Compatibility and Uniqueness Analyses of Steady State Solution for Multi-variable Predictive Control Systems

The multi-variable control systems can be structurally classified into the square and non-square ones,with the latter further into fat and thin ones.For the fat and thin,the output offset and non-determinedness of the steady state input,respectively,can occur in predictive control systems.From the steady-state relationship between the control input and the controlled output,the two issues are tackled as the compatibility and uniqueness,respectively,of the nonhomogeneous linear equations set.The reason why the compatibility and uniqueness issues can arise is analyzed based on the determination theorem for non-homogeneous linear equations set,and the solutions based on the double-layer(two-layer) control structure are given.The upper level steady state optimization not only tackles the compatibility issue for the thin system,but also finds the optimal solution from the infinite many consistent ones for the fat system.The lower level predictive control algorithm,integrated with the control input target,guarantees the uniqueness of the steady state solution for fat system,and algorithmically unifies both the square and nonsquare systems.Simulation results have validated the effectiveness of the double-layered predictive control algorithm,i.e.,the steady state solutions of the multi-variable predictive control system are consistent and unique.