Architecture, performance and stability analysis of a formula-based fuzzy I - fuzzy P - fuzzy D controller
In this paper, a formula-based fuzzy integral minus fuzzy proportional minus fuzzy derivative (FI - FP - FD) controller is proposed based on the modified conventional parallel PID controller, i.e. parallel integral minus proportional minus derivative (I - P - D) controller, in order to avoid some practical industrial process problems. It freezes the linear structure of conventional parallel I - P - D controller, with analytical formulas. The final shape of the controller is a discrete-time fuzzy version of conventional parallel I - P - D controller. Computer simulation is performed to evaluate the performance of FI - FP - FD controller for setpoint tracking and load-disturbance rejection for some complex processes, such as, first- and second-order process with delay, inverse response process with and without delay and higher order processes. The simulation is done using National Instrument (TM) software (LabVIEW (TM)). The response of FI - FP - FD controller is compared with the conventional parallel I - P - D controller, tuned with the Ziegler-Nichols tuning technique. It is observed that the FI - FP - FD controller performed much better than conventional I - P/I - P - D controller. Simulation results demonstrate the effectiveness and usefulness of proposed formula-based FI - FP - FD controller. Also, the bounded-input bounded-output (BIBO) stability of the overall fuzzy control system is established with sufficient conditions, using the famous "Small Gain Theorem".
pid i - p - d fi - fp - fd controller inverse response process dead time