General Integral Control Design via Singular Perturbation Technique

Liu, Baishun; Luo, Xiangqian; Li, Jianhui

doi:10.4236/ijmnta.2014.34019

Cited by 5 publications

(5 citation statements)

References 9 publications

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“…For general integral control design, there were various design methods, such as general integral control design based on linear system theory, sliding mode technique, Feedback linearization technique and Singular perturbation technique and so on, presented by [2]- [5], respectively. In addition, general concave integral control [6], general convex integral control [7], constructive general bounded integral control [8] and the generalization of the integrator and integral control action [9] were all developed by Lyapunov method.…”

Section: Introductionmentioning

confidence: 99%

Equal Ratio Gain Technique and Its Application in Linear General Integral Control

Liu¹

2015

IJMNTA

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In conjunction with linear general integral control, this paper proposes a fire-new control design technique, named Equal ratio gain technique, and then develops two kinds of control design methods, that is, Decomposition and Synthetic methods, for a class of uncertain nonlinear system. By Routh's stability criterion, we demonstrate that a canonical system matrix can be designed to be always Hurwitz as any row controller gains, or controller and its integrator gains increase with the same ratio. By solving Lyapunov equation, we demonstrate that as any row controller gains, or controller and its integrator gains of a canonical system matrix tend to infinity with the same ratio, if it is always Hurwitz, and then the same row solutions of Lyapunov equation all tend to zero. By Equal ratio gain technique and Lyapunov method, theorems to ensure semi-globally asymptotic stability are established in terms of some bounded information. Moreover, the striking robustness of linear general integral control and PID control is clearly illustrated by Equal ratio gain technique. Theoretical analysis, design example and simulation results showed that Equal ratio gain technique is a powerful tool to solve the control design problem of uncertain nonlinear system.

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Section: Introductionmentioning

confidence: 99%

Equal Ratio Gain Technique and Its Application in Linear General Integral Control

Liu¹

2015

IJMNTA

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“…For general integral control, there were various design techniques, such as Linearization technique [2], Sliding mode technique [3], Feedback linearization technique [4], Singular perturbation technique [5], Perturbation technique [6]- [9] and Equal ratio gain technique [10] [11]. Although Singular perturbation and Equal ratio gain techniques can all effectively deal with the uncertain nonlinear system, respectively, the results could be too conservative, especially for Singular perturbation technique.…”

Section: Introductionmentioning

confidence: 99%

Power Ratio Gain Technique and General Integral Control

Liu¹

2015

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In conjunction with general integral control, and synthesizing Singular perturbation and Equal ratio gain techniques, this paper proposes a new control design technique, named Power ratio gain technique, and then by Lyapunov method, theorem to ensure regionally as well as semi-globally asymptotic stability is established in terms of some bounded information. The highlight point is that it not only inherits all the essences of Singular perturbation and Equal ratio gain techniques but also makes up for their shortcomings, and then the conservatism of control input can be improved by compromising the Power ratio coefficients. Theoretical analysis, design example and simulation results show that Power ratio gain technique is a simple, practical and powerful tool to deal with the uncertain nonlinear system.

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“…For general integral control design, there were various design methods, such as general integral control design based on linear system theory, sliding mode technique, feedback linearization technique and singular perturbation technique and so on, which were presented by [2]- [5], respectively. In addition, general concave integral control [6], general convex integral control [7], constructive general bounded integral control [8] and the generalization of the integrator and integral control action [9] were all developed by using Lyapunov method and resorting to a known stable control law.…”

Section: Introductionmentioning

confidence: 99%

Output Feedback Nonlinear General Integral Control

Liu¹

2015

IJMNTA

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This paper proposes an output feedback nonlinear general integral controller for a class of uncertain nonlinear system. By solving Lyapunov equation, we demonstrate a new proposition on Equal ratio gain technique. By using Equal ratio gain technique, Singular perturbation technique and Lyapunov method, theorem to ensure regionally as well as semi-globally exponential stability is established in terms of some bounded information. Moreover, a real time method to evaluate the ratio coefficients of controller and observer are proposed such that their values can be chosen moderately. Theoretical analysis and simulation results show that not only output feedback nonlinear general integral control has the striking robustness but also the organic combination of Equal ratio gain technique and Singular perturbation technique constitutes a powerful tool to solve the output feedback control design problem of dynamics with the nonlinear and uncertain actions.

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General Integral Control Design via Singular Perturbation Technique

Cited by 5 publications

References 9 publications

Equal Ratio Gain Technique and Its Application in Linear General Integral Control

Equal Ratio Gain Technique and Its Application in Linear General Integral Control

Power Ratio Gain Technique and General Integral Control

Output Feedback Nonlinear General Integral Control

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