_REF] Bernier | Humus form dynamics during the sylvogenetic cycle in a mountain spruce forest[END_REF], allows determination of the percentage by volume of each class at a given depth. In the present study, 61 classes were identified (Table 2).

Data analysis

Data (percentages of occurrence of the 61 classes in the 40 samples) were subjected to correspondence analysis (CA), a multivariate method using the chi-square distance between individuals and between variables in a symmetrical manner [START_REF] Greenacre | Theory and Applications of Correspondence Analysis[END_REF][START_REF] Ponge | Biocenoses of Collembola in Atlantic temperate grass-woodland ecosystems[END_REF][START_REF] Loranger | Does soil acidity explain altitudinal sequences in collembolan communities[END_REF]. This method has also been called reciprocal averaging [START_REF] Hill | Reciprocal averaging: an eigenvector method of ordination[END_REF][START_REF] Hill | Correspondence analysis: a neglected multivariate method[END_REF]. The different classes of humus components were the active variables, coded by their percentage of occurrence by volume, estimated by the corresponding number of points divided by the total number of points counted [START_REF] Bernier | Humus form dynamics during the sylvogenetic cycle in a mountain spruce forest[END_REF]. The nature of the corresponding horizon (OL, OF, A, S), the year (1999,2002), the site (SI, SII, SIII) and the depth at which the samples were taken were treated as passive variables, i.e. they were projected on the factorial axes as if they had been involved in the analysis, without contributing to the factorial axes. They were coded as 1 or 0. The absence of contribution of passive variables to factorial axes is the main difference between simple correspondence analysis (CA) and canonical correspondence analysis or CCA [START_REF] Ter Braak | The analysis of vegetation-environment relationships by canonical correspondence analysis[END_REF]. The absence of correction of the 'arch effect' or detrending by rescaling data is the main difference between the original method (CA) and detrended correspondence analysis or DCA [START_REF] Hill | Detrended correspondence analysis: an improved ordination technique[END_REF]. We preferred CA to CCA because the second method violates several of the original principles of CA established by [START_REF] Benzécri | L'analyse des données. II. L'analyse des correspondances[END_REF], in particular that the model should follow the data and not the contrary. We preferred CA to DCA because the 'arch effect' appears when only one gradient is depicted by the data. In this case we prefer to project samples and variables on a single axis [START_REF] Ponge | Soil fauna and site assessment in beech stands of the Belgian Ardennes[END_REF][START_REF] Loranger | Does soil acidity explain altitudinal sequences in collembolan communities[END_REF], avoiding the use of scatter graphs which show a distorted cloud of points.

In order to give the same weight to all variables (active and passive) they were transformed to mean 20 and unit variance by

X = (x-m)/s + 20,
where x is the original value, m is the mean of a given variable and s is its standard deviation. The addition to each standardized variable of a constant 20 made all values positive, because correspondence analysis deals only with positive numbers, commonly counts (Greenacre, 1994). Following this transformation, factorial coordinates of variables can be interpreted directly in terms of their contribution to the factorial axes. The transformation used here gives to correspondence analysis most properties of the wellknown principal components analysis, while keeping the advantage of the simultaneous projection of variables and samples on the same factorial axes and the robustness due to the principle of distributional equivalence [START_REF] Greenacre | Theory and Applications of Correspondence Analysis[END_REF].

Results

Before pointing to the advantages of multivariate methods for the simultaneous analysis of all samples, we examine the information for the individual humus profiles.

Examination of individual humus profiles

Figures 1 to 3 represent the vertical distribution of main classes of humus components in the six profiles (Table 2). For simplifying the graphs, some classes were pooled. The graphic representation of humus components follows the method used commonly for results from pollen analyses and which [START_REF] Gillet | Humus forms and metal pollution in soil[END_REF] have recently applied to the vertical distribution of humus components by replacing plant species by humus components and time by depth. As expected, the holm oak leaves were rapidly transformed into fragments and animal faeces, and these became rapidly enriched in mineral matter (Figure 1). The humus forms is typical of the mull group. The distribution of entire leaves changes with altitude, the OL horizon becoming thicker at higher elevation (compare Figure 1 with Figures 2 and3).

Accordingly, fragmented leaves occur deeper in the soil and the OF horizon becomes thicker when altitude increases. Roots are found in the OF horizon, but they are more abundant in the A horizon and still more in the S horizon. Mycorrhizae symbiotic with the ascomycete Cenococcum geophilum Fr. (jet black and shiny, with erect hair hyphae) follow the distribution of the whole root system of holm oak but their role increases with altitude.

Rhizomorphs of Marasmius are present in OL and OF horizons, but disappear beneath.

Organic-dominant animal faeces (small epigeic earthworms, insects and undetermined fauna) are present in the OL horizon, increase in volume in the OF horizon then progressively disappear in the upper part of the A horizon. Mineral-dominant animal faeces (enchytraeids and undetermined fauna) are almost absent from the OL horizon, but they are abundant (up to 36% of the soil matrix) in the OF and in the A horizon. They decrease abruptly in the S horizon. Pure mineral matter increases steadily from OF to A then to S horizon, where it comprises the bulk of the soil matrix.

Correspondence analysis

The matrix analysed was composed of 40 columns (samples, see Table 1) and 61 rows (classes of humus components, see Table 2) with percentages of occurrence at the intercept, transformed as mentioned above. Axes 1 and 2 of correspondence analysis extracted 24% and 10% of the total variance, respectively. Classes of humus components (active variables) and of horizon names (passive variables) were projected in the plane of the first two factorial axes (Figure 4). The farther a variable was projected from the origin of the axes (barycentre) along a factorial axis, the more it contributed to this axis. We have not shown the projection of individual samples, because we prefer to deal with bulk variables such as depth levels, horizons, altitudes, years. This does not change anything to the analysis, but it simplifies the interpretation of the results. The cloud of humus components in the plane formed by the the first two factorial axes shows the existence of three poles, corresponding to OL, OF and S horizons, respectively. The A horizon is intermediate between OF and S, without any typical composition. The plane formed by the first two axes thus displays the vertical distribution of humus components. The simultaneous projection of depth indicators helps to visualize the vertical gradient. The OL horizon is most often restricted to the topmost centimetre, whereas the OF horizon is expressed mostly between 2 and 4 cm depth, the A horizon between 5 and 6 cm and the S horizon underneath. Notice that indicators of depth or horizon names help to reveal mean trends, without taking into account the variation which may occur from a humus profile to another.

A wide variety of litter components (24 among 61) are present in the OL horizon, expressing the variety of plant organs from several species which fall on the ground. Brown as well as bleached entire and nibbled oak leaves can be recognized (classes 1, 2, 3, 4), as well as herb leaves (8), Cistus leaves (9), Juniperus oxycedrus needles and galbuli (10, 11), and other organs such as acorns (12), buds (15), flowers (16), twigs (17), petioles (19), wood (22). Lichens ( 23), living and dead mosses (24, 25), rhizomorphs of Marasmius quercophilus (39, 40), entire and fragmented arthropod cuticles (60, 61) are also components of this superficial horizon, which reflects the composition of litter fall and the first stages of its degradation (nibbling by fauna, bleaching by white rot).

The OF horizon consists mainly of brown and bleached oak leaf fragments (classes 5, 6), bleached leaves skeletonized by fauna (7). Organic-dominant faeces (44,46,48), hemorganic enchytraeid faeces (43), mineral-dominant faecal masses (49), complex assemblages of holomineral faeces and mycelia, with (51) or without roots (50), and mycelial masses (42) constitute other typical components of this horizon. Thus this horizon is the main centre of microbial and faunal activities in the litter, and mineral matter is mixed with the litter there through the deposition of mineral or hemorganic faeces.

Although the composition of the A horizon is not as typical as that of other horizons, some components are more abundant in this horizon than in the others. This is so for fine roots (27), mycorrhizae (36, 41), unidentified plant fragments (26), unidentified mineraldominant faeces (47), but coarse sand (56) and gravels (59) are also present. The development of the feeder root system of oak is prominent in this hemorganic horizon.

The S horizon, in addition to its richness in fine sand (57) and weathered rock (58), is the centre for living and dead lignified roots (29,30,31,32,33), decaying unlignified fine roots and mycorrhizae (28,34,37), as well as roots and plant fragments embedded in mineral matter (35,55). Sclerotia of C. geophilum (38) are also present. Typically this horizon shows the anchorage of the root system of oak in the weathering parent rock. Note that in this horizon large roots (33) as well as fine roots (34) are often attacked by the mycorrhizal fungus C. geophilum, which gives them a jet black colour.

The projection of passive variables corresponding to sites (SI, SII, SIII) revealed the effects of altitude on the composition of humus profiles, although these effects are not as pronounced as depth (as shown by their distance to the origin, shorter than that of horizon names). In SI, situated on the positive side of axis 2, humus profiles show a more rapid transition from the OL horizon to the S horizon than in SII and SIII, projected on the negative side of Axis 2 (see also Figures 1,2,3). This phenomenon is better visualized by the projection of depth indicators when the three sites are distinguished (Figure 5). The SI run does not exhibit pronounced trends towards the negative side of Axis 2, in contrast to SII and more especially SIII. Moreover, the OL horizon is thicker at SIII than in the lower two sites, since in the upper site the OF horizon is not reached before 3-4 cm depth. The S horizon is reached as soon as 4-5 cm at SI, but not before 6-7 cm at SII, and 7-8 cm at SIII.

The projection of year indicators in the plane of the first two axes (Figure 4) reveals changes according to year, in particular changes in the respective development of horizons could be suspected. The projection of depth indicators separated by years may throw light on this pattern (Figure 6). In 1999, at 2-3 cm depth the litter exhibits a composition intermediate between that of an OL and that of an OF horizon, while in 2002 it has typically the composition of an OF horizon. This can be seen on Figures 1,2,3, by comparing the ultimate depths at which entire and nibbled leaves (which comprise the bulk of the OL horizon) are still present in 1999 (left side) and 2002 (right side). This means that the OL horizon was thicker in 1999 than in 2002, although this was not perceived to the naked eye in the field (see horizon thicknesses at the bottom of Figures 1 to 3, see also Table 1). Another trend depending on the year is the composition of the S horizon. In 2002 the composition of this horizon is clearly different from that of the A horizon, while differences between the two horizons are not so pronounced in 1999 (Figure 6). Examination of original data reveals that decaying roots (28,30,32,34), classified as typical of the S horizon by the analysis, were more abundant in 2002 than in 1999, reaching 18.4% of the total matrix in 2002 at SIII (compared to 8.6% in 1999(compared to 8.6% in ), 16.6% in 2002(compared to 8.6% in at SII (compared to 9.9% in 1999)). The same phenomenon was not observed at lower altitude (13.3% in 2002(13.3% in , 13.1% in 1999 at SI) at SI).

Discussion and conclusion

The humus profiles we examined under Q. rotundifolia contained much activity by fungi and fauna, despite the resistence to decay of the dead oak oak leaves. Dysmull, characterized by the presence of a thick OF horizon and an A horizon with a crumby structure [START_REF] Brêthes | Classification of forest humus forms: a French proposal[END_REF], was constant, in both years and at all three elevations. Fauna evidently had nibbled and skeletonized the holm oak leaves, even in the OL horizon, and had deposited of faecal pellets in the underlying OF horizon. Faeces from small earthworms (organic-dominant), enchytraeids (hemorganic) and insect larvae (holorganic) occurred in this horizon. Despite its crumby structure, the A horizon was imperfectly expressed. Rather, it was transitional between the OF horizon, enriched in mineral matter through the deposition of mineral faeces (mostly enchytraeids), and the S horizon, which was the source of mineral matter for these tiny oligochaetes. By the importance of enchytraeid activity, the observed Dysmull shares several properties with moder, except that in moder holorganic faeces accumulate, forming a dark, organic-dominant OH horizon [START_REF] Ponge | Horizons and humus forms in beech forests of the Belgian Ardennes[END_REF]. Under the Mediterranean climate, fauna are active deeper than under moister and colder climate, which favours the mixing of organic matter with mineral matter [START_REF] Peltier | Humus forms in mediterranean scrublands with aleppo pine[END_REF]. Causes can be found in (i) dryness of the litter during the summer, which makes it inaccessible to drought-intolerant animals, such as enchytraeids [START_REF] Babel | Influence of high densities of fine roots of Norway spruce on processes in humus covers[END_REF][START_REF] Abrahamsen | Ecological study of Enchytraeidae (Oligochaeta) in Norwegian coniferous forest soils[END_REF], and (ii) the deep development of roots, which makes them better protected from desiccation [START_REF] Salisbury | Plant Physiology[END_REF]. Roots are important food for animals living in the soil [START_REF] Baylis | A survey of the invertebrates feeding on living clover roots (Trifolium repens L.) using 32 P as a radiotracer[END_REF][START_REF] Gunn | The exploitation of food resources by soil meso-and macro invertebrates[END_REF]. In the humus profiles studied they were found mainly in the S horizon.

The influence of altitude appears mainly through an increase in the thickness of OF and A horizons (seen mainly in Site SII at 1700 m) and in the thickness of the OL horizon (seen mainly in Site SIII, at 1900 m). Lower temperature is the main cause of the decrease in soil biological activity at higher altitude [START_REF] Van Cleve | Respiration rates in the forest floor of birch and aspen stands in Interior Alaska[END_REF][START_REF] Djellali | Étude de l'activité biologique des sols de la steppe à alfa d'Algérie. Minéralisation du carbone et de l'azote[END_REF]. It seems that the increase in thickness of OF and A horizons (where most fauna are active) is due mainly to less microbial activity (slower mineralization of organic matter once incorporated into animal faeces), whilst the increase in thickness of the OL horizon is likely to be due to less faunal activity (slower fragmentation of litter, delaying the passage to the OF horizon). Note, however, that the humus form did not change with altitude, probably because the threshold of resilience of the mull type was not reached within the altitudinal range studied [START_REF] Belotti | Variability in space and time and redundancy as stabilizing principles of forest humus profiles[END_REF].

We did not measure litter fall for this study, and so we can only speculate about the effects of variations in litter input between the two years 1999 and 2002. The fact that more roots were dead in 2002, whilst litter was thinner, was possibly due to a lack of protection of the root system from desiccation during the warm season in years with a poor litter fall. If this is true, this may have consequences for the composition and the vertical distribution of animal and microbial communities in the soil, since it implies an alternation in the disposal of two important food sources: roots (in years with little litter input) and foliage (in years when there was much).

Correspondence analysis proved useful for the simultaneous analysis of several humus profiles, especially in the absence of replication, i.e. when dealing with heterogeneous environments.

Legends of figures

Figure 1 Vertical distribution of the main components of the soil matrix (class numbers indicated in Table 2) at Site SI (1500 m). Depth as abscissa. Percentage of the total matrix volume as ordinate (arbitrarily mirrorred on the negative axis for clarity).

Figure 2

 2 Figure 2 Vertical distribution of the main components of the soil matrix (class numbers

Figure 3

 3 Figure 3 Vertical distribution of the main components of the soil matrix (class numbers

Figure 4

 4 Figure 4 Correspondence analysis. Projection of humus components (categories, codes in

Figure 5

 5 Figure 5 Correspondence analysis. Projection of depth indicators (for each site) in the plane

Figure 6

 6 Figure 6 Correspondence analysis. Projection of depth indicators (for each year) in the plane

Fig. 3

 3 Fig.3

  Fig.4

Table 1

 1 Layers (with their thickness in cm) sampled in the three study sites. A dash means that the layer was not present in the profile studied

	5	2.0

Table 2

 2 The classes of humus components, coded by numbers

	55%								55%
				Brown entire leaves (1)				Brown entire leaves (1)
	55%								55%
				Bleached entire leaves (3)				Bleached entire leaves (3)
				Nibbled leaves (2 + 4)				Nibbled leaves (2 + 4)
				Leaf fragments (5 + 6)				Leaf fragments (5 + 6)
				Other leaves and plant organs (8 -22)			Other leaves and plant organs (8 -22)
		Roots (27 + 28 + 29 + 30 + 31 + 32 + 33 + 34)		Roots (27 + 28 + 29 + 30 + 31 + 32 + 33 + 34)
		Mycorrhizae Cenococcum geophilum
				(36 + 37)					Mycorrhizae Cenococcum geophilum (36 +
										37)
		Rhizomorphs Marasmius
			quercophilus						Rhizomorphs Marasmius quercophilus (39 +
				(39 + 40)						40)
				Organic-dominant faeces (44 + 45 + 46 + 48)				Organic-dominant faeces (44 + 45 + 46 + 48)
				Mineral-dominant faeces (43 + 47 + 49 + 50 + 51 + 52)			Mineral-dominant faeces (43 + 47 + 49 + 50 + 51 + 52)
		Hemorganic masses + plant fragments
		and roots embedded in mineral particles		Hemorganic masses + plant fragments and
				(35 + 54 + 55)					roots embedded in mineral particles (35 + 54
										+ 55)
		Mineral fraction (56 + 57 + 58 + 59)			Mineral fraction (56 + 57 + 58 + 59)
						Depth / cm		Depth / cm
	0
	0
	0	1	2	3 4	5	6	7	8.	0 1 2 3 4 5 6 7 8 9 10
	OL OF		A		6 S			OL	OF	A	S
				SI (1999)						SI (2002)
	Fig. 1