Theory and application of a novel fuzzy PID controller using a simplified Takagi–Sugeno rule scheme

Abstract

We first present a novel general-purpose nonlinear PID controller realized via fuzzy PID control that uses our newly-introduced simplified Takagi–Sugeno (TS) rule scheme. Analytical structure of the fuzzy PID controller is derived and its structure is analyzed in relation to the linear PID controller. The unique features of the fuzzy controller are as follows. First, the proportional, integral and derivative gains constantly vary with the output of the system under control. The gain variation leads to a shorter rise-time, a less overshoot and a smaller settling-time as compared to a comparable linear PID controller. Second, the characteristics of the gain variation are determined by the fuzzy rules, and can intuitively be designed. We have also investigated the local stability of the fuzzy PID control systems. As an application demonstration, we have developed a fuzzy PID control system to regulate, in computer simulation, blood pressure in postsurgical patients. We have chosen this particular control problem because the studies in the literature have established that, in order to achieve satisfactory control results, using a nonlinear controller with variable gains is necessary. The simulation results show that the fuzzy PID controller significantly outperforms its linear counterpart, and is safer and more robust over a wide range of patient condition.