Convergence analysis of cyclic iterative learning control scheme

Inam Ul Hasan Shaikh, Hassan H. Khalili, Martin Brown

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    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. © 2012 IEEE.
    Original languageEnglish
    Title of host publicationProceedings of 2012 9th International Bhurban Conference on Applied Sciences and Technology, IBCAST 2012|Proc. Int. Bhurban Conf. Appl. Sci. Technol., IBCAST
    Place of PublicationIslamabad, Pakistan
    PublisherIEEE
    Pages1-7
    Number of pages6
    ISBN (Print)9781457719295
    DOIs
    Publication statusPublished - 2012
    Event2012 9th International Bhurban Conference on Applied Sciences and Technology, IBCAST 2012 - Islamabad
    Duration: 1 Jul 2012 → …

    Conference

    Conference2012 9th International Bhurban Conference on Applied Sciences and Technology, IBCAST 2012
    CityIslamabad
    Period1/07/12 → …

    Keywords

    • bipedal walking robot
    • Convergence
    • Cyclic Iterative Learning Control

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