Observer design for motorcycle lean and steering dynamics estimation: A Takagi-Sugeno approach

Abstract

In this paper, a nonlinear motorcycle model is considered in order to estimate both the lean and steering dynamics. The model is transformed into a Takagi-Sugeno (T-S) form using the well-known sector nonlinearity approach. The first contribution of this work is the exactness of the obtained T-S model compared to the considered nonlinear model, where the weighting functions of the T-S model depend on unmeasured state variables. A novel approach to construct a nonlinear unknown input fast observer is proposed. The objective is the simultaneous reconstruction of the state variables and the rider's torque. The observer's convergence is studied using Lyapunov theory guaranteeing boundedness of the state and unknown input estimation errors which is expressed by the Input to State Practical Stability (ISpS). Stability conditions are then expressed in terms of Linear Matrix Inequalities (LMI). Finally, simulation results are provided to confirm the suitability of the proposed nonlinear observer.

Observer based controller for single track vehicles

“…The obtained model is the same as the one used in [6], [10]. We suggest readers to refer to this articles for more details on the matrices E,B andÃ(x) and their parameters.…”

“…More recently, a higher order sliding mode observer was proposed to estimate the lateral dynamics and steering torque in [12]. The same authors proposed also a study on state and unknown input estimation by exploring the Takagi-Sugeno systems and linear matrix inequalities in [6].…”

Robust Observer-Based H∞ Controller Design for Motorcycle Lateral Dynamics

“…Model of the Motorcycle. The model used in this work describes the motorcycle's lateral and roll dynamics, which are obtained by considering Sharp's motorcycle model [11] (see Figure 1). The dynamics of a motorcycle can be represented by a model with four equations [12,13] describing the lateral motion mainly caused by lateral forces ( , ) and the yaw and roll motions under rider's steering actions.…”

Estimation of lateral motorcycle dynamics and rider action with Luenberger observer

“…In practice to get better performance of the observer it is possible to transform the previous LMI (17) in an optimization problem by considering γ as a variable parameter of optimization. …”

“…In [17] an adaptive observer is used. Proportional multiple integral (PMI) observers and Kalman filter as discussed in previous paragraph are also used for PTW lateral estimation.…”