Fractional-order Iterative Learning Control Research Articles

Precise Position Control in Air-Bearing PMLSM System Using an Improved Anticipatory Fractional-Order Iterative Learning Control

Precise Position Control in Air-Bearing PMLSM System Using an Improved Anticipatory Fractional-Order Iterative Learning Control

Fractional-order iterative learning control for fractional-order systems with initialization non-repeatability

The effect of initialization non-repeatability on iterative learning control performance for fractional-order systems has not been sufficiently investigated. It is a hidden deficiency that leads directly to the breaking of perfect tracking conditions in both theoretical analysis and real-world applications. Therefore, under the framework of general fractional-order nonlinear systems, this paper proposes an open-close loop Dα-type iterative learning control scheme based on system preconditioning and strictly derives two convergence conditions. By applying the preconditioning optimization strategy based on the short-memory principle, the tracking error due to initialization nonrepetition can converge to any desired range. Compared with the existing results, the proposed iteration scheme fully considers the complexity of the initialization and initial conditions of fractional-order systems, and provides several practical preconditioning methods to improve the tracking efficiency. Two numerical examples are presented to validate the above conclusions.

Two-Dimensional Fractional Order Iterative Learning Control for Repetitive Processes

The convergence and robustness rejecting parameters variations and external disturbance of the system are crucial for repetitive processes. In this paper, a two-dimensional robust fractional-order iterative learning control (FOILC) is proposed for the repetitive motion process to enhance the convergence and robustness. A fractional-order proportional derivative function (FOPDF) is designed as the control variable to replace the tracking error of the integer-order iterative learning control (IOILC) algorithm. The required dynamic output fractional-order iterative learning controller is constructed by solving a set of linear matrix inequalities (LMI), and the control parameters are adjusted according to the given specifications. Simulation and experimental results in robot torque control are given to prove the effectiveness and feasibility of the proposed design method.

Fractional-order Iterative Learning Control with Nonuniform Trial Lengths

Fractional-order Iterative Learning Control with Nonuniform Trial Lengths

Iterative learning control of fractional-order linear systems with nonuniform pass lengths

Most previous studies about fractional-order iterative learning control (FOILC) assume fixed pass lengths in iteration domain and identical initial condition. These fundamental preconditions may be violated in practical applications. This paper introduces a novel FOILC strategy for tracking control of fractional-order linear systems. To relax the fixed pass lengths assumption, redefined tracking error is applied to formulate control input. Meanwhile, an initial state learning algorithm is introduced to relax the identical initial condition assumption. Strict convergence analysis of the tracking error in iteration domain is given. Finally, two illustrative simulation examples are applied to verify the efficiency and applicability of the proposed algorithm.

Iterative learning control for fractional order nonlinear system with initial shift

In this study, a closed-loop \({D^\alpha }\)-type iterative learning control (ILC) with a proportional D-type iterative learning updating law for the initial shift is applied to nonlinear conformable fractional order system. First, the system with the initial shift is introduced. Then, fractional order ILC (FOILC) frameworks that experience the initial shift problem for the path tracking of nonlinear conformable fractional order systems are addressed. Moreover, the sufficient condition for the convergence of tracking errors is obtained in the time domain by introducing \(\lambda \)-norm and Hölder’s inequality. Lastly, numerical examples are provided to illustrate the effectiveness of the proposed methods.

An improved fast error convergence topology for PD α -type fractional-order ILC

The monotonic convergence of the PD α -type fractional-order iterative learning control algorithm is considered for a class of fractional-order linear systems. First, a theoretical analysis of the monotonic convergence of 1st and 2nd order PD α -type control algorithms is carried out in the typical terms of Lebesgue-p (L p ), and the sufficient conditions for their monotonic convergence are comprehended and extended to the case of N-order control algorithms; then the speed of convergence of the two is explained in detail. It is concluded that the conditions for convergence of the control algorithm are determined by the learning gain and the system’s properties are together determined. Simulation experiment verifies the accuracy of proposed scheme and the validity of the control algorithm.

PDα-type iterative learning control with initial state learning for fractional-order systems

In order to eliminate the influence of the arbitrary initial state on the systems, open-loop and open-close-loop PDα-type fractional-order iterative learning control (FOILC) algorithms with initial state learning are proposed for a class of fractional-order linear continuous-time systems with an arbitrary initial state. In the sense of Lebesgue-p norm, the sufficient conditions for the convergence of PDα-type algorithms are disturbed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral. The results demonstrate that under these novel algorithms, the convergences of the tracking error are can be guaranteed. Numerical simulations support the effectiveness and correctness of the proposed algorithms.

Consensus Control of Multi-agent Robot System with State Delay Based on Fractional-Order Iterative Learning Control Algorithm

This paper mainly explores the consensus control of multi-agent robot system with repetitive motion under the constraints of a leader and fixed topology. To realize the consensus control, a fractional order iterative learning control (FOILC) algorithm was designed under the mode of distributed open-closed-loop proportional-derivative alpha (PDα). The uniform convergence of the algorithm in finite time was discussed, drawing on factional calculus, graph theory, and norm theory, resulting in the convergence conditions. Theoretical analysis shows that, with the growing number of iterations, each agent can choose the appropriate gain matrix, and complete the tracking task in finite time. The effectiveness of the proposed method was verified through simulation.

Fractional-Order Iterative Learning Control with Initial State Learning for a Class of Multiagent Systems

To solve the consensus problem of fractional-order multiagent systems with nonzero initial states, both open- and closed-loop PDα-type fractional-order iterative learning control are presented. Considering the nonzero states, an initial state learning mechanism is designed. The finite time convergences of the proposed methods are discussed in detail and strictly proved by using Lebesgue-p norm theory and fractional-order calculus. The convergence conditions of the proposed algorithms are presented. Finally, some simulations are applied to verify the effectiveness of the proposed methods.

Consensus Tracking of Fractional-Order Multiagent Systems via Fractional-Order Iterative Learning Control

In this work, the consensus problem of fractional-order multiagent systems with the general linear model of fixed topology is studied. Both distributed PDα-type and Dα-type fractional-order iterative learning control (FOILC) algorithms are proposed. Here, a virtual leader is introduced to generate the desired trajectory, fixed communication topology is considered, and only a subset of followers can access the desired trajectory. The convergence conditions are proved using graph theory, fractional calculus, and λ norm theory. The theoretical analysis shows that the output of each agent completely tracks the expected trajectory in a limited time as the iteration number increases for both PDα-type and Dα-type FOILC algorithms. Extensive numerical simulations are given to demonstrate the feasibility and effectiveness.

Consensus Control of Fractional-Order Multi-Agent Systems With Time Delays via Fractional-Order Iterative Learning Control

This paper considers the leader-following consensus tracking problem of fractional-order multi-agent systems (FOMASs) that contain communication time delays. By combining the iterative learning control (ILC) approach and fractional-order calculus, a distributed PD α -type fractional-order iterative learning control (FOILC) and a distributed D α -type FOILC algorithm are proposed, respectively. Based on graph theory and λ-norm theory, the consensus problems of the proposed algorithms are discussed, and their convergence conditions are identified. The theoretical analysis demonstrates that as the number of iterations increases, all fractional-order agents with communication time delays can realize consensus exactly on the desired output trajectory by selecting suitable gain matrices of FOILC over a finite time interval. Illustrative examples are presented, on which the performances of the proposed method are evaluated.

Rectified fractional order iterative learning control for linear system with initial state shift

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.

Fractional-order iterative learning control with initial state learning design

In this paper, we present a fractional-order iterative learning control (ILC) framework with initial state learning for the tracking problems of linear time-varying systems. Both open-loop and closed-loop $$D^{\alpha }$$ -type iterative learning updating laws are considered. To design ILC scheme for practical control systems, initialization assumption, i.e., the system initial states should be the same at each repetition, is removed by using an initial state learning scheme together with the $$D^{\alpha }$$ -type ILC updating law. Sufficient conditions of convergence to the desired trajectory is theoretically proved for a linear time-varying mechanical system. Numerical simulation results are presented to illustrate effectiveness of the control strategies. Moreover, we also show that the proposed learning scheme can be applied to the motion control of robot manipulators under some reasonable conditions.

Design and Analysis of Fractional Order PD α -Type Iterative Learning Control

Abstract This paper is concerned with fractional-order iterative learning control (ILC) for the tracking problems of a class of linear time-varying systems. Both open-loop and closed-loop PD α -type iterative learning updating laws are considered. Sufficient conditions for the convergence of the tracking errors are obtained. Finally the efficiency of the methods are verified by numerical simulations.

INTELLIGENT FRACTIONAL ORDER ITERATIVE LEARNING CONTROL USING FEEDBACK LINEARIZATION FOR A SINGLE-LINK ROBOT

In this paper, iterative learning control (ILC) is combined with an optimal fractional order derivative (BBO-Da-type ILC) and optimal fractional and proportional-derivative (BBO-PDa-type ILC). In the update law of Arimoto's derivative iterative learning control, a first order derivative of tracking error signal is used. In the proposed method, fractional order derivative of the error signal is stated in term of 'sa' where  to update iterative learning control law. Two types of fractional order iterative learning control namely PDa-type ILC and Da-type ILC are gained for different value of a. In order to improve the performance of closed-loop control system, coefficients of both  and  learning law i.e. proportional , derivative  and  are optimized using Biogeography-Based optimization algorithm (BBO). Outcome of the simulation results are compared with those of the conventional fractional order iterative learning control to verify effectiveness of BBO-Da-type ILC and BBO-PDa-type ILC

Fractional order iterative learning control with randomly varying trial lengths

In this paper, we establish a uniform framework to deal with varying tracking problem in the finite time interval for fractional order system. In order to tracking the reference trajectory associated with nonlinear fractional differential systems with randomly varying trial lengths, we design a new type iterative learning control of the output equation with nonlinear input involving an integral term. As a result, convergence analysis results for several classes of learning laws with local average operator are given. Finally, some examples are given to illustrate our results.

Sliding mode based fractional-order iterative learning control for a nonlinear robot manipulator with bounded disturbance

In this paper a new type of sliding mode based fractional-order iterative learning control (ILC) is proposed for nonlinear systems in the presence of uncertainties. For the first time, a sliding mode controller is combined with fractional-order ILC. This sliding mode based [Formula: see text] and [Formula: see text]-type ILC is applied on a nonlinear robot manipulator. Convergence of the proposed method is investigated when the stability is also proved. In this method, the control signal at any iteration is generated in two parts. The first section comes from the sliding mode controller while the second part is output of the fractional-order ILC. The latter signal is assessed using its previous amount and the sliding mode error signal. The achieved control law is capable of controlling nonlinear iterative processes, perturbed by bounded disturbances with high accuracy. The same frequent disturbance is eliminated by the iterative learning part, while the effect of nonrepetitive uncertainty is improved by the sliding mode part. The sliding mode based [Formula: see text]-type ILC (as an adaptive control law) is proposed to control a single-link arm robot. The controller is then improved to sliding mode based [Formula: see text]-type ILC. The effectiveness of the proposed method is again investigated on a single-link robot manipulator through a simulation approach. It is shown that the controller for [Formula: see text] provides performance by means of faster response together with more accuracy with respect to a conventional ILC.

A Survey on Fractional-Order Iterative Learning Control

In this paper, an overview of fractional-order iterative learning control (FOILC) is presented including main developments of this field since 2001. Many theoretical and experimental results are provided to show the advantages of FOILC such as the improvement of transient and steady-state performances. Some unique characters of fractional-order operators are illustrated to show the new features and techniques of FOILC. A number of unsolved problems are briefly presented.