Relay Auto Tuning of Decentralized PID Controllers for Unstable TITO Systems

An improved method, taking into account the higher order harmonics, is presented for the analysis of decentralized relay feedback for an unstable multivariable process. Smith method [Smith, “Intelligently Tune PID Controllers”, Chem. Eng., pp. 56–62 (2003)] is used for calculating the integral and derivative times of the Proportional-Integral-Derivative controllers. A simple method is provided for the calculation of the minimum value of the controller gain. The design value for the controller gain is considered as the average value of the corrected maximum and minimum values of the gain of the controller. The simulation results are given for (i) a two-input and two-output (TITO) system with unstable transfer function models for one of the input variables and (ii) a TITO system with unstable diagonal elements having unequal poles. The improved auto-tuning method yields superior responses and reduced interactions over the conventional method of analysing the relay auto-tune method.