Fast periodic oscillations in singularly perturbed relay control systems and sliding modes

As a mathematical model of chattering in the small neighbourhood of switching surface in the sliding mode systems we examine the singularly perturbed relay control systems (SPRCS). The sufficient conditions for existence of fast periodic solutions in such systems are found. Their stability is investigated. It is proved that the slow motions in such SPRCS are approximately described with equations obtained from the equations for the slow variables of SPRCS by averaging along fast periodic motions. It is shown that in the case when the original SPRCS contains the relay control linearly the averaged equations and equations which describe the motions of the reduced system in the sliding mode are coincide. The algorithm is proposed which allows to solve the problem of eigenvalues assignment for averaged equations using the additional dynamics of fast actuator

On the asymptotic analysis of singularly perturbed systems with sliding mode

In this paper we study singularly perturbed systems with discontinuity surfaces. This means that we have a system of ordinary differential equations with a small parameter and a piecewise smooth vector field. The state where the trajectory moves on the discontinuity surface is called sliding mode. We present an asymptotic representation for trajectories with temporary sliding and apply the result to stick-slip vibrations

Decentralised control for complex systems - An invited survey

© 2014 Inderscience Enterprises Ltd. With the advancement of science and technology, practical systems are becoming more complex. Decentralised control has been recognised as a practical, feasible and powerful tool for application to large scale interconnected systems. In this paper, past and recent results relating to decentralised control of complex large scale interconnected systems are reviewed. Decentralised control based on modern control approaches such as variable structure techniques, adaptive control and backstepping approaches are discussed. It is well known that system structure can be employed to reduce conservatism in the control design and decentralised control for interconnected systems with similar and symmetric structure is explored. Decentralised control of singular large scale systems is also reviewed in this paper

Time-Varying Gain Differentiator: A Mobile Hydraulic System Case Study

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Dual layer barrier functions based adaptive higher order sliding mode control

International audienceThis article presents an adaptive discontinuous higher ordersliding mode control (HOSMC) strategy for a disturbed chain ofintegrators of order <i&gtn</i&gt. This strategy employs a barrierfunction-based dual layer adaptation and it ensures the convergenceof the sliding variable and its (<i&gtn</i&gt − 1) first derivatives tozero without requiring any information on the bounds of thedisturbances or their derivatives. It consists in applying abarrier function-based adaptive super-twisting methodologycompensating Lipschitz disturbances with some error, and a growinggain-based adaptive HOSMC which just needs to counteract thiserror. Real-time simulation platform is used to test the efficacyof the proposed strategy to control a linear induction motorconsidering dynamic end effects

Dual layer barrier functions based adaptive higher order sliding mode control

International audienceThis article presents an adaptive discontinuous higher ordersliding mode control (HOSMC) strategy for a disturbed chain ofintegrators of order <i&gtn</i&gt. This strategy employs a barrierfunction-based dual layer adaptation and it ensures the convergenceof the sliding variable and its (<i&gtn</i&gt − 1) first derivatives tozero without requiring any information on the bounds of thedisturbances or their derivatives. It consists in applying abarrier function-based adaptive super-twisting methodologycompensating Lipschitz disturbances with some error, and a growinggain-based adaptive HOSMC which just needs to counteract thiserror. Real-time simulation platform is used to test the efficacyof the proposed strategy to control a linear induction motorconsidering dynamic end effects

Robust orbital stabilization: A Floquet theory–based approach

The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC) methodology. The main contribution of the article is to provide a constructive procedure for designing the time-invariant switching function used in the SMC synthesis. More specifically, its zero-level set (the sliding manifold) is designed using a real Floquet–Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a transverse linearization. This ensures asymptotic stability of the periodic orbit when the system is confined to the sliding manifold, despite any system uncertainties and external disturbances satisfying a matching condition. The challenging task of oscillation control of the underactuated cart–pendulum system subject to both matched- and unmatched disturbances/uncertainties demonstrates the efficacy of the proposed scheme