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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 510738, 12 pages
Research Article

Robust Adaptive PID Controller for a Class of Uncertain Nonlinear Systems: An Application for Speed Tracking Control of an SI Engine

1Department of Industrial Engineering, Khon Kaen University, Khon Kaen 40002, Thailand
2Department of Mechanical Engineering, Khon Kaen University, Khon Kaen 40002, Thailand

Received 12 October 2014; Accepted 25 February 2015

Academic Editor: Kacem Chehdi

Copyright © 2015 Tossaporn Chamsai et al. 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.


The sliding mode control (SMC) technique with a first-order low-pass filter (LPF) is incorporated with a new adaptive PID controller. It is proposed for tracking control of an uncertain nonlinear system. In the proposed control scheme, the adaptation law is able to update the PID controller online during the control process within a short period. The chattering phenomenon of the SMC can be alleviated by incorporation of a first-order LPF, while the robustness of the control system is similar to that of the sliding mode. In the closed-loop control analysis, the convergence condition in the reaching phase and the existence condition of the sliding mode were analyzed. The stability of the closed-loop control is guaranteed in the sense of Lyapunov’s direct method. The simulations and experimental applications of a speed tracking control of a spark ignition (SI) engine via electronic throttle valve control architecture are provided to verify the effectiveness and the feasibility of the proposed control scheme.