Abstract
Active and semi-active suspensions for passenger cars have been traditionally used to enhance ride comfort through body control, and vehicle handling by reducing the tyre load variations induced by road irregularities. Active suspensions can also be designed to track a desired yaw rate profile through the control of the anti-roll moment distribution between the front and rear axles. Such control action alters the load transfer distribution, which in turn provokes a lateral tyre force variation.
The first purpose of this work is to provide control formulations for semi-active and active suspension actuators to control the yaw, roll, pitch, and heave dynamics excited by the driving actions. To begin with, a combined feedforward and feedback front-to-total anti-roll moment distribution controller, aiming to improve vehicle yaw rate response in both steady-state and transient-state conditions, is presented. The influence of load transfer on the lateral axle force and the tyre cornering stiffness is analysed, and leads to a new linearised lateral axle force model formulation that is used in the frequency domain for the design of the feedback part of the controller. Then, an offline optimisation based on a quasi-static vehicle model is exploited to determine the reference yaw rate as well as the nonlinear feedforward part of the proposed controller to achieve driver-preferred vehicle understeer characteristics. Simulations and real experiments demonstrate the effectiveness of the proposed controller in reference yaw rate tracking, vehicle roll stabilizing, and yaw response oscillation reduction. Secondly, two novel real-time-capable implicit nonlinear model predictive control (i-NMPC) formulations, excluding and including cost function weight adaptation, are proposed and compared with the passive vehicle, and the controlled vehicle with two combinations of skyhook and active roll control, the first one based on a pseudoinverse decoupling transformation for obtaining the damping force contributions, and the second one using an inverse formulation. The algorithms are assessed through an experimentally validated simulation model, along manoeuvres corresponding to sub-limit and limit handling operation, to analyse the trade-off between body motion reduction and cornering response enhancement. The results show that the NMPC configuration with adaptable cost function weights provides the best performance in all scenarios, including consideration of significant variations of the main vehicle and tyre parameters. The NMPC algorithm is also applied to a vehicle equipped with only controllable dampers, and the preview functionality based on the future steering wheel angle profile is added for generating the reference yaw rate and improving cornering response. The performance of the proposed preview controller is evaluated for two different internal model formulations, for different prediction horizon lengths, and through robustness analysis with respect to the estimation inaccuracies of the steering wheel angle input.
The second objective of this study is to design a controller to enhance ride comfort. A regionless explicit model predictive controller (e-MPC) for an active suspension system with preview is introduced and assessed through simulations and experiments on a sport utility vehicle demonstrator with controllable hydraulic suspension actuators. The results show how the inclusion of the preview provides the best performance in reducing the root mean square of the heave and pitch accelerations of the sprung mass with respect to the baseline MPC configuration (without preview) and the benchmarking skyhook controller.