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Journal of Applied Mathematics
Volume 2013, Article ID 854631, 9 pages
http://dx.doi.org/10.1155/2013/854631
Research Article

Generalized Kalman-Yakubovich-Popov Lemma Based I-PD Controller Design for Ball and Plate System

1Graduate School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan
2Department of Science and Engineering, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan

Received 23 June 2013; Accepted 9 September 2013

Academic Editor: Baocang Ding

Copyright © 2013 Shuichi Mochizuki and Hiroyuki Ichihara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The ball-on-plate balancing system has a camera that captures the ball position and a plate whose inclination angles are limited. This paper proposes a PID controller design method for the ball and plate system based on the generalized Kalman-Yakubovich-Popov lemma. The design method has two features: first, the structure of the controller called I-PD prevents large input signals against major changes in the reference signal; second, a low-pass filter is introduced into the feedback loop to reduce the influence of the measurement noise produced by the camera. Both simulations and experiments are used to evaluate the effectiveness of the design method.