Iterative Learning Control Law Research Articles

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.

Adaptive Boundary Iterative Learning Control for an Euler-Bernoulli Beam System With Input Constraint.

This paper addresses the vibration control and the input constraint for an Euler-Bernoulli beam system under aperiodic distributed disturbance and aperiodic boundary disturbance. Hyperbolic tangent functions and saturation functions are adopted to tackle the input constraint. A restrained adaptive boundary iterative learning control (ABILC) law is proposed based on a time-weighted Lyapunov-Krasovskii-like composite energy function. In order to deal with the uncertainty of a system parameter and reject the external disturbances, three adaptive laws are designed and learned in the iteration domain. All the system states of the closed-loop system are proved to be bounded in each iteration. Along the iteration axis, the displacements asymptotically converge toward zero. Simulation results are provided to illustrate the effectiveness of the proposed ABILC scheme.

Iterative learning fault-tolerant control for differential time-delay batch processes in finite frequency domains

This paper develops a fault-tolerant iterative learning control law for a class of differential time-delay batch processes with actuator faults using the repetitive process setting. Once the dynamics are expressed in this setting, stability analysis and control law design makes use of the generalized Kalman–Yakubovich–Popov (KYP) lemma in the form of the corresponding linear matrix inequalities (LMIs). In particular, sufficient conditions for the existence of a fault-tolerant control law are developed together with design algorithms for the associated matrices. Under the action of this control law the ILC dynamics have a monotonicity property in terms of an error sequence formed from the difference between the supplied reference trajectory and the outputs produced. An extension to robust control against structured time-varying uncertainties is also developed. Finally, a simulation based case study on the model of a two-stage chemical reactor with delayed recycle is given to demonstrate the feasibility and effectiveness of the new designs.

A novel iterative learning control design for linear discrete time systems based on a 2D Roesser system

This paper is mainly devoted to the iterative learning control (ILC) design for a class of linear discrete time systems. By providing a 2D analysis of the learning process, the ILC design for such systems can be transformed into the problem of state feedback or output feedback control for 2-D systems described by Roesser models. Then, a Lyapunov approach can be used to obtain an ILC law that achieves asymptotical convergence of the tracking error. Sufficient stability conditions are provided in terms of linear matrix inequalities, which can determine learning gains as well. The theoretical results are also verified through simulation tests.DOI: http://dx.doi.org/10.5755/j01.itc.45.4.13391

Iterative learning control for one-dimensional fourth order distributed parameter systems

This paper addresses the problem of iterative learning control algorithm for high order distributed parameter systems in the presence of initial errors. And the considered distributed parameter systems are composed of the one-dimensional fourth order parabolic equations or the one-dimensional fourth order wave equations. According to the characteristics of the systems, iterative learning control laws are proposed for such fourth order distributed parameter systems based on the P-type learning scheme. When the learning scheme is applied to the systems, the output tracking errors on $L^2$ space are bounded, and furthermore, the tracking errors on $L^2$ space can tend to zero along the iteration axis in the absence of initial errors. Simulation examples illustrate the effectiveness of the proposed method.

Iterative learning control for a class of mixed hyperbolic-parabolic distributed parameter systems

This paper deals with the problem of iterative learning control algorithm for a class of mixed distributed parameter systems. Here, the considered distributed parameter systems are composed of mixed hyperbolic-parabolic partial differential equations. The domain of the system is divided into two parts in which the system is hyperbolic and parabolic, respectively, with transmission conditions at the interface. According to the characteristics of the systems, iterative learning control laws are proposed for such mixed hyperbolic-parabolic distributed parameter systems based on P-type learning scheme. Using the contraction mapping method, it is shown that the scheme can guarantee the output tracking errors on L 2 space converge along the iteration axis. A simulation example illustrates the effectiveness of the proposed method.

Adaptive Iterative Learning Boundary Control of a Flexible Manipulator with Guaranteed Transient Performance

AbstractThis paper investigates the iterative learning control (ILC) problem of a flexible manipulator in the presence of external disturbances and output constraints. The dynamic behavior of the flexible manipulator is represented by partial differential equations (PDEs). We propose an ILC law to track the desired trajectory and suppress the vibration of the elastic deflection. The control scheme is based on a prescribed performance bound (PPB) which characterizes the maximum restrictions and convergence rate of the tracking error and deflection error. It is shown that the errors satisfy the prescribed performance bond all the time at any iterations. The established theoretical results are illustrated using numerical simulations for control performance verification.

Vector Lyapunov functions for stability and stabilization of differential repetitive processes

Differential repetitive processes arise in the analysis and design of iterative learning control algorithms. They belong to a class of mathematical models whose dynamic properties are defined by two independent variables, such as a time and a spatial coordinate, also known as 2D systems in the literature. Moreover, standard stability analysis methods cannot be applied to such processes. This paper develops a vector Lyapunov function-based approach to the exponential stability analysis of differential repetitive processes and applies the resulting conditions to develop linear matrix inequality based iterative learning control law design algorithms in the presence of model uncertainty.

Iterative learning control for linear discrete‐time systems with high relative degree under initial state vibration

For linear discrete-time multiple-input–multiple-output (MIMO) systems with high relative degree, this study presents three average operator-based iterative learning control (ILC) algorithms to investigate the effect of initial state vibration on ILC tracking error. The proposed ILC laws include an initial rectifying action against initial state vibration at certain time points, and pursue the reference trajectory tracking beyond the initial time points. It is proved that, when the proposed ILC laws are applied to linear discrete-time MIMO systems with high relative degree, the effect of the initial state vibration on ILC tracking error beyond the initial time points can be exactly decided. Moreover, the ILC tracking error beyond the initial time points can be driven to zero against a progressive fixed initial state error. Numerical examples are used to illustrate the effectiveness of the proposed ILC laws.

Predictive iterative learning control with experimental validation

This paper develops an iterative learning control law that exploits recent results in the area of predictive repetitive control where a priori information about the characteristics of the reference signal is embedded in the control law using the internal model principle. The control law is based on receding horizon control and Laguerre functions can be used to parameterize the future control trajectory if required. Error convergence of the resulting controlled system is analyzed. To evaluate the performance of the design, including comparative aspects, simulation results from a chemical process control problem and supporting experimental results from application to a robot with two inputs and two outputs are given.

Experimentally verified generalized KYP Lemma based iterative learning control design

This paper considers iterative learning control law design for plants modeled by discrete linear dynamics using repetitive process stability theory. The resulting one step linear matrix inequality based design produces a stabilizing feedback controller in the time domain and a feedforward controller that guarantees convergence in the trial-to-trial domain. Additionally, application of the generalized Kalman–Yakubovich–Popov (KYP) lemma allows a direct treatment of differing finite frequency range performance specifications. The results are also extended to plants with relative degree greater than unity. To support the algorithm development, the results from an experimental implementation are given, where the performance requirements include specifications over various finite frequency ranges.

Design of an Iterative Learning Control Law for a Class of Switched Repetitive Systems

This paper is concerned with the design of an iterative learning control (ILC) law, which is developed to improve the tracking performance of a class of switched repetitive systems with time-varying delay. Firstly, the ILC scheme is introduced and a two-dimensional (2D) switched model is proposed to describe the switched repetitive system. Secondly, sufficient conditions for the exponential stability with $${l_2}$$l2-gain performance of the 2D switched system are derived by choosing a Lyapunov---Krasovskii functional. The ILC gains are then obtained by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.

Dissipativity and stabilization of nonlinear repetitive processes

Repetitive processes are characterized by repeated executions of a task defined over a finite duration with resetting after each execution is complete. Also the output from any execution directly influences the output produced on the next execution. The repetitive process model structure arises in the modeling of physical processes and can also be used to effect in the control of other systems, the design of iterative learning control laws where experimental verification of designs has been reported. The existing systems theory for them is, in the main, linear model based. This paper considers nonlinear repetitive processes using a dissipative setting and develops a stabilizing control law with the required conditions expressed in terms of vector storage functions. This design is then extended to stabilization plus disturbance attenuation.

Monotonically convergent hybrid ILC for uncertain discrete-time switched systems with state delay

This paper is mainly devoted to a monotonically convergent iterative learning control (ILC) design for a class of uncertain discrete-time switched systems with state delay (UDTSDSs). By taking advantage of output error and state information, a hybrid ILC law for a class of UDTSDSs is proposed. After the ILC process is transformed into a 2D system, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived by using a multiple Lyapunov–Krasovskii-like functional approach and a quadratic performance function. It is shown that if certain LMIs are met, the tracking error 2-norm converges monotonically to zero along the iteration direction, while the learning gains could be determined directly by solving the LMIs. The simulation results are provided to illustrate the theoretical analysis.

PID-type iterative learning control for impulsive ordinary differential equations

In this paper, we consider PID-type iterative learning control law for nonlinear impulsive ordinary differential equations. We obtain convergence results for open-loop and closed-loop iterative learning schemes with initial error in the sense of \(\lambda \)-norm. Finally, a numerical example is given to demonstrate the validity of the design methods.

Robust finite frequency design of iterative learning control schemes

This paper considers the problem of designing an iterative learning control law for discrete linear systems using repetitive process stability theory The resulting design produces a stabilizing output feedback controller in the time domain and a feedforward controller that guarantees monotonic convergence in the trial-to-trial domain. An extension to design with limited frequency range specifications for uncertain plants is developed. All design computations required for the new results in this paper can be computed using linear matrix inequalities (LMIs). A simulation example is given to illustrate the theoretical developments.

Stability of a Class of Nonlinear Repetitive Processes with Application to Iterative Learning Control

The paper considers a discrete repetitive process described by the state-space model with static nonlinearity satisfying quadratic constraints (in particular, the SISO case with the sector bounded nonlinearity). Based on the vector Lyapunov function approach developed by the authors, sufficient conditions of pass profile exponential stability are obtained in the form of linear matrix inequalities. These conditions are then applied to the design of an iterative learning control law for a simple nonlinear mechanical system.

An Iterative Learning Control Design Method for Nonlinear Discrete-Time Systems with Unknown Iteration-Varying Parameters and Control Direction

An iterative learning control (ILC) scheme is designed for a class of nonlinear discrete-time dynamical systems with unknown iteration-varying parameters and control direction. The iteration-varying parameters are described by a high-order internal model (HOIM) such that the unknown parameters in the current iteration are a linear combination of the counterparts in the previous certain iterations. Under the framework of ILC, the learning convergence condition is derived through rigorous analysis. It is shown that the adaptive ILC law can achieve perfect tracking of system state in presence of iteration-varying parameters and unknown control direction. The effectiveness of the proposed control scheme is verified by simulations.

Repetitive process based design and experimental verification of a dynamic iterative learning control law

This paper gives new results on iterative learning control (ILC) design and experimental verification using the stability theory of linear repetitive processes. Using this theory a control law can be designed in one step to force error convergence and produce acceptable transient dynamics. Previous research developed algorithms for the design of a static control law with supporting experimental verification. Should a static law not give the required levels of performance one option is to allow the control law to have internal dynamics. This paper develops a procedure for the design of such a control law with supporting experimental verification on a gantry robot, including a comparative performance against a static law applied to the same robot. The resulting ILC design is an efficient combination of linear matrix inequalities and optimization algorithms.

Stabilization of differential repetitive processes

Differential repetitive processes are a subclass of 2D systems that arise in modeling physical processes with identical repetitions of the same task and in the analysis of other control problems such as the design of iterative learning control laws. These models have proved to be efficient within the framework of linear dynamics, where control laws designed in this setting have been verified experimentally, but there are few results for nonlinear dynamics. This paper develops new results on the stability, stabilization and disturbance attenuation, using an H ∞ norm measure, for nonlinear differential repetitive processes. These results are then applied to design iterative learning control algorithms under model uncertainty and sensor failures described by a homogeneous Markov chain with a finite set of states. The resulting design algorithms can be computed using linear matrix inequalities.