Analytical Tuning of Predictive Control for a Multivariable Fractional Dead Time System

In this study, we propose an analytical model predictive control (MPC) tuning approach for a multivariable system described by first order plus fractional dead time model for each subsystem. Initially, the multivariable fractional dead time system is transformed into the state space form. Subsequently, an MPC optimization problem is constructed based on the aforementioned model, and an analytical expression can be obtained for the control signal. In addition, the decoupling analysis of the closed-loop control system reveals the quantitative relation between the predictive controller parameters of the model and the closed-loop performance of the system. Therefore, the parameter tuning problem can be redefined as a pole placement problem, and the MPC tuning formulas that ensure closed-loop performance are developed. Finally, the simulation results denote the effectiveness of the proposed analytical parameter tuning method.