Convergence analysis of cyclic Iterative Learning Control scheme

Abstract

Iterative Learning Control (ILC) is a learning control technique for the systems operated repeatedly. The Iterative Learning Controller learns to generate the desired set of input signals to compensate for the output tracking errors. Conventionally the performance of ILC algorithms has been based on the convergence of the output tracking error. In this paper, the convergence of the control input is investigated down to the sample-time level. Two scenarios are considered: Firstly, when the control input is updated with same initial conditions at the start of each batch/repetition/iteration/trial and secondly for varying initial conditions. The batch to batch evolution of control inputs at each sample time within a batch is formulated. Convergence of the control input signals has been based on the Eigen analysis of this relationship. This provides deeper insight about the ILC algorithms and exact factors affecting the convergence could be monitored. Limits of the learning process are clearly demonstrated as well. Performance of D-type & PD-type ILC algorithms has been investigated for a simple pendulum and further extended to bipedal locomotion. Bipedal walking robot is an interesting control problem but involves complexity being a hybrid system. It comprises of single support, impact with ground and double support phases. The non-linear impacts pose challenge since they cause non-zero initial errors for each step. For reasons of energy efficiency, passive dynamics has been chosen for compass gait model of the biped. Stable gait achieved from a fine-tuned PD controller provides the set of desired inputs for the joints of the compass gait robot. ILC learns/adapts the joint control for repetitive gaits. It represents learning a sequence of action by muscles. Due to the transfer of state error in a cyclic manner from the end of a previous step/repetition to the recent step/repetition, the convergence has to be established in joint control and state space. The steady gait is achieved for bipedal locomotion on flat surface as demonstrated through simulations.