Direct discrete time design of robust state derivative feedback control laws

Abstract

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.

Robust state derivative feedback LMI-based designs for discretized systems.

“…Assumption 1. The control is updated immediately after the state derivativeẋ(kT (α 2 )) is measured at each sampling time (Rossi et al (2018)).…”

“…Accelerometers are one of the most used sensors either in field or in laboratory scale experiments. It turns out that the displacement estimation from this sensors tends to be biased (Rossi et al (2018) and references). Therefore, in engineering applications instead of using a state feedback control law based on displacements and velocities, it may be more convenient to use a state derivative feedback control law.…”

“…Regarding contributions concerning state derivative feedback, it is important to highlight that most research efforts have been devoted to the design of continuous-time controllers (Duan et al (2005), Faria et al (2009), Tseng and Hsieh (2013), Beteto et al (2018), among others). On the other hand, several methods treat the problem of discretization of uncertain systems through of the first order Taylor series expansion to circumvent the difficulty of dealing with the exponential of an uncertain matrix (Cardim et al (2009), Rossi et al (2018)). To the author's knowledge, in context of state derivative feedback, there exists a lack of methods that allows to handle systematic treatment of the high order terms in the discretization procedure, specially when the sampling period is not sufficiently small such that the quadratic and higher-order terms in the Taylor series expansion can not be neglected in the uncertain representation.…”

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

“…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).…”

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

“…Projetos de controladores para sistemas mecânicos, incluindo o controle de vibrações, utilizando realimentacão derivativa podem ser encontrados em Abdelaziz and Valásek (2004), Abdelaziz and Valásek (2005), Cardim et al (2007) e Rossi et al (2018).…”