Neural Network-Based Model Predictive Control of a Servo-Hydraulic ...

IEEE AFRICON 2009

23 - 25 September 2009, Nairobi, Kenya

Neural Network-Based Model Predictive Control of a Servo-Hydraulic Vehicle Suspension System o. A. Dahunsi School of Mechanical Aeronautical and Industrial Engineering University of the Witwatersrand Johannesburg, South Africa olurotimi.dahunsi @students.wits.ac.za

J.

o. Pedro

School of Mechanical Aeronautical and Industrial Engineering University of the Witwatersrand Johannesburg, South Africa [email protected]

Abstract- This paper presents the design of a multi-layer feedforward neural network-based model predictive controller (NNMPC) for a two degree-of-freedom (DOF), quarter-car servohydraulic vehicle suspension system. The nonlinear dynamics of the servo-hydraulic actuator is incorporated in the suspension model and thus a suspension travel controller is developed to indirectly improve the ride comfort and handling quality of the suspension system. A SISO feedforward multi-layer perceptron (MLP) neural network (NN) model is developed using input-output data sets obtained from the mathematical model simulation. Levenberg-Marquandt algorithm was employed in training the NN model. The NNMPC was used to predict the future responses that are optimized in a sub-loop of the plant for cost minimization. The proposed controller is compared with an optimally tuned constant-gain PID controller (based on Ziegler-Nichols tuning method) during suspension travel setpoint tracking in the presence of deterministic road input disturbance. Simulation results demonstrate the superior performance of the NNMPC over the generic PID - based in adapting to the deterministic road disturbance.

Keywords: Neural Networks, Model Predictive Control, PID Control, Ride Comfort, Suspension System, Servo-hydraulics. I. INTRODUCTION

Research interest in active vehicle suspension system has continued to grow since the late 1960s due to progress in random vibrations research and optimal control theory[l], [2]. Greater prospect is feasible for active vehicle suspension system (AVSS) with the current rapid advances in electronics and intelligent control. Active vehicle suspension control problem is a disturbance rejection or vibration isolation problem where the road roughness profile is seen as the external disturbance [3], [4]. Major design objectives for vehicle suspensions systems are: ride comfort, which is related to the body heave acceleration; road handling, which is related to the body pitch and roll accelerations; road holding, which is related to the relative displacement between the wheel and the road; and suspension travel, which is the relative displacement between the body and the wheel. It is difficult to simultaneously satisfy these design requirements because of their conflicting nature. Hence a trade-off between these requirements is needed.

O. T. Nyandoro School for Electrical and Information Engineering University of the Witwatersrand Johannesburg, South Africa [email protected]

A good vehicle suspension is typically indicated by the vehicle's ride comfort and road handling quality within a permissible range of the suspension travel [5], [6]. Suspension travel is one of the readily measurable signal that makes the ASS design and analysis realistic especially in feedback structure [7], [8]. Application of optimal and robust control techniques has enabled ASS to achieve better trade-off of design parameters despite the presence of the following drawbacks [9], [10], [11]: higher cost; inherent system nonlinearities and uncertainties; hardware complexity (evident in measurement complications; performance degradation due to chattering in hydraulic actuators; and complications due to additional external power requirement); actuator dynamics complications; and varying operating conditions of the vehicle. Actuation force in ASS is commonly achieved through the use of the electro-hydraulic or electro-pneumatic actuators, but the electro-hydraulic systems are preferred due to their: superior power-to-weight ratio, fast response, high stiffness, lower cost and the fact that force can be generated with it for a long time without the risk of overheating. However, the effects of actuator dynamics and nonlinearities due to the other suspension elements were often ignored in the published works [3], [9], [11]. The proportional, integral and derivative (PID) control is a generic control loop feedback mechanism that is widely used, but tuning the three constants in this algorithm is often done intuitively. PID controllers have drawbacks in terms of robustness, linearity and high loop gains [12]. This motivates for the augmentation of the PID controllers with genetic algorithm (GA) and fuzzy logic [10], [13]. The GA is used to obtain the optimum PID gains. Gaspar et al. [14], and Fialho and Balas [15] presented linear parameter varying (LPV) control technique for a nonlinear active vehicle suspension system with actuator dynamics. LPV theory is mainly useful to tackle measurable

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and bounded nonlinearities [16]. LPV design is also one of the fixed-gain strategies that are designed to be optimal for nominal parameter set and specific operating condition. Model predictive control (MPC) is an iterative, finite horizon optimization control technique. It relies more on linear empirical models obtained by system identification. MPC predicts the outputs based on current plant measurements, setpoints of regulatory controllers and the modelled dynamic system. While many MPC schemes have been developed; MPC based on the polynomial nonlinear autoregressive external input (NARX) model is generally desirable because of the plant nonlinearities [24].

NNMPC has so many metallurgical process, chemical plants, food and pharmaceutical procesing applications as made evident in the quantity of available literature [25] , the converse is the case for ASS problems. The prevailing need for real-time control of ASS with adequate handling of design constraints is a motivation for this study. In this paper, NNMPC is proposed for the suspension travel control of an electro-hydraulically actuated vehicle suspension system in the presence of a deterministic road disturbance. The novelty of this paper lies in the application of this controller to significantly improve the ride comfort and road handling quality of the ASS; and also to reduce the control inputs throughout the tracking process.

NN have found wide applications in the field of control because of the following reasons: its ability to approximate arbitrary nonlinear mapping, its highly parallel structure allows parallel implementation, thereby making it more fault-tolerant than conventional schemes, its ability to learn and adapt on-line, its good application for multivariable systems [17], [18], [19], [20].

The paper is structured as follows; firstly, the nonlinear model of the system is addressed after which the suspension travel control methodology is introduced. PID control and tuning is then explained along with NN-based suspension travel controller training and control. Various simulation results are analysed before concluding the paper.

NN model may also be easier to develop than a polynomial NARX model, especially when applied to multivariable systems. Hence, MPC is often used with other techniques like neural network when dealing with highly nonlinear control applications [21].

A. Physical Modelling

NNMPC involves the generation of values for plant inputs as solutions of an online optimization problem. This is done based on prediction of the future plant performance through a NN model obtained for the nonlinear plant [22].

II. SYSTEM OVERVIEW AND MODELLING

Figure 1 shows the quarter-car active suspension system model. The sprung mass m s , represents the car chassis, while the unsprung mass m u represents the wheel assembly. The spring k s and damper bs represent a passive spring and shock absorber that are placed in-between the car body and the wheel assembly. The spring kt represents the spring constant due to the compressibility of the pneumatic tyre. The vertical

A thorough review of the contemporary intelligent control methodologies for active vehicle suspension system is presented in [18]. These include adaptive fuzzy, adaptive fuzzy sliding mode, adaptive neural network and GA based adaptive control. Renn and Wu [23] showed that the body displacement responses of a PID controlled nonlinear, quarter-car model compared well with a NN controlled one. However, the NNbased control clearly suppressed the vehicle body acceleration better. Eski and Yildrim [20] compared the suspension deflection response of a linear, full-car ASS with PID control to a NNMPC of the same ASS model. Good profile tracking was achieved. Actuator dynamics and system nonlinearities were ignored. Approximate predictive control (APC), one of the variants of NNMPCs is used in the current work. APC uses an indirect design approach by applying the instantaneous linearization principle. APC can be readily tuned by intuitive means, it is good for systems with time delay and it is flexible, thus effective in a wide spectrum of control application [24].

1 - _ - l Power,Signal Amplifier, Computer and Control Unit

Fig. 1. Simplified quarter car model

displacement of the car body, wheel and the road disturbance are represented by X l , X2 and w respectively. The actuator force, F due to the hydraulic actuator is applied in between the sprung and unsprung mass. The relative displacement between the vehicle body and the wheel, ( X2 - X l ) , represents the suspension travel, while the relative displacement between the wheel and the road, (X2 - w ), is the parameter used to characterize road holding.

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B. Mathematical Modelling

Application of Newton's law to the quarter car model shown in Fig.l yields the following governing equations which indicates the nonlinear nature of the system [14], [15]:

Xl

X3

(1)

~

~

m

k~(X2 - xd

msX3

P,

J~~

P,

J~

+ k~I(X2 -

Xl )3 +b~(X4 - X3) - b: - x31 +b~l VlX4 - x3lsgn(X4 - X3) - AX5 -k~(X2 - Xl) - k~I(X2 - xd 3 y mlx4

mux4

X5

-b~(X4 - X3) + b: y mlx4 - x31 _b~l VlX4 - x3lsgn(x4 - X3) -kt( X2 - w) + AX5 ')'