Iterative learning control of multivariable plants

摘要

In recent years, many researchers have proposed different iterative learning
\ncontrollers, which unfortunately mostly require that the plants under control be
\nregular. Therefore, in order to remove this limitation, various analogue and digital
\niterative learning controllers are proposed in this thesis.
\nIndeed, it is shown that analogue iterative learning controllers can be designed for
\nplants with any order of irregularity using initial state shifting or initial impulsive
\naction. However, such analogue controllers have to be digitalised for purpose of
\nimplementation. In addition, in the synthesis of their control laws, such controllers
\nrequire some knowledge of the plants' Markov parameters. Ilerefore, new digital
\niterative learning controllers are proposed. Such digital controllers circumvent the
\nneed for detailed mathematical models of the plants in any form. Indeed, the
\nproposed digital iterative learning controllers rely on input/output data in the
\nsynthesis of their control laws. It is shown that digital iterative learning controllers
\ncan be readily designed for multivariable plants of any order or irregularity using only
\nsuch input/output data in the form of step-responsem atrices.
\nThe learning rates achievable in both the analogue and digital iterative learning
\ncontrol of linear multivariable plants are investigated. It is shown that the irregularity
\nand stability characteristics of the plants under control impose severe constrains on the
\nachievable learning rates. Indeed, it is shown that the learning parameter in the case
\nof digital iterative learning controllers increases as the order of plant irregularity
\nincreases. This increase in the learning parameter affects the learning performance
\nand the speed of convergence adversely. This discovery led to the introduction of
\ncompensators in the design of digital iterative learning controllers for irregular plants which help to improve the learning performance and convergence by reducing the
\neffective learning parameter. Since such digital iterative learning controllers use stepresponse
\nmatrices in the synthesis of their control laws and since the step-response
\ncharacteristics can be identified in real time, it is shown in this thesis that iterative
\nlearning controllers can readily be rendered adaptive in case plant dynamics are
\ninitially unknown or time-varying.
\nIn order to demonstrate the applicability of these results to the control of robotic
\nmanipulators, both analogue and digital iterative learning controllers are designed for
\na two-link manipulator in both joint and task spaces. Finally, digital iterative
\nlearning controllers are designed and practically implemented in the real-time
\npositional control of a dc servo actuator.