Stability analysis and design of a class of MIMO fuzzy control systems
Stability analysis and design of a class of MIMO fuzzy control systems
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DOI：
10.3233/ifs-2012-0621
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发表时间：
2013
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通讯作者：
Radu-Emil Precup;Marius-Lucian Tomescu;S. Preitl;E. Petriu;J. Fodor;C. Pozna
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文献类型：
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作者：
Radu-Emil Precup;Marius-Lucian Tomescu;S. Preitl;E. Petriu;J. Fodor;C. Pozna
针对一类模糊控制系统FCS控制多输入多输出多输入多输出非线性过程，提出了一种新的稳定性分析方法。通过对多输入多输出模糊控制系统中各模糊规则的稳定性分析，利用Lasalle全局不变集理论对模糊控制系统的稳定性进行了分析。这样不仅降低了稳定性分析的复杂性，而且可以方便地增加新的模糊规则；这种模糊逻辑结构的改进只需要满足本文提出的稳定性分析定理中的一个条件。本文提出的稳定性分析方法的另一个优点是，与Lyapunov稳定性定理中必须负定的Lyapunov函数相比，候选Lyapunov函数的导数必须是负定的。这样就降低了稳定性条件的保守性，从而方便了Flcs的设计。以一个典型的MIMO过程为例，对三球罐系统的液位控制进行了数值仿真，验证了理论结果的适用性和有效性。
This paper presents a new stability analysis method dedicated to a class of fuzzy control systems FCSs controlling multi input-multi output MIMO nonlinear processes by means of Takagi-Sugeno-Kang fuzzy logic controllers FLCs. The stability analysis of the FCSs is carried out using LaSalle's global invariant set theorem by the separate stability analysis of each fuzzy rule in MIMO fuzzy control systems. Therefore the complexity of the stability analysis is reduced and the adding of new fuzzy rules can be conducted easily; this modification of FLC structure requires the fulfillment of only one of the conditions of the stability analysis theorem suggested in this paper. Another advantage of the stability analysis approach proposed in this paper is that the derivative of the Lyapunov function candidate must be only negative semi-definite in comparison with Lyapunov's stability theorem where it must be negative definite. The conservativeness of stability conditions is thus reduced, and this enables the convenient design of FLCs. The applicability and efficiency of the theoretical results are illustrated by numerical simulations for a representative MIMO process which deals with the level control in a three spherical tank system.