DocumentCode :
2259354
Title :
Robust stability of fuzzy logic control systems
Author :
Farinwata, Shehu S. ; Vachtsevanos, George
Author_Institution :
Ford Motor Co., Mevindale, MI, USA
Volume :
3
fYear :
1995
fDate :
21-23 Jun 1995
Firstpage :
2267
Abstract :
An approximate method is formulated for analyzing the performance of a broad class of linear and nonlinear systems controlled using fuzzy logic. It is assumed that an approximate model of the nominal plant is available. Stability in the presence of small, bounded parametric uncertainty and external disturbance of a known origin is considered. The method is based on an appropriate formulation of a performance measure as a Lyapunov-like function of the nominal plant. A heuristic measure of the system´s error sensitivity with respect to the parameters of interest is incorporated into this performance expression which is to be minimized. By applying a Lyapunov-like stability condition, the robustness of the system is analyzed by observing a definiteness condition of a simple matrix. The theory is developed in two parts. First, it is assumed that the states are decoupled in the sense that a parameter perturbation in a particular state has no effect on other states. The main robust stability result is developed based on this assumption. In the second part, some interaction is allowed to exist between states as a result of parameter variation. Estimates of the measure of the interactions are derived on stability grounds. A more general result for robust stability is then given. The point of stability convergence is the system´s specified target point. Thus, stability convergence to this point, in the presence of parameter perturbations and external load inherently addresses the robust stability of the closed-loop system. Finally, inequality bounds are derived for the sensitivity, error deviation and parameter deviations in terms of fuzzy quantities. A measure for robustness is then formulated using singular values. A fuzzy automotive engine idle speed controller is used to illustrate the methodology
Keywords :
Lyapunov methods; closed loop systems; control system analysis; fuzzy control; fuzzy systems; linear systems; matrix algebra; nonlinear control systems; robust control; Lyapunov-like function; Lyapunov-like stability condition; bounded parametric uncertainty; closed-loop system; definiteness condition; error deviation; error sensitivity; external disturbance; external load; fuzzy automotive engine idle speed controller; fuzzy logic control systems; heuristic measure; inequality bounds; linear systems; nonlinear systems; parameter deviations; parameter perturbations; performance measure; robust stability; robustness; simple matrix; stability convergence; Control systems; Convergence; Fuzzy control; Fuzzy logic; Nonlinear control systems; Nonlinear systems; Performance analysis; Robust stability; Robustness; Stability analysis;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
American Control Conference, Proceedings of the 1995
Conference_Location :
Seattle, WA
Print_ISBN :
0-7803-2445-5
Type :
conf
DOI :
10.1109/ACC.1995.531375
Filename :
531375
Link To Document :
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