The article is about steering control of cars by drivers, concentrating on following the lateral profile of the roadway, which is presumed visible ahead of the car. It builds on previously published work, in which it was shown how the driver's preview of the roadway can be combined with the linear dynamics of a simple car to yield a problem of discrete-time optimal-linear-control-theory form. In that work, it was shown how an optimal ‘driver’ of a linear car can convert the path preview sample values, modelled as deriving from a Gaussian white-noise process, into steering wheel displacement commands to cause the car to follow the previewed path with an attractive compromise between precision and ease. Recognizing that real roadway excitation is not so rich in high frequencies as white-noise, a low-pass filter is added to the system. The white-noise sample values are filtered before being seen by the driver. Numerical results are used to show that the optimal preview control is unaltered by the inclusion of the low-pass filter, whereas the feedback control is affected diminishingly as the preview increases. Then, using the established theoretical basis, new results are generated to show time-invariant optimal preview controls for cars and drivers with different layouts and priorities. Tight and loose controls, representing different balances between tracking accuracy and control effort, are calculated and illustrated through simulation. A new performance criterion with handling qualities implications is set up, involving the minimization of the preview distance required. The sensitivities of this distance to variations in the car design parameters are calculated. The influence of additional rear wheel steering is studied from the viewpoint of the preview distance required and the form of the optimal preview gain sequence. Path-following simulations are used to illustrate relatively high-authority and relatively low-authority control strategies, showing manoeuvring well in advance of a turn under appropriate circumstances. The results yield new insights into driver steering control behaviour and vehicle design optimization. The article concludes with a discussion of research in progress aimed at a further improved understanding of how drivers control their vehicles.
Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation
