Keywords: active suspension, ride comfort, road-holding ability, control force, optimal control theory, stationary random process.

Demands for better ride comfort and controllability of road vehicles have motivated many automotive industries to consider the use of active suspension systems. These electronically controlled suspension systems can potentially improve ride comfort as well as road-holding ability of the vehicle. Active suspensions offer the potential of being adaptable to the quality of the roadway surfaces, vehicle speed and different comfort requirements.

Active suspension employs pneumatic or hydraulic actuators which in turn creates the desired force in the suspension system, [1,2]. Electro-rhelogical fluid dampers are also used in realizing active suspension systems, [3]. The actuator is secured in parallel with a spring and a damper. Active suspensions may consume large amounts of energy [4] in providing the control force, and therefore, in the design procedure for the active suspension the power limitations of actuator should also be considered as an important factor.

In any vehicle suspension system, there are a variety of performance parameters, which need to be optimized. Among them, ride comfort, road-holding ability and rattle space are three important quantities, which should be considered carefully in designing a suspension system. The main advantage of controlled suspension system is that a better set of design trade-off is possible in comparison to passive systems, [5].

The state of the art review by Goodall and Kortum [6] covers important developments in active suspension systems design, including theoretical formulation and analysis, and practical aspects of hardware realization and implementation. Sinha et al., [7] and Caundil et al., [8] have used linear optimal theory to design active suspension controllers for railroad vehicles.

In this paper, the suspension system is optimised with respect to ride comfort, road-holding ability, rattle space and control force expenditure. The passenger acceleration has been used as indicator of ride comfort. Rattle space is the state of the system, and road-holding ability is related to the tire deflection. The control force limits the size and cost of the suspension system.

A two-degrees-of-freedom vehicle model and optimal control theory are used to develop active suspension system with optimised suspension parameters. The optimisation procedure consists of determining the spring stiffness () and damping co-efficient () which minimise the performance index, . The performance index, represents the performance characteristic requirement as well as the controller input force limitations.

The control force gain matrix of the active suspension system is computed by Riccati equation. The results are obtained for the vehicle model moving on a rough road with a constant speed, which is considered as stationary random (Gaussian) process. For the controller design, it is assumed that all the states are available and also can be measured exactly. The simulated results indicate that the use of optimised passive spring and damping elements is advantageous in an active suspension system, because they reduce control forces, not appreciably influencing the performance of the system.

1

Esmailzadeh, E., "Servo-valve controlled pneumatic suspension," Journal of Mech. Engg. Science 21(1):7-18, 1979. doi:10.1243/JMES_JOUR_1979_021_004_02

2

Wright, P.G., Williams, D.A., "The applications of active suspension to high performance road vehicles," IMech E, C239184, 1984.

3

Burton, S.A., Makins, N., Konstantopouloulos, I., Antsaklis, P.J., "Modelling the response of ER damper: Phenomenology and emulation," Journal of Engg. Mechanics, 122, 897-906, 1966. doi:10.1061/(ASCE)0733-9399(1996)122:9(897)

4

Karnopp, D., "Power Requirement for Vehicle Suspension Systems", Journal of vehicle system dynamics, 21(2), 65-72, 1992.

5

Miller, L.R., "Tuning passive, semi-active and fully active suspension systems," IEEE proc. of the 27th conf. On Decision and Control," 2047-2053, 1988. doi:10.1109/CDC.1988.194694

6

Goodall., R.M., Kortum., W., "Active controls in ground transportinal: A review of the state of the art and future potential", Journal of Vehicle Systems Dynamics, 12, 225-257, 1983. doi:10.1080/00423118308968755

7

Sinha, P.K., Wormely, D.N., Hedrick, J.K., "Rail passenger vehicle lateral dynamic performance improvement through active control", ASME publication,78-WA/DSC-14, 1978.

8

Caudill, R.J., Sweet, L.M., Oda.K., "Magnetic guidance of conventional rail road vehicles", ASME J. of Dynamic systems, Measurement and Control, 104(1):36- 42, 1982.

9

Kwakernaak, H., Sivan, R., "Linear optimal control systems", John Wiley and Sons, New York, 1972.

10

Nigam, N.C., Narayanan, S., "Applications of random vibrations", Narosa Publishing House, 280-283, 1990.

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