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

Contents 5.4. Observer structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.4.1. Measurement inputs . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.4.2. Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.5. Considerations for the calculation of the longitudinal tire forces . . . . . . 103 5.5.1. Estimation of the longitudinal slip . . . . . . . . . . . . . . . . . . 104 5.5.2. Estimation of the slip angles . . . . . . . . . . . . . . . . . . . . . 105 5.5.3. Wheel’s torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6. Results and conclusion 107 6.1. Strong acceleration manoeuvre with constantµmax . . . . . . . . . . . . . 107 6.1.1. Results without resampling step . . . . . . . . . . . . . . . . . . . 108 6.1.2. Results with resampling step . . . . . . . . . . . . . . . . . . . . . 110 6.1.3. Resampling step with particle re-initialisation . . . . . . . . . . . . 111 6.2. Strong braking manoeuvre with varyingµmax . . . . . . . . . . . . . . . . 113 6.3. Gentle braking manoeuvre on varyingµmax . . . . . . . . . . . . . . . . . 117 6.4. Braking manoeuvre onµ split conditions . . . . . . . . . . . . . . . . . . . 119 6.5. Comparison of results with requirements of an AEB . . . . . . . . . . . . 122 6.6. Discussion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7. Summary 127 A. Friction potentials in literature 131 B. Tire model TMsimple and tire dynamics 133 B.1. Parameter relationships between static tire model . . . . . . . . . . . . . . 133 B.2. Modelling time function τy . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 C. Vehicle model structure for sensitivity analysis 137 C.1. Numerical implementation of vehicle model for automatic differentiation . 138 C.1.1. Find maximum out of two values . . . . . . . . . . . . . . . . . . . 139 C.1.2. Absolute value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 D. Vehicle and tire model parameters 141 E. Longitudinal velocity estimation 145 E.1. Estimation of the longitudinal velocity using only ESC sensors . . . . . . 145 E.2. Observer-based estimation of the longitudinal velocity . . . . . . . . . . . 146 E.3. Radar-based estimation of the longitudinal velocity . . . . . . . . . . . . . 147 xxi