Fast sampling control of a class of differential linear repetitive processes

Repetitive processes are a distinct class of 2D linear systems of practical and theoretical interest. Most of the available control theory for them is for the case of linear dynamics and focuses on systems theoretic properties such as stability and controllability/observability. This paper uses an extension of standard, or 1D, feedback control schemes to control a physically relevant sub-class of these processes

<i>H</i>₂ and mixed <i>H</i>₂/<i>H</i>_∞ Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation

H2/H∞ output information-based disturbance attenuation for differential linear repetitive processes

Repetitive processes propagate information in two independent directions where the duration of one is finite. They pose control problems that cannot be solved by application of results for other classes of 2D systems. This paper develops controller design algorithms for differential linear processes, where information in one direction is governed by a matrix differential equation and in the other by a matrix discrete equation, in an H2/H∞ setting. The objectives are stabilization and disturbance attenuation, and the controller used is actuated by the process output and hence the use of a state observer is avoided

Robust L2–L∞ control of uncertain differential linear repetitive processes

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdFor two-dimensional (2-D) systems, information propagates in two independent directions. 2-D systems are known to have both system-theoretical and applications interest, and the so-called linear repetitive processes (LRPs) are a distinct class of 2-D discrete linear systems. This paper is concerned with the problem of L2–L∞ (energy to peak) control for uncertain differential LRPs, where the parameter uncertainties are assumed to be norm-bounded. For an unstable LRP, our attention is focused on the design of an L2–L∞ static state feedback controller and an L2–L∞ dynamic output feedback controller, both of which guarantee the corresponding closed-loop LRPs to be stable along the pass and have a prescribed L2–L∞ performance. Sufficient conditions for the existence of such L2–L∞ controllers are proposed in terms of linear matrix inequalities (LMIs). The desired L2–L∞ dynamic output feedback controller can be found by solving a convex optimization problem. A numerical example is provided to demonstrate the effectiveness of the proposed controller design procedures.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Dissipative stability theory for linear repetitive processes with application in iterative learning control

This paper develops a new set of necessary and sufficient conditions for the stability of linear repetitive processes, based on a dissipative setting for analysis. These conditions reduce the problem of determining whether a linear repetitive process is stable or not to that of checking for the existence of a solution to a set of linear matrix inequalities (LMIs). Testing the resulting conditions only requires compu- tations with matrices whose entries are constant in comparison to alternatives where frequency response computations are required

Constrained optimal control theory for differential linear repetitive processes

Differential repetitive processes are a distinct class of continuous-discrete two-dimensional linear systems of both systems theoretic and applications interest. These processes complete a series of sweeps termed passes through a set of dynamics defined over a finite duration known as the pass length, and once the end is reached the process is reset to its starting position before the next pass begins. Moreover the output or pass profile produced on each pass explicitly contributes to the dynamics of the next one. Applications areas include iterative learning control and iterative solution algorithms, for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modeling of numerous industrial processes such as metal rolling, long-wall cutting, etc. In this paper we develop substantial new results on optimal control of these processes in the presence of constraints where the cost function and constraints are motivated by practical application of iterative learning control to robotic manipulators and other electromechanical systems. The analysis is based on generalizing the well-known maximum and $\epsilon$-maximum principles to the

Finite-region boundedness and stabilization for 2D continuous-discrete systems in Roesser model

This paper investigates the finite-region boundedness (FRB) and stabilization problems for two-dimensional continuous-discrete linear Roesser models subject to two kinds of disturbances. For two-dimensional continuous-discrete system, we first put forward the concepts of finite-region stability and FRB. Then, by establishing special recursive formulas, sufficient conditions of FRB for two-dimensional continuous-discrete systems with two kinds of disturbances are formulated. Furthermore, we analyze the finite-region stabilization issues for the corresponding two-dimensional continuous-discrete systems and give generic sufficient conditions and sufficient conditions that can be verified by linear matrix inequalities for designing the state feedback controllers which ensure the closed-loop systems FRB. Finally, viable experimental results are demonstrated by illustrative examples

Stability Tests for a Class of 2D Continuous-Discrete Linear Systems with Dynamic Boundary Conditions

Repetitive processes are a distinct class of 2D systems of both practical and theoretical interest. Their essential characteristic is repeated sweeps, termed passes, through a set of dynamics defined over a finite duration with explicit interaction between the outputs, or pass profiles, produced as the system evolves. Experience has shown that these processes cannot be studied/controlled by direct application of existing theory (in all but a few very restrictive special cases). This fact, and the growing list of applications areas, has prompted an on-going research programme into the development of a 'mature' systems theory for these processes for onward translation into reliable generally applicable controller design algorithms. This paper develops stability tests for a sub-class of so-called differential linear repetitive processes in the presence of a general set of initial conditions, where it is known that the structure of these conditions is critical to their stability properties

Output frequency response function-based analysis for nonlinear Volterra systems

Analysis of nonlinear systems has been studied extensively. Based on some recently developed results, a new systematic approach to the analysis of nonlinear Volterra systems in the frequency domain is proposed in this paper, which provides a novel insight into the frequency domain analysis and design of nonlinear systems subject to a general input instead of only specific harmonic inputs using input-output experimental data. A general procedure to conduct an output frequency response function (OFRF) based analysis is given, and some fundamental results and techniques are established for this purpose. A case study for the analysis of a circuit system is provided to illustrate this new frequency domain method

On the Control of Distributed Parameter Systems using a Multidimensional Systems Setting

The unique characteristic of a repetitive process is a series of sweeps, termed passes, through a set of dynamics defined over a finite duration with resetting before the start of the each new one. On each pass an output, termed the pass profile is produced which acts as a forcing function on, 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 which increase in amplitude in the pass-to-pass direction. Such behavior cannot be controlled by standard linear systems approach and instead they must be treated as a multidimensional system, i.e. information propagation in more than one independent direction. Physical examples of such processes include long-wall coal cutting and metal rolling. In this paper, stability analysis and control systems design algorithms are developed for a model where a plane, or rectangle, of information is propagated in the passto- pass direction. The possible use of these in the control of distributed parameter systems is then described using a fourthorder wavefront equation