Iterative learning control of multivariable plants
In recent years, many researchers have proposed different iterative learning controllers, which unfortunately mostly require that the plants under control be regular. Therefore, in order to remove this limitation, various analogue and digital iterative learning controllers are proposed in this thesis. Indeed, it is shown that analogue iterative learning controllers can be designed for plants with any order of irregularity using initial state shifting or initial impulsive action. However, such analogue controllers have to be digitalised for purpose of implementation. In addition, in the synthesis of their control laws, such controllers require some knowledge of the plants' Markov parameters. Ilerefore, new digital iterative learning controllers are proposed. Such digital controllers circumvent the need for detailed mathematical models of the plants in any form. Indeed, the proposed digital iterative learning controllers rely on input/output data in the synthesis of their control laws. It is shown that digital iterative learning controllers can be readily designed for multivariable plants of any order or irregularity using only such input/output data in the form of step-responsem atrices. The learning rates achievable in both the analogue and digital iterative learning control of linear multivariable plants are investigated. It is shown that the irregularity and stability characteristics of the plants under control impose severe constrains on the achievable learning rates. Indeed, it is shown that the learning parameter in the case of digital iterative learning controllers increases as the order of plant irregularity increases. This increase in the learning parameter affects the learning performance and the speed of convergence adversely. This discovery led to the introduction of compensators in the design of digital iterative learning controllers for irregular plants which help to improve the learning performance and convergence by reducing the effective learning parameter. Since such digital iterative learning controllers use stepresponse matrices in the synthesis of their control laws and since the step-response characteristics can be identified in real time, it is shown in this thesis that iterative learning controllers can readily be rendered adaptive in case plant dynamics are initially unknown or time-varying. In order to demonstrate the applicability of these results to the control of robotic manipulators, both analogue and digital iterative learning controllers are designed for a two-link manipulator in both joint and task spaces. Finally, digital iterative learning controllers are designed and practically implemented in the real-time positional control of a dc servo actuator.