Abstract
This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.
Highlights
Iterative learning control (ILC) is an effective technique for improving the performance of systems that operate repetitively over a fixed time interval [1,2,3,4]
Distributed parameter systems are a class of complicated infinite-dimensional systems, whose states depend on both spatial position and time [8,9,10,11]
The purpose of this paper is to present a second order P-type iterative learning control (ILC) algorithm with initial state learning for fractional order linear distributed parameter systems
Summary
Iterative learning control (ILC) is an effective technique for improving the performance of systems that operate repetitively over a fixed time interval [1,2,3,4]. For a class of single-input single-output coupling nonlinear distributed parameter systems, a P-type learning controller was designed, and the convergence conditions, speed and robustness of the iterative learning algorithm were discussed in [14]. By using the Gronwall–Bellman inequality, a close-loop P-type iterative learning algorithm is proposed for linear parabolic distributed parameter systems in [19]. The purpose of this paper is to present a second order P-type ILC algorithm with initial state learning for fractional order linear distributed parameter systems. (1) By analyzing the control and learning processes, the second order P-type ILC design problem for fractional order linear distributed parameter systems is converted to a stability problem for a discrete system. (3) The proposed design method can be extended to ILC for fractional order parabolic distributed parameter systems involving time-delay, locally Lipschitz, as well as bounded external disturbance.
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