On the Design of Yaw Rate Control via Variable Front-to-Total Anti-Roll Moment Distribution

Abstract

In vehicle dynamics, yaw rate control is used to improve the cornering response in steady-state and transient conditions. This can be achieved through an appropriate anti-roll moment distribution between the front and rear axles of a vehicle with controllable suspension actuators. Such control action alters the load transfer distribution, which in turn provokes a lateral tire force variation. With respect to the extensive set of papers from the literature discussing yaw rate tracking through active suspension control, this study presents: i) A detailed analysis of the effect of the load transfer on the lateral axle force and cornering stiffness; ii) A novel linearized single-track vehicle model formulation for control system design, based on the results in i); and iii) An optimizationbased routine for the design of the non-linear feedforward contribution of the control action. The resulting feedforward-feedback controller is assessed through: a) Simulations with an experimentally validated model of a vehicle with active anti-roll bars (case study 1); and b) Experimental tests on a vehicle prototype with an active suspension system (case study 2).

On the model-based design of front-to-total anti-roll moment distribution controllers for yaw rate tracking

“…Hence, a system of two equations outputs c 1,i and c 2,i : Figure 5 compares the lateral axle force characteristics from the magic formula, Model A and Model B. The reference operating points, highlighted by the square markers, are defined for nominal values of F y,i,0 , α i,0 and F z,i,0 , corresponding to a y = 3, 6 and 9 m/s 2 , obtained for steady-state cornering through the quasi-static model in [30,[32][33][34]. For all models, the results are reported for:…”

“…where A, B and E are the state, input and disturbance matrices, and C, D and F are the respective output equation matrices. In the equations, α i,0 , F z,i,0 , r 0 and f 0 are obtained from the nonlinear quasi-static model from [30], suitable for the analysis of the steadystate cornering behaviour; F y,i,0 , F y,i,0 and C i,0 are calculated through the manipulation of the magic formula, whereas β 0 , ϕ 0 and S 0 result from (21), by imposing q(x 0 , u 0 , w 0 ) = 0.…”

“…Figure 10 is a simplified schematic of the implemented front-to-total anti-roll moment distribution controller. f is given by the combination of two contributions: (i) a nonlinear feedforward contribution, f FF , computed offline via an optimisation routine based on a quasi-static model, see [30] and [32][33][34], which provides the desired cornering response in nominal steady-state conditions; and (ii) a feedback contribution, f FB , generated by a PI controller, which is the focus of this study.…”

“…its gains are expected to be negative, as the increase of the vehicle yaw rate requires a decrease of the control action. The reference yaw rate, r Ref , and the feedforward contribution, f FF , are modified based on the value of the rear axle sideslip angle, β RA , and a y , to avoid unstable vehicle behaviour in critical conditions, see [30] and [36]. Starting from the resulting f , the front and rear anti-roll moment generator calculates the front and rear active anti-roll moments, M AR,Act,F and M AR,Act,R , which are sent to the suspension actuators.…”

“…In the integrated chassis controller of [29], the front-to-total anti-roll moment distribution parameter is controlled through an empirical law, using a sideslip-based stability index and the yaw rate error, without model-based control. In [30] Ricco et al present an anti-roll moment distribution controller consisting of nonlinear feedforward and linear feedback contributions; however, the study does not include the frequency response analysis of the model for feedback control design.…”