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™ software (LabVIEW™). 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”.