Variable structure control of time-delay systems with a simulation study on stabilizing combustion in liquid propellant rocket motors

Zheng, Feng; Cheng, Ming; Gao, Wei-Bing

doi:10.1016/0005-1098(95)00012-l

Cited by 34 publications

(13 citation statements)

References 8 publications

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“…According to . -k s(t) a|s( -p(t) s(t)J1 +sT(t) (T2+K7) , xQt) [12], we can conclude that xi(t)|, i=1,2, n, are bounded a within [02+KT[12 , tr+a oncud. ta .…”

Section: V(t) = St(t)[-kjs(t)ja Sgns(t) -P(t)sgns(t) +(T2 +Ktl)f(xt)]mentioning

confidence: 92%

“…shows the responses of the switching function s(t) and the From [12], it can be concluded that limx(t) = 0.…”

Section: V(t) = St(t)[-kjs(t)ja Sgns(t) -P(t)sgns(t) +(T2 +Ktl)f(xt)]mentioning

confidence: 97%

“…F 0.1 0.037 the stability of (20), that is limTz(t) =limz(t) =0 If In order to shorten the reaching time and attenuate the according to [12], we can obtain chattering, we select k = 30, = 0.5. Fig.1 shows the system control responses with the given initial conditions.…”

Section: V(t) = St(t)[-kjs(t)ja Sgns(t) -P(t)sgns(t) +(T2 +Ktl)f(xt)]mentioning

confidence: 99%

“…The second phase is to Substituting (12) into (lOa), the dynamics of the sliding design an appropriate control law so that the system state motionis describedby trajectories can be attracted to the designed sliding manifold in Proof: Using V(t) = (1/ 2)sT (t)s(t) as a Lyapunov function According to [11] we give the following sufficient candidate, then we have condition for unmatched case.…”

Section: Panghp123gl63commentioning

confidence: 99%

“…Considering Assumption 2, where A = AO + ehAAA, B =BO + ehABI. the fictitious optimal control law can be obtained as By applying the defined linear transformation, the original pl (t) (12) system (1) is transformed into an uncertain delay-free system 2(t) Q2l1A1 (1) described by (7). Both systems share the same poles and where the positive-definite symmetric matrix P is the provide the equivalent input/output mapping [2], so we can solution to the following Riccati equation study the behaviour of the transformed system (7) and then reflected back to original time-delay system (1).…”

Section: Panghp123gl63commentioning

confidence: 99%

See 4 more Smart Citations

Sliding Mode Control for Linear Uncertain Systems with Input and State Delays

Pang

Liu

Meng

2006

2006 IEEE International Conference on Information Acquisition

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The problem of designing sliding mode controllers investigated the feasibility of the sliding surface combined for a class of linear systems with uncertainties and both input with a predictor to compensate for the input delay of the and time state delays is investigated. A particular linear system. Robust integral sliding mode control for uncertain transformation is defined to transform the time-delay system into stochastic systems with time-varying delay was researched by a delay-free form first. Then, the sliding mode controller is Niu and Ho [9]. designed based on the transformed system. Optimal control The study of uncertain systems with either state-delay or theory is adopted to construct the optimal sliding manifold with a quadratic performance index minimized. The selected control nput-delay has been pad much attention in the past decade law can ensure the existence of the sliding mode and alleviate[7]-[1O]. However, with regard to the control of system chattering effectively in the sliding motion. About the featuring both state and input delays, only a few studies have uncertainties, the cases of matched condition and unmatched been reported in the literature. In this paper, based on SMC, a condition are studied respectively. Furthermore, a sufficient class of linear uncertain systems with both input delay and condition that guarantees the global asymptotic stability of the state delay are investigated. A novel systematic SMC system original system is derived. Finally, a numerical example is given design methodology is proposed. to illustrate the proposed approach.This paper is organized as follows. The next section describes the system that will be studied. In Section III a linear Index Terms -Sliding mode control, uncertain systems, timetransformation is defined to map the original system into a delay systems, optimal control. delay-free form. Section IV presents the design of the sliding I. INTRODUCTION mode controller in detail. The optimal sliding manifold design based on optimal control theory is presented in Section A. Time delay is quite common in various engineering systemsThe design of the control law that consists of a continuous such as chemical processes, hydraulic systems, biological control action and a discontinuous control action is carried out systems and economic systems. Compared to the systems in Section B. A sufficient condition for the asymptotic without delay, the presence of delay makes it more difficult to stability of the original system with the proposed control law achieve the satisfactory performance of the systems. Another is given in Section C. Section V performs a simulation major problem in real-world systems is the robust control to example to verify the effectiveness of the proposed scheme. minimize the effects of uncertainties. In recent years, there is II. PROBLEM STATEMENTS an increasing interest in the development of robust control systems for processes having time delays and uncertainties.Consider the uncertain retarded system described by Many approaches have be...

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“…According to . -k s(t) a|s( -p(t) s(t)J1 +sT(t) (T2+K7) , xQt) [12], we can conclude that xi(t)|, i=1,2, n, are bounded a within [02+KT[12 , tr+a oncud. ta .…”

Section: V(t) = St(t)[-kjs(t)ja Sgns(t) -P(t)sgns(t) +(T2 +Ktl)f(xt)]mentioning

confidence: 92%

“…shows the responses of the switching function s(t) and the From [12], it can be concluded that limx(t) = 0.…”

Section: V(t) = St(t)[-kjs(t)ja Sgns(t) -P(t)sgns(t) +(T2 +Ktl)f(xt)]mentioning

confidence: 97%

Section: V(t) = St(t)[-kjs(t)ja Sgns(t) -P(t)sgns(t) +(T2 +Ktl)f(xt)]mentioning

confidence: 99%

Section: Panghp123gl63commentioning

confidence: 99%

Section: Panghp123gl63commentioning

confidence: 99%

See 3 more Smart Citations

Sliding Mode Control for Linear Uncertain Systems with Input and State Delays

Pang

Liu

Meng

2006

2006 IEEE International Conference on Information Acquisition

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Compensation of time-delay for control of civil engineering structures

Agrawal

Yang

2000

Earthquake Engng. Struct. Dyn.

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SUMMARYTime-delay is an important issue in structural control. Applications of unsynchronized control forces due to time-delay may result in a degradation of the control performance and it may even render the controlled structures to be unstable. In this paper, a state-of-the-art review for available methods of time-delay compensation is presented. Then, "ve methods for the compensation of "xed time-delay are presented and investigated for active control of civil engineering structures. These include the recursive response method, state-augmented compensation method, controllability based stabilization method, the Smith predictor method and the Pade approximation method, all are applicable to any control algorithm to be used for controlled design. Numerical simulations have been conducted for MDOF building models equipped with an active control system to demonstrate the stability and control performance of these time-delay compensation methods. Finally, the stability and performance of the phase shift method, that is well-known in civil engineering applications, have also been critically evaluated through numerical simulations.

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Reliable memory feedback design for a class of non‐linear time‐delay systems

Yue

Lam

2003

Intl J Robust & Nonlinear

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SUMMARYThis paper is concerned with the robust controller design of uncertain time-delay systems with unknown nonlinearity and actuators failures. New methods for designing stabilizing controllers and reliable controllers are proposed. The stability criteria of the closed-loop system, which are dependent on the magnitudes of the delay and its derivative, are derived in the form of linear matrix inequalities. Numerical and simulation results are provided to demonstrate the effectiveness of the proposed results, as well as the reduction of conservativeness when compared with existing ones.

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Variable structure control of time-delay systems with a simulation study on stabilizing combustion in liquid propellant rocket motors

Cited by 34 publications

References 8 publications

Sliding Mode Control for Linear Uncertain Systems with Input and State Delays

Sliding Mode Control for Linear Uncertain Systems with Input and State Delays

Compensation of time-delay for control of civil engineering structures

Reliable memory feedback design for a class of non‐linear time‐delay systems

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