ANALYSIS OF ITERATIVE LEARNING CONTROL WITH CURRENT CYCLE FEEDBACK

Abstract

This thesis contains a study of a new iterative learning control algorithm and its application in the control of robots. A relatively simple algorithm is used to improve the performance of linear and nonlinear plants by repetitive learning. The algorithm is analysed in time domain as well as in the frequency domain. In the frequency domain, it can be proved that one of the parameters f involved in the selection of the control gain ? is directly related to the "cutoff" frequency within which learning can be guaranteed. A critical choice of this parameter ensures that with a chosen control gain, performance improvement of the system is attained with a rapid convergence of output errors. For this purpose, simulation studies are performed with a linear system as well as nonlinear systems of first order and of second order. A group of inputs is typically selected to depict improvement in performance of the systems in the simulations, for instance when the input contains frequencies lesser than the "cutoff" frequency, and when the input contains frequencies higher than the “cutoff” frequency as well as when the input contains a combination of lower and higher frequencies than the "cutoff" frequency. The application of this learning control strategy in the control of robotic manipulators is explored next. The conditions which ensure convergence in error in the learning process are derived. Simulation studies are performed initially with a simple single link manipulator and then with a more complex two link manipulator. Leaming performance is studied when the strategy is applied without reset in position, velocity and acceleration variables as well as when these variables are reset to zero at the beginning of each trial. The dynamic model for the two link manipulator is derived rigorously using Lagrangian formulation. The two link manipulator represents a multi-input, multi-output system and thus the learning control algorithm is extended to MIMO systems. A comparison is drawn between the results obtained with this strategy and the results obatained by other existing strategies such as Arimoto's strategy and Tso and Ma's strategy. The last part of this thesis discusses the effect of multiperiod learning on learning performance. The use of more than one set of past control information can enhance the convergence of the simple learning control law studied thus far. A theoretical justification for such an improved learning control strategy is elaborated. This modified strategy is also applied to a single link manipulator and a two link manipulator. Simulation studies indicate the improvement in their performance to track a desired trajectory.