scholarly journals Experimental Implementation of a Hybrid Nonlinear Control Design for Magnetostrictive Actuators

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
William S. Oates ◽  
Phillip G. Evans ◽  
Ralph C. Smith ◽  
Marcelo J. Dapino
Keyword(s):  
Optimal Control ◽  
Nonlinear Control ◽  
Tracking Control ◽  
High Speed ◽  
Control Design ◽  
Nonlinear Optimal Control ◽  
Open Loop ◽  
Energy Model ◽  
Switching Behavior ◽  
Homogenized Energy Model

A hybrid nonlinear optimal control design is experimentally implemented on a magnetostrictive Terfenol-D actuator to illustrate enhanced tracking control at relatively high speed. The control design employs a homogenized energy model to quantify rate-dependent nonlinear and hysteretic ferromagnetic switching behavior. The homogenized energy model is incorporated into a finite-dimensional nonlinear optimal control design to directly compensate for the nonlinear and hysteretic magnetostrictive constitutive behavior of the Terfenol-D actuator. Additionally, robustness to operating uncertainties is addressed by incorporating proportional-integral (PI) perturbation feedback around the optimal open loop response. Experimental results illustrate significant improvements in tracking control in comparison to PI control. Accurate displacement tracking is achieved for sinusoidal reference displacements at frequencies up to 1 kHz using the hybrid nonlinear control design, whereas tracking errors become significant for the PI controller for frequencies equal to or greater than 500 Hz.

Adjoint-Based Optimization Procedure for Active Vibration Control of Nonlinear Mechanical Systems

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Carmine M. Pappalardo ◽  
Domenico Guida
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Control Problem ◽  
Numerical Solution ◽  
Optimal Control Theory ◽  
Numerical Procedure ◽  
Nonlinear Optimal Control ◽  
Open Loop ◽  
Adjoint Equations ◽  
Loop Control

In this paper, a new computational algorithm for the numerical solution of the adjoint equations for the nonlinear optimal control problem is introduced. To this end, the main features of the optimal control theory are briefly reviewed and effectively employed to derive the adjoint equations for the active control of a mechanical system forced by external excitations. A general nonlinear formulation of the cost functional is assumed, and a feedforward (open-loop) control scheme is considered in the analytical structure of the control architecture. By doing so, the adjoint equations resulting from the optimal control theory enter into the formulation of a nonlinear differential-algebraic two-point boundary value problem, which mathematically describes the solution of the motion control problem under consideration. For the numerical solution of the problem at hand, an adjoint-based control optimization computational procedure is developed in this work to effectively and efficiently compute a nonlinear optimal control policy. A numerical example is provided in the paper to show the principal analytical aspects of the adjoint method. In particular, the feasibility and the effectiveness of the proposed adjoint-based numerical procedure are demonstrated for the reduction of the mechanical vibrations of a nonlinear two degrees-of-freedom dynamical system.

Integrated Structure/Control Design of High Speed Flexible Robots Based on Time Optimal Control

1995 ◽  
Vol 117 (4) ◽  
pp. 503-512 ◽  
Author(s):  
Sudhendu Rai ◽  
Haruhiko Asada
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
High Speed ◽  
Control Design ◽  
Design Criterion ◽  
Time Optimal Control ◽  
Design Parameters ◽  
Element Analysis ◽  
Structure Control ◽  
Time Optimal

This paper presents the integrated structure/control design of high speed single link robots based on time-optimal control and finite element analysis. First, the solutions of a time optimal control problem are analyzed with respect to the arm link inertia and its structural flexibility. A new technique is developed to further reduce the optimal traveling time by redesigning the arm structure through the trade-off analysis between the arm inertia and its natural frequency. In the latter half of the paper, the design criterion is extended to multiple indices by considering residual vibrations, load bearing capacity and other design constraints. For suppressing residual vibrations, a simple feedback control is designed and its dynamic performance with respect to pole-zero locations is improved along with other criteria through mechanical structure modification. The finite element method is used as a modeling tool and the shape of the arm geometry is modified as design parameters. An arm is designed which performs much better as compared to the design which is done without considering the interactions between physical structure and control. The newly designed arm is tested by constructing an experimental setup. The results show significantly improved performance.

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