Sliding surface design for discrete VSS using LQR technique with a preset real eigenvalue

This paper presents an LQR-based sliding surface design procedure that takes, in addition to the desired weighting matrix, a preset real eigenvalue consequential in discrete VSS as inputs. A weighting matrix that simultaneously stays``closest'' to the desired one and yields the preset eigenvalue is sought. Sliding surface is then determined from the optimal gain matrix and the preset eigenvalue. The existence and non-uniqueness of feasible weighting matrices, the uniqueness of solution and convexity of the constrained optimization problem, as well as the use of least-squares to simplify and solve the problem are studied. The paper ends with two MATLAB examples that illustrate the design procedure. This paper proposes a decentralized sliding mode control law for a class of large scale switching systems. It is assumed that some parts of the switching structures are fixed, and the design of the decentralized sliding mode control laws for the switching and fixed parts are carried out independently. The inclusion principle is developed so that one can expand a switching system, possibly performing sliding modes, into a higher dimensional switching system, design decentralized sliding mode controllers in the expanded space, then contract the solution for implementation on the original system. Some design issues, like connective reachability of the sliding manifold and the stability of the sliding mode equations in the expanded and original state spaces are examined. Finally, an example is given to illustrate the effectiveness of the design methodology. Sliding mode control systems are valued for their robust accommodation of uncertainties and their ability to reject disturbances. In this paper, a design methodology is proposed to eliminate the chattering phenomenon affecting sliding mode controlled plants with input unmodeled actuator dynamics of second order or greater. The proposed controller design is based on the relative degrees of the plant and the unmodeled actuator dynamics and the ranges of the uncertainties of the plant and actuator. The controller utilizes the pass filter characteristics of the physical actuating device to provide a smoothing effect on the discontinuous control signal rather than introducing any artificial dynamics into the controller design thus eliminating chattering in the system's output response. In this study, a parameterized output feedback dynamic sliding mode controller is proposed and internal stability, BIBO stability, and external disturbance rejection problem of generalized plant is studied. The proposed controller is described by a a solution of bezout equation and is parameterized by a Youla's free parameter. It …