Parallel Fuzzy P+Fuzzy I+Fuzzy D Controller:Design and Performance Evaluation

In this paper, a parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative （FP＋FI＋FD） controller is proposed. It is derived from the conventional parallel proportional-integral-derivative （PID） controller. It preserves the linear structure of a conventional parallel PID controller, with analytical formulas. The final shape of the controller is a discrete-time fuzzy version of a conventional parallel PID controller. Computer simulations are performed to evaluate the performance of the FP＋FI＋FD controller for setpoint tracking and load-disturbance rejection for some complex processes, such as first- and second-order processes with delay, inverse response process with and without delay and higher order processes. Also, the performance of the proposed fuzzy controller is evaluated experimentally on highly nonlinear liquid-flow process with a hysteresis characteristic due to a pneumatic control valve. The simulation and real time control is done using National InstrumentTM hardware and software （LabVIEWTM）. The response of the FP＋FI＋FD controller is compared with the conventional parallel PID controller, tuned with the Ziegler-Nichols （Z-H） and /~strSm- H^gglund （A-H） tuning technique. It is observed that the FP＋FI＋FD controller performed much better than the conventional PI/PID controller. Simulation and experimental results demonstrate the effectiveness of the proposed parallel FP＋FI＋FD controller.

Some Investigations on Fuzzy P+Fuzzy I+Fuzzy D Controller for Non-stationary Process

The paper addresses the adaptive behaviour of parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP+FI+FD) controller. The parallel FP+FI+FD controller is actually a non-linear adaptive controller whose gain changes continuously with output of the process under control. Two non-stationary processes, whose characteristics change with time, are considered for simulation study. Simulation is performed using software LabVIEW TM . The set-point tracking response of parallel FP+FI+FD is compared with conventional parallel proportional plus integral plus derivative (PID) controller, tuned with the Ziegler-Nichols (Z-N) tuning technique. Simulation results show that conventional PID controller fails to track the set-point and becomes unstable as the process changes its characteristic with time. But the parallel FP+FI+FD controller shows considerably much better set-point tracking response and does not deviate from steady state. Also, a huge spike is observed in the output of PID controller as the reference set-point and process parameters are changed, while the FP+FI+FD controller gives spike free control signal.

Stability Analysis of Parallel Fuzzy P + Fuzzy I + Fuzzy D Control Systems

The study presented in this paper is in continuation with the paper published by the authors on parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative （FP ＋ FI ＋ FD） controller. It addresses the stability analysis of parallel FP ＋ FI ＋ FD controller. The famous＂small gain theorem＂ is used to study the bounded-input and bounded-output （BIBO） stability of the fuzzy controller. Sufficient BIBO-stability conditions are developed for parallel FP ＋ FI ＋ FD controller. FP ＋ FI ＋ FD controller is derived from the conventional parallel proportional plus integral plus derivative （PID） controller. The parallel FP ＋ FI ＋ FD controller is actually a nonlinear controller with variable gains. It shows much better set-point tracking, disturbance rejection and noise suppression for nonlinear processes as compared to conventional PID controller.