Elsevier

Neurocomputing

Volume 306, 6 September 2018, Pages 130-140
Neurocomputing

Variable universe fuzzy control for vehicle semi-active suspension system with MR damper combining fuzzy neural network and particle swarm optimization

https://doi.org/10.1016/j.neucom.2018.04.055Get rights and content

Abstract

This study proposes a novel variable universe fuzzy control design for vehicle semi-active suspension system with magnetorheological (MR) damper through the combination of fuzzy neural network (FNN) and particle swarm optimization (PSO). By constructing a quarter-vehicle test rig equipped with MR damper and then collecting the measured data, a non-parametric model of MR damper based on adaptive neuro-fuzzy inference system is first presented. And then a Takagi–Sugeno (T–S) fuzzy controller is designed to achieve the effective control of the input current in MR damper by using the contraction-expansion factors. Furthermore, an appropriate FNN controller is proposed to obtain the contraction-expansion factors, in which particle swarm optimization and back propagation are introduced as the learning and training algorithm for the FNN controller. Lastly, a simulation investigation is provided to validate the proposed control scheme. The results of this study can provide the technical foundation for the development of vehicle semi-active suspension system.

Introduction

The main functions of vehicle suspension system, no matter what kind of suspension system such as passive, active and semi-active suspensions, are to absorb the shock vibrations caused by uneven road surfaces and simultaneously keep the firm uninterrupted contact of vehicle wheels to rough road in improving ride comfort and handling stability [1–2]. As compared to an active suspension control, semi-active suspension (SAS) can offer both of the stability of passive suspension and the control effect of active suspension without requiring too much external energy. Moreover, SAS can adjust its damping force in real time according to the controller requirements, which are usually based on vehicle suspension dynamics. Therefore, over the past decades, vehicle SAS system has received considerable attentions in the fields of vehicle applications [[3], [4], [5], [6], [7]]. More importantly, a MR damper is often utilized as the promising semi-active device in SAS because it can change its viscosity continuously and produce the controllable damping force using MR fluid.

For the controller design and optimization of vehicle SAS system, many researchers and scholars have proposed a number of control approaches such as H control [8,9], sliding-mode control [10,11], adaptive backstepping control [12,13] and T–S fuzzy control [14,15]. Among these control schemes, T–S fuzzy control of vehicle semi-active suspension system with MR damper has been widely and extensively investigated in the current studies due to its being independent of the controlled model. For example, the development and implementation of a novel fuzzy hybrid control of PID and fuzzy logic have been conducted for a quarter-car model in the presence of various road disturbances [16,17]. It was found that the hybrid fuzzy controller can achieve a better performance as compared to the conventional PID controller. In another article, a reliable fuzzy H controller was designed for active suspension system with actuator delay and fault [18], in which T-S fuzzy model approach was used to describe the model uncertainties. Considering the actuator nonlinearities and vehicle body mass uncertainties simultaneously, an adaptive sliding-mode controller was designed via T–S fuzzy approach to guarantee the improvement of suspension dynamic performances and satisfaction of suspension safety constraints [19]. Moreover, a state-observer-based T–S fuzzy controller was presented for a semi-active quarter-car suspension with MR damper, and a quarter-car test rig and control system hardware were developed to demonstrate the benefits of the proposed controller [20]. Simply summarizing the above-mentioned literatures with respect to T–S fuzzy control, the ride comfort and vehicle maneuverability can be improved in some sense, yet there exists a significant reliance on the expert experience when designing controllers, which will lead to the degradation of the control performance or even the instability of the closed-loop system.

To this end, variable universe fuzzy control was proposed to overcome the disadvantages of the conventional T–S fuzzy control, and it is noted that the universe range of fuzzy variable is becoming compact with a decreasing of the system error, and vice versa [21]. In the present studies, the universe variation can be performed through the tunable contraction–expansion factors. However, there are no uniform descriptions on the contraction–expansion factors currently. T–S fuzzy model was employed to make the online adapting regulation for the input and output universes of discourse, which was comprised of a variable universe fuzzy logic controller [22,23]. Additionally, the T–S fuzzy approach is also utilized to describe the variation of input and output contraction-expansion factors in [24,25]. However, it is too difficult to accurately depict them by means of a fuzzy function model, because it will bring out the same problem like fuzzy control. In other words, it will be too much dependent on the expert experiences when choosing the contraction–expansion factors. For this reason, an enhanced variable universe fuzzy controller design was presented for a vehicle semi-active suspension system in our previous study [26], wherein the conventional variable universe fuzzy control algorithm and fuzzy neural network control theory were combined together to derive the designed controller with better control performances. It should be noted that back propagation (BP) algorithm was used to realize the training of fuzzy neural networks, while using BP algorithm separately will yield to the local optimization problem.

Motivated by the above discussion, this paper conducts the experimental study to establish a relatively accurate non-parametric model of MR damper based on adaptive neuro-fuzzy inference system and further to obtain a half-vehicle SAS system as the control plant, then a novel variable universe fuzzy control design is proposed via combing FNN and PSO, referred as VUFC-FNNPSO controller. In which, the appropriate FNN controller is designed to adjust the two input universes of discourse based on PSO and BP algorithm, and a T–S fuzzy controller is designed to realize the input current control of MR damper by using the two contraction-expansion factors obtained from the FNN controller. Finally, a numerical simulation investigation is provided to illustrate the effectiveness of the proposed controller under bump, random and rough road surface.

The rest of this paper is organized as follows: Section 2 presents the modeling and characterizing of MR damper based on the measured data. The dynamic model establishment of half-vehicle suspension system is described in Section 3. The proposed variable universe fuzzy controller is specifically discussed in Section 4. In Section 5, simulation investigation is given to verify the effectiveness of the designed controller. Finally, the conclusions are summarized in Section 6.

Section snippets

Modeling and characterizing of MR damper

It is noted that the MR device installed on Land Rover Aurora 2016 Sport Utility Vehicle (SUV) car is considered in this study, and the structure and its components are revealed in Fig. 1, which is composed of MR fluid, piston, conductive coil, floating plug and spring. The work principle of MR damper is that the arrangements of magnetic molecules change by means of adjusting the current in coil, therefore achieving a continuous adjustable damping force for this MR damper.

As a popular MR model,

The half-vehicle dynamic model establishment

In this section, a half-vehicle dynamic model using the above-discussed MR damper is shown in Fig. 5, and it is employed to describe the essential characteristics of vehicle SAS system, which is extensively used in the previous literatures [1,17] due to its symmetry.

In this model, a and b denote the distances of the front and rear axles to the center of vehicle body; zs and θ denote the vertical and pitch angular displacements at the gravity center of vehicle body, respectively; ms and Is

The variable universe fuzzy controller design

The basic idea of variable universe fuzzy control may originate from the desire that universe can be compressed or expanded when the input variable decreases or increases, which contributes to make the fuzzy rules more valuable, so as to improve the control accuracy. Assume that Xi= [-Ei, Ei] (i = 1, 2, …, n) represents the fuzzy domain of input variable xi (i = 1, 2, …, n), Y = [-U, U] represents the fuzzy domain of output variable y. Ai = {Aij} (1 ≤ j ≤ m) and B = {Bj} (1 ≤ j ≤ m) represent

Simulation investigation and discussion

In this section, a simulation case is provided to verify the effectiveness of the proposed control scheme under bump, random and rough road excitation. The half-vehicle model parameters are listed in Table 1 [49], and the vehicle dynamic performances z¨s,θ¨, and the safety constraint indictors such as suspension deflection △y and tire dynamic load Ft are chosen as the measured output performances to conduct the simulation investigation.

Conclusions

In this paper, a novel variable universe fuzzy controller has been developed for vehicle semi-active suspension system with MR damper via the combination of FNN and PSO. A non-parametric model of MR damper based on adaptive neuro-fuzzy inference system is first presented using the measured data collected from a quarter-vehicle suspension test rig. And then a Takagi–Sugeno (T–S) fuzzy controller is designed to fulfill the control input current of MR damper by using the contraction–expansion

Acknowledgments

This work is supported by National Natural Science Foundation of China under Grant 51675423 and 51305342, and Primary Research & Development Plan of Shannxi Province under Grant 2017GY-029.

Hui Pang received the B.S. degree in Mechanical Manufacturing and Automation from Zhengzhou Institute of Aeronautical Industry Management, Zhenzhou, China, in 2002, and the M.S. and Ph.D. degrees in Mechanical Engineering from Northwestern Polytechnical University, Xi'an, China, in 2005 and 2009, respectively. He is currently an Associate Professor in School of Mechanical and Precision Instrument Engineering, Xi'an University of Technology. During 2016–2017, he was a visiting scholar in the

References (51)

  • YuJ. et al.

    Evolving artificial neural networks using an improved PSO and DPSO

    Neurocomputing

    (2008)
  • H. Melo et al.

    Gaussian-PSO with fuzzy reasoning based on structural learning for training a Neural Network

    Neurocomputing

    (2016)
  • O. Cordon

    A historical review of evolutionary learning methods for Mamdani-type fuzzy rule-based systems: designing interpretable genetic fuzzy systems International

    Int. J. Approx. Reason.

    (2011)
  • KuoR.J. et al.

    An intelligent stock trading decision support system through integration of genetic algorithm based fuzzy neural network and artificial neural network

    Fuzzy Sets Syst

    (2001)
  • E. Momeni et al.

    Prediction of uniaxial compressive strength of rock samples using hybrid particle swarm optimization-based artificial neural networks

    Measurement

    (2015)
  • A. Ismail et al.

    An optimised product-unit neural network with a novel PSO-BP hybrid training algorithm: applications to load-deformation analysis of axially loaded piles

    Eng. Appl. Artif. Intell.

    (2013)
  • CaoD. et al.

    Editor's perspectives: road vehicle suspension design, dynamics, and control

    Veh. Syst. Dyn.

    (2011)
  • DuH. et al.

    Semi-active variable stiffness vibration control of vehicle seat suspension using an MR elastomer isolator

    Smart Mater. Struct.

    (2011)
  • M. Zapateiro et al.

    Semi-active control methodologies for suspension control with magnetorheological dampers

    IEEE Trans. Mechatron.

    (2012)
  • ChenH. et al.

    Non-linear modelling and control of semi-active suspensions with variable damping

    Veh. Syst. Dyn.

    (2013)
  • YinX. et al.

    Robust control of networked systems with variable communication capabilities and application to a semi-active suspension system

    IEEE Trans. Mechatron.

    (2016)
  • ZongL.H. et al.

    Semi-active H control of high-speed railway vehicle suspension with magnetorheological dampers

    Veh. Syst. Dyn.

    (2013)
  • ChenB.C. et al.

    Sliding-mode control for semi-active suspension with actuator dynamics

    Veh. Syst. Dyn.

    (2011)
  • M. Zapateiro et al.

    Real-time hybrid testing of semiactive control strategies for vibration reduction in a structure with MR damper

    Struct. Control Health Monit.

    (2010)
  • DuH. et al.

    Direct voltage control of magnetorheological damper for vehicle suspensions

    Smart Mater. Struct.

    (2013)
  • Cited by (0)

    Hui Pang received the B.S. degree in Mechanical Manufacturing and Automation from Zhengzhou Institute of Aeronautical Industry Management, Zhenzhou, China, in 2002, and the M.S. and Ph.D. degrees in Mechanical Engineering from Northwestern Polytechnical University, Xi'an, China, in 2005 and 2009, respectively. He is currently an Associate Professor in School of Mechanical and Precision Instrument Engineering, Xi'an University of Technology. During 2016–2017, he was a visiting scholar in the Department of Automotive Engineering, Clemson University, Greenville, South Carolina, USA. His interests include nonlinear robust control and fuzzy sliding mode control, and their applications in vehicle dynamics control.

    Fan Liu received the B.S. and M.S. degree in Automotive Engineering from Xi'an University of Technology, Xi'an, China, in 2015 and 2018, respectively. His research interests include nonlinear control theory and vehicle dynamics control.

    Zeren Xu received the B.S. and M.S. degree in Materials Science and Engineering from Chongqing University, Chongqing, China, in 2009 and 2012, respectively. He received his Ph.D. degree in Automotive Engineering from the Department of Automotive Engineering, Clemson University, Greenville, South Carolina, USA, in 2017. His current research interests focus on manufacturing and materials, signal processing and nonlinear control methods.

    View full text