Optimal I-PD controller design for setpoint tracking of integrating processes with time delay

Abstract

Processes including one or more integrators in their transfer functions can frequently be encountered in industry. In this study, integral-proportional-derivative (I-PD) controllers are proposed to control these type of processes. Analytical and optimal tuning rules are derived to tune the I-PD controllers for setpoint tracking of integrating plus first order plus dead time (IFOPDT) processes and double IFOPDT processes. Optimal tuning rules for setpoint tracking are achieved by minimising time moment weighted integral performance criteria. Obtained I-PD tuning formulas are in terms of process' transfer function parameters, namely the gain, time delay and time constant. Simulation examples are given to demonstrate the use of the proposed method. Comparisons are provided to show the superior closed-loop performance of the proposed approach than existing proportional-integral-derivative and I-PD controller designing methods. In addition, the practical implementation of the proposed designing method is presented by controlling the position of a cart on an experimental setup.