Quantitative design and analysis of fuzzy proportional-integralderivative control a step towards autotuning

In this paper, a thorough mathematical analysis is proposed for designing and tuning fuzzy proportional ± integral± derivative (FZ-PID) control in order to achieve a better performance and simpler design. The quantitative model of FZ-PID, derived for the mathematical analysis and gain design, consists of a nonlinear relay and a nonlinear proportional ± integral ± derivative (PID) controller. This nonlinear model can be treated as of a PID nature around the equilibrium state under certain approximations. Through direct comparison with the conventional PID control, the connection between the scaling gains and the control actions is expressed in an explicit mathematical form. This theoretical analysis reveals that FZ-PID leads to more damping and hence less oscillation than do its conventional counterparts. This could be one of the reasons why fuzzy logic control can achieve a robust performance. A less coupled gain structure is further proposed to decouple the in ̄ uence of the scaling gains and to disclose the major contribution of each gain to the di€ erent aspects of the control performance. Consequently, the systematic design and tuning method of the conventional PID control can be applied to the initial gain design and the ® ne tuning of the FZ-PID control. The simulation results con ® rm the e€ ectiveness of the method proposed. This research is actually an important step towards the possible autotuning of the fuzzy controller.