Optimal control of rotation of a flexible arm

Passive optimal feedback control of an articulated flexible arm

Journal of Vibration and Control ◽

10.1177/1077546320956763 ◽

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.

Download Full-text

Optimal Design and Control of a Rotating Flexible Arm With ACLD Treatment

Aerospace ◽

10.1115/imece2003-41245 ◽

2003 ◽

Cited By ~ 1

Author(s):

E. H. K. Fung ◽

D. T. W. Yau

Keyword(s):

Optimal Control ◽

Optimal Design ◽

Shear Modulus ◽

Optimal Control Problem ◽

Control Problem ◽

Performance Index ◽

Flexible Arm ◽

Design Variables ◽

And Control ◽

Optimal Design And Control

In this paper, the optimal design and control of a rotating clamped-free flexible arm with fully covered active constrained layer damping (ACLD) treatment are studied. The arm is rotating in a horizontal plane in which the gravitational effect and rotary inertia are neglected. The piezo-sensor voltage is fed back to the piezo-actuator via a PD controller. Finite element method (FEM) in conjunction with Hamilton’s principle is used to derive the governing equations of motion of the system which takes into account the effects of centrifugal stiffening due to the rotation of the beam. The damping behavior of the viscoelastic material (VEM) is modeled using the complex shear modulus method. The design optimization objective is to maximize the sum of the first three open-loop modal damping ratios divided by the weight of the damping treatment. A genetic algorithm, differential evolution (DE), combined with a gradient-based algorithm, sequential quadratic programming (SQP), is used to determine the optimal design variables such as the thickness and storage shear modulus of the VEM core. Next for the determined optimal design variables, the optimal control problem is performed to determine the optimal control gains which minimize a quadratic performance index. The control performance index is normalized with respect to the initial conditions and the optimal control problem is posed to solve a min-max optimization problem. The results of this study will be useful in the optimal design and control of adaptive and smart rotating structures such as rotorcraft blades or robotic arms.

Download Full-text