Rectified fractional order iterative learning control for linear system with initial state shift
نویسنده
چکیده
*Correspondence: [email protected] Department of Applied Mathematics, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, P.R. China Abstract In this paper, a new rectifying action is combined into different proportional-α-order-derivative-type iterative learning control algorithms for a class of fractional order linear time-invariant systems. Unlike the existing fractional order iterative learning control techniques, the proposed algorithms allow the initial state value of a fractional order iterative learning control system at each iteration to shift randomly. By introducing the Lebesgue-p norm and using the method of fractional integration by parts and the generalized Young inequality of convolution integral, the tracking performances with respect to the initial state shift under the proposed algorithms are analyzed. These analyses show that the tracking errors are incurred by such a shift and improved by tuning the rectifying gain. Numerical simulations are performed to demonstrate the effectiveness of the proposed algorithms.
منابع مشابه
Fractional-Order Iterative Learning Control for Fractional-Order Linear Systems
In this paper, we discuss in time domain the convergence of the iterative process for fractional-order systems. Fractional order iterative learning updating schemes are considered. The convergent conditions of the fractional-order and integer-order iterative learning schemes are proved to be equivalent. It is shown in Matlab/Simulink results that the tracking speed is the fastest when the syste...
متن کاملNon-linear Fractional-Order Chaotic Systems Identification with Approximated Fractional-Order Derivative based on a Hybrid Particle Swarm Optimization-Genetic Algorithm Method
Although many mathematicians have searched on the fractional calculus since many years ago, but its application in engineering, especially in modeling and control, does not have many antecedents. Since there are much freedom in choosing the order of differentiator and integrator in fractional calculus, it is possible to model the physical systems accurately. This paper deals with time-domain id...
متن کاملThe convergence analysis of P-type iterative learning control with initial state error for some fractional system
In this paper, the convergence of iterative learning control with initial state error for some fractional equation is studied. According to the Laplace transform and the M-L function, the concept of mild solutions is showed. The sufficient conditions of convergence for the open and closed P-type iterative learning control are obtained. Some examples are given to illustrate our main results.
متن کاملFractional order nonlinear systems with delay in iterative learning control
Keywords: Fractional order with delay Generalized Gronwall inequality Iterative learning control a b s t r a c t In this paper, we discuss a P-type iterative learning control (ILC) scheme for a class of fractional order nonlinear systems with delay. By introducing the k-norm and using Gronwall inequality, the sufficient condition for the robust convergence of the tracking errors is obtained. Ba...
متن کاملPerfect Tracking of Supercavitating Non-minimum Phase Vehicles Using a New Robust and Adaptive Parameter-optimal Iterative Learning Control
In this manuscript, a new method is proposed to provide a perfect tracking of the supercavitation system based on a new two-state model. The tracking of the pitch rate and angle of attack for fin and cavitator input is of the aim. The pitch rate of the supercavitation with respect to fin angle is found as a non-minimum phase behavior. This effect reduces the speed of command pitch rate. Control...
متن کامل