Discrete Linear Repetitive Processes Research Articles

Dynamic ILC for Linear Repetitive Processes Based on Different Relative Degrees

The current research on iterative learning control focuses on the condition where the system relative degree is equal to 1, while the condition where the system relative degree is equal to 0 or greater than 1 is not considered. Therefore, this paper studies the monotonic convergence of the corresponding dynamic iterative learning controller systematically for discrete linear repetitive processes with different relative degrees. First, a 2D discrete Roesser model of the iterative learning control system is presented by means of 2D systems theory. Then, the monotonic convergence condition of the controlled system is analyzed according to the stability theory of linear repetitive process. Furthermore, the sufficient conditions of the controller existence are given in linear matrix inequality format under different relative degrees, which guarantees the system dynamic performance. Finally, through comparison with static controllers under different relative degrees, the simulation results show that the designed schemes are effective and feasible.

Robust feedback feed-forward PD-type iterative learning control for uncertain discrete systems over finite frequency ranges

This paper proposes a robust feedback feed-forward proportional-derivative type (PD-type) iterative learning control (ILC) scheme for a class of linear discrete systems with polytopic uncertainty over finite frequency ranges. First, the ILC process is transformed into an equivalent discrete linear repetitive process. Then, with the help of the generalized Kalman–Yakubovich–Popov lemma, the issue of a robust control law design algorithm in the process model is converted into the problem of solutions to the corresponding linear matrix inequality conditions. This procedure not only meets the robust performance specifications along the trial, but also guarantees the monotonic converge of the trial-to-trial error dynamics over finite frequency ranges. Finally, the simulations for a direct current servo motor system are adopted to show the effectiveness and superiority of the proposed method. Compared with previously established works, the new algorithm is more effective in delivering higher performance and achieving better tracking effect.

New relaxed stability and stabilization conditions for both discrete and differential linear repetitive processes

The paper develops new results on stability analysis and stabilization of linear repetitive processes. Repetitive processes are a distinct subclass of two-dimensional (2D) systems, whose origins are in the modeling for control of mining and metal rolling operations. The reported systems theory for them has been applied in other areas such iterative learning control, where, uniquely among 2D systems based designs, experimental validation results have been reported. This paper uses a version of the Kalman–Yakubovich–Popov Lemma to develop new less conservative conditions for stability in terms of linear matrix inequalities, with an extension to control law design. Differential and discrete dynamics are analysed in an unified manner, and supporting numerical examples are given.

On the reduction of repetitive processes into singular and non-singular Roesser models

In this paper we present new methods for the reduction of a polynomial system matrix describing a discrete linear repetitive process, to equivalent singular and non-singular 2-D state space representations. Particularly, a zero coprime system equivalence transformation resulting in a singular Roesser state space model, preserving the core algebraic structure of the original system matrix, is proposed. As a second step utilizing the singular Roesser model introduced, we further reduce the system to a non-singular, zero coprime system equivalent Roesser model. Both models are constructed by inspection or by applying elementary matrix manipulations and have significantly smaller dimensions compared to similar reductions found in the literature.

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.

Fusion estimation for multi-rate linear repetitive processes under weighted try-once-discard protocol

In this paper, the fusion estimation problem is studied for a class of discrete time-varying multi-rate linear repetitive processes (LRPs) under weighted try-once-discard protocol. The LRPs are measured by multiple sensors that are allowed to have different sampling periods, and the state updating period of the LRPs is also allowed to be different from the sampling periods of the asynchronous sensors. To facilitate the estimator design, the lifting technique is applied to transform the multi-rate LRPs to single-rate ones. Moreover, due to limited communication capability, the weighted try-once-discard protocol is adopted to schedule the asynchronous sensors. A set of local estimators is designed such that the upper bounds on the local estimation error covariances are guaranteed, and such upper bounds are then minimized by appropriately designing the estimator gains. Furthermore, the estimates from the local estimators are fused by recurring to the sequential covariance intersection fusion method. Finally, a simulation example is given to demonstrate the effectiveness of the proposed fusion estimation scheme.

Equivalence of wave linear repetitive processes and the singular 2-D Roesser state-space model

This paper develops a direct method for transforming a polynomial system matrix describing a discrete wave linear repetitive process to a 2-D singular state-space Roesser model description where all relevant properties, including the zero coprimeness properties of the system matrix, are retained. It is shown that the transformation is zero coprime system equivalence. The structure of the resulting system matrix in singular form and the transformation are also established.

Equivalent 2-D nonsingular Roesser models for discrete linear repetitive processes

ABSTRACTThe elementary operations algorithm is used to establish that a system matrix describing a discrete linear repetitive process can be transformed to that of a 2-D nonsingular Roesser model where all the input–output properties are preserved. Moreover, the connection between these system matrices is shown to be input–output equivalence. The exact forms of the resulting system matrix and the transformation involved are established. Some areas for possible future use/application of the developed results are also briefly discussed.

Reduction of discrete linear repetitive processes to nonsingular Roesser models via elementary operations

A method based on the elementary operations algorithm (EOA) is developed that reduces a system matrix describing a discrete linear repetitive process to a 2-D nonsingular Roesser form such that all the input-output properties, including the transfer-function matrix, are preserved. Some areas for possible future use/application of the developed results will also be briefly discussed.

Parameter-Dependent Lyapunov Functions in the Robust Control of Discrete Linear Repetitive Processes Using Previous Pass-Windowed Information

Abstract The variables in multidimensional systems are functions of more than one indeterminate, and such systems cannot be controlled by standard systems theory. This paper considers a subclass of these systems that operate over a subset of the upper-right quadrant of the two-dimensional (2D) plane in the discrete domain with a specified recursive structure known as repetitive processes. Physical examples of such processes are known and also their representations can be used in the analysis of other classes of systems, such as iterative learning control. This paper gives new results on the use of the parameter-dependent Lyapunov functions for stability analysis and controls law design of a subclass of repetitive processes that arise in application areas. These results aim to eliminate or reduce the effects of model parameter uncertainty.

New results on strong practical stability and stabilization of discrete linear repetitive processes

Discrete linear repetitive processes operate over a subset of the upper-right quadrant of the 2D plane. They arise in the modeling of physical processes and also the existing systems theory for them can be used to effect in solving control problems for other classes of systems, including iterative learning control design. This paper uses a form of the generalized Kalman–Yakubovich–Popov (GKYP) Lemma to develop new linear matrix inequality (LMI) based stability conditions and control law design algorithms for the strong practical stability property. Relative to alternatives, the LMIs for stability have a simpler structure and it is not required to impose particular structures on the matrix variables. These properties are extended to control law design, including those where state vector access is not required. Illustrative numerical simulation examples conclude the paper.

Repetitive Processes Based Iterative Learning Control Designed by LMIs

This paper addressed the stability analysis along the pass and the synthesis problem of linear 2D/repetitive systems. The algorithms for control law design are developed using a strong form of stability for discrete and differential linear repetitive processes known as stability along the pass. In particular, recent work on the use of linear matrix inequalities- (LMIs-) based methods in the design of control schemes for discrete and differential linear repetitive processes will be highlighted by the application of the resulting theory of linear model. The resulting design computations are in terms of linear matrix inequalities (LMIs). Simulation results demonstrate the good performance of the theoretical scheme.

Robust control with finite frequency specification for uncertain discrete linear repetitive processes

This paper is dedicated to the study of robust stability and controller synthesis for discrete linear repetitive processes with polytopic uncertainty. In the robust control domain, conditions based on parameter dependent Lyapunov functions are proposed in order to reduce the conservatism related to uncertainty problems. The solution is a class of Lyapunov functions that depends in a polytopic way on the uncertain parameters and that can be derived from linear matrix inequality conditions. Nevertheless, in many cases in practice, the frequency range of reference signals, noises and disturbances are known beforehand. Therefore, performing controller synthesis in the full frequency range is not practically suited and may introduce conservatism to some extent. Based on generalized Kalman–Yakubovich–Popov Lemma, a finite frequency controller is derived for uncertain discrete linear repetitive processes which are the most investigated class of 2D systems. Hence, the designer can specify a frequency range where the prescribed control performance is required, where, for example, this range could be determined by inspection of frequency spectrums of the available signals.

Control of discrete linear repetitive processes using strong practical stability and [formula omitted] disturbance attenuation

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest. This paper develops algorithms for control law design to ensure stabilization and a prescribed level of disturbance attenuation as measured by an H∞ norm.

Control law design for discrete linear repetitive processes with non-local updating structures

Repetitive processes are a class of 2D systems where information propagation in one direction is of finite duration. These processes make a series of sweeps, termed passes, through a set of dynamics and on completion of each pass resetting to the starting position occurs ready for the start of the next pass. The control problem is that the previous pass output, termed the pass profile, acts as a forcing function on the current pass and can result in oscillations that increase in amplitude from pass-to-pass. In the case of discrete dynamics, these processes have structural links with 2D systems described by the well known Roesser and Fornasini–Marchesini state-space models but some applications require updating structures that cannot be represented by these models. This requirement arises either in adequately modeling the dynamics or as a result of the control law structure and requires the development of a systems theory for eventual use in applications. In this paper such a theory is advanced through the development of new control law design algorithms.

Strong practical stability and stabilization of uncertain discrete linear repetitive processes

SUMMARYRepetitive processes are a distinct class of 2D systems of both theoretical and practical interest. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass, respectively, where the former is a necessary condition for the latter. Recently applications have arisen where asymptotic stability is too weak, and stability along the pass is too strong for meaningful progress to be made. This, in turn, has led to the concept of strong practical stability for such cases, where previous work has formulated this property and obtained necessary and sufficient conditions for its existence together with Linear Matrix Inequality based tests, which then extend to allow robust control law design. This paper develops considerably simpler, and hence computationally more efficient, stability tests that also extend to allow control law design. Copyright © 2011 John Wiley & Sons, Ltd.

Reduced-order [formula omitted] filtering for discrete linear repetitive processes

This paper is concerned with the reduced-order H 2 filtering problem for discrete linear repetitive processes (LRPs). For a discrete linear repetitive process (LRP) assumed to be stable along the pass, our attention is focused on the design of a reduced-order filter, which guarantees the filtering error process to be stable along the pass, and minimizes an upper bound for the H 2 norm of its transfer function. Two different approaches are proposed to solve the reduced-order H 2 filtering problem: one is the convex linearization approach and the other is the projection approach. A numerical example is presented to illustrate the feasibility of the proposed methodologies.

Robust control of distributed parameter mechanical systems using a multidimensional systems approach

Robust control of distributed parameter mechanical systems using a multidimensional systems approach The unique characteristic of a repetitive processes is a series of sweeps, termed passes, through a set of dynamics defined over a finite duration. On each pass an output, termed the pass profile is produced which acts as on forcing function, and hence contributes to, the dynamics of the next pass profile. This leads to the possibility that the output, i.e. the sequence of pass profiles, will contain oscillations that increase in amplitude in the pass-to-pass direction. Such behavior cannot be controlled by application of standard linear systems control laws and instead they must be treated as two-dimensional (2D) systems where information propagation in two independent directions, termed pass-to-pass and along the pass respectively, is the defining feature. Physical examples of such processes include long-wall coal cutting and metal rolling. In this paper, stability analysis and control law design algorithms are developed for discrete linear repetitive processes where a plane, or rectangle, of information is propagated in the pass-to-pass direction. The possible use of such a model in the control of distributed parameter systems has been investigated in previous work and this paper considers an extension to allow for uncertainty in the model description.

Modelling and Control of Bi-Directional Discrete Linear Repetitive Processes

Repetitive processes are characterized by a series of sweeps or passes through a set of dynamics defined over a finite duration where the output produced on any pass acts as a forcing function on, and hence contributes to, the dynamics of the next pass. The resulting control problem is that the output sequence of pass profiles can contain oscillations that increase in amplitude in the pass-to-pass direction. This paper considers bi-directional operation, i.e. a pass is completed and at the end the next one begins but in the opposite direction. In particular, a model for such a process in the case of discrete dynamics is first proposed and new results on stability and control law design for stabilization and performance developed.

On controllability and control laws for discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by the direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. This article develops significant new results on the relationships between one physically motivated concept of controllability for the so-called discrete linear repetitive processes and the structure and design of control laws, including the case when disturbances are present.