Figure 2 shows the semi-active control of a half-car vehicle model supported on a damper-controlled variable-spring-stiffness suspension system using a force generator. Figures 6 to 9 show the transmissibility curves of bounce and pitch of sprung mass both with and without wheel velocity feed-back. For lower mass ratios, when the wheel velocity feedback is not used, the peak transmissibility at the first resonance frequency reduces significantly, but it increases drastically at the second resonance frequency. When the velocity feedback is taken from the wheel, then the value at the first peak increases. This effect is visible in Figs 6 and 7. With the use of wheel velocity feedback, the peak value first increases and then damps out at higher mass ratios. This can be visualized in Fig. 8. It is clear from Fig. 9 that the pitch values are much less at the second peak with the use of wheel velocity feedback. Therefore, it can be concluded that the force generators can minimize the power required to control the damper.
Comparison between the transmissibility curves for a damper-controlled variable-spring-stiffness suspension and both control forces u and u1 are shown in Figs 10 to 17. At lower mass ratios m and lower damping ratios d, the peak transmissibility at the first resonance frequency increases, but it is the same at the second peak, as shown in Fig. 10. Figure 11 shows the pitch values. The amplitude ratio is less than the damper-controlled variable-spring-stiffness suspension at the first peak, but it is more at the second peak. Both the control forces u (dashed curve) and u1 (curve with open diamonds) give nearly the same results. Increasing the damping ratio reduces the amplitude of the control forces. This effect is shown in Figs 12 and 13. For higher mass ratios, the peak transmissibility of the control forces is slightly higher at the first peak and it coincides at the second peak in comparison with the damper-controlled variable-spring-stiffness as can be seen in Figs 14 to 17. The choice of the optional feedback gain is a compromise. For example, better sprung mass control can be achieved by increasing the gains. However, this reduces control of the other variables in the system, such as wheel hop. Therefore, choice of gain depends upon the design of the actuators. Very high values of gain cannot be utilized as this leads to an increase in consumption of power and further increases complexity.