European nuclear nationalism

UK and French perspectives on nuclear disarmament

Nick Ritchie and Benoit Pelopidas

The UK and France were the first sub-superpowers to develop nuclear forces after participating in the US Manhattan Project. Despite critiques in the two countries, the British and French decision-making elites never felt that a US pledge of extended nuclear deterrence could substitute for what they regarded as independent nuclear forces (Pelopidas 2015a). In both countries, the development of a nuclear arsenal coincided with the loss of a colonial Empire, the brutalizing impact of six years of "total war" against Nazi Germany, and the forging of an uncertain new world order. Both countries have justified the continued possession of nuclear weapons through reference to notions of "strict sufficiency" (French Government 2008: 120, 168, author's translation;French Government 2013: 73; Simon-Michel 2014a: 2) to meet evolving conceptions of "minimum deterrence" throughout the nuclear age. After the Cold War, both countries initiated modernization programs for their nuclear forces (French Government 2008: 170) while at the same time reducing their numbers, which is now the general tendency across nuclear-armed states [START_REF] Mecklin | Disarm and modernize[END_REF]. Since the Ottawa declaration of 1974, 1 the two nations, both founding members of NATO, have argued that their nuclear forces contribute to the deterrent capacity of the Alliance (North Atlantic Council 1974: para 6;NATO 2010: para 18). In 2010, the two countries signed a fifty-year treaty to develop and operate joint nuclear warhead diagnostic facilities in the UK and France, which cemented a nuclear-armed path dependency for both nations for the foreseeable future (Harries 2012). Beyond these commonalities, France and the UK have had different approaches to the possibility of nuclear disarmament; these derive from the different post-Second World War national narratives in which the development of nuclear weapons has been embedded. This started from two different attitudes toward the NATO Alliance and its nuclear component, two different sets of lessons learned from the 1956 Suez crisis (Pelopidas 2015a), and it culminated in two different reactions to the increase in nuclear disarmament advocacy worldwide, which is the focus of this chapter.

The UK conducted its first nuclear test in 1952, becoming the third country to do so. In 1957, it entered the ranks of the thermonuclear 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 powers with the detonation of a 1.8 megaton shot off Christmas Island in the central Pacific. Three years later, in February 1960, France detonated its first A-bomb in the Algerian desert. In October 1964, the air component of the French nuclear forces entered service and, in 1968, Paris detonated its first H-bomb. In 1971, the land-based component was finalized in Provence with eighteen silos built on the plateau d'Albion, where short-range Pluton and Hades missiles would be placed. In 1972, the first French ballistic missile submarine, Le redoutable, entered service. In the 1990s, the land-based component of the French nuclear forces and the test site in the Pacific Ocean were dismantled.

The UK currently has a nuclear stockpile of 225 warheads that arm its US-designed and built Trident II (D5) submarine-launched ballistic missiles deployed aboard four Vanguard class ballistic missile submarines. The system is collectively referred to as "Trident," which encompasses the missiles, submarines, and warheads. The UK embarked on a long, expensive, and controversial project to replace the Trident system in 2007, beginning with the procurement of a new class of ballistic missile submarines. 2 The intention is to retain a strategic nuclear weapons capability well into the second half of the twenty-first century after the new submarines enter into service in the 2020s and 2030s.

The French arsenal is similarly expected to last for the next two to three decades at least, with the recent addition of modified nuclear-tipped airto-air missiles (ASMPA) and the four French ballistic missile submarines that are being adapted to deploy the new M-51 submarine-launched ballistic missiles, a new version of which is being developed. The French President has ordered preparatory studies for the third generation of ballistic missile submarines, the replacement of Mirage 2000N by Rafale, and the evolution of the ASMPA cruise missile, as well as the preparation of the successor generation, ASN4G, which are referred to in laws detailing the military programs for 2014-2019(French Government 2014: 38).

The UK decision to replace the Trident system was driven by a number of factors, notably the perceptions of strategic national security threats from nuclear-armed adversaries and an abiding belief in the efficacy of nuclear deterrence (what [START_REF] Booth | Beyond nuclearism[END_REF] call "nuclearism"). 3 Other factors include the importance of reproducing the "special relationship" with the USA, industrial concerns about retaining a sovereign capability to build nuclear-powered submarines, and, perhaps most importantly, a particular elite conception of national identity in terms of who "we" think we are and how we think "we" should act in the international political arena. The latter reflects what Hennessy (2007a) labels a "gut instinct" that the UK should be and must remain a nuclear power.

There is, however, resistance to "business-as-usual" for another generation of nuclear weaponry. This is reflected in deep disquiet within the UK government and among the general public about the necessity and wisdom of investing heavily in reproducing a strategic nuclear weapons capability procured in a different era to deter an adversary that no longer exists, despite difficult relations with Russia over its annexation of Crimea in 2014 and the strategic destabilization of Ukraine. It is rooted in concerns about cost in an era of welfare austerity and significant cuts in the defense budget. It reflects a different hierarchy of national security challenges in which nuclear weapons have little value, as well as a desire to support the nuclear Non-Proliferation Treaty (NPT) by taking significant steps toward nuclear disarmament (Ritchie 2012). This last point of resistance was transformed by the resurgence of an international nuclear disarmament agenda in January 2007, just a month after the Labour government under Tony Blair published the White Paper The Future of the United Kingdom's Nuclear Deterrent in December 2006, setting out the case for the replacement of Trident.

Since the late 1970s, with the conversion of the French socialist party to nuclear deterrence and the progressive decline of the communist party, which similarly gave up criticizing nuclear deterrence, French officials have shown no similar discomfort with the possession of nuclear weapons by the Republic and no major governing party is opposed to a continued possession of nuclear weapons. The green parties oppose both nuclear weapons and nuclear power, which puts them at a political disadvantage in a national context in which more than 70 percent of electricity comes from nuclear sources. It would be false, however, to argue that there has not been any criticism of those weapons in France. Critical voices are simply left out of official circles (Pelopidas 2012(Pelopidas , 2015b)). For example, non-violent movements (religious or not), environmentalists, and military personnel willing to preserve the link between the army and the nation have formulated critiques for a long time. In 1964, the year when the first component of the French nuclear arsenal entered service, Georges Izard, a lawyer who would soon become a member of the Académie française, published his Lettre affligée au général de Gaulle [Afflicted letter to General de Gaulle] [START_REF] Izard | Lettre affligée au général de Gaulle [Afflicted letter to General de Gaulle[END_REF], which summarized almost all the non-communist and non-moral critiques that are voiced today. The weapon system was described as: primarily dangerous due to the impossibility of protecting populations against a nuclear strike and the status of primary target granted by the possession of nuclear weapons; potentially useless and resulting from a misguided inability to accept that France was now a middle power; and, finally, too onerous. [START_REF] Izard | Lettre affligée au général de Gaulle [Afflicted letter to General de Gaulle[END_REF] suggested that, instead of accepting its status as a middle power, France used the bomb to compensate for the loss of both its empire and its rank among the nations of the world. In the military, a majority was opposed to a French A-bomb between the end of the Second World War and the Reggane test in 1960. Even before the test, several anti-nuclear traditions had made powerful cases against nuclear weapons. One opposed the nuclearization of the country in the name of the priority that should be given to the preservation of the empire. Others voiced a civic critique that nuclear weapons were tantamount to a technocratic elite dispossessing the body politic of its control over its own defense and, as a consequence, citizens were likely to lose their sense of responsibility for the defense of the nation as they lost their sense of voluntary sacrifice for it. A third critique started with the latter assessment of a loss of responsibility and sense of sacrifice, but saw it as the source of a weakening of the population in the case of a conventional war.

Nuclear disarmament resurgent

In both the UK and France, the positive response to renewed advocacy in favor of a world without nuclear weapons was mostly based on a strategy of creating the conditions for nuclear disarmament rather than practicing it, even if the UK's rhetorical commitment to the goal is less ambiguous than the French.

In the UK, the Labour government responded to the powerful call by et al. (2007) for "a world free of nuclear weapons" by declaring its full commitment to this aim and a determination to take an active leadership role in examining the practical steps and challenges involved. In June 2007, the UK Foreign Secretary Margaret Beckett declared that, "When it comes to building this new impetus for global nuclear disarmament, I want the UK to be at the forefront of both the thinking and the practical work. To be, as it were, a 'disarmament laboratory' " (Becket 2007). In January 2008, the UK Prime Minister Gordon Brown pledged that the UK ". . . will be at the forefront of the international campaign to accelerate disarmament among possessor states, to prevent proliferation to new states, and to ultimately achieve a world that is free from nuclear weapons" [START_REF] Brown | Speech at the Chamber of Commerce in Delhi[END_REF]. In February 2008, the UK Defense Secretary Des Browne gave a speech entitled "Laying the foundations for multilateral disarmament" at the Conference on Disarmament in Geneva. He said, ". . . the UK has a vision of a world free of nuclear weapons and, in partnership with everyone who shares that ambition, we intend to make further progress toward this vision in the coming years."

In February 2009, the UK Foreign Secretary David Miliband published a policy information paper Lifting the Nuclear Shadow: Creating the Conditions for Abolishing Nuclear Weapons, which said, "We need an assertive and cooperative strategy, founded on the premise that the goal of a nuclear weapons free world is achievable" (Foreign and Commonwealth Office 2009: 3). The following month, Prime Minister Gordon Brown declared in a speech that the UK would develop ". . . a credible roadmap toward disarmament by all the nuclear weapons states -through measures that will command the confidence of all the non-nuclear weapons states" [START_REF] Brown | Speech on nuclear energy and proliferation[END_REF]. The roadmap was published later that year (Cabinet Office 2009). The UK hosted a conference of the five recognized nuclear weapons states (the UK, France, China, Russia, and the USA) in September 2009 in London to explore confidence-building measures toward nuclear disarmament, the first conference of its kind. Follow-up meetings took place in Paris, Washington, and Geneva, and then again in London (Ritchie 2013).

Outside the UK government, four former foreign and defense secretaries, Malcolm Rifkind, David Owen, Douglas Hurd, and George Robertson, mirrored their transatlantic colleagues with an article in The Times in June 2008 that said the world must "[s]tart worrying and learn to ditch the bomb." They argued: Substantial progress towards a dramatic reduction in the world's nuclear weapons is possible. The ultimate aspiration should be to have a world free of nuclear weapons. It will take time, but with political will and improvements in monitoring, the goal is achievable. We must act before it is too late, and we can begin by supporting the campaign in America for a non-nuclear weapons world. (Rifkind et al. 2008) Their call was endorsed by 277 MPs in a parliamentary Early Day Motion on the Nuclear Security Project the following month [START_REF] Willett | Nuclear Security Project. Early Day Motion 2053[END_REF]).

In the coalition government that came to power in 2010, the Conservative Party's pre-election Green Paper on National Security stated, "In the context of progress in nuclear disarmament and reduction, the UK must be prepared to take a rigorous look at whether we can take our excellent record in this area further forward" (Conservative Party 2009: 13). Conservative MP David Lidington, later Minister for Europe at the Foreign and Commonwealth Office, said: . . . [the] party welcomes the specific proposals that have been put forward by Schultz, Kissinger, Perry and Nunn. . . . We agreed too with the long-term objective of a world free of nuclear weapons, though we think that the path to that goal is likely to be slow and painstaking. [START_REF] Lidington | Speech at the Nuclear Policy Lab at the Royal Society[END_REF] Some changes to UK nuclear weapons policy were subsequently made in the Coalition's Strategic Defence and Security Review published in October 2010 (Cabinet Office 2010). The review announced further reductions in the UK's nuclear stockpile and an updated negative security assurance to non-nuclear weapons states party to the NPT. The Liberal Democrats, as the junior party in the Coalition, consistently supported the idea of a world free of nuclear weapons. They argued that the UK can and should take further steps "down the nuclear ladder"' by cutting the nuclear force yet further and removing it from permanent alert (Liberal Democrats 2013;Ritchie 2009) Tertrais 2007Tertrais , 2009aTertrais , 2009bTertrais , 2010[START_REF] Tertrais | Defence of Deterrence. The Relevance, Morality and Cost-Effectiveness of Nuclear Weapons[END_REF]. As a result, the goal of a world without nuclear weapons is almost never mentioned by high-level public officials in France.

The February 2015 speech by French President Francois Hollande is an exception as he declared that France ". . . does not want to give up on the goal of disarmament itself, including that of nuclear disarmament" (Hollande 2015, authors' translation). In 2012, his election as President of the French Republic led some observers to anticipate a change in the French reluctance toward nuclear disarmament, mostly because he was the first left-wing president in seventeen years and that, in a context of austerity, the defense budget was expected to decrease. However, the incoming president had emphasized his continued attachment to French nuclear weapons during the presidential campaign and, once elected, made sure that the false impression would not last by choosing to embark on the most recent French ballistic missile submarine, Le Terrible, on July 4, 2012, only a few months after his inauguration. This is symbolically powerful as no French president had made such a visit since Valery Giscard d'Estaing in 1974. In February 2015, President Hollande clearly stated, "The international context does not allow any weakness and shows that the era of nuclear deterrence is not over" (Hollande 2015, authors' translation). Consequently, we can mostly see continuity between the December 5, 2008 letter by President Sarkozy to the United Nations Secretary-General Ban Ki-Moon about nuclear disarmament, while France was still assuming the rotating presidency of the European Union, and the later practice of President Hollande. The focus of the letter was on the goal of "a safer world" and on measures of arms control and transparency away from immediate 1 2 3 4 5 6 7 8 9

European nuclear nationalism 231 1 2 3 4 5 6 7 8 9

nuclear disarmament practice (Sarkozy 2008a). Similarly, Sarkozy had campaigned in 2007 on the idea of being "at odds" ("la rupture") with his predecessors, but his nuclear weapons policy showed demonstrable continuity with the policy followed since the 1970s (Pelopidas 2012). However, the rise of nuclear disarmament advocacy has had a significant impact on the former policy elites in France and triggered a limited debate in Parliament and among civil society. A 2012 report from the Working Group on the Future of French Nuclear Forces within the Commission on Foreign Affairs, Defense and Armed Forces of the Senate noted that:

. . . if we had to design a format of army today starting from scratch, it is very likely that the necessity to acquire a nuclear force de frappe, with two legs, would not be part of our ambitions for defense.

(French Senate Commission on Foreign Affairs, Defense and Armed Forces 2012)

This paragraph has had a significant impact, in particular on critical voices against nuclear weapons [START_REF] Desportes | Interview with one of the authors[END_REF]Quilès et al. 2013: 92). Similar to the phenomenon described in the UK, groups mixing personalities from the right and left of the political spectrum have appeared in France and joined forces under the European Leadership Network headed by (now Lord) Des Browne. The only high-level government official who has been publicly opposed to nuclear weapons for a long time is former French Prime Minister Michel Rocard. He participated in the 1996 Canberra Commission and has since then been writing introductions and forewords to books trying to bring nuclear disarmament back into the French debate. In 1996, he wrote a long, partly autobiographical foreword to the French version of the report of the Canberra Commission (Rochard 1996) and, in 2009, did the same for the critique of the illogic of the nuclear arms race by Le Guelte (Rochard 2009). In the spring of 2015, he wrote the foreword to the French translation of disarmament advocate Ward Wilson's book Five Myths about Nuclear Weapons (Rocard 2015). As he himself confessed in December 2013, he had been preaching alone in the desert for a long time (Pascallon 2015). However, starting in the late 2000s, a French "gang of four" gathered around him (Rocard, Juppé, Richard, and Norlain) and published an article in the French newspaper Le Monde (Rocard et al. 2009). General Bernard Norlain is a former director of the Institute for National Defense Studies and was head of the military cabinet for the French Prime Ministers Michel Rocard and Jacques Chirac; Alain Juppé is a former French Prime Minister and Alain Richard is a former Defence Minister. Since then, Alain Richard and Alain Juppé have stayed away from nuclear disarmament advocacy, but former Defence Ministers Paul Quilès (1985)(1986) and Herve Morin (2007Morin ( -2010) ) have become vocal about the issue. Quilès created an association Arrêter A few prominent scientists and public intellectuals joined the discussion, including physicist Albert Jacquard and former diplomat Stephane Hessel (Hessel and Jacquard 2012) and, in a context of austerity, a few military voices advocated the dismantlement of the air leg of the French arsenal, or at least the opening of a serious debate about it [START_REF] Desportes | L'arme nucléaire oubliée du débat français [Nuclear weapons, forgotten from the French debate[END_REF][START_REF] Desportes | Interview with one of the authors[END_REF]. In spite of these differences, we examine in the next section how the political leaderships in the UK and France have maintained a commitment to nuclear weapons.

UK and French commitment to nuclear weapons

The formal UK response to the global zero initiative sparked by Shultz et al. (2007) and cemented by US President Barack Obama's speech in Prague in April 2009 [START_REF] Obama | Remarks by President Barack Obama in Prague[END_REF]) was generally positive. The validity of a world free of nuclear weapons was accepted and a desire to be at the forefront of developments among the nuclear weapons states was strong, particularly for Labour and the Liberal Democrats.

Nevertheless, the legitimacy of UK nuclear weapons and the practice of nuclear deterrence have not been questioned in Whitehall (Ministry of Defence and the Foreign and Commonwealth Office 2006: 17). None of the main Westminster political parties is committed to relinquishing nuclear weapons. All are committed to replacing Trident in some form and retaining nuclear weapons well into the future, with the Conservatives and Labour committed to a like-for-like replacement of the current system [START_REF] Coaker | Speech at the Royal United Services Institute[END_REF]Hansard 2010;Hammond 2013). Anything less than such "essential protection" risks fatally undermining the nation's security, they argue (Robertson et al. 2013). The debate led by the Liberal Democrats over possible alternatives is about the more limited aim of rethinking nuclear deterrence to reduce the salience of nuclear weapons, while retaining the capability to deploy them within a specific period of time should a major military threat to the survival of the state ever re-emerge. Successive UK governments have acknowledged that the UK currently faces no major direct nuclear threat and has not faced such a threat since the early 1990s (Cabinet Office 2008: 12). "Unilateralism" remains a dirty word in Westminster after Labour's sojourn into the political wilderness in the 1980s, partly as a result of its electorally unpopular platform of nuclear disarmament (Stott 2006).

What we have witnessed, then, is an aspirational, but conditional, rhetorical commitment to the idea of a world free of nuclear weapons. The commitment is one of working to "create the conditions" for a "step-bystep" approach to nuclear disarmament through multilateral negotiations between the nuclear-armed states (Cabinet Office 2010: 37). In this context, the UK insists that now is not the time for it to get rid of its own nuclear weapons, but to forge ahead with the Trident replacement program. Nuclear weapons are judged to provide a vital insurance against an uncertain future. In fact, necessity and insurance in the face of uncertainty is the central theme of contemporary UK nuclear weapons policy. It is a mantra that was developed under Tony Blair and adopted by David Cameron, who has repeatedly asserted that UK nuclear weapons are ". . . the ultimate insurance policy against blackmail or attack by other countries. That is why I believe it is right to maintain and replace it [Trident]" (Hansard 2011) and that "Trident and its replacement are non-negotiable. They are an absolutely vital part of this nation's security" (Hansard 2015). The UK will therefore retain its weapons for as long as other states possess them and until there is ". . . global adherence to obligations not to proliferate nuclear weapons or related technology, under the NPT and other treaties and export control regimes" (Ministry of Defence and the Foreign and Commonwealth Office 2006: 15). Furthermore, the UK will only consider entering a multilateral nuclear disarmament process after further significant nuclear force reductions by the US and Russia. For example, Alistair Burt, Parliamentary Under-Secretary of State at the Foreign and Commonwealth Office, said:

In order for the UK to offer to include its small number of nuclear weapons in multilateral disarmament negotiations there would first need to be further reductions in the much larger nuclear weapons stockpiles held by other states and greater assurances that no new major threats will emerge that could threaten the UK or its vital interests.

(Hansard 2013)

Significant qualitative changes in UK nuclear weapons policy to complement its post-Cold War quantitative force reductions have also been fiercely resisted, such as proposals to de-alert the nuclear arsenal advocated by the Liberal Democrats [START_REF] Miller | UK cannot afford to be complacent[END_REF]. Instead, the marker of the UK's commitment to nuclear disarmament has been periodic "salami slicing" of the UK nuclear arsenal. While force reductions are clearly to be welcomed, an exclusive focus on quantitative reductions has sidelined international expectations of the much wider and deeper qualitative changes required to meet Article VI disarmament commitments under the NPT (Ritchie 2014).

Nevertheless, the juxtaposition of the global zero agenda with the initiation of the Trident replacement process gave some presentational problems for the UK. There is an evident diplomatic tension between commencing the Trident replacement program underpinned by an enduring commitment to the logic of nuclear deterrence and remaining a firm supporter of the logic of nuclear disarmament in the NPT. The UK has been criticized in the NPT, along with other nuclear weapons states, for the continued modernization of its nuclear weapons and delivery systems because they reinforce the value of nuclear weapons and the practice of nuclear deterrence [START_REF] Minty | Statement to Preparatory Committee for the 2010 NPT Review Conference, Cluster 1 Issues[END_REF]. This has made it difficult for the UK government to credibly support a universal norm against nuclear proliferation while insisting that it needs these weapons for its own security for the foreseeable future, particularly when the UK faces no strategic nuclear threat (Ritchie 2007). As Director General of the International Atomic Energy Agency Mohammed El Baradei said in February 2007, the UK cannot ". . . modernize its Trident submarines and then tell everyone else that nuclear weapons are not needed in the future" [START_REF] Blair | UN nuclear watchdog call Trident hypocritical[END_REF]. This criticism has also been leveled at home. Writing in The Times in January 2009, three former senior military figures, Field Marshal Lord Bramall, General Lord Ramsbotham, and General Sir Hugh Beach, argued, "The UK does not need a nuclear deterrent" and that:

. . . it is difficult to see how the UK can exert any leadership and influence on this issue [nuclear disarmament] if we insist on a costly successor to Trident that would not only preserve our own nuclear-power status well into the second half of this century but might actively encourage others to believe that nuclear weapons were still, somehow, vital to the secure defence of self-respecting nations. [START_REF] Bramall | UK does not need a nuclear deterrent[END_REF] The UK has attempted to manage the tension between the two by pursuing a nuclear posture of "minimum deterrence" and demonstrating political leadership on nuclear disarmament. This has required extensive discursive labor to legitimize the long-term retention of nuclear weapons through the expensive recapitalization of Trident system while framing the UK as a nuclear disarmament champion. suggested earlier, President Hollande inscribed his defense policy within a framework in which nuclear disarmament remains a long-term possibility.

Since the end of the Cold War, the size of the French nuclear forces has diminished significantly to less than 300 warheads and France still wants to appear at the forefront of progress toward a safer world while renewing its commitment to nuclear weapons. After 1995, France stopped nuclear testing, signed and ratified the Comprehensive Test Ban Treaty, and started advocating its entry into force. By 1998, the Mururoa test site in the Pacific, the fissile material production facilities, and the land-based component of the nuclear forces had been dismantled; the number of ballistic missile submarines permanently at sea was reduced to one and the level of alert of the French nuclear forces was reduced twice. Following the announcement by President Sarkozy in 2008 (Sarkozy 2008b), the size of the air leg of the French nuclear forces has been reduced by one-third. During the 2014 Preparatory Committee to the NPT Review Conference, the French Ambassador announced that he would sign the protocol to the Nuclear Weapon Free Zone Treaty in Central Asia and that France was also prepared to sign the protocol to the Southeast Asian Nuclear Weapon Free Zone Treaty (Simon-Michel 2014a, 2014b). Those accomplishments coexist with the modernization of the arsenal outlined above (Journé 2011: 131-138).

The two dynamics are articulated via the invocation of an unpredictable and dangerous post-Cold War international context in which nuclear weapons remain the ultimate guarantor of French "vital interests," both in presidential speeches and in the White Paper on Defence and National Security (French Government 1994: 52;2008: 69, 315;2013: 127). The latest instance can be found in Hollande (2015). Already in the military realm in 1994, the preservation of nuclear deterrence was conceived within the framework of ". . . less immediate risks than before, more diffuse and varied risks, but persisting ones or maybe increasing ones in the foreseeable period" (French Government 1994: 57, authors' translation). The 2008 White Paper reuses this motif of an increasingly dangerous and unpredictable world (French Government 2008: 11, 14, 300, 315) in which nuclear weapons need to be maintained and modernized. This unpredictability opens the possibility of strategic surprises and technological breakthroughs. In such a context, the reliance on an air-based component and not only on a submarine-based nuclear force is presented as protecting ". . . our deterrence against [. . .] an unexpected technological breakthrough in the fields of air defense, missile defense or submarine detection (French Government 2008: 169-170, authors' translation). Here we can see similar justificatory narratives in the UK and France rooted in uncertainty, necessity, and insurance metaphors.

Most importantly, in France, nuclear disarmament is never isolated from conventional disarmament and the broader security context (Sarkozy 2008a(Sarkozy , 2008b;;Simon-Michel 2014a, 2014b: 3;Hollande 2015) disarmament is portrayed as a multilateral and incremental process toward general and complete disarmament and, while France keeps talking about ". . . exerting its responsibilities when it comes to disarmament" (Simon-Michel 2014a, 2014b), the framework in which this is supposed to be done is within the Permanent 5 process, where the focus is on transparency in the number of warheads and verification. Transparency is then presented as necessary to create the conditions for nuclear disarmament and as a sign of French progressive policies in that matter, but it is also compatible with classic policies of arms control and deterrence (Hollande 2015; Simon-Michel 2014b). From the French official perspective, ". . . the next logical step of multilateral disarmament" is the negotiation of a Fissile Material Cut-Off Treaty within the Conference on Disarmament (Simon-Michel 2014a: 3, authors' translation). In the end, a world without nuclear weapons is simply not the end goal; the consistent end goal from the French official perspective remains ". . . a safer world for all and to create the conditions for a world without nuclear weapons" (Simon-Michel 2014a: 4, authors' translation) which fundamentally relies on nuclear deterrence in the face of an uncertain future.

The French attachment to nuclear weapons and nuclear deterrence is also visible in the boundaries of what is publicly debated on the issue in France, within the very limited space this debates occupies (see Pelopidas 2015a). Both the pro-and anti-nuclear deterrence camps accept the fact that nuclear deterrence is technologically driven and that there is a ". . . preeminence of technology over doctrine" (Quilès et al. 2013: 14). While the opponents are trying to use this fact as a critique, the pro-nuclear weapons camp regards it as a reality of the sector. Even the former commander-in-chief of the French Oceanic Strategic Force recognized this [START_REF] Desportes | Interview with one of the authors[END_REF][START_REF] Desportes | Interview with one of the authors[END_REF]Pascallon 2015). This does not mean that France will deploy any nuclear technology, but, as a result, modernization and technological developments never have to be justified by a strategic or doctrinal purpose; they become acceptable as determinants of the national arsenal. Moreover, the limited French debate is not really about nuclear deterrence. It is rather a debate in the name of nuclear deterrence. In spite of the context of austerity, the law defining military programs for 2014-2019, as well as the presidential speeches, emphasize the need for both legs of the French nuclear arsenal to perform its mission of deterrence credibly. In the name of their perpetuation, modernization is presented as necessary (Hollande 2015; French Government 2014). To clarify that the debate on the possibility of limiting the mission of nuclear deterrence to submarines would not have consequences in the next electoral cycle, French Minister of Defense Jean-Yves Le Drian opened a conference in November 2014 to celebrate the fiftieth anniversary of the French Air Strategic Force and restate its continued relevance (Le Drian 2014).

Overall, political elites in the UK and France remain committed to nuclear weapons and, in spite of their diverging degree of public commitment to the goal of a world free of nuclear weapons, both use similar rhetorical strategies to negotiate the tensions between the long-term goal of abolition and the continued need for nuclear weapons. In both countries, the policy goal is not to disarm, but to create the conditions for nuclear disarmament; while nuclear weapons keep being portrayed as an insurance against the unforeseeable, minimum deterrence or strict sufficiency are presented as signs that both countries are ahead of others as far as nuclear disarmament is concerned.

Identity and fear

The UK's desire to play a global leadership role in nuclear disarmament and retain nuclear weapons as a major power, highlights the significance of identity in nuclear politics. In fact, the "ontological insecurity" [START_REF] Mitzen | Ontological security in world politics: state identity and the security dilemma[END_REF]) generated by the prospect of becoming a nuclear weaponless state is a core driver of the UK's determination to replace Trident. This is reflected in the party political fear of a partisan attack by the right-wing press for being "weak" on defense if a radical change in UK nuclear weapons policy is pursued. For many, a decision to become a non-nuclear weapons state by not replacing Trident would signal a dramatic downgrading of the UK's "rank" in the international hierarchy of states (Willet 2007). The Conservative Mayor of London Boris Johnson declared in February 2015:

If a Labour-Scottish National Party coalition were to junk Trident, Britain would be vulnerable to nuclear blackmail; but it is worse than that. We would suffer a public and visible diminution of global authority; we would be sending a signal that we no longer wished to be taken seriously; that we were perfectly happy to abandon our seat on the UN Security Council to some suit from Brussels; that we were becoming a kind of military capon. [START_REF] Johnson | If we want to be taken seriously, we have to defend ourselves[END_REF] The possession of nuclear weapons has been an important part of the UK's identity in international politics since the late 1940s. Throughout the Cold War this "nuclear" identity centered on Britain's wider self-identity as a major world power, the USA's primary political and military ally, and a vital part of the Western bulwark against the Soviet ideological and military threat. The Soviet Union has long since been consigned to history and no major strategic nuclear threat has emerged to take its place, but the UK's identity as a major power remains firm and the historical association in the UK between major "powerdom" and the possession of nuclear weaponry remains equally strong. part of the currency of being a major power" (Smith 2005: 449). From the mid-1990s, Tony Blair and later Gordon Brown reproduced this identity within a New Labour framework and renewed the long-standing association between Britain's identity as a major power and its possession of nuclear weapons. The coalition government has continued this theme and reproduced a post-Cold War identity of the UK as a responsible nuclear power deploying purely defensive and therefore benign nuclear arms in support of international peace and stability. The possession of nuclear weapons reaffirms and, in part, constitutes the collectively held identity of the UK as an interventionist, "pivotal" power and defender of the international community operating alongside the USA through NATO. It reflects a historical narrative originating in the initial acquisition of a nuclear capability and chronicled in detail by Hennessy (2007b). It is a powerful collective identity, the reproduction of which generates a "national interest" in the continued deployment of strategic nuclear weapons. In essence, if we want to be "the UK" according to this collective identity, then we must have nuclear weapons both as a representation of our major power identity and as a means of enabling the UK to act in the world according to this identity. This association suggests an implicit axiom that the UK is a nuclear weapons state both in fact and in identity (Ritchie 2012: chapter 5).

This was evidenced in the debate on the referendum on Scottish independence held in September 2014. The Scottish government, led by the Scottish National Party (SNP) has long insisted that ". . . an independent Scotland would be a nuclear free Scotland. The UK's nuclear submarines would have to be removed from Scottish waters, encouraging the UK, we hope, to end its dangerous reliance on an outdated nuclear deterrent" (Scottish National Party 2005). In 2012, the SNP's then-leader Alex Salmond insisted that a nuclear weapon-free status would be written into a new constitution for an independent Scotland and this was set out in the Scottish government's draft constitution published in June 2014 [START_REF] Johnson | Independent Scotland would ban nuclear weapons but join Nato[END_REF]Scottish Government 2014: 6). The SNP intended to remove Trident by 2020 within the first parliament of an independent Scotland after a general election in May 2016, twenty months after a successful independence referendum [START_REF] Carrell | Alex Salmond targets 2016 Trident withdrawal date[END_REF]Scottish National Party 2014). This caused deep anxiety for the Westminster political and defense establishment in terms of the UK's capacity to engage in expeditionary warfare, its "special"' relationship with Washington, the retention of a sophisticated nuclear arsenal, and the future of its permanent membership of the United Nations Security Council (Blick and Whitman 2013: 7-8). Former NATO Secretary-General and Labour Defence Secretary, Lord George Robertson alarmingly claimed in April 2014 that Scottish independence would leave the UK as: . . . a diminished country whose global position would be open to question. . . . The loudest cheers for the breakup of Britain would be from . . . our relationship with the United States, our status as a leading military power and even our permanent membership of the UN Security Council would all probably be lost. We would be reduced to two struggling nations on Europe's periphery.

(Graham 2014)

Similarly, the possession of nuclear weapons has been a significant part of the post-Second World War French national identity, which combines an attachment to nuclear power and to nuclear weapons (Pelopidas 2012; Hecht 1998). This attachment is connected to the image of a protective and responsible world power.

Beyond claims of adaptation of the doctrine and the capabilities (Bentégeat 2014), nuclear weapons have remained central as a response to the fear of a loss of independence, security, sovereignty, and freedom of action. The four White Papers on Defense, then the White Papers on Defense and National Security published since the creation of French strategic nuclear forces (in 1972, 1994, 2008, and 2013) show this eloquently. While the attempt at nuclear blackmail by the Soviets and abandonment by the USA during the Suez crisis is interpreted in the UK as meaning that, from that moment on, no major intervention abroad would be possible without consultation with the USA, the French remember it as the founding episode justifying a quest for independence via nuclear weapons (Pelopidas 2015b; Heuser 1998: chapter 3). We are not claiming that the Suez crisis changed the priorities toward the development of nuclear weapons, but instead that its memory retrospectively legitimized the course of action already taken in Paris.

Being a nuclear weapons state was a significant part of French antihegemonic policies and the refusal of the bipolar order during the Cold War (for a typical example, see de Gaulle's discussion with US Ambassador James Gavin on May 26, 1962;French Government 1962). It has largely persisted after the end of the so-called bipolar order. The 2013 White Paper states that "France's strategy has evolved over time. In the 1972 White Paper, its chief focus was nuclear deterrence" (French Government 2013: 67). Twenty-two years later, after the end of the Cold War, ". . . the need to possess nuclear weapons in the new strategic context remains politically a major component of the independence of France" (French Government 1994: 57, authors' translation) deterrence which serve as ". . . the ultimate guarantor of national security and independence" (French Government 2008: 69, 315, authors' translation 315). Five years later, the meaning is stable, ". . . nuclear deterrence is the ultimate guarantee of the security, protection and independence of the Nation" (French Government 2013: 73). In the post-Cold War context, independence is still defined vis-à-vis NATO (French Government 1994: 37;2008: 110, 317, authors' translation;[START_REF] Carrell | Alex Salmond targets 2016 Trident withdrawal date[END_REF] and vis-à-vis any other actor that that would restrict France's freedom of action. The 2013 White Paper on defense and national security states that nuclear deterrence ". . . rules out any threat of blackmail that might paralyze [France's] freedom of decision and action" (French Government 2013: 67). The emphasis was similar five years earlier: nuclear deterrence ". . . is one of the conditions of our strategic autonomy, and of the freedom of judgment, decision and action of the Head of State" (French Government 2008: 69, authors' translation). "Nuclear blackmail" was similarly considered as "plausible" in the 1994 White Paper (French Government 1994: 67, authors' translation) and freedom of action was to be pursued at least in part with nuclear weapons (French Government 1994: 52). This freedom of action has to do with the ability of France to exert its responsibility as a world power. In the post-Cold War context, this is notably portrayed as an ability to protect its allies. "By its mere existence, French nuclear deterrence [. . .] contributes to Europe's security" (French Government 2008: 70, authors' translation). The 2008 White Paper on defense and national security adds, within the discussion of France's independence and freedom of action that, ". . . the Ottawa declaration and the 1999 strategic concept, which recognize the contribution of its forces [. . .] to the deterrent capability of the alliance" (French Government 2008: 110, authors' translation). In 2013, the idea of a protective relationship vis-à-vis the European and NATO allies as a result of the possession of nuclear weapons is restated in almost equivalent terms: "France's deterrence capability contributes by its very existence to the security of the Atlantic Alliance and that of Europe" (French Government 2013: 72). Indeed, the focus on freedom of action is explicitly linked to and constrained by ". . . the framework of [France's] international responsibilities" (French Government 2013: 73).

Pressure to disarm unilaterally in the context of the Trident replacement process, the Global Zero agenda, and the Scottish independence referendum presented a major ontological challenge for the UK political elite. This took a new twist after the 2010 NPT Review Conference through the emergence of a "humanitarian initiative" to delegitimize the use and possession of nuclear weapons based on the unmanageable and unacceptable humanitarian consequences of use (Borrie and Caughley 2013). This process has at the time of writing involved three major international conferences on the humanitarian impact of nuclear weapons in Oslo, Norway (March 2013) Vienna conference, where it rejected the idea of a humanitarian imperative to ban nuclear weapons: "The UK considers that this approach fails to take account of, and therefore jeopardizes, the stability and security which nuclear weapons can help to ensure" (Foreign and Commonwealth Office 2014). France did not send representatives to any of the conferences on the humanitarian consequences of nuclear weapons. Its statements during the NPT review process emphasized the need for a step-by-step multilateral approach to nuclear disarmament that recognizes the NPT review process as the only legitimate framework in which nuclear disarmament progress can be made. "Recent initiatives" calling for more urgent action on nuclear disarmament are accused of being counter-productive because they challenge the legitimacy of this framework (Simon-Michel 2014b). France maintains that its nuclear disarmament record is exemplary and includes such statement in the latest White Paper on defense and national security:

Since dismantling its nuclear testing site in the Pacific, France has continued to set an example by taking unilateral measures, such as the irreversible dismantling of its installations for producing fissile materials for nuclear weapons. It has indicated that its arsenal includes fewer than 300 nuclear warheads. France was the first country to take these concrete steps towards nuclear disarmament.

(French Government 2013: 73)

The political authority of the humanitarian initiative rests on a world view that privileges human security, the international rule of law, including international humanitarian law applicable in armed conflict, human rights, and a conception of common humanity that underpins rationales for the "responsibility to protect." The humanitarian focus exacerbates the tension between French and UK identities as a stalwart supporter and defender of these facets of international politics or protective states on the one hand, and states prepared to inflict massive nuclear damage in the name of their own national security on the other. Both the UK and France routinely self-identify as a "force for good" on the international stage and, in doing so, they conflate responsible and civilized state behavior with nuclear defense of the post-Second World War international order. The Global Zero agenda and the humanitarian initiative have challenged this conflation and set the reproduction by the UK and France of a strategic nuclear capability for another generation against the image of responsible statehood in terms of their own value commitments.

Opportunities for the UK

The Global Zero agenda provided an opportunity for the UK to exercise international leadership by exploring further steps toward a world free of nuclear weapons, but keeping its own nuclear arsenal as part of Margaret Beckett's "disarmament laboratory" concept [START_REF] Beckett | A World Free of Nuclear Weapons? Keynote address presented at the Carnegie International Nonproliferation Conference[END_REF]). Yet Whitehall has chosen not to do so in any significant way for a variety of reasons, not least the politics of nuclear identity outlined in this chapter. The opportunity presented in the context of the Trident replacement debate is to rethink "minimum deterrence" by further reducing both the size and operational readiness of the UK's nuclear weapons or by relinquishing nuclear weapons altogether. On the former, the UK could adopt the "preserved deterrence" option outlined in the Trident Alternatives Review (Cabinet Office 2013). This was described as:

No deterrent platforms would be regularly deployed but the UK would maintain the ability to deploy if the context changed. The platforms might be deployed without nuclear weapons for training purposes and could conduct conventional duties as long as they could be made available for deterrent duties if required.

(Cabinet Office 2013: 5)

In such a circumstance, the UK would become what William Walker describes as a "disarmament threshold state" with a fully de-alerted nuclear arsenal (Walker 2010: 447). Such a move would clearly indicate that the UK no longer sees a compelling reason to deploy nuclear weapons for immediate use, but is temporarily retaining these weapons pending global elimination. A de-alerted posture would all but eliminate any intention to use nuclear weapons first in a crisis at short notice, thereby reinforcing political and legal commitments to non-nuclear weapons states and providing a degree of strategic reassurance to other possessors of nuclear weapons. It would signify an important "de-coupling" (Brown 1997: 47) of nuclear weapons from the broad, day-to-day calculus of national security by demonstrating that the UK is prepared to learn to live without nuclear weapons operationally deployed at sea on a permanent basis as a precursor to learning to live without nuclear weapons at all.

The UK could, of course, go a step further and relinquish nuclear weapons altogether. This would represent the most significant case of "deproliferation" to date and a potential turning point in the global nuclear order [START_REF] Müller | The little known story of de-proliferation: why states give up nuclear weapon activities[END_REF]. The decision would be of special significance for a number of reasons. First, the development of nuclear weapons originated in London when the Maud Committee first met in 1940 to consider the practicality of a uranium atom bomb, three years before UK scientists arrived at Los Alamos in New Mexico to build the first atomic bombs under the Manhattan Project. Second, the UK is a depository state of the NPT along with the USA and Russia. Third, the UK is one of the original members of the "nuclear club". Finally, such a decision would unambiguously signal the declining utility of nuclear weapons for a stillpowerful, influential, and activist country and would represent a clean break between the pernicious correlation between a nuclear capability and permanent membership of the United Nations Security Council (the UK would not lose its seat -it would have to vote itself off to do that) (Walker 2007: 167). General Jack Sheehan, former Supreme Allied Commander, Atlantic for NATO and Commander-in-Chief, US Atlantic Command, concurred in January 2009, arguing, "I think it is entirely possible that the British government, for a lot of good reasons, could do it [relinquish nuclear weapons] and it would lead the world" and have a significant international impact (Sheehan 2009). Others, such as former UK Defence Secretary Liam Fox, have argued that other states would be "utterly underwhelmed by gesture unilateralism" (Hansard 2007).

If the UK continues with business-as-usual, however, the prospects for significant progress toward nuclear disarmament begins to look bleak as observers ponder the practicability of a world without nuclear weapons, if even a self-styled "reluctant" possessor of nuclear weapons operating at "minimum" nuclear posture cannot make a decision to radically rethink its commitment to nuclear deterrence when the strategic rationales for retention are so thin, the opportunity costs for the armed forces are significant, public opinion is ambivalent or hostile to the replacement program, and the commitment to the NPT and a desire to exercise leadership on nuclear disarmament is strong. This has been compounded by efforts to revalidate UK nuclear weapons following Russia's annexation of Crimea and the strategic destabilization of Ukraine. The UK then-Defence Secretary Philip Hammond, for example, stated in March 2014 that, "What those events do show is that we have been right throughout in maintaining the need to continue with a strategic nuclear deterrent as the ultimate guarantor of Britain's sovereignty and freedom of action" (Hansard 2014; for a convincing critique of the counter-facts that a nuclear-armed Ukraine would prevent the Russian annexation of Crimea, see Rublee 2015).

For now, at least, the UK stands at a crossroads. As the WMD Commission's report Weapons of Terror: Freeing the World of Nuclear, Chemical and Biological Arms noted:

France and the UK will have to decide whether it will be meaningful to retain costly nuclear arsenals that were developed for an enemy that no longer exists, in order to meet hypothetical threats against which such weapons are of questionable value. Both countries are now at a crossroads: going down one road would show their conviction that nuclear weapons are not necessary for their security, while the other would demonstrate to all other states a belief that these weapons continue to be indispensable. (Blix 2006: 90) The tension between a firm policy of non-proliferation, as expressed by the firm attitude of the French toward Iran (Pelopidas 2012), and a continued commitment to a small nuclear arsenal as the ultimate guarantor of national security and independence, which is presented as good value for money and relatively risk-free, is also at the heart of the French stance. The usual reaction is to justify the French policy of strict sufficiency by contrasting it with the US-Soviet nuclear arms race and overkill. Nevertheless, the tension remains strong when we consider that the countries suspected of proliferating will not take the USA as an example, but might rather refer to the French anti-hegemonic nuclear politics of the 1950s and 1960s. The absence of debate of this issue in France is also more of a problem than in the UK, but, in both cases, nuclear vulnerability is at best imperfectly recognized; the public is not presented with consistent justifications of the reasons to continue nuclear vulnerability and any relationship between their continued possession of nuclear weapons and sustaining a permissive global environment for nuclear proliferation is vehemently denied. 4

Notes 1 UK strategic forces were formally committed to NATO in the 1962 Nassau Agreement that paved the way for the Polaris Sales Agreement. 2 The government's case was set out in detail by the Ministry of Defence and Foreign and Commonwealth Office (2006). 3 The notion that nuclear weapons and the practice of nuclear deterrence are an inevitable, necessary, and enduring component of major power stability. 4 For this problem in the UK, see Pelopidas and Weldes (2014).

  bombe [Stop the bomb], along with General Norlain and defense analyst and the French representative of Parliamentarians for Nuclear Nonproliferation and Disarmament Jean-Marie Collin, and later published two books on the issue (Quilès 2012; Quilès et al. 2013).

  Trident on permanent alert. The Trident Alternatives Review was released in declassified form in July 2013 (Cabinet Office 2013). It set out a range of alternative nuclear postures for the UK and applied these to a number of different delivery systems. The Liberal Democrats subsequently went into the 2015 General Election with a commitment to: Retain our Trident independent nuclear deterrent through a Contingency Posture of regular patrols, enabling a "surge" to armed patrols when the international security context makes this appropriate. This would enable us to reduce the UK warhead stockpile and procure fewer Vanguard successor submarines, and would help the UK to fulfill our nuclear non-proliferation treaty commitments.

	replacement of	1 1
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	. To that end, in May 2011
	they successfully sought agreement with the Conservatives for a formal
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(Liberal Democrats 2014: 75)

The French government was originally taken by surprise by the renewed advocacy of nuclear disarmament in 2007-2008. French officials, as well as most of the few French nuclear experts, remain convinced that this push is temporary, that the history of the nuclear age is that of nuclear proliferation, and that a world without nuclear weapons is in the end not desirable

(Pelopidas 2012;[START_REF] De Champchesnel | Un monde sans armes nucleaires. L'utopie du zero [A world without nuclear weapons[END_REF]

  The 1998 Strategic Defence Review, for example, described this as ". . . retain[ing] our nuclear deterrent with fewer warheads to meet our twin challenges of minimum credible deterrence backed by a firm commitment to arms control" and ". . . work[ing] to create conditions in which even a minimum level of nuclear deterrence is no longer necessary" (Ministry of Defence 1998: paras 8 and 55). Colin Gray described it as ". . . running with the nuclear fox and riding with the disarmament hounds" (Gray 2001: 233). So far, however, the commitment to nuclear deterrence has prevailed to the extent that a like-for-like replacement of Trident remains the path of least political, financial, and operational resistance in Whitehall. Replacing the Trident system is perfectly legitimate under the NPT as far as the UK is concerned[START_REF] Browne | The United Kingdom's Nuclear Deterrent in the 21st Century. Speech at King's College London[END_REF] Ministry of Defence and Foreign and Commonwealth Office 2006: 14).France's more steadfast defense of nuclear deterrence creates a more limited presentational problem than that observed in the UK even if, as

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  from our enemies. For the second military power in the West to shatter this year would be cataclysmic in geopolitical terms. . . . The force of darkness would simply love it (Robertson 2014) Vice-Admiral John McAnally similarly insisted in March 2014 that:

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  . The idea is restated and reinforced in the 2008 White Paper, which portrays nuclear weapons as instruments of

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  , Nayarit, Mexico (February 2014), and Vienna, Austria (December 2014). The UK declined to attend the first two conferences, but it did attend the

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 HC, vol. 458, no. 61, col. 392 (March 14, 2007). Hansard, HC, vol. 516, no. 54, col. 807 (October 19, 2010). Hansard, HC, vol. 528, no. 160, col. 338 (May 18, 2011). Hansard, HC, vol. 556, no. 99, col. 997W (January 18, 2013). Hansard, HC, vol. 557, no. 137, col. 550 (March 17, 2014). Hansard, HC, vol. 594, no. 123, col. 296 (March 11, 2015). Harries, M. ( 2012


Didier Theilliol
email: didier.theilliol@cran.uhp-nancy.fr

Cédric JOIN ‡ Youmin Zhang

ACTUATOR FAULT-TOLERANT CONTROL DESIGN BASED ON RECONFIGURABLE REFERENCE INPUT

Keywords: Fault tolerant control (FTC), Actuator fault accommodation, Reconfigurable reference input

The prospective work reported in this paper explores a new approach in order to enhance the performance of an Active Fault Tolerant Control System. This proposed technique is based on a modified recovery/trajectory control system which considered a reconfigurable reference input when performance degradation occurs on system due to faults in actuators dynamics. The added value of this work is to reduce the energy spent to achieve desired closed-loop performance. The feasibility of this work is illustrated using a three-tank system for slowly varying reference inputs corrupted by actuators faults.

INTRODUCTION

Sensor or actuator failures, equipment fouling, feedstock variations, product changes and seasonal influences may affect controller performance and as many as 60% of industrial control problem [START_REF] Harris | A review of performance monitoring and assessment techniques for univariate and multivariate control systems[END_REF]. The objective of Fault Tolerant Control System (FTCS) is to maintain current performances close to the desirable performances and preserve stability conditions in the presence of component and/or instrument faults; in some circumstances reduced performance could be accepted as a trade-off (Zhang and Jiang, 2003a).

In fact, many FTC methods have been recently developed [START_REF] Patton | Fault-tolerant control: the 1997 situation[END_REF], [START_REF] Noura | Fault-tolerant control in dynamic systems: application to a winding machine[END_REF], [START_REF] Blanke | Diagnosis and Fault-Tolerant Control[END_REF]. Almost all the methods can be categorized into two groups [START_REF] Zhang | Bibliographical review on reconfigurable fault tolerant control systems[END_REF]: passive and active approaches. Passive FTC deals with a presumed set of system component failures based on the actuator redundancy at the controller design stage. The resulting controller usually has fixed structure and parameters. However, the main drawback of a passive FTCS is that as the number of potential failures and the degree of system redundancy increase, controller design could become very complex, and the performance of the resulting controller (if exists) could become significantly conservative. Moreover, if an unanticipated failure occurs, passive FTC cannot ensure system stability and cannot reach again nominal performance of the system. Controllers switching underlines the fact that many faulty system representations had to be identified so as to synthesize off-line pre-computed and stabilized controllers. These requirements are sometimes difficult to obtain and it is restrictive. Active FTCS is characterized by an on-line FDI process and control reconfiguration mechanism. According to the FDI module, a control reconfiguration mechanism is designed in order to take into account the possibility of fault occurrence [START_REF] Theilliol | Fault diagnosis and accommodation of a three-tank system based on analytical redundancy[END_REF]. Advanced and sophisticated controllers have been developed with fault accommodation and tolerance capabilities, in order to meet pre-fault reliability and performance requirements as proposed by (Gao and Antsaklis,1991) [START_REF] Jiang | Design of reconfigurable control system using eigenstructure assignments[END_REF] for model matching approaches or by [START_REF] Gao | Reconfigurable control systems design via perfect model following[END_REF] to track trajectory but also with degraded ones as suggested by [START_REF] Jiang | Accepting performance degradation in fault-tolerant control system design[END_REF]. Moreover, the importance of improving the system behaviour during the fault accommodation delay has been, recently, considered by [START_REF] Staroswiecki | Progressive accommodation of parametric faults in linear quadratic control[END_REF] in order to reduce the loss of performance. This paper addresses a new approach in order to increase the performance of an Active Fault Tolerant Control System. This novel technique consists on taking into account a modified recovery/trajectory control system when performance degradation occurs on system due to faults in actuators dynamics. The developed method preserves the system performance through an appropriate reconfigurable reference in order to preserve the output dynamic properties and to limit the energy of control inputs as well.

The paper is organized as follows. Section 2 recalls the actuator fault representation and the controller synthesis for LTI system. Section 3 is devoted both to remind a classical fault tolerant controller considered in this paper and to define the novel reconfigurable reference input technique. A simulation example of a well-know three-tank system with slowly varying reference inputs subject to actuators faults has been used, in Section 4, to illustrate the effectiveness and performance of active fault tolerant control system. Conclusions and further work are discussed in Section 5.

Basic Concept

Control system synthesis

Consider the discrete linear system given by the following state space representation:

⎪ ⎩ ⎪ ⎨ ⎧ = = + = + k k k r k k k 1 k x C w x C y Bu Ax x (1)
where

n n R A × ∈ , p n R B × ∈ , n m R C × ∈ and n h r R C × ∈
are the state, the control, the output and tracking output matrices, respectively.

n R x∈ is the state vector, p R u ∈ is the control input vector, m R w∈
corresponds to the measured output vector and h R y∈ represents the system outputs that will track the reference inputs h R r∈ . It can notice that, in order to maintain controllability, the number of outputs h that can track a reference input vector r , cannot exceed the number of control inputs h p ≥ .

The study considered in this paper is suitable, not only in regulation, but also in the tracking control problem. The eigenstructure assignment (EA) or the linear quadratic regulators (LQR) are among the most popular controller design techniques for multiinput and multi-output systems. Since the feedback control,

k nom feedback x K - can only
guarantee the stability and the dynamic behaviour of the closed loop system, a complementary controller is required to cause the output vector y to track the reference input vector r in the sense that the steady state response is:

r y lim k = +∞ → (2)
To achieve steady-state tracking of the reference input, different techniques have developed. Among them, a feedforward control law based on a command generator tracker [START_REF] Zhang | Active fault-tolerant control system against partial actuator failures[END_REF] can be considered such as:

k nom feedback k nom forward nom k x K r K u - - = (3)
where the feedforward gain nom forward K is synthesized based on the closed-loop modelfollowing principle .

As proposed by [START_REF] D'azzo | Linear Control System Analysis and Design, Conventional and Modern[END_REF], another solution to track the reference input consists of adding a vector comparator and integrator (

h nom R z ∈ ) that satis- fies: ( ) ( ) k r k s nom k k k s nom k nom 1 k x C r T z y r T z z - + = - + = + (4)
Therefore, the state feedback control law is computed by:

k nom feedback nom k nom forward nom k x K z K u - - = (5)
where the feedforward gain nom forward K (different from (3)) is synthesized based on an augmented state space representation with a desired behaviour of a plant in closed loop.

In the following, matrix C is assumed to be equal to an identity matrix: the outputs are the state variables. However, the control law could be computed using the estimated state variables.

Actuator fault model

In most conventional control systems, controllers are designed for fault-free systems without taking into account the possibility of fault occurrence. Let us recall the faulty representation.

Due to abnormal operation or material aging, actuator faults can occur in the system. An actuator can be represented by additive and/or multiplicative faults as follows:

j0 j j k f j u u α u + = (6)
where j u and f j u represent the j th normal and faulty control actions. j0 u denotes a constant offset when actuator is jammed and/or

1 0 k ≤ ≤ α denotes a gain degrada- tion of the j th component [ ] p j L 1 ∈ ∀
(constant or variable). In this paper, only the reduction in effectiveness is considered i.e.:

1 0 ≤ < = j k j j k f j α with u α u (7)
Such modelling can be viewed as multiplicative faults which affect matrix B as:

[ ] u B u α α B u u u B f p k k 1 k T f p f j f 1 = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = L M O O M O L 0 0 0 0 0 0 α (8) Matrix f
B represents the actuator fault distribution matrix relates to the nominal constant control input matrix B . Therefore, the discrete state space representation defined in (1) with actuator faults modelled by control effectiveness factors becomes as:

⎪ ⎩ ⎪ ⎨ ⎧ = + = + k k k f k k Cx w u B Ax x 1 (9)
or in a faulty case, if 7) is rewritten such as ( )

[ ] p j L 1 ∈ ∀ equation (
1 0 1 ≤ < - + = j k j j k j f j α with u α u u
. According to (8), equation ( 1) is described based on an alternative representation following an additive representation:

⎪ ⎩ ⎪ ⎨ ⎧ = + + = + k k a k a k k k Cx w f F Bu Ax x 1 (10)
where

p n a R F × ∈
represents the actuator fault distribution matrix ( B F a = ) and

p a R f ∈
is the faulty vector.

In the presence of actuator faults, the faulty actuators corrupt the closed-loop behaviour. Moreover, the controller aims at cancelling the error between the measurement and its reference input based on fault-free conditions. In this case, the controller gain is away from the "optimal" one and may drive the system to its physical limitations or even to instability.

Under the assumption that an efficient fault diagnosis module is integrated in the reconfigurable control to provide sufficient information, an active fault tolerant control system based on the fault accommodation principles is developed in the next section in order to preserve the output dynamic properties and to limit the energy of control inputs.

Actuator fault tolerant control design

Actuator fault accommodation: Reconfigurable control gain synthesis or fault compensation principle

In order to annihilate the actuator fault effect which appears at sample

f k k =
on the system, various methods have been proposed to recover as close as possible the performance of the pre-fault system according to the considered fault representation. Among methods, two main classical approaches have been developed. One is based on a model matching principle where the control gain is completely re-synthesised on-line and the other method is based on fault compensation added to the nominal control law.

Based on multiplicative fault representation, defined in (9), some extensions of the classical Pseudo-Inverse Method (PIM) have been proposed to guarantee both the performance and the stability of the pre-fault system. Using constrained optimization [START_REF] Gao | Stability of the pseudo-inverse method for figurable control systems[END_REF] and [START_REF] Staroswiecki | Fault tolerant control: the pseudo-inverse method revisited[END_REF] have synthesized a suitable feedback control accom feedback K . Moreover, [START_REF] Zhang | Active fault-tolerant control system against partial actuator failures[END_REF] and (Guenab et al., 2006) have proposed to compute a reconfigurable feedforward gain accom forward K controller in order to eliminate the steady-state tracking error in faulty case. Therefore, the control signal applied to the system at sample

f r k k k > =
is represented such as:

k accom feedback k accom forward FTC k x K r K u - - = (11)
However, under an additive faulty representation, defined in (10), [START_REF] Noura | Fault-tolerant control in dynamic systems: application to a winding machine[END_REF], [START_REF] Theilliol | Fault diagnosis and accommodation of a three-tank system based on analytical redundancy[END_REF] and [START_REF] Rodrigues | Fault tolerant control design for polytopic LPV system[END_REF] have proposed to add a new control law acc u to the nominal control law synthesised as presented in §2.1. The total control signal to be applied to the system at sample

f r k k k > = is repre- sented as follows: ( ) ( ) acc k k nom feedback nom k nom forward acc k nom k FTC k u x K z K u u u + - - = + = (12)
According to the new control law in ( 12), the discrete state space representation defined in (10) becomes as:

⎪ ⎩ ⎪ ⎨ ⎧ = + + + = + k k a k a acc k nom k k k Cx w f F u B u B Ax x 1 (13)
whereupon, the additional control law acc u must be computed such that the faulty system is as close as possible to the nominal one, therefore:

0 f F Bu a k a acc k = + ( 14
)
Using the estimation of the fault magnitude a k f ˆ obtained from the fault diagnosis module, the solution of ( 14) can be obtained by the following relation if matrix B is of full row rank:

a k a acc k f F B u + - = (15)
where + B is the pseudo-inverse of matrix B .

In both cases, a fault tolerant controller has been designed to compensate faults by computing a new control law in order to minimize the effects on the system performance, and consequently to achieve the desired dynamic and stability performance of the faulty closed-loop system. Furthermore, the reconfigurable control mechanism requires some adjustments of the control inputs and consequently reduces the "lifespan" of various components from a reliability point of view.

Actuator fault accommodation: recovery/trajectory control system

From control point of view, in the tracking assumption, the reconfigurable control mechanism requires more energy to reach the target and to guarantee steady-state performance. Thus, the energy variable k E associated to the accommodated control law is defined as:

( ) ( ) ∑ ∑ = = × = × = k 0 τ T FTC τ FTC τ k 0 τ T τ τ k u u u u E ( 16
)
In order to reduce k E , the proposed technique is to modify, during the reconfigura- tion transient, the reference input vector r . To achieve this goal, when the fault is detected and reconfigured at sample When the fault is detected and controller is reconfigured, the new reference acc r has been considered. For r k k > , the fault accommodation control signal applied to the system based on the reconfigurable gain synthesis is computed such as:

k accom feedback acc k accom forward RFTC k x K r K u - - = (18)
or if the fault compensation principle is considered, the fault accommodation control signal, defined in ( 12), becomes to:

( ) ( ) acc k k nom feedback acc k nom forward acc k recon k RFTC k u x K z K u u u + - - = + = (19)
where acc z corresponds to the integrator vector defined as:

( )

k acc k s acc k acc 1 k y r T z z - + = + (20)
A reconfigurable control mechanism has been proposed to limit the drawback of a fault accommodation strategy which requires more energy to reach the target and to guarantee steady-state performance. To demonstrate the effectiveness of the prospective work, the well-known three-tank system [START_REF] Join | Nonlinear filter design for fault diagnosis: application to the three-tank system[END_REF] has been considered around one operating point. In the presence of actuator fault, the nominal controller (NL), the fault accommodation principle without (FTC) and with (RFTC) reconfigurable reference input have been evaluated and compared.

An illustrative example

Process description

The process is composed of three cylindrical tanks with identical cross section S. The tanks are coupled by two connecting cylindrical pipes with a cross section S n and an outflow coefficient μ 13 . The nominal outflow is located at tank 2, it also has a circular cross section S n and an outflow coefficient μ 2 . Two pumps driven by DC motors supply tanks 1 and 2. The flow rates through these pumps are defined by the calculation of flow per rotation. All three tanks are equipped with sensors for measuring the levels of the liquid (l 1 , l 2 , l 3 ).

Pump 1 Pump 2 q 1 q 2 q 20 l 1 l 3 l 2
Tank 1 Tank 3 Tank 2 q 32 q 13 S S n μ 13 μ 32 μ 20

Fig. 1. Synoptic of the three-tank-system

Plant modelling

The non-linear system can be simulated conveniently using Matlab/Simulink by means of non-linear mass balance equations.

As all the three liquid levels are measured by level sensors, the output vector is

[ ] T 3 l 2 l 1 l y = . The control input vector is [ ] T 2 1 q q u =
. The purpose is to control the system around an operating point. Thus, it has been linearized around an operating point which is given by

[ ] T 0 0.3 0.2 0.4 y = (m) and [ ] 4 T 0 10 0.33 0.35 u - = (m 3 /s).
Using the Torricelli rule, for l 1 >l 3 >l 2 , the linearized system can then be described by a discrete state space representation with a sampling period T s = 1s with: and C is an identity matrix.

⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = 0.
Levels 1 l and 2 l have to follow reference input vector 2 R r ∈ . These outputs are controlled using the multivariable control law described previously. Control matrix pair of the augmented plant is controllable, and the nominal tracking control law, designed by a LQ+I technique conducts to a feedback/forward gain matrices equal to:

4 10 4 19 9 . 2 5 3 6 . 21 - × ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ - - = nom feedback K (21a) 4 10 91 . 0 3 . 0 32 . 0 95 . 0 - × ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ - - - - = nom forward K (21b)

Results and comments

The validation of the tracking control with the linearized model is shown in Fig. 2 where step responses with respect to set-point changes are considered for a range of 3000s. Reference inputs r are step changes of 12.5% for 1 l (and 2 l -not presented here) of their corresponding operating values. The dynamic responses demonstrate that a tracker is synthesized correctly (NL -fault-free case in Fig. 2).

Then, in a similar way, an actuator fault has been applied. A gain degradation of pump 1 (clogged or rusty pump, ….) is considered and appears abruptly at sample s 1000 k k f = = on the system during the steady-state operation. To do so without breaking the system, the control input applied to the system is equal to the control input computed by the controller multiplied by a constant system ( 2 0 1 . = α and 0 u 10 = ). Since an actuator fault acts on the system as a perturbation, and due to the presence of the integral error in the controller, the system outputs reach again their nominal values (NL -faulty case in Fig. 2). Fig. 2. Level 1 l in fault-free case and with fault on pump 1

Under the assumption that a fault detection, isolation and estimation module will provide to the FTC system the information about the occurrence of the actuator fault at sample

s 1010 k k k f r = > =
, the re-adjusted control reference acc r is defined following the technique proposed in Section 3.2. A second-order impulse response is chosen to modify the initial reference r on level 1 l . This level is corrupted by the faulty pump associated to the tank 1. The second-order impulse response is considered with a natural frequency ω and damping ratio ξ calculated in a discrete form with a sampling period T s = 1s based on the following classical transfer function:

+ + = s s s G ( 22
)
where s is a Laplace variable.

As shown in Fig. 3 for a specific 5 . 10 = ξ , the re-adjusted control reference input acc r is "revised" just after the occurrence of the fault and finally returned to the initial reference input r after a short period. Fig. 3. Reference input for level 1 l in fault-free case and recovery principle

The compensation control law is computed in order to reduce the fault effect on the system. Indeed, since an actuator fault acts on the system as a perturbation (

s 1000 k k f = =
), the system outputs reach again their nominal values, as illustrated in Fig. 4. With the fault accommodation methods (FTC or RFTC with 5 . 10 = ξ

), the output decrease less than the case of a classical control law (NL), then they reach the nominal values quicker because the fault is estimated and the new control law is able to compensate for the fault effect at instant

s 1010 k k k f r = > =
when the fault is isolated. It can be easily seen that after the fault occurrence, the time response and the dynamic behaviour of the compensated outputs in both FTC and RTFC cases are not similar and completely different from the fault-free case. l with fault on pump 1 with nominal control law (NL), fault accommodation without FTC and with RFTC recovery reference input.

These results can be confirmed by the examination of control input q 1 (Fig. 5). In the classical law (NL), the control input increases slowly trying to compensate for the fault effect on the system. In the accommodation approach, the RTFC control input increases quickly and enables rapid fault compensation on the controlled system outputs in similar way than with the FTC control input. ) emphasizes the performance of the approach as presented in Table 1. With two fault accommodation methods (RFTC and FTC), tracking error norms for outputs 1 l and 2 l are very close and slightly lager than the nominal one but it is still significantly smaller than the case with classical control law (NL) under the fault condition. 2 where the energy (13) associated to flow rate 1 q δ around the reference r on level 1 l is calculated between k=2000s and k=2400s. In view of the above figures and the energy computation illustrated in Table 2 for the experiments, it appears clearly that the RFTC preserves the output dynamic properties and limits the energy of control inputs compared to the classical FTC. As discussed previously, the performances of a novel recovery/trajectory control are linked to the damping ratio ξ . As illustrated in Fig. 6, the tracking error norm Φ (---) vs. damping ratio ξ for RFTC.

The computation of the two performance indexes is realized for a time period around the fault occurrence started at k=2000s and finished at k=2400s. The data provided in the two previous tables are included in Fig. 6 ( 5 . 10 = ξ ). It is interesting to note that for a large value of damping ratio ξ the performance indexes are closed to a classical accommodation (FTC): the second order impulse response is closed to zero when the damping ratio ξ increases. Consequently, an optimal damping ratio ξ needs to be found in order to preserve the output dynamic properties and to limit the energy of control inputs.

CONCLUSION

This paper has presented an active fault tolerant control system design strategy which takes into account a modified trajectory/reference input for system reconfiguration. Classical fault accommodation methods have been considered to design the fault tolerant controller. The design of an appropriate recovery/trajectory control reference input provides to the fault accommodation controller the capabilities to, simultaneously, , reach their nominal dynamic and steady-state performances and to preserve the reliability of the components [START_REF] Finkelstein | A note on some aging properties of the accelerated life model[END_REF]. The application of this method to the well-known three tank system example gives encouraging results. Future work concerns the theoretical definition of the optimal impulse response for flatness control [START_REF] Fliess | Flatness and defect of non-linear systems: introductory theory and examples[END_REF] in the FTC framework [START_REF] Mai | An example of flatness based fault tolerant control using algebraic derivative estimation[END_REF].

  as an impulse which excites a non-periodic system. The dynamic behaviour of this system is chosen according to the criteria to reach the nominal reference as well as to reduce k E . This recovery/trajectory control reference

Fig. 4 .

 4 Fig.4. Zoom on level 1 l with fault on pump 1 with nominal control law (NL), fault accommodation without FTC and with RFTC recovery reference input.

Fig. 5 .

 5 Fig.5. Zoom on flow rate 1 q with fault on pump 1 and with nominal control law (NL), fault accommodation without FTC and with RFTC recovery reference input.

Fig

  Fig. 6. Performance indexes

Table 1 .

 1 Norms of tracking error computed between k=2000s and k=2400s.

				Fault free case	Faulty case
	with		NL	NL	FTC	RFTC
	1 l e	2	0.0211	0.2989	0.0514	0.0540
	l e	2	2	0.0197	0.1087	0.0223	0.0219
	Effectiveness of the reconfiguration strategy based on a novel recovery/trajectory
	control is highlighted in Table

Table 2 .

 2 Variation of energy computed between k=2000s and k=2400s.

					Fault free case		Faulty case
	with		NL	NL	FTC	RFTC
	Φ	×	10 -	4	0	1.3048	1.1432	1.0624