Quantitative design and analysis of fuzzy proportional-integral-derivativecontrol - a step towards autotuning

In this paper, a thorough mathematical analysis is proposed for designing a nd 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. Th,is nonlinear model can be treated as of a PID nature around the equilibrium state under certain approximations. Through direct compari son with the conventional PID control, the connection between the scaling g ains and the control actions is expressed in an explicit mathematical form. This theoretical analysis reveals that FZ-PID leads to more damping and he nce less oscillation than do its conventional counterparts. This could be o ne of the reasons why fuzzy logic control can achieve a robust performance. A less coupled gain structure is further proposed to decouple the influenc e of the scaling gains and to disclose the major contribution of each gain to the different aspects of the control performance. Consequently, the syst ematic design and tuning method of the conventional PID control can be appl ied to the initial gain design and the fine tuning of the FZ-PID control. T he simulation results confirm the effectiveness of the method proposed This research is actually an important step towards the possible autotuning of the fuzzy controller.