Decoupled Smith predictor for multivariable nonsquare systems with multiple time delays

The classical multivariable Smith predictor is extended to multivariable nonsquare systems with multiple time delays where the number of process inputs is higher than the process outputs. Pairing for input and output variables is carried out using the block relative gain technique. Simplified decoupling method is applied to design the decouplers. The decoupled processes are modeled as first-order plus time-delay model or second-order plus timedelay model with positive/negative zero. The controllers are designed individually based on the identified models. For the delay-compensated system, decentralized multivariable proportional-integral controllers are designed by internal model control method for FOPTD models. To show the improvement, PI controllers for the uncompensated system are also designed by simplified internal model control method. For SOPTD models, a method similar to Chien et al. [Simple PID controller tuning method for processes with inverse response plus dead time or large overshoot response plus dead time, Ind. Eng. Chem. Res., 42, 4461–4477 (2003)] is proposed for controller design in the delay compensator. The proposed method is applied to shell standard control problem (3 input and 2 output), hot oil fractionator (4 input and 2 output) and mixing tank (3 input and 2 output). Simulation studies were carried out for both servo and regulatory problems. Robustness studies were carried out for uncertainty in all the process model parameters. It is shown that the performance of the multivariable delay-compensated system with decentralized PI controllers is significantly better than that of the multivariable control system without any delay compensator.