LMI approach to digital redesign of linear time-invariant systems

Chang, Wook; Park, J.B.; Lee, H.J.; Joo, Young Hoon

doi:10.1049/ip-cta:20020430

Cited by 54 publications

(12 citation statements)

References 8 publications

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“…See, for example, Sunkel, Shieh, and Zhang (1991), Shieh, Wang, and Zheng (1997), Chang, Park, Lee, and Joo (2002), Lee, Park, and Joo (2003), Tsai, Tsai, and Guo (2007), respectively, and references therein. By comparison, relatively few related results seem to be tractable for nonlinear systems (Guo, Shieh, Chen, and Lin 2000;Chang, Park, and Joo 2003;Nesˇic´and Gru¨ne 2005Gru¨ne, Worthmann, and Nesˇic´2008;Lee, Shieh, and Kim 2008).…”

Section: Introductionmentioning

confidence: 98%

Controlling linear systems with nonlinear perturbations under sampled-data output feedback: digital redesign approach

Kim¹,

Lee²

2010

International Journal of Control

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This article develops a digital redesign (DR) technique for sampled-data observer-based output-feedback control of a continuous-time linear system with nonlinear perturbation. It is assumed that the nonlinear perturbation is a locally Lipschitz function. To deal with the discrete-time modelling error in nonlinear systems, as opposed to the previous approach, the DR problem is configured as a stabilisation one for error dynamics between the closedloop system of nominal linear model under an analogue state-feedback controller and that of the linear system with the nonlinear perturbation under a sampled-data output-feedback controller. A constructive DR condition is formulated in the format of linear matrix inequalities. The stability of the actual sampled-data control system is guaranteed within the DR procedure. The effectiveness of the proposed DR methodology is demonstrated through a numerical simulation.

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Section: Introductionmentioning

confidence: 98%

Controlling linear systems with nonlinear perturbations under sampled-data output feedback: digital redesign approach

Kim¹,

Lee²

2010

International Journal of Control

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“…Such a technique of designing a discrete control law is known as digital redesign [8], [9]. The resultant discretetime system with digitally redesigned controller would have a better performance as compared to the one obtained by the application of continuous-time sliding mode control to the plant under sampling.…”

Section: Introductionmentioning

confidence: 99%

Digital Redesign of Sliding Mode Control Algorithms Using Saturation Function: State and Multirate Output Feedback Approach

Abera

Bandyopadhyay

Janardhanan

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Though continuous-time sliding mode control has a variety of desirable properties, its discrete-time counterpart does not guarantee the same performance. This is due to the fact that most of the discrete-time sliding mode control algorithms are based on reaching laws that are only approximations of continuous-time reaching laws and thus may not give a performance close to continuous-time sliding mode control. This paper presents a method for digital redesign of sliding mode control using saturation function based on state feedback. The method is extended to multirate output feedback case. It is shown that performance of the proposed controller is close to the performance of a pre-designed continuous-time sliding mode control algorithm. The method is illustrated by a numerical example.

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“…This was due to the nonsymmetry of matrix for the controller synthesis, condition that was necessary to the LMI development when the controller synthesis matrix was = −1 . The solution found was using the idea of the optimization procedure for redesign presented in [15]. Thus, in [8] the new optimization method adequacy was proposed, with the minimization of a scalar obeying the relation < with the Lyapunov function, to the new relaxed parameters through the following theorem.…”

Section: Optimization Of Norm Usingmentioning

confidence: 99%

Less Conservative Optimal Robust Control of a 3-DOF Helicopter

Buzachero

Assunção

Teixeira

et al. 2015

Journal of Control Science and Engineering

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This work proposes an improved technique for design and optimization of robust controllers norm for uncertain linear systems, with state feedback, including the possibility of time-varying the uncertainty. The synthesis techniques used are based on LMIs (linear matrix inequalities) formulated on the basis of Lyapunov's stability theory, using Finsler's lemma. The design has used the addition of the decay rate restriction, including a parameter in the LMIs, responsible for decreasing the settling time of the feedback system. Qualitative and quantitative comparisons were made between methods of synthesis and optimization of the robust controllers norm, seeking alternatives with lower cost and better performance that meet the design restrictions. A practical application illustrates the efficiency of the proposed method with a failure purposely inserted in the system.

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LMI approach to digital redesign of linear time-invariant systems

Cited by 54 publications

References 8 publications

Controlling linear systems with nonlinear perturbations under sampled-data output feedback: digital redesign approach

Controlling linear systems with nonlinear perturbations under sampled-data output feedback: digital redesign approach

Digital Redesign of Sliding Mode Control Algorithms Using Saturation Function: State and Multirate Output Feedback Approach

Less Conservative Optimal Robust Control of a 3-DOF Helicopter

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