K Galkowski

Stability and controllability of a class of 2-D linear systems with dynamic boundary conditions

Discrete linear repetitive processes are a distinct class of two-dimensional (2-D) linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2-D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. In this paper a complete characterization of stability and so-called pass controllability (and several resulting features), essential building blocks for a rigorous systems theory, under a general set of initial, or boundary, conditions is developed. Finally, some significant new results on the problem of stabilization by choice of the pass state initial vector sequence are developed.

New 2D models and a transition matrix for discrete linear repetitive processes

This paper reports further results on the development of a control theory for discrete linear repetitive processes. In particular, Roesser and Fornasini Marchesini state space model equivalent descriptions for the dynamics of these processes are constructed and then used to develop new stability tests which involve only computations on matrices with constant entries. Also, they are used to develop a transition matrix, or fundamental matrix sequence, for these processes which isa then used to define and characterize so-called local reachability and controllability properties in the form of matrix rank-based tests.

Strong practical stability and stabilization of uncertain discrete linear repetitive processes

SUMMARY Repetitive 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

Strong practical stability and control of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest. The stability theory for these processes currently consists 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 paper develops the concept of strong practical stability for such cases together with LMI based necessary and sufficient conditions. These are then used as a basis for control law design.

On the design of ILC schemes for finite frequency range tracking specifications

Many industrial systems perform the same task over a finite duration. For example, a robot placing objects on a conveyer where the exact sequence of operations is collect an object from a given location, transfer it over a finite time, place it on a moving conveyor and then return to the same location for the next one and so on. Iterative learning control emerged as a setting for controller design in such cases where information from previous executions, also termed trials, is used to update the control signal to be used on the next trial and thereby sequentially improve performance. Control laws designed in this setting can be activated in a number of ways, one of the most common is feedforward from the previous trial to track a specific reference signal or reject a repeating disturbance. Another option is to combine the feedforward term with feedback action on the current trial. For plants with linear dynamics, the learning filter, termed the L-filter in some of the literature, is a common approach to guarantee convergence in the trial-to-trial direction and is often combined with a robustness filter, termed the Q-filter in some literature. In this paper, we use the generalized Kalman-Yakubovich-Popov lemma to design the L and Q filters over a finite, as opposed to the complete, frequency range which is more practically relevant in many cases.

SCILAB compatible software for analysis and control of repetitive processes

In this paper the development of a SCILAB compatible software package for the analysis and control of repetitive processes is described. The core of the package consists of a simulation tool which enables the user to inspect the process dynamics with or without control laws applied. Reliable and numerically efficient algorithms for stability analysis and the control law design have been included. Illustrative examples are also given and areas of ongoing development are discussed

Experimentally verified Iterative Learning Control based on repetitive process stability theory

This paper gives new results on the design and experimental evaluation of an Iterative Learning Control (ILC) law in a repetitive process setting. The experimental results given are from a gantry robot facility that has been extensively used in the benchmarking of linear model based ILC designs. An example is also given to demonstrate that this new design offers much superior performance in comparison to some previous designs based on the Roesser model for 2D linear systems.

MATLAB based tools for 2D linear systems with application to iterative learning control schemes

Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest. For example, they arise in the study of industrial processes such as long-wall coal cutting operations and also in the modeling of classes of iterative learning control schemes. This paper describes the development of MATLAB based tools for control related analysis/controller design in the case of so-called discrete linear repetitive processes with particular emphasis on the iterative learning control application. Some areas for short to medium term further development are also briefly noted.

Control of a Class of

Repetitive processes are a distinct class of two-dimensional (2D) systems (i.e. information propagation in two independent directions occurs) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or (most often) 2D systems theory. In this paper we define a new model for these processes necessary to represent dynamics which arise in some applications areas and which are not included in the currently used models. Then we proceed to define quadratic stability for this case, obtain conditions for its existence, and also solve the problem of designing a control law to stabilize the process dynamics (including the case when there is uncertainty associated with the defining state space model)

The influence of feedback/feedforward control on relaxed pass profile controllability of 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 direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here we give the first results on how feedback/feedforward control action can be used to influence one form of controllability for processes with discrete dynamics.