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Research Papers

Minimax Input Shaper Design Using Linear Programming

[+] Author and Article Information
Tarunraj Singh

Department of Mechanical and Aerospace Engineering, SUNY at Buffalo, Buffalo, NY 14260

J. Dyn. Sys., Meas., Control 130(5), 051010 (Aug 04, 2008) (9 pages) doi:10.1115/1.2963039 History: Received May 04, 2007; Revised May 13, 2008; Published August 04, 2008

The focus of this paper is on the design of robust input shapers where the maximum value of the cost function over the domain of uncertainty is minimized. This nonlinear programming problem is reformulated as a linear programming problem by approximating a n-dimensional hypersphere with multiple hyperplanes (as in a geodesic dome). A recursive technique to approximate a hypersphere to any level of accuracy is developed using barycentric coordinates. The proposed technique is illustrated on the spring-mass-dashpot and the benchmark floating oscillator problem undergoing a rest-to-rest maneuver. It is shown that the results of the linear programming problem are nearly identical to that of the nonlinear programming problem.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Approximation of circle with lines

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Figure 2

Approximation of sphere with planes

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Figure 3

Barycentric examples

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Figure 4

Division of 2-simplex

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Figure 5

Error in approximating hypersphere with hyperplanes

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Figure 6

Energy and norm plots

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Figure 7

Energy and norm plots

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Figure 8

Input shaped control profile

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Figure 9

Minimax cost sensitivity

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Figure 10

Floating oscillator

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Figure 11

Recursive division

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Figure 12

l2 Minimax control

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Figure 13

l2 Minimax control

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