Variable Structure Systems: Survey

Coordinated Science Laboratory was formerly known as Control Systems Laborator

Control of the reaching mode in variable structure systems

This paper focuses on the behaviour of variable structure systems with dynamic control, particularly during the reaching mode of operation. It is shown that stability problems may arise during this reaching phase. The causes of these problems are closely related with the problems of windup commonly found in conventional control systems with actuator constraints. Methods for stabilization of the reaching mode are proposed which are based on the concepts of 'realizable reference' and observers. Well-known algorithms that have been previously proposed from empiric ideas, can now be rigorously derived using these concepts. The theoretical framework developed by Kothare and co-workers in the context of windup is generalized to study and design control algorithms for the reaching mode

Control of the reaching mode in variable structure systems

This paper focuses on the behaviour of variable structure systems with dynamic control, particularly during the reaching mode of operation. It is shown that stability problems may arise during this reaching phase. The causes of these problems are closely related with the problems of windup commonly found in conventional control systems with actuator constraints. Methods for stabilization of the reaching mode are proposed which are based on the concepts of 'realizable reference' and observers. Well-known algorithms that have been previously proposed from empiric ideas, can now be rigorously derived using these concepts. The theoretical framework developed by Kothare and co-workers in the context of windup is generalized to study and design control algorithms for the reaching mode.Facultad de Ingenierí

Switching Flow-Graph nonlinear modeling technique

A unified graphical modeling technique, “Switching Flow-Graph” is developed to study the nonlinear dynamic behavior of pulse-width-modulated (PWM) switching converters. Switching converters are variable structure systems with linear subsystems. Each subsystem can be represented by a flow-graph. The Switching Flow-Graph is obtained by combining the flowgraphs of the subsystems through the use of switching branches. The Switching Flow-Graph model is easy to derive, and it provides a visual representation of a switching converter system. Experiments demonstrate that the Switching Flow-Graph model has very good accuracy

A New Framework for the Simulation of Equation-Based Models with Variable Structure

Many modern models contain changes that affect the structure of their underlying equation system, e.g. the breaking of mechanical devices or the switching of ideal diodes. The modeling and simulation of such systems in current equation-based languages frequently poses serious difficulties. In order to improve the handling of variable-structure systems, a new modeling language has been designed for research purposes. It is called Sol and it caters to the special demands of variable-structure systems while still representing a general modeling language. This language is processed by a new translation scheme that handles the differential-algebraic equations in a highly dynamic fashion. In this way, almost arbitrary structural changes can be processed. In order to minimize the computational effort, each change is processed as locally as possible, preserving the existing computational structure as much as possible. Given this methodology, truly object-oriented modeling and simulation of variable-structure systems is made possible. The corresponding process of modeling and simulation is illustrated by two examples from different domains

Adaptive control using variable structure systems.

Adaptive control is employed in control systems required to operate satisfactorily regardless of parameter variations, external disturbances and changes in the environment. A conceptually simple approach to adaptive control is the model reference approach which yields a nonlinear feedback system. In a model reference control system the system output is made to follow the output of a specified model. There are numerous approaches to the design of model reference adaptive control systems (MRAC). In this thesis the theory of variable structure systems (VSS) is studied and applied in the design of MRAC systems. VSS are inherently nonlinear feedback systems which exhibit certain adaptive properties including insensitivity to a range of parameter variations and certain external disturbances when operating in the sliding mode. The application of VSS theory to the problem of adaptive model-following has demonstrated the simplicity of the design. It also ensures the asymptotic stability of the controlled system and provides direct control over the error transient. The notion of system zeros arises naturally when tackling the problem of output model-following control systems. Certain interrelations between VSS, system zeros and the output model following problem have suggested a new method for computing the zeros of linear multivariable square systems. A fundamental operator in VSS is shown to be a projector. The employment of projector theory in the study of VSS provides further insight into their operation. Furthermore new methods for constructing the switching hyperplanes matrix are formulated by utilizing projector theory. The linear control law ensuring output model-following and the necessary order reduction is shown to be identical to the equivalent control encountered in VSS. The control law also decouples the system, assigns arbitrary poles and possesses certain adaptive properties. The extension of VSS theory to output model following systems using output information is also discussed

Observer design for piecewise smooth and switched systems via contraction theory

The aim of this paper is to present the application of an approach to study contraction theory recently developed for piecewise smooth and switched systems. The approach that can be used to analyze incremental stability properties of so-called Filippov systems (or variable structure systems) is based on the use of regularization, a procedure to make the vector field of interest differentiable before analyzing its properties. We show that by using this extension of contraction theory to nondifferentiable vector fields, it is possible to design observers for a large class of piecewise smooth systems using not only Euclidean norms, as also done in previous literature, but also non-Euclidean norms. This allows greater flexibility in the design and encompasses the case of both piecewise-linear and piecewise-smooth (nonlinear) systems. The theoretical methodology is illustrated via a set of representative examples.Comment: Preprint accepted to IFAC World Congress 201

Control of the reaching mode in variable structure systems

This paper focuses on the behaviour of variable structure systems with dynamic control, particularly during the reaching mode of operation. It is shown that stability problems may arise during this reaching phase. The causes of these problems are closely related with the problems of windup commonly found in conventional control systems with actuator constraints. Methods for stabilization of the reaching mode are proposed which are based on the concepts of 'realizable reference' and observers. Well-known algorithms that have been previously proposed from empiric ideas, can now be rigorously derived using these concepts. The theoretical framework developed by Kothare and co-workers in the context of windup is generalized to study and design control algorithms for the reaching mode.Facultad de Ingenierí

Design of stable fuzzy controllers for an AGV

Fuzzy logic control is a relatively new technology and hence it needs rigorous comparative analyses with other well-established conventional control schemes. Further, fuzzy controller stability analysis is a major hindrance for its popularity among control engineers. This paper shows how stable fuzzy controllers may be synthesized for a typical AGV from the perspective of variable structure systems (VSS) theory. VSS or sliding model control (SMC) is an established robust non-linear control methodology. The AGV is characterized by highly non-linear, coupled and configuration dependent dynamics, with uncertainty in model parameters. Similarity in performance of the fuzzy controllers to the SMC controller is demonstrated through experimental results obtained for steer control of the AGV

Uniform finite time stabilisation of non-smooth and variable structure systems with resets

This thesis studies uniform finite time stabilisation of uncertain variable structure and non-smooth systems with resets. Control of unilaterally constrained systems is a challenging area that requires an understanding of the underlying mechanics that give rise to reset or jumps while synthesizing stabilizing controllers. Discontinuous systems with resets are studied in various disciplines. Resets in states are hard nonlinearities. This thesis bridges non-smooth Lyapunov analysis, the quasi-homogeneity of differential inclusions and uniform finite time stability for a class of impact mechanical systems. Robust control synthesis based on second order sliding mode is undertaken in the presence of both impacts with finite accumulation time and persisting disturbances. Unlike existing work described in the literature, the Lyapunov analysis does not depend on the jumps in the state while also establishing proofs of uniform finite time stability. Orbital stabilization of fully actuated mechanical systems is established in the case of persisting impacts with an a priori guarantee of finite time convergence between t he periodic impacts. The distinguishing features of second order sliding mode controllers are their simplicity and robustness. Increasing research interest in the area has been complemented by recent advances in Lyapullov based frameworks which highlight the finite time Convergence property. This thesis computes the upper bound on the finite settling time of a second order sliding mode controller. Different to the latest advances in the area, a key contribution of this thesis is the theoretical proof of the fact that finite settling time of a second order sliding mode controller tends to zero when gains tend to infinity. This insight of the limiting behaviour forms the basis for solving the converse problem of finding an explicit a priori tuning formula for the gain parameters of the controller when and arbitrary finite settling time is given. These results play a central role ill the analysis of impact mechanical systems. Another key contribution of the thesis is that it extends the above results on variable structure systems with and without resets to non-smooth systems arising from continuous finite time controllers while proving uniform finite time stability. Finally, two applications are presented. The first application applies the above theoretical developments to the problem of orbital stabilization of a fully actuated seven link biped robot which is a nonlinear system with periodic impacts. The tuning of the controller gains leads to finite time convergence of the tracking errors between impacts while being robust to disturbances. The second application reports the outcome of an experiment with a continuous finite time controller