Predictive Control

5Predictive Control for MIMO Constrained Systems

In the above chapters, both introducing typical predictive control algorithms and investigating the quantitative relationship between the design parameters and the closed‐loop performances are all for unconstrained SISO systems. Although predictive control can be adopted in single‐loop control to replace the PID controller, its utility is more embodied in controlling constrained multivariable systems. In this chapter, based on the basic algorithms and principles introduced above, we will take the DMC algorithm as an example and introduce the predictive control algorithm for MIMO systems with constraints, which is closer to its real application status.

5.1 Unconstrained DMC for Multivariable Systems

In this section, we first introduce the DMC algorithm for multivariable systems without considering constraints [1]. As introduced in Section 2.1, the single‐variable DMC algorithm is based on the following basic principles:

1. Output prediction based on the prediction model using proportion and superposition properties of linear systems;
2. Online rolling optimization based on optimal output tracking and control increment suppression;
3. Error prediction and correction based on real‐time measured output.

Obviously these principles can be easily extended to multivariable systems.

Consider a stable MIMO plant with m control inputs and p outputs. Assume that the unit step response of each input u_j to each output y_i has been measured as