Design and analysis of a multistage fuzzy PID controller

Classical PID controllers remain one of the simplest, most effective, robust, and easily certifiable control strategies. However, this simplicity comes with a price. Design tradeoffs between integral and derivative gain in a linear PID controller often make it difficult to achieve optimal performance. For example, increasing the integral term to reduce steady-state error causes undesired behavior during the transient phase of the system response. Intuitively, the integral term should only be active during the steady-state portion of the response to either reduce or eliminate the steady-state error. This can be achieved by implementing a switching multistage PID controller that consists of a first stage PD controller followed by a second stage PI controller. Difficulty arises in designing the switching circuit to appropriately engage the integral controller without jeopardizing stability. It has been shown that a fuzzy logic PD controller is able to reduce the steady-state error while maintaining the speed and damping of the system. However, like the classical counterpart, a fuzzy PD controller can not completely eliminate the error. To eliminate this error, the design of a multistage fuzzy PID controller is presented in this paper. The simulation results show the effectiveness of the fuzzy PID controller in removing the steady-state error while maintaining the speed and stability of the system. Finally, fuzzy control systems have not been widely accepted by the control community due to lack of systematic stability analysis. To address this concern, this paper demonstrates some preliminary work, using simulation aided formal analysis to derive the global stability region of fuzzy based Hybrid System.