The presence of fast and slow modes in suspension systems is utilized in the design of two reduced-order active suspension control strategies. The first strategy is obtained by combining the solutions of slow and fast control sub-problems. The second strategy is based on a two-level hierarchical control design. The local level requires measurements of local fast variables, namely the unsprung mass velocities. The coordinating level relies on measurements of slow variables, namely, suspension deflections, sprung mass velocity, and mass pitch rate. Neither strategy requires tire deflection measurements. In spite of their simplified structure, simulation results indicate that their performance is comparable to that of the full-state feedback design.

SUMMARYNeighbouring extremals of dynamic optimization problems with a known parameter vector 8 and an unknown parameter vector T are considered in this paper. The parameter vector T and the control are to be optimally determined to minimize a cost functional with a given 8. With some simplifications, the neighbouring extremal problem is reduced to one of solving a linear, time-varying, two-point boundary value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Example problems are solved to illustrate the validity and usefulness of the solution technique.KEY WORDS Backward sweep method Parameter variations Second variation Neighbouring optimal feedback laws

The high-speed cruising stability of passenger vehicles may be enhanced with stability augmentation systems. These systems would modify the driver’s steering command to the vehicle’s front wheels, and steer the rear wheels according to measured vehicle conditions such as its yaw-rate. In this simulation study, an explicit driver model is used in the design of these stability augmentation systems. For ease of implementation, only low-order controllers are synthesized using parameter optimization. The high-speed, straight-line stability of a passenger vehicle in a cross-wind is simulated to evaluate steering performance with these controllers. Our results show that stability augmented steering has the potential to improve the directional stability of passenger vehicles.