Iterative learning control of integer and noninteger order: An overview

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Iterative learning control of integer and noninteger order: An overview

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Lazarević, Mihailo

This paper provides an overview of the recently presented and published results relating to the use of iterative learning control (ILC) based on and integer and fractional order. ILC is one of the recent topics in control theories and it is a powerful control concept that iteratively improves the behavior of processes that are repetitive in nature. ILC is suitable for controlling a wider class of mechatronic systems - it is especially suitable for motion control of robotic systems that attract and hold an important position in biomechatronical, technical systems involving the application, military industry, etc. The first part of the paper presents the results relating to the application of higher integer order PD type ILC with numerical simulation. Also, another integer order ILC scheme is proposed for a given robotic system with three degrees of freedom for task-space trajectory tracking where the effectiveness of the suggested control is demonstrated through a simulation procedure. In the second part, the results related to the application of the fractional order of ILC are presented where PDα type of ILC is proposed firstly, for a fractional order linear time invariant system. It is shown that under some sufficient conditions which include the learning operators, convergence of the learning system can be guaranteed. Also, PIβDα type of ILC is suggested for a fractional order linear time delay system. Finally, sufficient conditions for the convergence in the time domain of the proposed ILC were given by the corresponding theorem together with its proof.