Smith delay compensator for multivariable non-square systems with multiple time delays

The classical multivariable Smith delay compensator is extended to multivariable non-square systems with multiple time delays where there is more number of inputs than the outputs. For the delay compensated system, centralized multivariable PI controllers are designed by an extended version of Davison method with a pseudo inverse for the steady-state gain matrix. A method is proposed to select the two tuning parameters in Davison method. To show the improvement, PI controllers for the uncompensated system are also designed by the Davison method. The proposed method is applied to shell standard control problem (3 input and 2 output) and hot oil fractionator (4 input and 2 output). Simulation studies are carried out for both servo and regulatory problems. Robustness studies are carried out for uncertainty in all the process model parameters. The performance of the multivariable delay compensated system with the centralized PI controllers is improved by 25–35% when compared to that of the multivariable control system without any delay compensator. It is also shown that the performance and robustness of the delay compensator are significantly better for the non-square systems than that of the squared down systems.