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 pseudo-inverse-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.
Pole Placement for Time-Delayed Systems Using Galerkin Approximations
Indian Institute of Technology Hyderabad,
Sangareddy, Telangana 502285, India
James H. Clark Center,
318 Campus Drive,
Stanford, CA 94305
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received February 27, 2018; final manuscript received December 24, 2018; published online January 29, 2019. Assoc. Editor: Dumitru I. Caruntu.
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Kandala, S. S., Uchida, T. K., and Vyasarayani, C. P. (January 29, 2019). "Pole Placement for Time-Delayed Systems Using Galerkin Approximations." ASME. J. Dyn. Sys., Meas., Control. May 2019; 141(5): 051012. https://doi.org/10.1115/1.4042465
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