Reduced order LQG control design for port Hamiltonian systems

Wu, Yongxin; Hamroun, Boussad; Gorrec, Yann Le; Maschke, Bernhard

doi:10.1016/j.automatica.2018.05.003

Cited by 21 publications

(19 citation statements)

References 13 publications

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“…There are many methods available of calculating and minimizing the expected cost E[J]. The implementation of a LQG control design method [23] to linearized port Hamiltonian system defined by (6) to derive the dynamic observer based controller Figure 5. Where the state of the controller x represents the estimation of the state x of the system, the feedback gains are:…”

Section: Lqg: Linear Quadratic Gaussianmentioning

confidence: 99%

An implementation of optimal control methods (LQI, LQG, LTR) for geostationary satellite attitude control

Djaballah¹,

Mohammed²,

Boughanmi³

2019

IJECE

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This paper investigates a new strategy for geostationary satellite attitude control using Linear Quadratic Gaussian (LQG), Loop Transfer Recovery (LTR), and Linear Quadratic Integral (LQI) control techniques. The sub-system satellite attitude determination and control of a geostationary satellite in the presence of external disturbances, the dynamic model of sub-satellite motion is firstly established by Euler equations. During the flight mission at 35000 Km attitude, the stability characteristics of attitude motion are analyzed with a large margin error of pointing, then a height performance-order LQI, LQG and LTR attitude controller are proposed to achieve stable control of the sub-satellite attitude, which dynamic model is linearized by using feedback linearization method. Finally, validity of the LTR order controller and the advantages over an integer order controller are examined by numerical simulation. Comparing with the corresponding integer order controller (LQI, LQG), numerical simulation results indicate that the proposed sub-satellite attitude controller based on LTR order can not only stabilize the sub-satellite attitude, but also respond faster with smaller overshoot.

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Section: Lqg: Linear Quadratic Gaussianmentioning

confidence: 99%

An implementation of optimal control methods (LQI, LQG, LTR) for geostationary satellite attitude control

Djaballah¹,

Mohammed²,

Boughanmi³

2019

IJECE

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“…It is impossible to find the approximated sub variable space by only considering the open loop behavior of the system. As a consequence, in order to find an appropriate approximation scheme, the authors in [12,13] have combined the approximation problem with the LQG control design problem for finite-dimensional port-Hamiltonian systems. Furthermpre, the approach has been generalized to the infinitedimensional port-Hamiltonian systems in [14].…”

Section: Figure 1: Silicon Made Micro-grippersmentioning

confidence: 99%

“…In order to preserve the passivity and the Hamiltonian structure in the closed loop system using the LQG controller, we shall consider an Hamiltonian structure preserving LQG control design method as follow: Theorem 3. [13] Denote the LQG Gramians P f , solution of the filter Riccati equation (23) and P c , solution of the control Riccati equation (26). Consider the LQG problem with the following relation between the covariance matrix R w and the weighting matrixR…”

Section: Control By Interconnection With Lqg Control and Reduced Ordementioning

confidence: 99%

LQG control for flexible micro-grippers with additional integral action

Ramírez

Gorrec

2019

2019 Chinese Control Conference (CCC)

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This paper deals with the stabilizing control design for a class of micro-grippers for DNA manipulation using boundary controlled infinite-dimensional port-Hamiltonian systems. In practical applications, the controllers are implemented as finitedimensional systems actuating at the boundaries of an infinite-dimensional system. The design of the finite-dimensional controllers is still a challenge, especially for hyperbolic PDEs. For this purpose, the LQG balancing reduction method is suitable for the reduced order control design since it considers the closed loop behavior in the reduction procedure. This paper presents the application of this recently proposed method combined with integral action in order to improve the robustness of the closed-loop system. It is shown by means of simulation that the addition of integral action effectively rejects constant perturbations while assuring global closed-loop stability.

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“…Second, the late lumping approach consists in designing the control law on the infinite dimensional system or on a high order approximation of the system and then in proceeding to the reduction of the controller. This closed-loop reduction/control design method has been developed using port Hamiltonian formulations for large scale finite dimensional systems in [2] but has been hardly considered in the infinite dimensional case. More precisely in [2] LQG control, balanced realization and structure preserving reduction are combined for the efficient design of reduced order controllers for large scale systems.…”

Section: Introductionmentioning

confidence: 99%

Reduced Order LQG Control Design for Infinite Dimensional Port Hamiltonian Systems

Hamroun

Gorrec

et al. 2021

IEEE Trans. Automat. Contr.

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This paper proposes a method that combines LQG control design and structure preserving model reduction for the reduced order control of Infinite Dimensional Port Hamiltonian Systems (IDPHS). For that purpose the weighting operators used in LQG control design are chosen such that the resulting dynamic controller is passive and the closed-loop system equivalent to control by interconnection. The method of Petrov-Galerkin is then used to approximate the balanced realization of the IDPHS by a finite dimensional port Hamiltonian system and to provide the associated reduced order LQG controller. The main advantages of the proposed method are that, first, both control and reduction are driven by closed-loop performances and that, second, due to the passivity properties of the controller the closed-loop stability is guaranteed when the finite dimensional controller is applied to the infinite dimensional system.

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Reduced order LQG control design for port Hamiltonian systems

Cited by 21 publications

References 13 publications

An implementation of optimal control methods (LQI, LQG, LTR) for geostationary satellite attitude control

An implementation of optimal control methods (LQI, LQG, LTR) for geostationary satellite attitude control

LQG control for flexible micro-grippers with additional integral action

Reduced Order LQG Control Design for Infinite Dimensional Port Hamiltonian Systems

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