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Pole placement for time-delayed systems using Galerkin approximations

[+] Author and Article Information
Shanti Swaroop Kandala

Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502285, Telangana, India
me14resch01001@iith.ac.in

Thomas K. Uchida

Department of Bioengineering, Stanford University, James H. Clark Center, 318 Campus Drive, Stanford, California 94305, U.S.A.
tuchida@uottawa.ca

Chandrika Prakash Vyasarayani

Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502285, Telangana, India
vcprakash@iith.ac.in

1Corresponding author.

ASME doi:10.1115/1.4042465 History: Received February 27, 2018; Revised December 24, 2018

Abstract

Many dynamic systems of practical interest have inherent time delays and thus are governed by delay differential equations (DDEs). Because DDEs are infinite dimensional, time-delayed systems may be difficult to stabilize using traditional controller design strategies. We apply the Galerkin approximation method using a new pseudoinverse-based technique for embedding the boundary conditions, which results in a simpler mathematical derivation than has been presented previously. We then use the pole placement technique to design closed-loop feedback gains that stabilize time delayed systems, and verify our results through comparison to those reported in the literature. Finally, we perform experimental validation by applying our method to stabilize a rotary inverted pendulum system with inherent sensing delays as well as additional time delays that are introduced deliberately. The proposed approach is easily implemented and performs at least as well as existing methods.

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