Optimal linear time-invariant preview steering control for motorcycles

Abstract

Prior research into the application of optimal linear preview control theory to the steering of a car by a driver is extended into the domain of the motorcycle. The simple car model employed previously is replaced by a much more elaborate motorcycle model, and the control mode is changed from a fixed control for the car to a free control for the motorcycle. Handlebar torque is always the main control input but, in some cases, the rider's upper body lean torque is also included as a control. The machine speed is considered to be constant. The objective of the optimal control is to minimize a weighted sum of path-tracking errors and control power. The time-invariant control corresponding to an infinite optimization horizon and a white noise disturbance is found for each of several cases, involving variations in machine speed and performance priorities. Results demonstrate the relatively minor role of body lean torque control and the strong relationship between the optimal tracking steering control and the motorcycle oscillatory modes of motion. The extent of rider preview necessary for full control is found for cases involving two controls and only one control. The optimal controls are installed on the machine for which they were derived, and simulation results from tracking tasks are shown. The simulations demand the transformation of the problem from a global description, in which the optimal control is found, to a local description corresponding to the rider's view. It is concluded that a motorcycle rider model representing a useful combination of steering control capability and computational economy has been established. The model yields new insights into the rider and motorcycle behaviour.