Model reference robust control for MIMO systems.

摘要

In this dissertation, Model Reference Robust Control (MRRC) is being extended to Multiple Input-Multiple Output (MIMO) systems. Considered in this dissertation are MIMO systems which are partially linear with a nonlinear part that is assumed to be a disturbance bounded by a known continuous function. The nominal linear MIMO plant is uncertain in that one does not have absolute certainty of plant parameter values. The aim of the thesis is to develop nonlinear robust controls for MIMO uncertain nominal plants, controls that compensate for plant uncertainties and nonlinear disturbances while achieving model following and stability.; It is shown in this dissertation that MRRC of MIMO systems is an extension of model reference control (MRC) of MIMO systems and MRRC of Single Input-Single Output (SISO) systems. The extension is complicated due to the fact the one is dealing with matrix systems. An additional complication is the fact that the back-stepping procedure used in non Strictly Positive Real (SPR) SISO systems cannot be directly applied to MIMO non SPR systems.; Unwanted coupling exists in many physical MIMO systems. It is shown that MRRC decouples MIMO systems using only input and output measurements rather than state feedback techniques. Using input and output information for control is a very desirable property, since in many instances state information is not available or state measurements are corrupted by noise.; MRC of systems where one has perfect knowledge is reviewed. Assumptions are listed for the application of MRRC for MIMO systems. Reference model selection is presented as the right Hermite normal form of the plant transfer function matrix. MRRC is derived for strictly positive real (SPR) MIMO systems, and systems which are not SPR. Robust control laws are presented and are verified using stability proofs based on Lyapunov's second method.; It is shown in this dissertation that SPR MIMO plants considered herein plus nonlinear robust controller achieves asymptotic stability and that non SPR plants achieves uniform ultimate boundedness.; Examples are presented of MIMO plants with significant nonlinear disturbances to illustrate the effectiveness of the nonlinear robust control laws. Two physical systems are presented which show the control's practical application. Discussions on extensions to MIMO plants with multiplicative unmodeled dynamics are presented and future research is discussed.