Naslov:Analiza stabilnosti nelinearnih sustava vođenih analitičkim neizrazitim regulatorom : doktorski rad / Josip Kasać
Ostali naslovi:Stability Analysis of Nonlinear Systems controlled by Analytic Fuzzy Controller
Predmet:Roboti, Upravljanje, Automatsko upravljanje, Nelinearni sustavi, Mehanički sustavi, Stabilnost
Datum objave: 2005
The subject of this thesis is the stability analysis of nonlinear mechanical systems in closed loop with analytic fuzzy PID controller. The analytic fuzzy control is a nonconventional approach that uses an analytic function for output determination, instead of a fuzzy rule base. The stability analysis is based on the Lypunov’s direct method and doesn ot require representation of the plant dynamics in the form of Takagi-Sugeno’s fuzzy model. The stability analysis is divided in four principal parts. First, error equations for closed loop system is determined. Second, Lyapunov function candidate is proposed. Then, stability criterion on system parameters is established. Finally, LaSalle invariance principle is invoked to guarantee the asymptotic stability. The local stability condition which involve only few control systems parameters are obtained. On the base of obtained results, some modification of analytic fuzzy controllers which ensure global asymptotic stability are considered. Further, the Lyapunov functions of analyzed controllers are employed for performance evaluation and determination of the optimal values of controller parameters. The proposed approach is based on construction of a parameter dependent Lyapunov function. With the appropriate choice of the free parameter an estimation of integral performance index is obtained. The estimated performance index depends on controller parameters and few parameters which characterize the robot dynamics. The optimal values of the controller gains are obtained by minimization of the performance index. The obtained tuning rules are demonstrated by using simulation models of two robot manipulators with different structures.
Keywords: robot control, analytic fuzzy control, Lyapunov stability analysis, global stability, performance evaluation, nonlinear control
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