SGER: New Approaches to the Design of Fixed Order Controllers

SGER：固定阶数控制器设计的新方法

• 批准号: 0330800
• 负责人: S. Bhattacharyya
• 金额: $ 8万
• 依托单位: Texas A&M Engineering Experiment Station
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-15 至 2007-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0330800&HistoricalAwards=false
• 关键词: SGER; New; Approaches; Design; Fixed

Control theory is at a eculiar crossroad.Much of the elegant theory developed over the last 43 years hasrun its course and now appeals to a dwindling number of academics,while it has generated little interestfrom industry and is mostly irrelevant for engineering design.On the other hand the real design roblemsfaced by control engineers remain unresearched,lack theoretical foundation,are of a fundamental natureand theoretically extremely challenging,and there is a crying need for analytical and computer aideddesign ap roaches.Our roposal attem ts to address this gap and to work towards its resolution.The exploratory research described here deals with the develo ment of new approaches to the design of.xed order and structure controllers.The need for this research stems from the following:a)The o timalcontrol theory developed intensively since 1960 by control theorists result in high order controllers thatare model-based and the theory cannot handle the constraint of .xed order,which is ever present inindustrial applications;this makes modern theory inapplicable to even such widely used controllers asPID and lead/lag,for instance.b)O timal and high order controllers can have severe structural andsensitivity roblems as shown dramatically in the 1997 paper "Robust,Fragile or Optimal?"h(IEEE T-ACAugust 1997)by Keel and Bhattacharyya.This a er showed that controllers designed by H2,H ",l1and techniques could be acutely sensitive to erturbations in the controller coe .cients rendering themunusable.Since then no systematic solution to the fragility roblem has emerged despite signi .cantactivity in this area.c)An important need in practical design roblems is to have sets of feasiblesolutions meeting various objectives such as stability,robustness,time-delay tolerance etc so that designtradeo .s can be intelligently compared.The resent theory of .xed order controllers is far from answeringsuch questions-indeed it cannot in most cases determine if even nominal stabilization is ossible at all.With the above background as motivation our roposed research sets out to explore some new ap-proaches to solve the .xed order controller design roblem.The .rst step in this,necessarily,is thedetermination of the stabilizing set.This is a di .cult and longstanding unsolved roblem in controltheory.We have recently obtained a breakthrough in two s ecial cases.Speci .cally we obtained a mixedanalytical/com utational solution to the roblem of determining whether a .rst order or PID controllercan stabilize a given lant.Our solution can determine the complete set of stabilizing controllers andshows that this set is not convex or even connected.In view of this it is not clear how erformanceconstraints can be e .ectively imposed.Moreover the solution technique used by us in these cases doesnot seem to extend to the general case.We intend to explore two approaches for the general case.The .rst will be an attempt to approximatethe .xed order controller stabilizing sets,which are disconnected in general,through unions of convexsets.We will explore the use of the interlacing conditions for stability to generate these and it appearsossible that we can get a good and tight approximation to the stabilizing sets as unions of convexsets.This can open the door to the im osition of erformance constraints and their satisfaction throughcomputationally tractable methods such as linear rogramming and convex optimization,despite thecomplicated to ology of the stabilizing sets.The second approach that we intend to explore is theuse of a hybrid Nyquist/D-Decomposition technique that we have found to be useful in simple cases.This method has the additional otential advantage that it may be ossible to determine stabilizing setsfrom frequency domain data only thus making the design based exclusively on experimental data andessentially "gmodel-free "h.In this setting achieving robustness of the design to the data should also bedevelo ed.In summary the exploratory research pro osed here addresses the design of fixed but arbitrary or-der,robust,non-fragile controllers based on classical as well as modern erformance criteria.This is alongstanding and di .cult open control roblem.Nevertheless it needs to be solved in general for thetheory and ractice of the .eld to rogress.In the roposal we describe some seemingly romising newapproaches which are signi .cant departures from the optimization and model based approaches thatdominate the .eld at resent.We intend to explore how far these approaches can be develo ed intodesign e .ective rocedures.We believe that such procedures will bene .t control engineering ractice aswell as academic research and hel close the looming theory-practice gap in our .eld.

控制理论正处于一个特殊的十字路口。在过去43年中发展起来的许多优雅的理论已经走完了它的历程，现在吸引越来越少的学者，而它几乎没有引起工业界的兴趣，而且大多与工程设计无关。另一方面，控制工程师所面临的真实的设计问题仍然没有研究，缺乏理论基础，具有基本的性质，在理论上极具挑战性，因此，迫切需要分析和计算机辅助设计方法。我们的研究试图解决这一问题，并朝着解决这一问题的方向努力。本文所述的探索性研究涉及设计定阶和定结构控制器的新方法的发展。这项研究的需要源于以下几点：a）自1960年以来，控制理论家们大力发展的最优控制理论导致了高阶控制器的模型，该理论不能处理工业应用中经常出现的定阶约束;这使得现代理论甚至不适用于诸如PID和超前/滞后这样广泛使用的控制器。B）如1997年的论文“Robust，脆弱还是最佳？“h（IEEE T-AC 1997年8月）。这表明，由H2，H“，l1和技术可能对控制器系数的扰动非常敏感，从而使它们无法使用。自那时以来，尽管在这方面有显著的进展，但还没有系统的解决方案。在实际的设计过程中，一个重要的需求是要有一套可行的解决方案，满足各种目标，如稳定性，鲁棒性，目前的定阶控制器理论还远远不能回答这些问题，事实上，在大多数情况下，它甚至不能确定名义稳定是否可能。探讨了解决定阶控制器设计问题的方法，其中第一步必然是，稳定集的确定是控制理论中一个长期未解决的难题，最近我们在两种特殊情况下取得了突破性的进展，特别是得到了一个混合解析解。本文给出了确定一阶或PID控制器是否能镇定给定对象的问题的一种计算方法。我们的解能确定镇定控制器的完整集合，并表明这一集合不是凸的，甚至不是连通的。鉴于此，不清楚性能约束是如何确定的本文试图探讨一般情况下的两种方法：第一种是试图近似固定阶控制器稳定集，它一般是不连通的，第二种是试图近似固定阶控制器稳定集，第三种是试图近似固定阶控制器稳定集。我们将探索使用交错条件的稳定性，以产生这些，它似乎是我们可以得到一个很好的，作为凸集的并集的稳定集的紧逼近。这可以通过计算上易处理的方法，如线性规划和凸优化，第二种方法，我们打算探索的是使用混合奈奎斯特/D-我们发现，这种分解技术在简单情况下是有用的。这种方法还有一个潜在的优点，即可能仅从频域数据确定稳定集，从而使设计完全基于实验数据，基本上是“无模型“的。h.在这种情况下，还应发展设计对数据的稳健性。总之，这里提出的探索性研究涉及固定但任意顺序的设计，稳健，非基于经典和现代误差准则的脆弱控制器，这是一个长期而困难的开放控制问题，然而，为了使该领域的理论和实践向前发展，需要普遍地解决这个问题。然而，我们描述了一些看似令人满意的新方法，它们与目前在该领域占主导地位的最优化和基于模型的方法有着显著的不同。我们打算探索这些方法在多大程度上可以发展成为设计有效程序。我们相信，这些程序将贝内控制工程实践以及学术研究，并有助于缩小我们老年人中迫在眉睫的理论与实践的差距。