Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State‐Derivative Feedback

Anais Do 14º Simpósio Brasileiro De Automação Inteligente

et al. 2019

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This paper considers a class of linear systems with time-invariant uncertainties, subject to actuator saturation, where only the derivative of the state vector is considered for feedback. In this scenario, the presented strategy uses an auxiliary dynamics, whose state is accessible for feedback, to control the original plant. It is proposed a switched control design procedure by means of linear matrix inequalities. If the conditions are feasible, they assure that the origin of the state space of the closed-loop system is locally asymptotically stable, for all initial for all initial conditions in an ellipsoidal region, which is within a given region defined for this new dynamics. Although the proposed design includes an auxiliary dynamics, it ensures the stability and decay rate proprieties for the original plant. A simulation example illustrates the effectiveness of the proposed approach. Resumo: Neste artigo considera-se uma classe de sistemas lineares com incertezas invariantes no tempo, sujeitoà saturação do atuador, onde apenas a derivada do vetor de estadoé considerada para realimentação. Neste cenário, a estratégia proposta utiliza uma dinâmica auxiliar, cujo estado está disponível para realimentação, para controlar a planta original. Propõe-se um procedimento de projeto de controle chaveado por meio de desigualdades matriciais lineares. Se as condições forem satisfeitas, elas asseguram que a origem do espaço de estados do sistema em malha fechadaé localmente assintoticamente estável, para todas as condições iniciais em uma região elipsoidal, que está dentro de uma determinada região definida para essa nova dinâmica. Embora o projeto proposto inclua uma dinâmica auxiliar, ele garante as propriedades de estabilidade e taxa de decaimento para a planta original. Um exemplo de simulação ilustra a eficácia da abordagem proposta.

Section: Controle Derivativo Com Saturação Do Atuadorunclassified

Controle Chaveado de Sistemas Lineares Incertos Sujeitos à Saturação no Atuador Usando Realimentação Derivativa

Silva¹,

Alves

Anais Do 14º Simpósio Brasileiro De Automação Inteligente

et al. 2019

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“…Applying a similar strategy, but incorporating a scalar value > 0 into the inequalities, one can obtain less conservative solutions, obviously with an adequate value of [5].…”

Section: Controller Design With Stability Condition Decay Rate and mentioning

confidence: 99%

“…Figure 10 represents the transitory response considering the methodology proposed in [5]. The system was subject to the same conditions showed in the practical implementation.…”

Section: Derivate State Feedback Using D-stability Constraintsmentioning

confidence: 99%

“…In [4], a geometric theory for dynamical systems with state derivative feedback for singular systems was shown. In [5], the theory was presented to the design of a less conservative controller for linear systems with polytopic uncertainties via derivative feedback ensuring the stability and robustness of the system. An approach to the stability and robustness with derivative feedback, including the weakness, can be seen in [6].…”

Section: Introductionmentioning

confidence: 99%

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Design of Gain Scheduling Control Using State Derivative Feedback

Llins

Assunção

Mathematical Problems in Engineering

et al. 2017

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In recent years, the study of systems subject to time-varying parameters has awakened the interest of many researchers. The gain scheduling control strategy guarantees a good performance for systems of this type and also is considered as the simplest to deal with problems of this nature. Moreover, the class of systems in which the state derivative signals are easier to obtain than the state signals, such as in the control for reducing vibrations in a mechanical system, has gained an important hole in control theory. Considering those ideas, we propose sufficient conditions via LMI for designing a gain scheduling controller using state derivative feedback. The D-stability methodology was used for improving the performance of the transitory response. Practical implementation in an active suspension system and comparison with other methods validates the efficiency of the proposed strategy.

“…Subsequent extensions of this technique were concerned with D-stability specifications (Faria et al, 2009) and generalisations to descriptor systems . Less conservative LMI conditions were developed in Silva, Assunção, Teixeira, Faria, and Buzachero (2011), Silva, Assunção, Teixeira, and Buzachero (2012) by using parameter-dependent Lyapunov functions. LMI formulations for time delay systems have also been reported (Amri, Soudani, & Benrejeb, 2011;Jing, Shen, Dimirovski, & Jiang, 2009).…”

Section: Introductionmentioning

confidence: 99%

Direct discrete time design of robust state derivative feedback control laws

Rossi

Galvão

International Journal of Control

et al. 2016

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This paper is concerned with the problem of designing robust state derivative feedback control laws in discrete time. The main contribution consists of a method for recasting a continuous time state space model in the form of a discrete time model formulated in terms of the state derivative. Uncertain input delays and parametric uncertainties in polytopic form can be propagated from the original state space representation to the resulting state derivative model. Therefore, robust control techniques originally developed for discrete time state space models can be directly employed to design the state derivative feedback law. Three computational examples are presented for illustration. The first example highlights the importance of accounting for the effect of sampling in the design procedure. More specifically, a linear quadratic regulation problem involving the state derivative is addressed. The second example involves the design of a robust predictive controller in the presence of input constraints and uncertain time delay. Finally, the third example is concerned with robust pole placement in the presence of parametric uncertainty.