Control of the Continuum Model of a Large Flexible Space Structure

Aerospace ◽  
2006 ◽  
Author(s):  
Armaghan Salehian ◽  
T. Michael Seigler ◽  
Daniel J. Inman
Keyword(s):  
Continuum Model ◽  
Vibration Suppression ◽  
Space Structure ◽  
Truss Structure ◽  
Distributed Parameter ◽  
Beam Model ◽  
Control Force ◽  
Linear Quadratic ◽  
Distributed Parameter Model ◽  
Lqr Problem

An analytical approach is presented here to develop a continuum model of a space radar antenna and the truss structure for the purpose of the control and vibration suppression. Kinetic and potential energy expressions are given for the equivalent homogenized 1-D model. Hamilton's principle is applied to find the governing partial differential equations for this structure. The equations for bending are similar to an extended Timoshenko beam model. A Linear, Quadratic, Regulator (LQR) problem is solved to find the optimal solution for feedback control design of the distributed parameter model. The control force designed this way is applied to a Finite Element Model (FEM) of the truss structure for the purpose of validation. Results from the FEM are shown to be in good agreement with the distributed parameter model.

scholarly journals An adaptive LQR controller based on PSO and maximum predominant frequency approach for semi-active control scheme using MR damper

2018 ◽  
Vol 19 (1) ◽  
pp. 109
Author(s):  
Gaurav Kumar ◽  
Ashok Kumar ◽  
Ravi S. Jakka
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Mr Damper ◽  
Control Force ◽  
Linear Quadratic ◽  
Swarm Optimization ◽  
Predominant Period ◽  
Weighting Matrix ◽  
Lqr Problem ◽  
Lqr Controller

In the linear quadratic regulator (LQR) problem, the generation of control force depends on the components of the control weighting matrix R. The value of R is determined while designing the controller and remains the same later. Amid a seismic event, the responses of the structure may change depending the quasi-resonance occurring between the structure and the earthquake signal. In this situation, it is essential to update the value of R for conventional LQR controller to get optimum control force to mitigate the vibrations due to the earthquake. Further, the constant value of the weighting matrix R leads to the wastage of the resources using larger force unnecessarily where the structural responses are smaller. Therefore, in the quest of utilizing the resources wisely and to determine the optimized value of the control weighting matrix R for LQR controller in real time, a maximum predominant period τpmax and particle swarm optimization-based method is presented here. This method comprises of four different algorithms: particle swarm optimization (PSO), maximum predominant period approach τpmax to find the dominant frequency for each window, clipped control algorithm (CO) and LQR controller. The modified Bouc-Wen phenomenological model is taken to recognize the nonlinearities in the MR damper. The assessment of the advised method is done on a three-story structure having a MR damper at ground floor subjected to three different near fault historical earthquake time histories. The outcomes are equated with those of simple conventional LQR. The results establish that the advised methodology is more effective than conventional LQR controllers in reducing inter-story drift, relative displacement, and acceleration response.

scholarly journals Convergence results for an averaged LQR problem with applications to reinforcement learning

2021 ◽  
Author(s):  
Andrea Pesare ◽  
Michele Palladino ◽  
Maurizio Falcone
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Current System ◽  
Numerical Test ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lqr Problem ◽  
Quadratic Optimal Control

AbstractIn this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution $$\pi $$ π on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience that the agent obtains while exploring the environment, approximating with increasing accuracy the underlying dynamics. Under these assumptions, we will show that the optimal control obtained by solving the “average” linear quadratic optimal control problem with respect to a certain $$\pi $$ π converges to the optimal control driven related to the linear quadratic optimal control problem governed by the actual, underlying dynamics. This approach is closely related to model-based reinforcement learning algorithms where prior and posterior probability distributions describing the knowledge on the uncertain system are recursively updated. In the last section, we will show a numerical test that confirms the theoretical results.

scholarly journals Modified LQG/LTR Control Methodology in Active Structural Control

2003 ◽  
Vol 22 (2) ◽  
pp. 97-108 ◽  
Author(s):  
Yan Sheng ◽  
Chao Wang ◽  
Ying Pan ◽  
Xinhua Zhang
Keyword(s):  
Structural Control ◽  
Signal To Noise Ratio ◽  
Open Loop ◽  
Control Force ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Control Approach ◽  
Active Structural Control ◽  
Loop Transfer Recovery ◽  
Control Methodology

This paper presents a new active structural control design methodology comparing the conventional linear-quadratic-Gaussian synthesis with a loop-transfer-recovery (LQG/LTR) control approach for structures subjected to ground excitations. It results in an open-loop stable controller. Also the closed-loop stability can be guaranteed. More importantly, the value of the controller's gain required for a given degree of LTR is orders of magnitude less than what is required in the conventional LQG/LTR approach. Additionally, for the same value of gain, the proposed controller achieves a much better degree of recovery than the LQG/LTR-based controller. Once this controller is obtained, the problems of control force saturation are either eliminated or at least dampened, and the controller band-width is reduced and consequently the control signal to noise ratio at the input point of the dynamic system is increased. Finally, numerical examples illustrate the above advantages.

scholarly journals Open-loop temperature control for a distributed parameter model of a pipe

2020 ◽  
Vol 53 (2) ◽  
pp. 7765-7770
Author(s):  
Simon Bachler ◽  
Jens Wurm ◽  
Frank Woittennek
Keyword(s):  
Temperature Control ◽  
Open Loop ◽  
Distributed Parameter ◽  
Distributed Parameter Model

Robustness of Natural Controls of Distributed-Parameter Systems

1996 ◽  
Vol 118 (1) ◽  
pp. 56-63 ◽  
Author(s):  
Jai Hyuk Hwang ◽  
Doo Man Kim ◽  
Kyoung Ho Lim
Keyword(s):  
Closed Loop ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Control Force ◽  
Spatial Discretization ◽  
Actual System ◽  
Discretization Errors

In this paper, the effect of parameter and spatial discretization errors on the closed-loop behavior of distributed-parameter systems is analyzed for natural controls. If the control force designed on the basis of the postulated system with the parameter and discretization errors is applied to control the actual system, the closed-loop performance of the actual system will be degraded depending on the degree of the errors. The extent of deviation of the closed-loop performance from the expected one is derived and evaluated using operator techniques. It has been found that the extent of the deviation is proportional to the magnitude of the parameter and discretization errors, and that the proportional coeffecient depends on the structures of the natural controls.

Active Vibration Absorption Using Delayed Resonator With Relative Position Measurement

1995 ◽  
Author(s):  
Nejat Olgac ◽  
Martin Hosek
Keyword(s):  
Relative Position ◽  
Primary Structure ◽  
Vibration Suppression ◽  
Control Force ◽  
Range Analysis ◽  
Position Measurement ◽  
Harmonic Force ◽  
Stability Range ◽  
Vibration Absorption ◽  
Active Vibration

Abstract A novel active vibration absorption technique, the Delayed Resonator, has been introduced recently as a unique way of suppressing undesired oscillations. It suggests a control force on a mass-spring-damper absorber in the form of a proportional position feedback with a time delay. Its strengths consist of extremely simple implementation of the control algorithm, total vibration suppression of the primary structure against a harmonic force excitation and full effectiveness of the absorber in a semi-infinite range of disturbance frequency, achieved by real-time tuning. All this development work was done using the absolute displacements of the absorber in the feedback. These displacement measurements may be difficult to obtain and for some applications impossible. This paper deals with a substitute and easier measurement: the relative motion of the absorber with respect to the primary structure. Theoretical foundations for the Delayed Resonator (DR) are briefly recapitulated and its implementation on a single-degree-of-freedom primary structure disturbed by a harmonic force is introduced utilizing both absolute and relative position measurement of absorber mass. Methods for stability range analysis and transient behavior are presented. Properties acquired for the same system with these two different feedback are compared. Relative position measurement case is found to be more advantageous in most applications of the Delayed Resonator method.

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