67
Introduction
O
ver the last few decades, the challenge of creating more accurate models for active safety systems is increased. However, without a precise knowledge of the system’s parameters, any modelling effort stay insufficient to evaluate the system’s dynamics. In the automotive research, the ability to get the pertinent vehicles parameters, a prior or in real-time, allows to develop attractive efficient active safety applications or model based vehicle control (Limroth,2009and Edwards,2008).The parametric identification consists in determining the best values of system’s parameters. It can be formulated as an optimization problem where its resolution can becomes quickly arduous as the number of parameters to be identified increases. One can distinguish two main classes of techniques to solve an optimization problem. The first class are based on gradient computation of the objective function to be minimized while the other class uses stochastic methods (Bartoli and Del Moral, 2001). The choice of the optimization method depends strongly on the complexity of the model. Usually, gradient descent methods are simple to implement and often gives good identification results, thus, they are generally applied in practical applications (Khobotov, 1987, Møller, 1993). Furthermore, multi-objective techniques applied to model identification have achieved great results in many cases, as shown in (Yousefi, Handroos, and Soleymani, 2008, Herrero et al.,2007and Rodriguez-Vazquez and Fleming,1998). Among others, algebraic identification method have been investigated to obtain an accurate model of real system modelled as continuous-time linear transfer function (Fliess and Sira-Ramírez,2003) and, it has been widely applied for electrical and mechanical applications like flexible robots estimation, mass-spring-damper model, DC Motor and others (Mamani et al., 2007, Becedas et al., 2007b, Becedas et al., 2007a, Reger and Jouffroy, 2009). This approach does not require initial conditions and the algorithm can be implemented on-line. Further, almost references, the identification methods are designed under consideration for a specific systems form and their direct transposition to the more general problem case is not straightforward for many reasons. Furthermore, the parameter identification problem is closely related to persistence of excitation in order to enable the parameters to reach an optimal solutions (Hildebrand and Gevers,2002). Hence, for identification process, suitable rich input signals should be considered.
It is common belief that ITS use various vehicle parameters to produce a correct assistance and to minimize the likelihood of false warning. If some parameters are easy to obtain such that vehicle’s mass, CoG position and inertia, identifying or estimating others is much more complex especially in real-time like tire cornering stiffness. For the PTWV, a great effort has focused on state estimation of the vehicle dynamics and several works are published since many years ago (Gasbarro et al.,2004a, Teerhuis and Jansen,2012a, Ichalal et al., 2012, Dabladji et al., 2013, De Filippi et al.,2011b, Nehaoua et al., 2013b). However, to the author’s best knowledge, a very few works deals with the PTWV parameters identification. In fact, the motorcycle is a complex and strongly nonlinear system. Almost attempt for parameters identification used behavioural models and statistical methods. Also, the persistence is difficult to respect since it is not possible to freely apply rich excitation signals to solicit the different dynamics due to the PTWV’s mechanical constraints and instability.
For example, in (James, 2002), the author considers an auto-regressive model to describe the motorcycle lateral dynamics behaviour and next used to estimate a state space representation which has no relation with the physical parameters. Also, (Savaresi et al.,2008) and (Savaresi et al.,2006) have used a regression-based estimation methods to recover the available road friction. Moreover, non model-based identification method is described in (Corno and Savaresi,2010), where the authors present a black-box identification. This method allows to directly estimate the input/output engine-to-slip dynamics of sport motorbike from experiments, instead of using the classical approach of multi-body modelling. In (Cossalter et al.,2006a), the authors deal with the identification of the vibration characteristics of motorcycle riders. This work presents an analysis to identify the properties of a rider multi-body model, which is used to fit the experimental data excited by means of stepped sine testing. On the other hand, studies have shown that semi-active steering dampers for motorcycles can be used in the design of innovative control strategies to improve two-wheeled vehicles stability. In the study (Tanelli et al.,2009b), an analytical model of a two-wheeled vehicle tuned to capture the weave and wobble modes to study steering related instabilities. The model is derived from first principles and its parameters tuned to fit a hyper-sport motorcycle based on a grey-box identification procedure. Also, in (Schwab et al., 2012; Schwab, De Lange, and Moore, 2012), the authors assume a linear PID controller for the rider control model. First, this parametric control model is fitted to the experimental data using black-box finite impulse response (FIR) model. After that, a gray box model is fitted to the response of the
68
FIR model to identify the PID feedback gains. Then, these gains are used to compute the specific optimal control linear-quadratic regulator (LQR) which the rider is using to control the two-wheelers.
Braking and traction control systems are commonly designed considering an integrated step of identification.
In the study of (Cabrera et al.,2014), the authors consider wheel slip control when excessive torque is applied on driving wheels, using a fuzzy logic control block. The parameters that define the fuzzy logic controller have been tuned, first according to experience, then, by means of an evolutionary algorithm in order to design an augmented traction controller.
Other approaches have been investigated to study electric two-wheelers, in Wilhelm et al.,2012, the author describes an algorithms based on a grey-box model for estimating four characteristic parameters of a linear dynamics model, then the physical meaning has been interpreted from the identified parameter values.
Past works have been interested in motorcycle suspension system based on estimation theory. The recursive least squares algorithm which incorporates a fault detection scheme can be a suitable approach to estimate the time varying dynamics as proposed in (Ledwidge,1995). It is shown using software simulations, a mass, spring and damper model are selected to represent the dynamics of the suspension system, these parameters were estimated from static tests. Further, motorcycle simulator prototype has been investigated in the recent decades, due to the rising concern of the rider safety. Their modelling claims informations about different parameters, as reviewed in (Nehaoua and Arioui,2008), where, the authors present the dynamics modelling and parameters identification of a motorcycle simulator’s platform. The identified parameters can be used to improve control scheme, adapted to driving simulation application. Also, the roll motion parameters of a motorcycle simulator prototype were studied in (Shahar et al.,2014).
To summarize, parameters identification is a main step in motorcycle studies, either for control requirements, safety purpose or even in behaviour and stability analysis. Previous studies have used various approaches with some assumptions according to the model and the available driving data. However, the robustness of these approaches across different motorcycle architecture, models and riding behaviour still needs a thorough improvements. Withal, most of these works have been devoted at identifying only part of the dynamics.
Nonetheless, the identification of the full dynamic is a real challenge.
This part deals with the parameter identification for motorcycle model parameters. In the previous chapter 2, we have studied two lateral dynamics models, one rigid body and two-bodies model (Sharp’s model).
For Sharp’s model, more than 30 unknown parameters needs to be identified which is a hard task. We’ll describe several approaches for motorcycle parameters identification where the conventional methods have failed or are difficult to apply. To do this, we divided this part into two chapters. The first one deals with the rigid body model, we’ll discuss static identification, gradient decent algorithm and algebraic identification method The second chapter studied the two-rigid bodies model. We’ll present multi-objective optimization and Levenberg-Marquardt algorithms.
69