Two degrees of freedom PID multi-controllers to design a mathematical driver model: experimental validation and robustness tests

Abstract

This paper proposes a mathematical driver model based on PID multi-controllers having two degrees of freedom. Each PID controller making up this model is synthesised by the Ziegler–Nichols oscillation method, using the linear time invariant models which are obtained around their nominal operating points. Different PID controllers are combined using nonlinear optimisation and the H _∞ constraint. To demonstrate its robustness, it was tested on two models: a linear parameter variant model and a nonlinear four-wheel model. It was also tested in situations of high dynamic demand. The driver model showed good performance, stability and trajectory tracking. The performance tests were carried out using experimental data acquired by a Laboratory Peugeot 307 developed by INRETS-MA. This driver model was developed for an application known as ‘Itinerary Rupture DIagnosis’ (DIARI), which aims to evaluate the physical limits of a vehicle negotiating a bend. DIARI requires a tool to determine the steering commands to be applied to a vehicle model, making extrapolations with respect to speed.

Keywords:

• vehicle dynamics and experimental validation
• mathematical driver model
• PID multi-controllers
• switching control

Notes

Linear parameter-varying model ⇔ LPVM; Nonlinear four-wheel model ⇔ NL4WM.

The two first sites used in the study, located in the Côtes d'Armor area of Brittany, were selected for certain dangerous features by the French SARI project. It should be pointed out that the experimental results shown in this section are from the following sites: Site 1: Figures 15, 17–20 and all figures of the speed extrapolation test (from Figures 22–24). Site 2: Figures 16 and 21.