Abstract and Applied Analysis
Volume 2013 (2013), Article ID 912747, 12 pages
Research Article

Optimal Vibration Control for Half-Car Suspension on In-Vehicle Networks in Delta Domain

1School of Mathematics and Computer Science, Yunnan Nationalities University, Kunming 650500, China
2Key Laboratory in Software Engineering of Yunnan Province, Kunming 650091, China
3National Pilot School of Software, Yunnan University, Kunming 650091, China

Received 3 January 2013; Accepted 18 February 2013

Academic Editor: Valery Y. Glizer

Copyright © 2013 Jing Lei 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 paper explores the optimal vibration control design problem for a half-car suspension working on in-vehicle networks in delta domain. First, the original suspension system with ECU-actuator delay and sensor-ECU delay is modeled. By using delta operators, the original system is transformed into an associated sampled-data system with time delays in delta domain. After model transformation, the sampled-data system equation is reduced to one without actuator delays and convenient to calculate the states with nonintegral time delay. Therefore, the sampled-data optimal vibration control law can be easily obtained deriving from a Riccati equation and a Stein equation of delta domain. The feedforward control term and the control memory terms designed in the control law ensure the compensation for the effects produced by disturbance and actuator delay, respectively. Moreover, an observer is constructed to implement the physical realizability of the feedforward term and solve the immeasurability problem of some state variables. A half-car suspension model with delays is applied to simulate the responses through the designed controller. Simulation results illustrate the effectiveness of the proposed controller and the simplicity of the designing approach.