In this chapter, we revisit the original formulation of the model reference adaptive control (MRAC), examine its transient performance, and then propose a modification to improve the latter. Often in practice, it is the transient of a tracking controller that defines feasibility of the selected system. Tracking performance during the first few seconds of operation is often more important than its asymptotic behavior. For linear systems, we can quantify transients by invoking the classical notions, such as damping ratio, natural frequency, overshoot, and undershoot. As for MRAC, uniform transient performance characterization is not at all straightforward. To remedy this situation, we offer a design modification to enforce and quantify transients for a class of MRAC-controlled nonlinear dynamical systems with uncertainties. We begin by drawing a parallel between reference models in adaptive control and Luenberger asymptotic state observers (Luenberger DG, IEEE Trans Mil Electron MIL-8:74–80, 1964). Based on this comparison, we reformulate the MRAC reference model structure. Our design change consists of adding an observer-like tracking error feedback/mismatch term to the reference model dynamics. This term is also known as the “innovation process” in Kalman filtering problems. Similar to the observer design, we will show that such a modification allows the enforcing of sufficiently fast, and thus improved, tracking error dynamics in MRAC systems. We substantiate our method with Lyapunov-based arguments to show that it is capable of solving servomechanism tracking problems for a selected class of multi-input–multi-output dynamical systems with uncertainties.


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    Title :

    Adaptive Control with Improved Transient Dynamics


    Additional title:

    Adv. Textbooks Control, Signal Proc.


    Contributors:


    Publication date :

    2012-09-01


    Size :

    30 pages





    Type of media :

    Article/Chapter (Book)


    Type of material :

    Electronic Resource


    Language :

    English




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