Stabilizability and Disturbance Rejection with State‐Derivative Feedback

Anais Do 14º Simpósio Brasileiro De Automação Inteligente

et al. 2019

Self Cite

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

Self Cite

“…Remark 2.1: The invertibility of c is a standard assumption in the state derivative feedback literature, as can be seen for instance in Abdelaziz and Valášek (2004), Assunção et al (2007), Duan et al (2005), and Moreira et al (2010).…”

Section: Preliminaries and Notationmentioning

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.

“…Derivative feedback may be useful in the control of real plants in which the state-derivative signals are easier to obtain than the state signal. For instance, in the active automotive suspension system (Reithmeier and Leitmann 2003;da Silva et al 2011da Silva et al , 2013Assunção et al 2007;Yazici and Sever 2017b), in the mass-spring system with damping (Moreira et al 2010), in the vibration control of an offshore steel jacket platform (Yazici and Sever 2017a), in the design of controllers for mechanical systems and vibration damping systems Valásek 2004, 2005;Cardim et al 2007;da Silva et al 2012;Rossi et al 2018), in the control of vibrations in cable-suspended bridges (Duan et al 2005), in the optimization problem for a four-wheel-drive front-wheel-steerable vehicle (Fallah et al 2013) and in the attitude control system of refueling spacecraft in orbit (Abdelaziz 2017).…”

Section: Introductionmentioning

confidence: 99%

Derivative Feedback Control for a Class of Uncertain Linear Systems Subject to Actuator Saturation

Wolmuth

Alves

J Control Autom Electr Syst

et al. 2019

Self Cite

This manuscript considers a class of linear systems with time-invariant uncertainties, where only the derivative of the state vector is considered for feedback. In this scenario, the proposed strategy uses auxiliary dynamics, whose state is accessible for feedback, to control the original plant. It is proposed a design procedure by means of linear matrix inequalities, adding an auxiliary dynamics and subject to actuator saturation. If the conditions are feasible, they assure that the equilibrium point of the closed-loop system is locally asymptotically stable, for all initial conditions in an ellipsoidal region, which is within a given region defined for the plant and the new dynamics. Although the proposed design includes an auxiliary dynamics, it ensures the stability and decay rate proprieties for the original plant. Simulations examples illustrate the effectiveness of the proposed approach.