Page - 101 - in Maximum Tire-Road Friction Coefficient Estimation

5 Tire/road friction estimator Vehicle model F z,i ( b a x , b a y ) r e,i ( W v x ,w i ) s x,i ( W v x , W v y ) W v x (v x ,v y , b w z ) α i (v x ,v y , b w z ) Velocity estimator v x ,v y Sensor signals s x F z,i α i Observer µ G µ fl µ fr µ rl µ rr max max max max max b z(k) . b z(k) δ S M D,i b w z w i b a x b a y u(k) Particle filter Rotational equilibrium (wheels) r e,i M R,i MD,i F x,i Particles (tire model) µF x,i M D,i F z,i r e,i F x,i (µ) F x,i (M D,i ) Figure 5.4.: Schematic structure of tire/road friction estimator showing the driver’s in- puts u(k), the measurement inputs z(k) and z˙(k) on the left side and the estimation outputs xˆ(k) comprisingµmaxG (k) andµ max i (k) on the right side. The observer model consists of the vehicle model (cf. Section 3.2) and the velocityestimator,whichdeliver the inputsneededtocalculate theexpected Fx,i based on the wheel’s angular momentum and the tire forces from the horizontal tire model forN particles of µmax, which are then forwarded to the particle filter. achievable accuracy depends on the accuracy of the measured and calculated inputs for theparticlefilterandalso theaccuracyof thenecessaryvehicleandtireparameters. The required parameters are discussed in Section 5.4.2. Table 5.1 shows all measured signals necessary for the tire/road friction estimator, as shown in Figure 5.4. All these signals are available in a vehicle equipped with ESC, except for the accurate longitudinal and lateral velocities, which have to be estimated, see Section 5.5.1. For all measurements andevaluations shown inSection6, the sensor signalshavebeenmeasuredwithasample rate of 200 Hz. The accuracy of an estimate ofµmax with the proposed method mainly depends on the accuracy of the inputs longitudinal slip sx,i and wheel torqueMD,i. The longitudinal slipsx,i is necessary for the calculationof thehypotheses of the longitudinal tire forcesFx,i that depend on the the particles ofµ max. An accurate calculation ofFx,i and thus sx,i is particularly important. Therefore, these topics are discussed in more detail in Section 5.5. These hypotheses ofFx,i are compared to an expected value ofFx,i within the particle filter, which depends on the wheel torqueMD,i, the rolling resistance torqueMR,i and the wheel’s angular momentum Ir ·∆ωi, as shown in Equation 5.11. 101