Wu-Chung Su

An O(T/sup 2/) boundary layer in sliding mode for sampled-data systems

The use of a discontinuous control law (typically, sign functions) in a sampled-data system will bring about chattering phenomenon in the vicinity of the sliding manifold, leading to a boundary layer with thickness O(T), where T is the sampling period. However, by proper consideration of the sampling phenomenon in the discrete-time sliding mode control design, the thickness of the boundary layer can be reduced to O(T/sup 2/). In contrast to discontinuous control for continuous-time VSS, the discrete-time sliding mode control need not be of switching type.

Constructing discontinuity surfaces for variable structure systems: a Lyapunov approach

The problem of constructing discontinuity surfaces in variable structure systems is studied from a Lyapunov point of view. A switching surface determined by the control coefficient matrix and the associated Lyapunov function is able to ensure asymptotic stability for the system in sliding mode. The proposed method may also be used for systems with nonlinear dynamics and for linear systems with delays.

Brief paper: Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties

This paper considers the stabilization problem of a one-dimensional unstable heat conduction system (rod) modeled by a parabolic partial differential equation (PDE), powered with a Dirichlet type actuator from one of the boundaries. By applying the Volterra integral transformation, a stabilizing boundary control law is obtained to achieve exponential stability in the ideal situation when there are no system uncertainties. The associated Lyapunov function is used for designing an infinite-dimensional sliding manifold, on which the system exhibits the same type of stability and robustness against certain types of parameter variations and boundary disturbances. It is observed that the relative degree of the chosen sliding function with respect to the boundary control input is zero. A continuous control law satisfying the reaching condition is obtained by passing a discontinuous (signum) signal through an integrator.

Nonlinear control of a rodless pneumatic servoactuator, or sliding modes versus Coulomb friction

Abstract Coulomb friction remains one of the major difficulties arising in control design for mechanical systems. Control of a translational pneumatic servoactuator is a typical example of such a problem. The aim of this paper is to demonstrate that sliding-mode control can be successfully used to compensate the friction of the piston in the cylinder, which is both viscous and Coulomb. A fourth-order nonlinear state-space model of a rodless pneumatic servoactuator will be developed with both numerical simulation and experimental validation. The comparison of sliding-mode control with classic PID control will be presented.

Sliding mode with chattering reduction in sampled data systems

This paper deals with discrete time sliding mode control with chattering reduction for sampled data systems. The pre-filtering and post-filtering settings are implemented to eliminate chattering with robustness. The proposed method weakens some of the constraints due to the high frequency switching and full state accessibility requirements in continuous time variable structure control.<<ETX>>

Sliding mode control in discrete time linear systems

Abstract Due to the sample/hold processes in a discrete time system, a number of properties, which are valid in continuous time systems, no longer hold. For sliding mode control, the discrete time matching condition will not be satisfied in general even if the continuous time version holds. Yet one still can maintain the states in the vicinity of the sliding manifolds up to at least O ( T 2 ) at each sampling instant, where T is the sampling period. Moreover, for disturbances with sufficient smoothness, the accuracy can be promoted to O ( ( T r ) 2 ) ( r being an interger ) (r being an integer) if additional switchings in between measured samplings are allowed. It is seen that the system uncertainties due to exogenous disturbances can be rejected within O ( T 2 ) to O ( ( T r ) 2 ) ( r being an interger ) accuracy and that the effect caused by parameter variations will be attenuated to zero asymptotically.

A Sampled-Data Singularly Perturbed Boundary Control for a Heat Conduction System With Noncollocated Observation

This note presents a sampled-data strategy for a boundary control problem of a heat conduction system modeled by a parabolic partial differential equation (PDE). Using the zero-order-hold, the control law becomes a piecewise constant signal, in which a step change of value occurs at each sampling instant. Through the dasialiftingpsila technique, the PDE is converted into a sequence of constant input problems, to be solved individually for a sampled-data formulation. The eigenspectrum of the parabolic system can be partitioned into two groups: a finite number of slow modes and an infinite number of fast modes, which is studied via the theory of singular perturbations. Controllability and observability of the sampled-data system are preserved, irrelevant to the sampling period. A noncollocated output-feedback design based upon the state observer is employed for set-point regulation. The state observer serves as an output-feedback compensator with no static feedback directly from the output, satisfying the so-called dasialow-pass propertypsila. The feedback controller is thus robust against the observation error due to the neglected fast modes.

Discrete-time VSS temperature control for a plastic extrusion process with water cooling systems

The plastic extrusion process with water cooling is a variable structure system in nature. To implement discrete-time variable structure control, three important problems are considered. They are: choice of dynamic sliding surface for a system with relative degree greater than one, computation of the discrete-time dynamic sliding surface variable (s/sub k/), and self-tuning of the switching control magnitude to reduce chatterings. A simplified lumped parameter model is constructed to decouple the original multichannel system into multiple single-channel subsystems. Experimental results show the effectiveness of the proposed method.

Variable Structure Control for Singularly Perturbed Linear Continuous Systems With Matched Disturbances

A variable structure system can be studied using the singular perturbation theory. The discontinuous control that leads to a finite-time reaching of the sliding surface creates fast-time transients analogous to the stable boundary layer dynamics of a singularly perturbed system. As the sliding mode is attained, the slow-time dynamics prevails, just as that of a singularly perturbed system after the boundary layer dynamics fades away. In this technical note, the problem of sliding mode control for singularly perturbed systems in the presence of matched bounded external disturbances is investigated. A composite sliding surface is constructed from solutions of algebraic Lyapunov equations which are derived from both the fast and the slow subsystems. The resultant sliding motion ensures Lyapunov stability with disturbance rejection. Two proposed schemes that ensure the asymptotic stability of the system are presented. The effectiveness of the proposed methods is demonstrated in a numerical example of a magnetic tape control system.

Output Feedback Sliding Mode Control for Sampled-Data Systems

We address the output feedback sliding mode control problem for a sampled data linear system with external disturbances of the matching type. By taking into account the disturbance compensation, a deadbeat high gain output feedback control strategy with additional dynamics is able to attenuate the disturbances. In the framework of singular perturbation analysis, it is shown that the closed loop system exhibits good robustness against exogenous disturbances.