Performance assessment of MIMO control systems with time-variant disturbance dynamics

In this paper, we consider performance assessment problem for multivariable control systems subject to piecewise constant time varying disturbance dynamics. The problem is motivated by the observation that most industrial controllers are linear time invariant (LTI) but the process, particularly the disturbance dynamics, can be time varying. We consider a class of disturbance dynamics that can be modelled by piecewise linear disturbance models, namely piecewise linear time varying (LTV) disturbance dynamics. The problem is formulated as searching for a multi-input multi-output (MIMO) benchmark control that is LTI but optimal in regulating the LTV disturbances. The single-input single-output (SISO) case has been previously solved by minimizing the variance of a most representative disturbance or by the minimization of the sum of the weighted variances of all but one of major disturbances, while satisfying a structured regulatory performance requirement for the major disturbance. In this paper, the previous results are extended to MIMO systems. The counterparts of the two SISO benchmarks are defined as the regular linear time varying disturbances (LTVDs) benchmark and the weighted LTVD benchmark for MIMO control systems, respectively. In addition, a new yet more practical LTVD benchmark, the generalized LTVD benchmark, is also proposed, which minimizes the maximum total variance among all different disturbance dynamics. These three LTVD benchmarks are compared by simulation and industrial application examples. The results show that the weighted and generalized LTVD benchmarks can always lead to better trade-offs on the total output variances.