Optimal Vibration Feedback Control of an Euler-Bernoulli Beam: Toward Realization of the Active Sink Method

1999 ◽  
Vol 121 (2) ◽  
pp. 174-182 ◽  
Author(s):  
N. Tanaka ◽  
Y. Kikushima
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Control Point ◽  
Control Law ◽  
Bernoulli Beam ◽  
Control Laws ◽  
Reflected Waves ◽  
Feedback Control Systems ◽  
Active Wave ◽  
Euler Bernoulli Beam

This paper discusses the optimal vibration feedback control of an Euler-Bernoulli beam from a viewpoint of active wave control making all structural modes inactive (more than suppressed). Using a transfer matrix method, the paper derives two kinds of optimal control laws termed “active sink” which inactivates all structural modes; one obtained by eliminating reflected waves and the other by transmitted waves at a control point. Moreover, the characteristic equation of the active sink system is derived, the fundamental properties being investigated. Towards the goal of implementing the optimal control law that is likely to be non-causal, a “classical” velocity feedback control law (Balas, 1979) widely used in a vibration control engineering is applied, revealing a substantial shortcoming. Introduction of a “classical” displacement feedback to the velocity is found to realize the optimal control law in a restricted frequency range. Finally, two kinds of stability verification for closed feedback control systems are presented for distributed parameter structures.

Passive optimal feedback control of an articulated flexible arm

2020 ◽  
pp. 107754632095676
Author(s):  
Raja Tebbikh ◽  
Hicham Tebbikh ◽  
Sihem Kechida
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Closed Loop ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Convolution Operators ◽  
High Frequencies ◽  
Zero Initial Condition ◽  
Flexible Arm ◽  
Euler Bernoulli Beam

This article deals with stabilization and optimal control of an articulated flexible arm by a passive approach. This approach is based on the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Due to the specific propagative properties of the beam, such controls involve long-memory, non-rational convolution operators. Diffusive realizations of these operators are introduced and used for elaborating an original and efficient wave-absorbing feedback control. The globally passive nature of the closed-loop system gives it the unconditional robustness property, even with the parameters uncertainties of the system. This is not the case in active control, where the system is unstable, because the energy of high frequencies is practically uncontrollable. Our contribution comes in the achievement of optimal control by the diffusion equation. The proposed approach is original in considering a non-zero initial condition of the diffusion as an optimization variable. The optimal arm evolution, in a closed loop, is fixed in an open loop by optimizing a criterion whose variable is the initial diffusion condition. The obtained simulation results clearly illustrate the effectiveness and robustness of the optimal diffusive control.

Scheduling Strategy of Multiple Semi-Active Controllers With Information on the Disturbance and the Structural Response

2016 ◽  
Author(s):  
Kazuhiko Hiramoto ◽  
Taichi Matsuoka ◽  
Katsuaki Sunakoda
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Active Control ◽  
Structural Response ◽  
Design Parameters ◽  
Control Law ◽  
Control Performance ◽  
Multiple Control ◽  
Control Laws ◽  
Scheduling Strategy

A scheduling strategy of multiple semi-active control laws for various earthquake disturbances is proposed to maximize the control performance. Generally, the semi-active controller for a given structural system is designed as a single control law and the single control law is used for all the forthcoming earthquake disturbances. It means that the general semi-active control should be designed to achieve a certain degree of the control performance for all the assumed disturbances with various time and/or frequency characteristics. Such requirement on the performance robustness becomes a constraint to obtain the optimal control performance. We propose a scheduling strategy of multiple semi-active control laws. Each semi-active control law is designed to achieve the optimal performance for a single earthquake disturbance. Such optimal control laws are scheduled with the available data in the control system. As the scheduling mechanism of the multiple control laws, a command signal generator (CSG) is defined in the control system. An artificial neural network (ANN) is adopted as the CSG. The ANN-based CSG works as an interpolator of the multiple control laws. Design parameters in the CSG are optimized with the genetic algorithm (GA). Simulation study shows the effectiveness of the approach.

scholarly journals State Transfer via On-Line State Estimation and Lyapunov-Based Feedback Control for a N-Qubit System

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 751 ◽  
Author(s):  
Sajede Harraz ◽  
Shuang Cong
Keyword(s):  
Feedback Control ◽  
State Estimation ◽  
Open Quantum Systems ◽  
State Feedback Control ◽  
Quantum Master Equation ◽  
Control Law ◽  
Control Laws ◽  
Quantum State Estimation ◽  
State Transfer ◽  
On Line

In this paper, we propose a Lyapunov-based state feedback control for state transfer based on the on-line quantum state estimation (OQSE). The OQSE is designed based on continuous weak measurements and compressed sensing. The controlled system is described by quantum master equation for open quantum systems, and the continuous measurement operators are derived according to the dynamic equation of system. The feedback control law is designed based on the Lyapunov stability theorem, and a strict proof of proposed control laws are given. At each sampling time, the state is estimated on-line, which is used to design the control law. The simulation experimental results show the effectiveness of the proposed feedback control strategy.

Sliding Mode Control for a Membrane Mirror Strip Actuated Using Multiple Smart Actuators

2007 ◽  
Author(s):  
Jamil M. Renno ◽  
C. Konda Reddy ◽  
Daniel J. Inman ◽  
Eric J. Ruggiero
Keyword(s):  
Sliding Mode ◽  
Fiber Composite ◽  
Tensile Load ◽  
Control Law ◽  
Bernoulli Beam ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Euler Bernoulli Beam ◽  
Mode Technique ◽  
Membrane Strip

The sliding mode technique is used to control the deformation of a membrane mirror strip. A membrane mirror strip is augmented with two macro fiber composite (MFC) bimorphs. The first bimorph is actuated in bending whereas the second is actuated in tension. Membrane strips are usually tensioned uniformly. However, the presence of the tension bimorphs induces a local tension at its location. The membrane strip is modeled as an Euler-Bernoulli beam under tensile load, whereas the MFCs are modeled as monolithic piezoceramics. To cast the system into a finite dimensional state space form, the finite elements method (FEM) is used. The control action is switched when the membrane strip approaches its original undeformed shape. Simulation results demonstrate the effectiveness of the proposed control law.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

Optimal Control of a Distributed Parameter, Time-Lagged River Aeration System

1975 ◽  
Vol 97 (2) ◽  
pp. 164-171 ◽  
Author(s):  
M. K. O¨zgo¨ren ◽  
R. W. Longman ◽  
C. A. Cooper
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Control Law ◽  
Optimal Controls ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Characteristic Lines

The control of artificial in-stream aeration of polluted rivers with multiple waste effluent sources is treated. The optimal feedback control law for this distributed parameter system is determined by solving the partial differential equations along characteristic lines. In this process the double integral cost functional of the distributed parameter system is reduced to a single integral cost. Because certain measurements are time consuming, the feedback control law is obtained in the presence of observation delay in some but not all of the system variables. The open loop optimal control is then found, showing explicity the effect of changes in any of the effluent sources on the aeration strategy. It is shown that the optimal strategy for a distribution of sources can be written as an affine transformation upon the optimal controls for sources of unit strength.

Vibration Control of a Beam Using the Nearly Optimal Control Algorithm with a Disturbance Force Observer

2001 ◽  
Vol 17 (4) ◽  
pp. 173-177
Author(s):  
Der-An Wang ◽  
Yii-Mai Huang
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Vibration Control ◽  
Feedforward Control ◽  
Active Vibration Control ◽  
Asymptotic Properties ◽  
Control Law ◽  
Flexible Beam ◽  
Active Vibration ◽  
Modal Space

ABSTRACTActive vibration control of a flexible beam subjected to arbitrary, unmeasurable disturbance forces is investigated in this paper. The concept of independent modal space control is adopted. Both the feedforward and feedback control is implemented here to reduce the beam vibration. Because of the existence of the disturbance forces, the feedforward control is applied by employing the idea of force cancellation. A modal space disturbance force observer is then established in this paper to observe the disturbance modal forces for the feedforward control. For obtaining the feedforward and feedback control gains with the optimal sense, the nearly optimal control law is derived, where the modal disturbance forces are regarded as additional states. The vibration control performances and the asymptotic properties of the control law are discussed.

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