Vibration Control of a Semiactive Vehicle Suspension System Based on Extended State Observer Techniques

Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2014, Article ID 248297, 10 pages http://dx.doi.org/10.1155/2014/248297 Research Article Vibration Control of a Semiactive Vehicle Suspension System Based on Extended State Observer Techniques Ze Zhang,1 Hamid Reza Karimi,2 Hai Huang,1 and Kjell G. Robbersmyr2 1 2 School of Astronautics, Beihang University, Beijing 100191, China Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway Correspondence should be addressed to Hamid Reza Karimi; Received 3 March 2014; Accepted 2 May 2014; Published 20 May 2014 Academic Editor: Weichao Sun Copyright © 2014 Ze Zhang 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. A feedback control method based on an extended state observer (ESO) method is implemented to vibration reduction in a typical semiactive suspension (SAS) system using a magnetorheological (MR) damper as actuator. By considering the dynamic equations of the SAS system and the MR damper model, an active disturbance rejection control (ADRC) is designed based on the ESO. Numerical simulation and real-time experiments are carried out with similar vibration disturbances. Both the simulation and experimental results illustrate the effectiveness of the proposed controller in vibration suppression for a SAS system. 1. Introduction Vibration is a common and unpredicted phenomenon for dynamic and static bodies. Vibrations are detrimental to comfort in many places, and most of the applications in civil, mechanical, and electrical engineering are easily affected by undesirable vibration or even the complete system will lose functionality. Those vibrations are harmful and must be eliminated or reduced. Vibration reduction can be achieved in many different ways. From the difference of isolation components, vibration suppression systems can be divided into three categories: passive, semiactive, and active. In the automobile industry, the vibration suppression system is introduced for decades. In a wheeled vehicle the mechanical system of springs and shock absorbers connect the wheels and axles to the chassis form vibration suspension system. The suspension system can provide stiffening and damping when the vehicle is running on an irregular road surface to isolate the vehicle body and ensure the comfort of the passengers. Many efforts were made to make the suspension system work in an optimal condition by optimizing the parameters of the suspension system passively; however, they have limitation of frequency range. Active suspensions were also introduced in [1–7], but the system is complex and in the need of much more power supply because of the added actuators. Semiactive concept combines the advantages of both active and passive suspensions and results in good performance with less complexity and power acquirement [8]. One of the semiactive suspension systems currently used for vibration isolation is equipped with magnetorheological (MR) damper which creates braking torque by changing the viscosity of the MR fluid inside the brake [9]. MR fluid has magnetically sensitive rheological properties. Varying the magnetic field strength by changing the input current has the effect of changing the viscosity of the MR field and this leads to the changing of the damper torque output [10]. Thus, the output torque of the MR damper can be controlled by changing the input current. For a MR damper and spring suspension system, the input current must be controlled properly in order to suppress vibration. Usually a feedback control with the information of the body position is introduced, such as PID control [11], neural network control [12], backstepping control [13, 14], fuzzy logic control [15], LQG [16], and H∞ control [17]. In this paper, a practical feedback control solution for controlling the MR damper based on extended state observer (ESO), a part of active disturbance rejection control (ADRC) technology [18, 19], is applied. The ADRC has been successfully employed in many mechanical and electronic 2 Journal of Applied Mathematics Sprung mass car body MR damper Spring Encoder Encoder Unsprung mass car wheel Eccentricity Control and power box Driving motor with gear Emergency button Figure 1: Semiactive suspension (SAS) system. rb Uppe r2 eam 𝛼2 Spring Lower MR r1 Horizontal line beam 𝛼1 R Dx r Wheel Tire 𝛽 l0g Eccentric Figure 2: Geometrical diagram of SAS. systems [20–24]. A simulation is done based on the dynamic model of the semiactive suspension (SAS) system and ADRC technology. The experimental task is also carried out to measure the performance of the controller in the real system. Figure 2 depicts the geometrical view of the SAS system. The dynamic model of the SAS is described by the following differential equations, in which the detailed definition of the angles 𝛼(⋅) and the distances 𝑟(⋅) are referred to in the nomenclature. The dynamic equation of the upper beam is 2. Semiactive Suspension System The semiactive suspension (SAS) system studied here for vibration suppression is developed by the Polish Company Inteco Limited [25]. This SAS system can be used to analyze the vertical dynamics of the car wheel. As shown in Figure 1, the SAS laboratory model simulated a quarter of a wheeled vehicle, and it consists of an upper beam which represents the car body, a wheel, rotational MR damper, and a spring. It is driven by a DC motor with gear coupled to an eccentric small wheel. The suspended car wheel rolls due to the eccentric wheel rotation and oscillates up and down due to the small wheel eccentricity. The MR damper incorporated in SAS acts as an interface between sensors (encoders), control algorithms, and mechanical structure of the suspension, using the external damper coil current to adjust the damping. The torque generated by the MR damper depends on the rotary velocity of the damper and the magnetic field strength. 𝐽2 𝑑2 𝛼2 = 𝑇2 . 𝑑𝑡2 (1) 𝑇2 is the total torque added to the upper beam. It consists of the friction torque of the upper beam at the torsional joint at the MR damper point, the moment dual to gravity, the torque caused by the connecting spring, and the MR damper torque. The 𝑇2 is given as the following equation: 𝑇2 = 𝑘2 𝑑𝛼2 𝑑𝛼 𝑑𝛼 − 𝑀2 cos 𝛼2 + 𝑟2 𝑘𝑠 𝑙𝑠 + ( 1 − 2 ) 𝑀MR (𝑖) 𝑑𝑡 𝑑𝑡 𝑑𝑡 (2) with 2 2 𝑙𝑠 = 𝑙0𝑠 − √(𝑟2 cos 𝛼2 − 𝑟1 cos 𝛼1 ) + (𝑟2 sin 𝛼2 − 𝑟1 sin 𝛼1 ) . (3) Journal of Applied Mathematics 3 Define 𝑥1 = 𝛼2 and 𝑥2 = 𝑥1̇ = 𝛼̇2 ; then, we can rewrite (9) in the following: The dynamic equation of the lower beam is 𝐽1 𝑑2 𝛼1 = 𝑇1 . 𝑑𝑡2 (4) 𝑇1 is the total torque added to the lower beam. It consists of the friction torque of the lower beam at the torsional joint at the MR damper point, the moment dual to gravity, the torque caused by t (...truncated)