Optimum Vehicle Suspensions Minimizing RMS Rattlespace, Sprung-Mass Acceleration and Jerk

The optimal suspension structure for a simple one-degree-of-freedom vehicle model is derived using Linear-Quadratic regulator theory. In addition to rms rattlespace and acceleration, rms jerk is included in the performance index. The suspension structure contains a skyhook spring as well as the more well known skyhook damper to inertial ground and must be mechanized actively except for the shock isolation problem with no ground motion. When jerk weighting is predominant, the damping ratio ζ of the complex roots shifts from 0.707 to 0.5. Charts are presented which enable preliminary design calculations to be done graphically. Using frequency response and time response techniques, performance is compared to that of optimal suspensions disregarding jerk.