Design of a non-linear hybrid car suspension system using neural networks

doi:10.1016/S0378-4754(02)00029-0

Mathematics and Computers in Simulation

Volume 60, Issues 3–5, 30 September 2002, Pages 369-378

https://doi.org/10.1016/S0378-4754(02)00029-0 Get rights and content

Abstract

A methodology for the design of active/hybrid car suspension systems with the goal to maximize passenger comfort (minimization of passenger acceleration) is presented. For this reason, a neural network (NN) controller is proposed, who corresponds to a Taylor series approximation of the (unknown) non-linear control function and the NN is due to the numerous local minima trained using a semi-stochastic parameter optimization method. Two cases A and B (continuous and discontinuous operation) are investigated and numerical examples illustrate the design methodology.

Introduction

The basic idea of an active/hybrid suspension system is to use an actuator (e.g. a hydraulic cylinder) to increase the dynamic performance of a car, e.g. stability, comfort, etc., beyond the performance of a passive linear and sometimes non-linear (progressive spring) suspension system. Thus, it is generally expected that the control of the actuator is non-linear and intelligent (e.g. flexible).

The synthesis of such controllers has been investigated in the past by a number of researchers using non-linear control, as well as fuzzy-neural approaches. A survey of advanced suspension developments and related optimal control applications are presented in [4].The most recent papers are listed in [1], [2], [3], [4], [5], [6]. Nevertheless, active control is rarely realized. Reasons are the add-on cost and complexity of the active suspension and the energy consumption.

In the present paper, a new methodological approach using neural networks (NNs) is presented. The approach proposes a general type NNs non-linear controller based on a Taylor series approximation, trained by a semi-stochastic optimization algorithm. The remaining part of this paper is organized as follows. Section 2 contains a description of the car dynamics and the problem statement. The control problem is set up in Section 3. Results of numerical calculations are presented in Section 4, while the conclusions are given in Section 5.

Section snippets

Mathematical model

The mathematical model used is the (well known) quarter-car model with passive–active suspension system shown in Fig. 1. Wheel and axle (unsprung mass m₂) is connected to the car body through a spring (k)—damper (c)—actuator (f) suspension system, while the tire is modeled as a spring (k₂). The car body is represented by its mass m₁ and the road disturbance w(t).

The equations of motion taking into account the dynamics of the actuator (time constant T_act) are the following: $m_{1} x ̈_{1} +c(x ̇_{1} − x ̇_{2})+k(x_{1} −x$

Control problem

The control objective is to maximize the passenger comfort, respectively, to minimize the passenger acceleration, under road disturbances.

The unconstrained problem (|z| not constrained) can be solved for T_act=0 immediately; $x ̈_{1} =0$ is achieved if $u_{unc} =c(x ̇_{1} − x ̇_{2})+k(x_{1} −x_{2})$ which means that the resulting passive+active spring and damping constants (k_res, c_res) become 0, while x₂ is equal to $x ̈_{2,unc} +Ω^{2} x_{2,unc} =Ω^{2} w→x_{2,unc} =w(1− cos Ωt) k_{2} m_{2} = Ω^{2},w= const$ , indicate now clearly that a control law that can cope

Numerical results

Case A (continuous operation). It is assumed that the passive car dynamics are already defined, e.g. c=1000 Ns/m, k=16,812 N/m, and that a non-linear controller, acting all the time (“continuous operation”) has to be designed to increase the passenger comfort (see [1]).

In order to minimize passenger acceleration with the control law (7), the following goal and constraints are defined: $f(w)=| x ̈_{1} |_{forA=5cm} = minimum, g_{1} (w)=|z|−0.08 m ≤0 for A_{max} =11 cm, g_{2} (w)=|z|−0.08 m ≤0, for A_{mean} =5 cm, g_{3} (w)=5000−k+w_{1} ≤0 N/m, g_{4} (w$

Conclusions

In this paper the problem of the design of a non-linear hybrid car suspension system for ride qualities using NNs has been presented. It is shown that the discontinuous operation of the ride qualities controller has a lot of advantages, e.g. lower power consumption, greater life time, etc., compared to a continuous operation of the active part of the suspension system.

From the standpoint of methodology, the paper emphasizes a new technique based on NNs, where the structure of the NN controller

References (6)

F.J. D’Amato et al.
Fuzzy control for active suspensions
Mechatronics
(2000)
T. Yoshimura et al.
Active suspension of passenger cars using linear and fuzzy-logic controls
Contr. Eng. Prac.
(1999)
D. Hrovat
Survey of advanced suspension developments and related optimal control applications
Automatica
(1997)

There are more references available in the full text version of this article.

Cited by (18)

Analysis and experiment of time-delayed optimal control for vehicle suspension system
2019, Journal of Sound and Vibration
Citation Excerpt :
With the progress of the society and the development of science and technology, the requirements for the performance of the vehicle are becoming higher and higher. As an important part of the vehicle driving system, the performance of the suspension system has a direct impact on the comfort and safety of the occupants [1–4]. At present, there are three types of vehicle suspension system, including passive, semi-active and active suspension.
In this paper, the performance of vehicle suspension system under time-delayed optimal control is investigated. The effect of time delay on control stability of the active suspension system is discussed. The mathematical simulation is used to verify the correctness of the stable interval obtained by differential equation theory for linear systems with constant coefficients and time delay. In order to keep the stability of the system, time-delayed optimal control is designed through the method of state transformation and optimal control theory. The results show that the control strategy could not only guarantee the stability of the system regardless of the variation on control time delay, but also improve the performance of the suspension system. Additionally, influence of the designed active time delay on the amplitude of sprung mass acceleration, suspension deflection, rode holding are analyzed to provide guidance for its further practical engineering application. Vibration control experiments of the active suspension system under harmonic excitation with time-delayed optimal control are figured to compare with simulations. It is seen that the designed time-delayed optimal control strategy has the effectiveness and advantage.
Vibration control of vehicle active suspension system using a new robust neural network control system
2009, Simulation Modelling Practice and Theory
The main problem of vehicle vibration comes from road roughness. For that reason, it is necessary to control vibration of vehicle’s suspension by using a robust artificial neural network control system scheme. Neural network based robust control system is designed to control vibration of vehicle’s suspensions for full suspension system. Moreover, the full vehicle system has seven degrees of freedom on the vertical direction of vehicle’s chassis, on the angular variation around X-axis and on the angular variation around Y-axis. The proposed control system is consisted of a robust controller, a neural controller, a model neural network of vehicle’s suspension system. On the other hand, standard PID controller is also used to control whole vehicle’s suspension system for comparison.
Consequently, random road roughnesses are used as disturbance of control system. The simulation results are indicated that the proposed control system has superior performance at adapting random road disturbance for vehicle’s suspension.
Vibration control of suspension systems using a proposed neural network
2004, Journal of Sound and Vibration
This paper presents a neural scheme for controlling a bus suspension system. The suspension system, designed as quarter bus model, is used to simplify the problem to a one-dimensional spring–damper system. The proposed controller is such that the system is always operating in a closed loop, which should lead to better performance characteristics. For comparison, PID, PI and PD controllers are also utilized to control the bus suspension system. Simulation results give superior performance of the proposed neural control scheme. It was also shown that the designed suspension control system displayed robust performance with system model uncertainties.
A novel multi-objective quantum particle swarm algorithm for suspension optimization
2020, Computational and Applied Mathematics
Time-delayed feedback control of vehicle suspension system based on state transformation
2018, Nongye Gongcheng Xuebao/Transactions of the Chinese Society of Agricultural Engineering
Sliding mode approach in semi-active suspension control
2017, Sliding Mode Control of Vehicle Dynamics

View all citing articles on Scopus

View full text