Abstract
Iterative learning control (ILC) is one of the recent topics in control theories and it is suitable for controlling a wider class of mechatronic systems - it is especially suitable for the motion control of robotic systems. This paper addresses the problem of application of fractional order ILC for fractional order singular system. Particularly, we study fractional order singular systems in the pseudo-state space. An closed-loop fractional order PDalpha type ILC of the fractional-order singular system is investigated. Also, open-closed loop of the fractional order P-PDa type ILC is considered. Sufficient conditions for the convergence in the time domain of the proposed ILC schemes are given by the corresponding theorems and proved. Finally, numerical simulations show the feasibility and effectiveness of the proposed approach.
Highlights
ITERATIVE learning control (ILC) is one of the most active fields in control theory and it is a powerful intelligent control concept that iteratively improves behavior of the processes that are repetitive in nature [1,2,3]
Motivated by the mentioned investigations of ILC algorithms for ILC fractional order control in the tracking problems of these systems,closed-loop iterative learning control for given fractional-order singular systems described in the form of state space and output equations
In Section Open-loop fractional-order iterative learning control, the first main result is derived where the convergence is guaranteed by mathematical proof rigorously, which includes the extensions of some of the basic result ILC of singular fractional-order systems with order α ∈ (0, 1) to uncertain fractional-order singular system
Summary
ITERATIVE learning control (ILC) is one of the most active fields in control theory and it is a powerful intelligent control concept that iteratively improves behavior of the processes that are repetitive in nature [1,2,3]. ILC is a technique of controlling systems operating in a repetitive mode with the additional requirement that a specified output trajectory yd (t ) in an interval [0,T ] is followed to a high precision and through improving the performance from trial to trial in the sense that the tracking error is sequentially reduced. Motivated by the mentioned investigations of ILC algorithms for ILC fractional order control in the tracking problems of these systems, (open)closed-loop iterative learning control for given fractional-order singular systems described in the form of state space and output equations. In Section Open-loop fractional-order iterative learning control, the first main result is derived where the convergence is guaranteed by mathematical proof rigorously, which includes the extensions of some of the basic result ILC of singular fractional-order systems with order α ∈ (0, 1) to uncertain fractional-order singular system.
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