Two-dimensional model and analysis for a class of iterative learning control systems

The Iterative Learning Control System (ILCS) is a new approach to the problem of improving transient behavior using previously acquired experience for systems that execute repetitive tasks. However the theoretical frameworks on the fundamentals of ILCS have not heretofore been established. Theoretical results for two-dimensional (2-D) system theory has been developed during the last two decades. But few applications have been reported. In this dissertation research, the connections between these two research areas (ILCS and 2-D) are established. A class of iterative learning control systems is analyzed from a two-dimensional system point of view. A generic 2-D model for a class of ILCS is established which allows us to employ 2-D system theory to analyze and design the entire learning control system. A general structure of learning controller is given based on the 2-D model. The analysis of the 2-D error equation shows that the 2-D asymptotic stability of the 2-D model guarantees the learning convergence of ILCS. Several class of learning control algorithms have been proposed for which the learning convergence is proved. The learning gain matrices are obtained from a recursive 2-D estimator using the input and output data of the controlled plant obtained from previous operations. The estimation algorithms are derived for both time-invariant and time variant systems. Comparisons of the 2-D ILCS algorithm with other learning algorithms are given. The results demonstrate superior performance of the 2-D based learning control system.;The feasibility of applying proposed 2-D learning algorithms to engineering systems are investigated through two application case studies. In the first case study, the proposed 2-D learning algorithm is applied to a parallel link robotic manipulator executing a repetitive motion. The learning process converges in four iterations of learning and the actual trajectory of the manipulator follows the desired trajectory with acceptable accuracy. The second case study deals with the learning control problem for the Experimental Breeder Reactor II (EBR II) in a nuclear power plant. The tracking control tasks for the EBR II primary system and the steam generator system are implemented by employing the learning controller. The efficiency of the 2-D based learning algorithms are demonstrated by extensive simulations.