Chattering in Variable Structure Feedback Systems

Kwatny, Harry G.; Siu, Theo

doi:10.1016/s1474-6670(17)55104-6

Cited by 14 publications

(7 citation statements)

References 10 publications

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“…The required information for calculating the control 2, 4.4.5, 4.4.8, 4.4.9, and 4.4.10. Besides, as presented in many publications [Utkin 1978;Kwatny and Siu 1987;Bartolini 1989], the chattering that appears as a high-frequency oscillation at the vicinity of the desired manifold may be excited by unmodeled high-frequency dynamics of the system. The discontinuous controller was implemented for real-time control of the pendulum.…”

Section: Stabilization Of the Inverted Pendulummentioning

confidence: 99%

Sliding Mode Control of Pendulum Systems

2009

Sliding Mode Control in Electro-Mechanical Systems, Second Edition

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The design of sliding mode control for nonlinear multivariable systems has been extensively studied in many books and papers. The design procedure of such high-order nonlinear control systems may be complicated and varies from case to case. The objective of this chapter is to develop design methods for nonlinear mechanical systems governed by a set of second-order equations. The proposed approach assumes that the control systems can be transformed into a regular form (see Section 3.2), which enables decoupled control design. The control laws are illustrated for different inverted pendulum systems. Design MethodologyWhen controlling mechanical systems, we deal with a set of interconnected second-order nonlinear differential equations: = ( , , ). If the condition in Equation 4.1.6 holds, then z and z tend to zero. After z decays, y is found from the algebraic equation f 1 (0,y,0) = 0. Because the origin of the state space is the equilibrium point, f 1 (0,0,0) = 0, Downloaded by [Universite Laval (UNIVERSITE LAVAL PAVILLON JEAN CHARLES BONENFANT)] at 01:42 12 September 2016

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Section: Stabilization Of the Inverted Pendulummentioning

confidence: 99%

Sliding Mode Control of Pendulum Systems

2009

Sliding Mode Control in Electro-Mechanical Systems, Second Edition

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“…(2) time. The differential equation or reaching law of any sliding mode control algorithm should satisfy a finite time differential The first order finite-time differential equation can be of the form ± =-sig, (x) (5) The reaching law, in this case would be where, 0 < p <1. ur -sigp (or) (7) A second order finite-time differential equation is suggested as [12] and the control is directly computed from the reaching law (7) x =-sig' (x) -sign () (6) and would be of the form with a and /3 satisfying the constraints, 3 Since is has been assumed that or is a continuously differ-(2 -entiable function of x and sigrho (x) is continuous, it can Appropriate proofs for the finite time convergence of Eqns. be said from the control expression in (8) that the control is (5 and 6) can be found in [12].…”

Section: Fmentioning

confidence: 99%

“…constitutes a stable sub-manifold of the state space. A boundary layer based technique [5], [6], [7] was initially…”

mentioning

confidence: 99%

Relay-free Second Order Sliding Mode Control

Janardhanan

2006

2006 IEEE International Conference on Industrial Technology

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The paper presents an approach for achieving sec-the system is not abrupt and chattering is avoided. The control ond order sliding mode in continuous-time systems. The existing is so structured that finite reaching time is guaranteed. methods of second order sliding mode control are based on relayThe terminology "second order sliding mode" comes from control in the derivative of the input. Such a control, though the fact that using this technique, both the sliding function o continuous, is not smooth in close proximity of the sliding surface. and it that sl conuous funct i nbt The proposed control algorithm achieves second order sliding and its derivative & are continuous functions of time and both mode by using a smooth control signal which avoids the use of would become equivalently equal to zero after a finite amount a relay in the control. of time i.e., or C1. This is in contrast with the traditional or first order sliding mode control where &r is discontinuous. The aforementioned control strategy, though it guarantees I. INTRODUCTION smoothness in the system and avoids chattering, does not proSliding mode control[.], [2] is a control technique in which duce a control that is smooth (or continuously differentiable) * due to the discontinuity in it. Thus, the control u C C°. the closed loop system is rendered some desirable properties In theiscpaper,iwep o aTsimpe control aot to by confining the system to a pre-specified sub-manifold of the achieve seprosldn . mo e control syesithout state space by application of an appropriate control.Traditionally, sliding mode control methods have been de-the use of a relay in the control. Further, the proposed signed for systems of relative degree of one. Most of these algorithm guarantees a continuously differentiable or smooth control techniques are relay based techniques in which the control. The algorithm is illustrated for systems with relative degree of one or two with respect to the sliding function control switches between two structures based on the sign i.e, systems wherein u appears in the expression of & and of the sliding function[3], [4]. This type of control structure ' e' causes a serious problem during practical implementation. In practice, the actuators cannot switch at an infinite frequency along the sliding surface, as demanded by the theory of the relay based sliding mode control algorithms. This leads to Consider the n-th order system high frequency finite amplitude oscillations of the system f=() + g()u(1) representative point and the control signal, around the sliding surface. This phenomenon, termed as chattering, is undesirable g( ) > 0, Vx as it may excite unmodeled dynamics in the system and may and the sliding function o(X() with or being a continuously also lead to fatigue and actuator failure. differentiable function of x such that the sliding surface or = 0Many researchers have worked on a solution to this problem. constitutes a stable sub-manifold of the state space. A boundary layer based technique[5], [6], [7] was initiallyThe aim is to d...

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“…In [20], Young and Drakunov summarized two m ain approaches to reduce chattering. The first one is the use of continuous approximation in the boundary layer of the sliding manifold [24,26].…”

Section: P Ro B Lem S Ta Tem En Tmentioning

confidence: 99%

“…Chattering reduction has been studied by many researchers [22,23,24,25,20,26,12] for continuous tim e implementation. Slotine and Sastry proposed considering a static boundary layer in the vicinity of each discontinuity plane (s,-= 0) as a transition region in the state space [22].…”

mentioning

confidence: 99%

Implementation of variable structure control for sampled-data systems

Drakunov²,

Özgüner³

Robust Control via Variable Structure and Lyapunov Techniques

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Chattering in Variable Structure Feedback Systems

Cited by 14 publications

References 10 publications

Sliding Mode Control of Pendulum Systems

Sliding Mode Control of Pendulum Systems

Relay-free Second Order Sliding Mode Control

Implementation of variable structure control for sampled-data systems

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