Learn while tracking. (c2013)

Abstract

Controlling a plant and automatically driving its output to track a user-defined reference trajectory with sufficiently small error has been an important problem in control theory and application. This problem is referred to as output tracking problem and has been addressed extensively throughout the last five decades. This topic has been and remains a challenging problem encountered in various engineering applications. Tracking systems are basically characterized in terms of their transient response and steady-state tracking error. Most of the proposed control techniques aim at achieving stable asymptotic tracking, where output error converges to zero as time goes to infinity. One of the most often mentioned open problems in control theory is the output feedback stabilization problem. Few algorithms tackle the uniform output tracking problem, where error converges to zero at all time, without necessitating the use of full state feedback. In particular, iterative learning control (ILC) algorithms are shown to achieve uniform output tracking as the number of iterative cycles goes to infinity. However, the main drawback of ILC algorithms is that the system is required to operate repetitively over a fixed time interval. Learn While Tracking (LWT) algorithm aims at achieving uniform output tracking in the sense of attaining arbitrary small tracking errors as well as arbitrary small transient period. LWT is a multiple-input multiple-output (MIMO) non-repetitive static output feedback digital control law that is founded on high sampling rate. It incorporates information of output errors and control input from previous time samples into the construction of the present control action. The latter awards “learn while tracking” terminology. LWT makes use of high sampling rates in order to provide the controller with an ability to tune the input in a faster manner. This approach was proposed in 2007 but was never further studied. Convergence and robustness characteristics were presented. However, the selection of the controller gain was not well elaborated. In this thesis the basic theory of LWT is revisited. The controller gains of LWT controller are designed for a class of DC motors satisfying the sufficient conditions for convergence and robustness. These gains are experimentally applied to a DC motor. In order to illustrate the performance of LWT in comparison with ILC, numerical and experimental results are presented. Finally, with the intention to explore the potential of LWT to MIMO nonlinear systems, the algorithm is experimentally applied to an induction motor.