Experimental evaluation of iterative learning control performance for non-minimum phase plants

Abstract

This thesis describes the design and construction of a Single Input Single Output (SISO) non-minimum phase experimental test facilityan d the subsequent testing of a number of Iterative Learning Control (ILC) strategies. The system can be configured in three different ways in order to test the effect of increased plant complexity and non-linearity. The implementation of a number of both existing and new ILC strategies is detailed and results and analysis of their performance are presented. A principal objective has been to find the ILC controller that is most effective in forcing the output of the test-bed to follow a repetitive trajectory. The design and construction of the test-bed is explained in full and both linear and non-linear models of the system are produced. P-type, D-type and Delay-type ILC algorithms have been tested on the simplest form of the system. The phase-lead algorithm has been implemented and a method of establishing the optimum lead found, as well as a procedure to estimate unstable frequencies. Both causal and noncausal filters have been assessed for use with the algorithm. Phase-lead ILC has been implemented on the more complex plant and comparisons made with previous results. The use of a forgetting factor has been found to overcome the problem of instability, but at the expense of increased final error. The phase-lead algorithm has been vastly improved using additional phase-leads and this technique has been generalised to produce an novel optimisation routine which uses a large number of phase-leads. Its success has been confirmed with experimental results. A learning law utilising the plant adjoint fits naturally into this framework and practical results are presented. This method has been both reformulated into one which needs little plant knowledge, and also combined with deadbeat control to avoid truncation in the course of its implementation. Results are presented using these techniques and practical guidelines produced and tested. A simple method of increasing the learning at higher frequencies has been proposed and verified experimentally. An optimality based Repetitive Control algorithm has also been rigorously tested and the use of a relaxation parameter found to increase its robustness. Finally, a graphical method that represents both the robustness and the stability of an ILC algorithm applied to a known plant has been developed. This tool may find wide application when designing and developing future ILC strategies.

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Identifiers

ORCID for Paul Lewin: orcid.org/0000-0002-3299-2556

ORCID for Eric Rogers: orcid.org/0000-0003-0179-9398

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