Robust performance iterative learning control : Analysis, synthesis and experimental validation

Here the authors concerned with robust iterative learning control (ILC) for uncertain time-delay systems. They demonstrate that the design of a robust ILC is straightforward based on a performance index for the error system. The ILC algorithms under consideration are rather simple. They show that after the two-dimensional analysis of ILC, a Lyapunov-like approach can be used to directly obtain a stable algorithm that achieves monotonic convergence of the control input error. Sufficient stability conditions are provided in terms of linear matrix inequalities, which can determine learning gains as well. They also show that the Lyapunov-like approach can be applied to design robust ILC for uncertain systems with time-varying delay or multiple time delays. Numerical simulation results are presented to illustrate the effectiveness of the proposed ILC approach.

An iterative learning control (ILC) framework based on two-degree-of-freedom control is presented for a linear plant with perturbations. A sufficient condition in the frequency domain is obtained for robust convergence with the bounded asymptotic error in the existence of input disturbance, output disturbance and errors in initial states. Based on the sufficient condition, the problem of designing ILC can be converted to a robust performance problem and a robust ILC against disturbances and initialization errors is derived by structured singular value and mu synthesis

In this paper is proposed a robust higher-order iterative learning control (ILC) algorithm for discrete-time systems. In contrast to conventional discrete-time learning methods, the proposed learning algorithm is constructed based on both time-domain performance and iteration-domain performance. Also, the proposed learning algorithm use more than one past error in the iteration-domain. It is proved that the proposed method has robustness in the presence of external disturbances and, in absence of all disturbances, the convergence of the proposed learning algorithm is guaranteed. A numerical example is given to show the robustness in the presence of state disturbance and convergence property according to parameters change.

In this paper, a robust adaptive iterative learning control (ILC) scheme is developed for the high-precision attitude tracking control of spacecraft in the presence of parametric uncertainties and external disturbances. The proposed robust adaptive ILC law consists of three parts, i.e., the classic proportional-derivative (PD) feedback control term, the PD-type feedforward learning term, and the robust term. The adaptive updating laws are designed for the gain matrices of both the classic PD feedback control term and the PD-type feedforward learning term. The asymptotic stability of the whole closed-loop system is proved through the Lyapunov function–based convergence analysis. The proposed robust adaptive ILC scheme can not only compensate for the parametric uncertainties and repetitive disturbance, but also handle the nonrepetitive disturbance owing to the robust control concept. Moreover, the proposed robust adaptive ILC scheme can achieve the fast convergence speed benefiting from the adaptive technique. Numerical simulations illustrate the effectiveness and superiority of the proposed ILC scheme.

A Robust Iterative Learning Control with Neural Networks for Robot

SummaryA new robust iterative learning control scheme is presented for state tracking control of nonlinear MIMO systems. The main characteristic of the proposed controller lies in its ability to deal with unstructured uncertainties that are norm‐bounded but not globally or locally Lipschitz continuous as usual. The classical resetting condition of iterative learning control is removed and replaced with more practical alignment condition. The class of systems to be considered is further extended to more general scenarios, in which input distribution uncertainties are included. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed control scheme. Copyright © 2015 John Wiley & Sons, Ltd.

An iterative learning-based adaptive disturbance rejection control (ADRC) method is proposed to tackle control issues for three-dimensional (3D) overhead crane. The tracking differentiator (TD) and extended state observer (ESO) are employed to extract desired displacement and estimate system disturbances. A robust iterative learning control (ILC) law is constructed by integrating sliding mode control (SMC) with ILC. The stability of the closed-loop system is proved through Lyapunov stability theory, and simulations are conducted to verify the effectiveness and robustness of the proposed method.

This study first investigates robust iterative learning control (ILC) issue for a class of two‐dimensional linear discrete singular Fornasini–Marchesini systems (2‐D LDSFM) under iteration‐varying boundary states. Initially, using the singular value decomposition theory, an equivalent dynamical decomposition form of 2‐D LDSFM is derived. A simple P‐type ILC law is proposed such that the ILC tracking error can be driven into a residual range, the bound of which is relevant to the bound parameters of boundary states. Specially, while the boundary states of 2‐D LDSFM satisfy iteration‐invariant boundary states, accurate tracking on 2‐D desired surface trajectory can be accomplished by using 2‐D linear inequality theory. In addition, extension to 2‐D LDSFM without direct transmission from inputs to outputs is presented. A numerical example is used to illustrate the effectiveness and feasibility of the designed ILC law.

In practical applications, the durations of operations in uncertain batch processes may fluctuate due to security considerations, physical constraints, and environmental changes. Regarding this issue, this paper addresses iterative learning control (ILC) for a class of uncertain single‐input single‐output (SISO) batch processes with nonuniform batch lengths. The aim is to develop an optimization‐based ILC scheme that guarantees robustness while meeting input constraints requirements. Two robust optimal ILC algorithms resting upon the modified error update model are proposed for the nonuniform batch length problem, where the linear matrix inequality (LMI) optimization techniques are employed to deal with polytopic and ellipsoidal model uncertainties. Hence, the ILC design requirements are reduced to a convex optimization method involving LMIs, which results in iterative input update signals at the end of each batch. Also, the theoretical analyses of the proposed algorithms are presented. Finally, two numerical cases for batch processes are simulated to testify the feasibility and performance of the proposed methods.

In this paper we present a linear computational complexity framework for design and implementation of (constrained) lifted Iterative Learning Control (ILC) systems with quadratic cost. The problem of designing constrained lifted ILC with quadratic cost is formulated as a convex optimization problem. We solve this problem using the primal-dual interior point method. High computational complexity of the primal-dual method, which render this method computationally infeasible for high dimensional lifted ILC systems, is significantly decreased by exploiting the sequentially semi-separable (SSS) structure of lifted system matrices. More precisely, O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) computational cost of one iteration of the primal-dual method is reduced to O(N), where N characterizes the size of the lifted system matrices. Furthermore, by exploiting the SSS structure the large lifted system matrices can be efficiently stored in computer memory. We also show that SSS structure can be exploited to efficiently implement analytical solution of the unconstrained lifted ILC problem with quadratic cost and for calculation of the norm and stability radius of ILC system.

A novel iterative learning control (ILC) algorithm was developed and applied to an active flow control problem. The technique uses pulsed air jets to delay flow separation on a two-element high-lift wing. The ILC algorithm uses position-based pressure measurements to update the actuation. The method was experimentally tested on a wing model in a 0.9 m × 0.6 m low-speed wind tunnel at the University of Southampton. Compressed air and fast switching solenoid valves were used as actuators to excite the flow, and the pressure distribution around the chord of the wing was measured as a feedback control signal for the ILC controller. Experimental results showed that the actuation was able to delay the separation and increase the lift by approximately 10%–15%. By using the ILC algorithm, the controller was able to find the optimum control input and maintain the improvement despite sudden changes of the separation position.

In order to achieve stable steering and path tracking, a lateral robust iterative learning control method for unmanned driving robot vehicle is proposed. Combining the nonlinear tire dynamic model with the vehicle dynamic model, the nonlinear vehicle dynamic model is constructed. The structure of steering manipulator of unmanned driving robot vehicle is analyzed, and the kinematics model and dynamics model of steering manipulator of unmanned driving robot vehicle are established. The structure of vehicle steering system is analyzed, and the dynamic model of vehicle steering system is established. Vehicle steering angle model is established by taking vehicle path tracking error and vehicle yaw angle error as input. Combining with the typical iterative learning control law, the robust term is added to the control law, and a robust iterative learning controller for steering manipulator system of unmanned driving robot vehicle is designed. The proposed controller’s stability and astringency are proved. The effectiveness of the proposed method is verified by comparing it with other control methods and human driver simulation tests.

This paper considers the robust convergence problem of iterative learning control (ILC) for discrete-time systems in the presence of iteration-varying uncertain plant parameters. If the uncertain parameters all converge along the iteration axis, then the perfect tracking property of ILC can be achieved under certain conditions. Otherwise, the tracking objective of ILC can be achieved within a bound if some of the uncertain parameters are bounded, rather than convergent, along the iteration axis.

In this paper, an integrated tube robust iterative learning model predictive control (Tube‐RILMPC) strategy based on the dynamic partial least squares (DyPLS) identified algorithm is proposed. The problems of large amount of online data calculation and input and output variable dimensions disaster in the original variable space are solved. This integrated Tube‐RILMPC strategy enhances the tracking performance and robustness of two‐dimensional (2D) control system. The output trajectories of system are located in the tube the nominal trajectory, which reduces the modelling error caused by the uncertain model. Based on the worst‐case performance index of ellipsoidal uncertainty and polytopic uncertainty, a robust iterative learning control (ILC) strategy is designed. Finally, the superiority of the proposed control algorithm is verified by comparative simulation.

Iterative learning control (ILC) enables high performance for exactly repeating tasks in motion systems. Many motion systems also perform slightly varying tasks during normal operation. The achieved performance with ILC algorithms can significantly deteriorate in such cases. The aim of this paper is to develop a new framework based on frequency-domain ILC that achieves high performance for both repeating and varying tasks. The proposed ILC framework achieves high machine performance for motion systems, while relying on straightforward loop-shaping based design methods for both performance and robustness. Furthermore, basis functions are used to cope with variations in tasks. An experimental validation on a high-speed axis of an industrial wire-bonder is presented to show that high performance is obtained for both repeating and varying tasks.