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Experimental Study of NMP Sample and Hold Input Using an Inverted Pendulum

[+] Author Affiliations
Yingxu Wang, Guoming G. Zhu, Ranjan Mukherjee

Michigan State University, East Lansing, MI

Paper No. DSCC2018-8994, pp. V001T01A004; 8 pages
doi:10.1115/DSCC2018-8994
From:
  • ASME 2018 Dynamic Systems and Control Conference
  • Volume 1: Advances in Control Design Methods; Advances in Nonlinear Control; Advances in Robotics; Assistive and Rehabilitation Robotics; Automotive Dynamics and Emerging Powertrain Technologies; Automotive Systems; Bio Engineering Applications; Bio-Mechatronics and Physical Human Robot Interaction; Biomedical and Neural Systems; Biomedical and Neural Systems Modeling, Diagnostics, and Healthcare
  • Atlanta, Georgia, USA, September 30–October 3, 2018
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5189-0
  • Copyright © 2018 by ASME

abstract

Early research showed that a zero-order hold is able to convert a continuous-time non-minimum-phase (NMP) system to a discrete-time minimum-phase (MP) system with a sufficiently large sampling period. However the resulting sample period is often too large to adequately cover the original NMP system dynamics and hence not suitable for control application to take advantage of a discrete-time MP system. This problem was solved using different sample and hold inputs (SHI) to reduce the sampling period significantly for MP discrete-time system. Three SHIs were studied analytically and they are square pulse, forward triangle and backward triangle SHIs. To validate the finding experimentally, a dual-loop linear quadratic regulator (LQR) control configuration is designed for the Quanser single inverted pendulum (SIP) system, where the SIP system is stabilized using the Quanser continuous-time LQR (the first loop) and an additional discrete-time LQR (the second loop) with the proposed SHIs to reduce the cart oscillation. The experimental results show more than 75% reduction of the steady-state cart displacement variance over the single-loop Quanser controller and hence demonstrated the effectiveness of the proposed SHI.

Copyright © 2018 by ASME
Topics: Pendulums

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