Robust Iterative Learning Control Design Research Articles

Robust iterative learning control design based on iterative integral sliding mode for nonlinear systems with unrepeatable disturbance

For the repetitive tracking control tasks, the unrepeatable disturbance is an obstruction to learning control schemes. This paper discussed the robust iterative learning control (RILC) design based on the sliding mode control (SMC) technique for a class of nonlinear systems with unrepeatable disturbances. In order to make the tracking error converge to zero in the iteration domain under the sliding mode and eliminate the reaching phase of the SMC, an iterative integral sliding mode (IISM) surface design was proposed. The IISM leads to linear tracking error dynamics in the iteration domain, which guarantees the convergence if the sliding mode parameters meet the given condition. After that, the iterative learning control (ILC) based on the IISM was designed, which drove the sliding mode variable of the closed-loop system to reach the origin with iterations from the initial time instant, despite the effect of the unrepeatable disturbances. The robustness to the unrepeatable disturbance and the fast convergence were achieved. Finally, the proposed IISM method was applied to a one-link robotic manipulator, and the simulation results validated the performance of the proposed control design.

Robust PD-Type Iterative Learning Control of Discrete Linear Repetitive Processes in the Finite Frequency Domain

This paper studies a robust iterative learning control design for discrete linear repetitive processes in the finite frequency domain. Firstly, the state-space model of the iterative learning process is deduced. Then the dynamic performance condition of the control system in the finite frequency domain is derived by combining it with the stability theory of discrete linear repetitive processes. The system performances in the finite frequency domain are then transformed into the corresponding solutions of the linear matrix inequality by using the generalised KYP lemma. Finally, an integrated state feedback PD-type iterative learning control strategy is proposed. The robust control problem with norm-bounded uncertainty and convex polyhedral uncertainty are also considered in this paper. The simulation of the injection velocity in injection molding verified that the proposed methods in this paper are more effective than the P-type state feedback iterative learning control algorithm.

Robust ILC design with application to stroke rehabilitation

Iterative learning control (ILC) is a design technique which can achieve accurate tracking by learning over repeated task attempts. However, long-term stability remains a critical limitation to widespread application, and to-date robustness analysis has overwhelmingly considered structured uncertainties. This paper substantially expands the scope of existing ILC robustness analysis by addressing unstructured uncertainties, a widely used ILC update class, the presence of a feedback controller, and a general task description that incorporates the most recent expansions in the ILC tracking objective. Gap metric based analysis is applied to ILC by reformulating the finite horizon trial-to-trial feedforward dynamics into an equivalent along-the-trial feedback system, as well as deriving relationships to link their respective gap metric values. The results are used to generate a comprehensive design framework for robust control design of the interacting feedback and ILC loops. This is illustrated via application to rehabilitation engineering, an area where they meet an urgent need for high performance in the presence of significant modeling uncertainty.

Robust iterative learning control design for linear systems with time-varying delays and packet dropouts

This paper proposes the robust iterative learning control (ILC) design for uncertain linear systems with time-varying delays and random packet dropouts. The packet dropout is modeled by an arbitrary stochastic sequence satisfying the Bernoulli binary distribution, which renders the ILC system to be stochastic instead of a deterministic one. The main idea of this paper is to transform the ILC design into robust stability for a two-dimensional (2D) stochastic system described by the Roesser model with a delay varying in a range. A delay-dependent stability condition, which can guarantee mean-square asymptotic stability of such a 2D stochastic system, is derived in terms of linear matrix inequalities (LMIs), and formulas can be given for the ILC law design. An example for the injection molding is given to demonstrate the effectiveness of the proposed ILC method.

Robust fault-tolerant iterative learning control for discrete systems via linear repetitive processes theory

This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multiple-output discrete linear systems with actuator faults. The stability theory for linear repetitive processes is used to develop formulas for gain matrices design, together with convergent conditions in terms of linear matrix inequalities. An extension to deal with model uncertainty of the polytopic or norm bounded form is also developed and an illustrative example is given.

Robust iterative learning controller design using the performance weighting function of feedback control systems

Iterative learning controllers combined with existing feedback controllers have prominent capability of improving tracking performance in repeated tasks. However, the iterative learning controller has been designed without utilizing effective information such as the performance weighting function to design a feedback controller. In this paper, we deal with a robust iterative learning controller design problem for an uncertain feedback control system using its explicit performance information. We first propose a robust convergence condition in the ℒ2-norm sense for an iterative learning control (ILC) scheme. We present a method to design an iterative learning controller using the information on the performance of the existing feedback control system such as performance weighting functions and frequency ranges of desired trajectories. From the obtained results, several design criteria for iterative learning controller are provided. Through analysis on the remaining error, the loop properties before and after learning are compared. We also show that, in the ℒ2-norm sense, the remaining error can be less than the initial error under certain conditions. Finally, to show the validity of the proposed method, simulation studies are performed.

Experimental Validation of Robust Iterative Learning Control on an Overhead Crane Test Setup

This paper presents an experimental validation of a recently proposed robust norm-optimal iterative learning control (ILC). The robust ILC input is computed by minimizing the worst-case value of a performance index under model uncertainty, yielding a convex optimization problem. The proposed robust ILC design is experimentally validated on a lab scale overhead crane system, showing the advantages of the approach over classical ILC designs in monotonic convergence and tracking performance.

A convex optimization approach to robust iterative learning control for linear systems with time-varying parametric uncertainties

In this paper, we present a new robust iterative learning control (ILC) design for a class of linear systems in the presence of time-varying parametric uncertainties and additive input/output disturbances. The system model is described by the Markov matrix as an affine function of parametric uncertainties. The robust ILC design is formulated as a min–max problem using a quadratic performance criterion subject to constraints of the control input update. Then, we propose a novel methodology to find a suboptimal solution of the min–max optimization problem. First, we derive an upper bound of the worst-case performance. As a result, the min–max problem is relaxed to become a minimization problem in the form of a quadratic program. Next, the robust ILC design is cast into a convex optimization over linear matrix inequalities (LMIs) which can be easily solved using off-the-shelf optimization solvers. The convergences of the control input and the error are proved. Finally, the robust ILC algorithm is applied to a physical model of a flexible link. The simulation results reveal the effectiveness of the proposed algorithm.

Robust learning controller design for MIMO stochastic discrete‐time systems: An H∞‐based approach

AbstractThis paper is devoted to designing iterative learning control (ILC) for multiple‐input multiple‐output discrete‐time systems that are subject to random disturbances varying from iteration to iteration. Using the super‐vector approach to ILC, statistical expressions are presented for both expectation and variance of the tracking error, and time‐domain conditions are developed to ensure their asymptotic stability and monotonic convergence. It shows that time‐domain conditions can be tied together with an H∞‐based condition in the frequency domain by considering the properties of block Toeplitz matrices. This makes it possible to apply the linear matrix inequality technique to describe the convergence conditions and to obtain formulas for the control law design. Furthermore, the H∞‐based approach is shown applicable to ILC design regardless of the system relative degree, which can also be used to address issues of model uncertainty. For a class of systems with a relative degree of one, simulation tests are provided to illustrate the effectiveness of the H∞‐based approach to robust ILC design. Copyright © 2011 John Wiley & Sons, Ltd.

A convex optimization design of robust iterative learning control for linear systems with iteration‐varying parametric uncertainties

AbstractIn this paper, a new robust iterative learning control (ILC) algorithm has been proposed for linear systems in the presence of iteration‐varying parametric uncertainties. The robust ILC design is formulated as a min‐max problem using a quadratic performance criterion subject to constraints of the control input update. An upper bound of the maximization problem is derived, then, the solution of the min‐max problem is achieved by solving a minimization problem. Applying Lagrangian duality to this minimization problem results in a dual problem which can be reformulated as a convex optimization problem over linear matrix inequalities (LMIs). Next, we present an LMI‐based algorithm for the robust ILC design and prove the convergence of the control input and the error. Finally, the proposed algorithm is applied to a distillation column to demonstrate its effectiveness.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Anticipatory approach to design robust iterative learning control for uncertain time‐delay systems

AbstractThis paper is devoted to robust iterative learning control (ILC) design for time‐delay systems (TDS) with uncertainties in both model plant and delay time. An ILC law is considered by using anticipation in time to compensate for the effects of delay, which has three design parameters: the weighting function, the lead time and the learning gain. For iteration‐invariant TDS, it is shown that a necessary and sufficient condition can be obtained for the tracking error to converge for all admissible plant uncertainties. If the uncertainty is considered to be varying randomly from iteration to iteration, resulting in iteration‐varying TDS, then a necessary and sufficient condition can be derived to ensure the convergence of the expected tracking error. For TDS in both cases, it is also shown that the convergence is monotonic in the sense of the ℒ︁2‐norm, and the estimated delay is sufficiently anticipatory for the selection of the lead time to achieve the robust ILC design. Simulation results are included to verify the theoretical study.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Robust Iterative Learning Control for Linear Systems Subject to Time-Invariant Parametric Uncertainties and Repetitive Disturbances

This paper presents the design of a robust Iterative Learning Control (ILC) algorithm for linear systems in the presence of parametric uncertainties and repetitive disturbances. The robust ILC design is formulated as a min-max problem with a quadratic performance index subjected to constraints of the control input. Employing Lagrange duality, we can reformulate the robust ILC design as a convex optimization problem over linear matrix inequalities (LMIs). An LMI algorithm for the robust ILC design is then given. Finally, the effectiveness of the proposed robust ILC algorithm is demonstrated through a numerical example.

Robust iterative learning control design for uncertain time-delay systems based on a performance index

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.

Robust Iterative Learning Control Design: Application to a Robot Manipulator

This paper deals with robust iterative learning control design for uncertain single-input-single-output linear time-invariant systems. The design procedure is based upon solving the robust performance condition using the Youla parameterization and the mu-synthesis approach to obtain a feedback controller. Thereafter, a convergent iterative learning law is obtained by using the performance weighting function involved in the robust performance condition. Experimental results, on a CRS465 robot manipulator, are provided to illustrate the effectiveness of the proposed design method.

Robust iterative learning control design for batch processes with uncertain perturbations and initialization

AbstractA robust iterative learning control (ILC) scheme for batch processes with uncertain perturbations and initial conditions is developed. The proposed ILC design is transformed into a robust control design of a 2‐D Fornasini–Marchsini model with uncertain parameter perturbations. The concepts of robust stabilities and convergences along batch and time axes are introduced. The proposed design leads to nature integration of an output feedback control and a feedforward ILC to guarantee the robust convergence along both the time and the cycle directions. This design framework also allows easy enhancement of the feedback and/or feedforward controls of the system by extending the learning information along the time and/or the cycle directions. The proposed analysis and design are formulated as matrix inequality conditions that can be solved by an algorithm based on linear matrix inequality. Application to control injection packing pressure shows the proposed ILC scheme and its design are effective. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Monotonic Convergent Iterative Learning Controller Design Based on Interval Model Conversion

This note presents a robust iterative learning controller design method for plants subject to interval model uncertainty in the A-matrix of their state-space description. First-order perturbation theory is used to find bounds on the eigenvalues and eigenvectors of the powers of A when A is an interval matrix. These bounds are then used for calculation of the interval uncertainty of the Markov matrix. The bounds on the Markov matrix are then used to design an iterative learning controller that ensures monotonic convergence for all systems in the interval plant.

LMI-based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learning control (ILC) system is reformulated as a y-suboptimal H-infinity control problem via the linear fractional transformation (LFT) .A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities (LMIs) . Furthermore, the linear transfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.

Authors' Reply to “Comments on `Robust iterative learning control design is straightforward for uncertain LTI systems satisfying the robust performance condition'”

Index Terms—Iterative learning control (ILC), robust performance, uncertain linear time-invariant (LTI) systems.

Comments on “Robust Iterative Learning Control Design is Straightforward for Uncertain LTI Systems Satisfying the Robust Performance Condition”

For original paper see ibid., vol.48, p.101-6 (2003). The article comments on the result of the above paper. The authors of the original paper showed that Theorem 1 is only the sufficient condition of the convergence in the sense of the L/sub 2/-norm. In this note, Theorem 1 is proved to be the not only sufficient but also necessary condition using some mathematical manipulation.

Robust iterative learning control design is straightforward for uncertain LTI systems satisfying the robust performance condition

This note demonstrates that the design of a robust iterative learning control is straightforward for uncertain linear time-invariant systems satisfying the robust performance condition. It is shown that once a controller is designed to satisfy the well-known robust performance condition, a convergent updating rule involving the performance weighting function can be directly obtained. It is also shown that for a particular choice of this weighting function, one can achieve a perfect tracking. In the case where this choice is not allowable, a sufficient condition ensuring that the least upper bound of the /spl Lscr//sub 2/-norm of the final tracking error is less than the least upper bound of the /spl Lscr//sub 2/-norm of the initial tracking error is provided. This sufficient condition also guarantees that the infinity-norm of the final tracking error is less than the infinity-norm of the initial tracking error.