Keywords: slow-active suspension, wheelbase preview, optimal control, correlated random road inputs, car riding model.

Electronically controlled suspension systems have the potential to overcome limitations of passive systems and to reduce the need to compromise among a variety of operating conditions and among the generally conflicting goals of the suspension designs. Such goals include providing good vibration isolation of the vehicle body (ride comfort), maintaining uninterrupted contact between the tire and the road (road holding ability for ride handling), and stabilizing the vehicle body (ride safety). Many investigators have used full bandwidth suspension systems, which offer improvements in ride and handling qualities but may suffer from other problems such as complexity, high cost and power consumption and noise, vibration and harshness problems. Consequently, such fully active systems have been unattractive commercially for production cars. However, it has been demonstrated that limited bandwidth active (slow-active) systems can offer significant improvements in the control of body resonances, similar to full bandwidth systems. The slow-active systems may be envisaged as an actuator of limited bandwidth (around 3-5 Hz).

In recent years, there has been a great interest in the use of a preview of the road input in the design of active suspension systems, and very encouraging results in terms of improved performance have been obtained. Since the control law needs information on the road input some distance ahead of the front wheels, practical difficulties of measuring the road surface by a body-mounted road sensor are encountered.

Practically, however, as a vehicle travels straight on hard road surfaces, the rear wheel is subject to almost the road input as the front wheel with only a time delay. The wheelbase preview information can be incorporated in the control law designs for active vehicle suspension systems, and further performance improvements may be expected. The wheelbase preview control has recently been studied and promising results have been obtained. The benefits come without the additional costs for sensors.

In this paper, an optimal control design method based on the use of the correlation between the front and rear wheel inputs (wheelbase preview) is introduced and then applied to the optimum design of a slow-active suspension system. The suspension consists of a limited bandwidth actuator in a series with a passive spring, the combination being in parallel with a passive damper. A three-dimensional seven degree of freedom car riding model subjected to four correlated random road inputs is considered. The performance potential of the limited bandwidth system with wheelbase preview in comparison with the non-preview (uncorrelated inputs) case is investigated.

The simulation results have shown that the controller based on wheelbase preview moderately improves the general road performance of the slow-active suspensions. An improvement of about 11% at a speed of 5 m/s in ride comfort is obtained by using the wheelbase preview control strategy over that without preview. The preview control for the slow-active system makes it possible to have improvement up to 29% in the suspension working space over the non-preview control at a vehicle speed of 20 m/s (0.14 sec preview time). The slow-active suspension system has very good performance in comparison to that of a typical passive system. It provides damping of the body resonances very effectively.

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