0
Research Papers

The Optimal Control Approach to Dynamical Inverse Problems

[+] Author and Article Information
Wolfgang Steiner

Department of Mechanical Engineering,  University of Applied Sciences Upper Austria, Stelzhamerstr. 23, A-4600 Wels, Austriaw.steiner@fh-wels.at

Stefan Reichl

Department of Mechanical Engineering,  University of Applied Sciences Upper Austria, Stelzhamerstr. 23, A-4600 Wels, Austrias.reichl@fh-wels.at

J. Dyn. Sys., Meas., Control 134(2), 021010 (Jan 03, 2012) (13 pages) doi:10.1115/1.4005365 History: Received July 09, 2010; Revised September 09, 2011; Published January 03, 2012; Online January 03, 2012

This paper considers solution strategies for “dynamical inverse problems,” where the main goal is to determine the excitation of a dynamical system, such that some output variables, which are derived from the system’s state variables, coincide with desired time functions. The paper demonstrates how such problems can be restated as optimal control problems and presents a numerical solution approach based on the method of steepest descent. First, a performance measure is introduced, which characterizes the deviation of the output variables from the desired values, and which is minimized by the solution of the inverse problem. Second, we show, how the gradient of this error functional can be computed efficiently by applying the theory of optimal control, in particular by following an idea of Kelley and Bryson. As the major contribution of this paper we present a modification of this method which allows the application to the case where the state equations are given by a set of differential algebraic equations. This situation has great practical importance since multibody systems are mostly described in this way. For comparison, we also discuss an approach which bases an a direct transcription of the optimal control problem. Moreover, other methods to solve dynamical inverse problems are summarized.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Linear oscillator. The right mass is driven by a force u(t).

Grahic Jump Location
Figure 2

Linear Oscillator, Kelley-Bryson method: Drive signals after 150 iterations. β = 10, α = 0.01. The dashed line shows the analytical solution 66.

Grahic Jump Location
Figure 5

Linear Oscillator, subinterval optimization method: Drive signal. The dashed line shows the analytical solution 66.

Grahic Jump Location
Figure 6

Crane trolley attached to a string pendulum with varying length

Grahic Jump Location
Figure 7

Overhead crane, Kelley-Bryson method: Target signal x(t) after 200 iterations for β = 5 (thick solid line), β = 0 (thin solid line) and the desired signal xd (t) (dashed line)

Grahic Jump Location
Figure 8

Overhead crane, Kelley-Bryson method: (Negative) Target signal z(t) after 200 iterations for β = 5 (thick solid line), β = 0 (thin solid line) and the desired signal zd (t) (dashed line)

Grahic Jump Location
Figure 9

Overhead crane, Kelley-Bryson method: Drive signals after 200 iterations for β = 5 (thick solid line), β = 0 (thin solid line). The dashed line shows the analytical solution.

Grahic Jump Location
Figure 10

Overhead crane, Kelley-Bryson method: Decreasing performance measure with increasing number of iterations for β = 5 and β = 0

Grahic Jump Location
Figure 11

Overhead crane, subinterval optimization method: Drive signals (thick line). The thin line shows the analytical solution.

Grahic Jump Location
Figure 3

Linear Oscillator, Kelley-Bryson method: Drive signals after 50 iterations for different weighting of the velocity error, i.e. β = 10 and β = 0. The dashed line shows the analytical solution 66.

Grahic Jump Location
Figure 4

Linear Oscillator, Kelley-Bryson method: Decreasing performance measure with increasing number of iterations. β = 10, α = 0.01.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In