The Absolute Stability Analysis in Fuzzy Control Systems with Parametric Uncertainties and Reference Inputs

Bing-Fei WU, Li-Shan MA, Jau-Woei PERNG
2009 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
This study analyzes the absolute stability in P and PD type fuzzy logic control systems with both certain and uncertain linear plants. Stability analysis includes the reference input, actuator gain and interval plant parameters. For certain linear plants, the stability (i.e. the stable equilibriums of error) in P and PD types is analyzed with the Popov or linearization methods under various reference inputs and actuator gains. The steady state errors of fuzzy control systems are also addressed
more » ... n the parameter plane. The parametric robust Popov criterion for parametric absolute stability based on Lur'e systems is also applied to the stability analysis of P type fuzzy control systems with uncertain plants. The PD type fuzzy logic controller in our approach is a single-input fuzzy logic controller and is transformed into the P type for analysis. In our work, the absolute stability analysis of fuzzy control systems is given with respect to a non-zero reference input and an uncertain linear plant with the parametric robust Popov criterion unlike previous works. Moreover, a fuzzy current controlled RC circuit is designed with PSPICE models. Both numerical and PSPICE simulations are provided to verify the analytical results. Furthermore, the oscillation mechanism in fuzzy control systems is specified with various equilibrium points of view in the simulation example. Finally, the comparisons are also given to show the effectiveness of the analysis method. key words: steady state error, parametric absolute stability, fuzzy logic control system, Lur'e system, Popov criterion, robust Li-Shan Ma was born in Changhua, Taiwan in 1968. He received the B.S. and M.S. degrees in electrical engineering from Chung Yuan Christian University, Chungli, Taiwan, in 1995 and 1997, respectively. Since 1999, he has been with the
doi:10.1587/transfun.e92.a.2017 fatcat:fipqtrhtmfdxxorslie3a42xse