Iterative learning control is now well established for linear and nonlinear dynamics in terms of both the underlying theory and experimental application. This approach is specifically targeted at cases where the same operation is repeated over a finite duration with resetting between successive repetitions. Each repetition or pass is known as a trial and the key idea is to use information from previous trials to update the control input used on the current one with the aim of improving performance from trial-to-trial. In this paper, new results on ILC applied to systems that arise from discretization of bi-variate partial differential equations describing spatio-temporal systems or processes are developed. Theses are based on Crank-Nicholson discretization of the governing partial differential equation, resulting in an unconditionally numerically stable approximation of the dynamics. It is also shown that this setting allows the selection of a finite number of points for sensing and actuation. The resulting control laws can be computed using Linear Matrix Inequalities (LMIs). Finally, an illustrative example is given and areas for further research are discussed.
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. r
a b s t r a c tThis paper uses a 2D system setting in the form of repetitive process stability theory to design an iterative learning control law that is robust against model uncertainty. In iterative learning control the same finite duration operation, known as a trial over the trial length, is performed over and over again with resetting to the starting location once each is complete, or a stoppage at the end of the current trial before the next one begins. The basic idea of this form of control is to use information from the previous trial, or a finite number thereof, to compute the control input for the next trial. At any instant on the current trial, data from the complete previous trial is available and hence noncausal information in the trial length indeterminate can be used. This paper also shows how the new 2D system based design algorithms provide a setting for the effective deployment of such information.
Iterative Learning Control (ILC) is now well established in terms of both the underlying theory and experimental application. This approach is specifically targeted at cases where the same operation is repeated over a finite duration with resetting between successive executions. Each execution is known as a trial and the key idea is to use information from previous trials to update the control input used on the current one with the aim of improving performance from trial-to-trial. In this paper, the subject area is the application of ILC to spatio-temporal systems described by a linear partial differential equation (PDE) using a discrete approximation of the dynamics, where there are a number of construction methods that could be applied. Here explicit discretization is used, resulting in a multidimensional, or n D, discrete linear system on which to base control law design, where n denotes the number of directions of information propagation and is equal to the total number of indeterminates in the PDE. The resulting control laws can be computed using Linear Matrix Inequalities (LMIs) and a numerical example is given. Finally, a natural extension to robust control is noted and areas for further research briefly discussed.
SUMMARYThis paper considers iterative learning control for a class of uncertain multiple-input multiple-output discrete linear systems with polytopic uncertainties and actuator faults. The stability theory for linear repetitive processes is used to develop control law design algorithms that can be computed using linear matrix inequalities. A class of parameter dependent Lyapunov functions are used with the aim of enlarging the allowed polytopic uncertainty range for successful design. The effectiveness and feasibility of the new design algorithms is illustrated by a gantry robot case study.
This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multipleoutput 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.