Model reference robust control for MIMO systems

    Authors

    H. Ambrose;Z. Qu

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Int. J. Control

    Keywords

    Automation & Control Systems

    Abstract

    Model reference robust control (MRRC) 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 stale-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 MRRC of multiple input multiple output (MIMO) systems is an extension of model reference control (MRC) of MIMO systems and MRRC of SISO 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. 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. MRRC 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.

    Journal Title

    International Journal of Control

    Volume

    68

    Issue/Number

    3

    Publication Date

    1-1-1997

    Document Type

    Article

    Language

    English

    First Page

    599

    Last Page

    623

    WOS Identifier

    WOS:A1997WK54500009

    ISSN

    0020-7179

    Share

    COinS