Model reference robust control for MIMO systems

Abstract

Model reference robust control (M RRC) of single-input single-output (SISO) systems was introduced as a new means of designing I/O robust control (Qu et al. 1994). This I/O design is an extension of the recursive backstepping design in the sense that a nonlinear dynamic control (not static) is generated recursively. Backstepping entails the design of fictitious controls starting with the output state-space equation and backstepping until one arrives at the input state-space equation where the actual control can be designed. At each step the system is transformed and a fictitious control is designed to stabilize the transformed state (Naik and Kumar 1992). It is shown in this paper that M RRC of multiple input multiple output (MIMO) systems is an extension of model reference control (M RC) of MIMO systems and M RRC of SISO systems. Unwanted coupling exists in many physical MIMO systems. It is shown that M RRC decouples MIMO systems using only input and output measurements rather than state feedback. This is a very desirable property, because in many instances state information is not available. A diagonal transfer function matrix is strictly positive real (SPR) if and only if each element on the diagonal is SPR. The fact that complicates the development of robust control laws is that the recursive backstepping procedure used in non-SPR SISO systems cannot be directly applied to diagonal MIMO non-SPR systems without the introduction of the augmented matrix or a pre-compensator. MRC of systems where one has perfect plant knowledge is reviewed. Assumptions are listed for the application of model reference robust control for MIMO systems. Model selection is presented as the right Hermite normal form of the plant transfer function matrix. M RRC is derived for MIMO systems that have a right Hermite normal form which is SPR and diagonal, and then for systems whose right Hermite normal form is diagonal but not SPR. Robust control laws are generated for achieving stability using Lyapunov's second method. Future research will focus on MIMO systems which are not diagonal.