Bartlomiej Sulikowski

Output feedback control 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 new results on the relatively open problem of the design of physically based control laws. These results are for the sub-class of so-called discrete linear repetitive processes, which arise in applications areas such as iterative learning control.

Technical communique: PI control of discrete linear repetitive processes

Abstract 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. In this paper, we exploit their unique physical structure to show how two term, i.e. proportional plus integral (or PI) action, can be used to control these processes to produce desired behavior (as opposed to just stability).

LMI based stability analysis and controller design for a class of 2D continuous-discrete linear systems

Differential linear repetitive processes are a distinct class of 2D continuous-discrete linear systems of both applications and systems theoretic interest. In the latter area, they arise, for example, in the analysis of both iterative learning control schemes and iterative algorithms for computing the solutions of nonlinear dynamic optimal control algorithms based on the maximum principle. Repetitive processes cannot be analysed/controlled by direct application of existing systems theory and to date there are few results on the specification and design of control schemes for them. The paper uses an LMI setting to develop the first really significant results in this problem domain.

Proportional plus integral control of ladder circuits modeled in the form of two-dimensional (2D) systems

In this paper, a 2D systems setting is used to develop new results on control of active electrical ladder circuits. In particular, the proportional plus integral control method has been extended to this case and the problem of how to obtain some distributed along the circuit nodes desired (reference) signal, and how to completely decouple distributed disturbances has been solved.

Control and Disturbance Rejection 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 direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here we give new results on the relatively open problem of the design of physically based feedforward/feedback control laws to achieve desired performance and disturbance decoupling in the sense defined in the body of the paper.

Robust stability of ladder circuits from the 2D systems point of view

Ladder circuits can be considered as two-dimensional (2D) systems where information is propagated in two separate directions, i.e. along the time axis and along a space variable represented by a node number. Further, lifting along nodes is applied to obtain an equivalent 1D dynamical system model. Finally, the Linear Matrix Inequality (LMI) approach is used to develop robust stability conditions for uncertain active ladder circuits.

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

Proportional plus integral control and disturbance rejection for differential linear repetitive processes

Repetitive processes are a distinct class of two-dimensional systems (i.e. information propagates 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 in the associated literature) or two-dimensional (2D) systems theory. Most of the currently available results for them focus on fundamental properties such as stability, controllability etc. Recently, however, there has been a move (prompted by the progress in this earlier research) towards the development of a control theory, and associated design algorithms, for the subclasses of so-called differential and discrete linear repetitive processes which arise in applications such as iterative learning control. In this paper we continue this theme by investigating the role of proportional plus integral action in the differential case.

Stability and stabilisation of active ladder circuits modeled in the form of two-dimensional (2D) systems

Electrical ladder circuits can be considered as spatially interconnected systems of regular structure and can be viewed in the form of two dimensional (2D) systems, where one of the indeterminates is time and another is the number of subsystem in the overall structure. In this paper we develop a new 2D system based method of its stability analysis and stabilizing controller design with the use of Linear Matrix Inequalities (LMI) techniques.

Repetitive Process Control Theory Applied to the Modeling and Control of Ladder Circuits

Abstract Repetitive processes propagate information in two separate directions, one of which is temporal and the other can be spatial. A repetitive process makes a series of sweeps, or passes, through a set of dynamics over this finite duration and when each is complete the process resets. Moreover, the output produced on the previous pass explicitly contributes to the dynamics produced on the next one. Hence they can also be viewed as a class of periodic systems. They also pose control problems that cannot be solved by standard systems control theory and design algorithms. This paper gives new results on the application of the repetitive process control theory to the analysis of ladder networks.