Analysis, design, and tuning of the two-input two-output fuzzy control systems using the simplified fuzzy rules

Most work on fuzzy control theory and application in the literature has dealt with single-input single-output (SISO) cases only. While the significance of multiple-input multiple-output (MIMO) fuzzy control is well recognized, it is much more difficult to study than the SISO control due to the coupling of the output variables and a much larger amount of design parameters of MIMO fuzzy controllers. At present, there exist little rigorous MIMO fuzzy control results, let alone a comprehensive theory. The trial-and-error method is often used for SISO fuzzy control; but it cannot be effective to the MIMO cases partially due to the number of design parameters and coupling. This dissertation attempts to address these issues in an analytical manner. While extensible to MIMO situations, this work is mainly focused on two-input two-output cases.; This dissertation performs a systematic study of analysis, design, and tuning of the TITO Takagi-Sugeno (TS) fuzzy control systems. This study is applied to fuzzy control systems with relationship to their conventional Proportional-Integral-Derivative (PID) counterpart. In this dissertation, the simplified fuzzy rules scheme method is used to dramatically reduce the number of design parameters for TITO fuzzy controllers.; The fuzzy controller structure analysis is investigated. The analysis shows that each output of the TITO TS fuzzy PI, PD, and PID controllers are proved to be the sum of two nonlinear, variable gains PI, PD, and PID controllers, respectively. Also, the analysis shows that the TITO TS fuzzy PI, PD, and PID controllers are linearizable at an equilibrium point, respectively. Also, analysis shows that local stability of TITO TS fuzzy system can be determined using Lyapunov linearization method.; The simplified fuzzy rules scheme method shows a significant improvement to reduce the number of design parameters. The number of design parameters of the TITO TS fuzzy PI controller is reduced from 65 design parameters to only 7. The number of design parameters of the TITO TS fuzzy PID controller is reduced from 385 to 9.; In this dissertation, a new systematic design and tuning procedure is presented. This procedure is applied to TITO TS fuzzy control systems by carrying a well known conventional MIMO control tuning method over the TITO fuzzy controllers. Also, the systematic design and tuning procedure is applied to SISO TS fuzzy control systems.; Finally, a selection of examples in computer simulation is given to illustrate the effectiveness of the proposed study. The examples include tuning TITO practical model and SISO linear and nonlinear models.