CONTROLLER REDUCTION FOR NONLINEAR PLANTS—ANL2 APPROACH
CONTROLLER REDUCTION FOR NONLINEAR PLANTS—ANL2 APPROACH
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非线性对象的控制器简化——ANL2 方法
DOI：
10.1002/(sici)1099-1239(199705)7:5
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发表时间：
1997
影响因子：
3.9
通讯作者：
F. Fairman
中科院分区：
文献类型：
--
作者：
L. Pavel;F. Fairman
摘要 本文将 Mustafa-Glover 的线性植物的 H = 平衡截断方法扩展为输入非线性植物。非线性 H = 平衡截断用于获得降阶控制器。导出了确保该控制器稳定全阶对象的条件。这是通过将模型简化问题与具有非结构化扰动的鲁棒稳定问题相关联来完成的。此外，还获得了闭环系统相对于 2 增益的性能上限。当专门针对线性植物时，这个界限减少到 Mustafa-Glover 的结果。 ( 1997 by John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control, Vol. 7, 475—505 (1997) 当现代控制器设计算法应用于高阶设备时，所得控制器的阶数可能足够高，从而在其实现中产生问题。控制器缩减问题涉及降低控制器的阶数，以保持控制系统的稳定性并保持控制系统的性能。对此问题的早期研究 研究表明，使用开环模型简化技术降低全阶稳定控制器的阶数不足以保持闭环稳定性。此外，当通过设计低阶控制器来控制对象的降阶近似来获得低阶控制器时，也会遇到这个缺点。最近，在参考文献 1 和 2 中，在线性情况下，通过使用 H = 闭环平衡2 来降低阶数，克服了这一困难 植物的。为该降阶设备获得的控制器将是低阶的，并且当与降阶设备一起使用时仍然实现稳定性和 H = 界限。当该控制器与全阶对象一起使用时，稳定性的保持可以通过鲁棒稳定性理论来获得。3这是通过将因用全阶对象替换降阶对象而导致的对象变化视为 H = 有界非结构化不确定性来实现的。非线性 平衡方法及其在模型简化中的应用在参考文献 4 渐近稳定植物中介绍，并在参考文献 5-7 中扩展到不稳定植物。基于非线性 H = 平衡的设备/控制器简化程序在参考文献 6 和 7 中进行了研究。H = 奇异值函数的属性和降阶的一些属性“他的论文被编辑 I. Postlethwaite 推荐出版
SUMMARY This paper extends the H = balanced truncation approach of Mustafa—Glover for linear plants to input aƒne nonlinear plants. Nonlinear H = balanced truncation is used to obtain a reduced order controller. Conditions which ensure that this controller stabilizes the full order plant are derived. This is done by relating the model reduction problem to a robust stabilization problem with unstructured perturbation. In addition an upper bound on the performance of the closed loop system, with respect to the ‚ 2 gain, is obtained. When specialized to linear plants this bound reduces to Mustafa—Glover’s result. ( 1997 by John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control, Vol. 7, 475—505 (1997) When modern controller design algorithms are applied to high order plants the resulting controller may have order high enough to create problems with its implementation. The controller reduction problem is concerned with reducing the order of the controller so as to maintain the stability of the control system and preserve the control system performance. Early research on this problem revealed that reducing the order of a full order stabilizing controller using open loop model reduction techniques was not suƒcient to preserve closed loop stability. Moreover this drawback was also encountered when the low order controller was obtained by designing it to control a reduced order approximation of the plant. Recently in References 1 and 2 this diƒculty has been overcome, in the linear case, by using H = closed loop balancing,2 to reduce the order of the plant. The controller obtained for this reduced order plant will then be of low order and still achieve both stability and an H = bound when used with the reduced order plant. The preservation of stability when this controller is used with the full order plant is then obtained by resorting to robust stability theory.3 This is done by viewing the change in the plant resulting from replacing the reduced order plant by the full order plant as an H = bounded unstructured uncertainty. The nonlinear balancing method and its use in model reduction was introduced in Reference 4 asymptotically stable plants and extended to unstable plants in Reference 5—7. The plant/controller reduction procedure based on nonlinear H = balancing was studied in References 6 and 7. Properties of the H = singular value functions and some properties of the reduced order „his paper was recommended for publication by editor I. Postlethwaite