Design of an optimal state derivative feedback LQR controller and its application to an offshore steel jacket platform

Abstract

This paper concerns with the optimal state derivative feedback LQR controller design for vibration control of an offshore steel jacket platform having active tuned mass damper against the wave induced disturbances. Considering that the state derivative signals such as acceleration and velocity are easier to measure rather than the state variables such as displacement, state derivative feedback control strategy is proposed to obtain practically applicable and easily realizable synthesis method. On the basis of convex optimization approach, state derivative feedback LQR controller design is formulated in Linear Matrix Inequalities (LMIs) form to get an optimal feasible solution set. Finally, an offshore steel jacket platform subject to nonlinear self excited wave force is used to illustrate the effectiveness of the proposed approach through simulations. The results show that proposed state derivative LQR controller is very effective in reducing vibration amplitudes of each floor of modeled offshore steel jacket platform and achieves compitable control performance to classical LQR controller design.

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

“…A realimentação derivativa pode serútil no estudo de problemas práticos nos quais a derivada do vetor de estadó e mais fácil de se medir do que o vetor de estado, por exemplo, no sistema de suspensão ativa de automóveis (Reithmeier and Leitmann, 2003;da Silva et al, 2013;Assunção et al, 2007). Em Yazici and Sever (2017b)é proposto um projeto de controladores com realimentação derivativa de saída para o controle ativo de vibração de um sistema de suspensão de veículos; um controle de vibrações em pontes suspensas por cabos com realimentação derivativaé encontrado em Duan et al (2005); um projeto de controlador LQR de realimentação derivativa para um controle de vibração de uma plataforma offshore tipo jaqueta de açoé proposto em Yazici and Sever (2017a).…”

Gain scheduling LQI controller design for LPV descriptor systems and motion control of two-link flexible joint robot manipulator

“…Many researchers have recently considered the problem of robust controller design on linear parameter varying or linear time invariant systems in the regular statespace form such as in [1][2][3][4][5][6][7][8][9][10][11][12][13][14], where the systems are common linear parameter varying (LPV) systems. Unlike the regular state-space forms, descriptor systems enable an expression which includes algebraic conditions on physical factors.…”