Design of an Adaptive Throttle-by-Wire Control System for a Sport Motorbike

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1 Preprints of the 8th IFAC World Congress Milano (Italy) August 8 - September, Design of an Adaptive Throttle-by-Wire Control System for a Sport Motorbike Giulio Panzani Matteo Corno Sergio M. Savaresi Dipartimento di Elettonica e Informazione, Politecnico di Milano, P.za L. da Vinci 3, Milano, Italy ( {panzani, savaresi}@elet.polimi.it). Delft Center for Systems and Control, Delft University of Technology, Mekelweg, 68 CD Delft, The Netherlands ( m.corno@tudelft.nl) Abstract: Thispaperaddressestheservo-controllerdesignofanelectronicthrottlebody(ETB) designed for ride-by-wire applications in racing motorcycles. The dynamics of the system is identified and a model of the friction is derived from experimental data. It is shown how, by identifying the friction characteristic, it is possible to separately design a linear time invariant closed loop controller and a friction compensator. In the second part of the paper the friction compensator is made adaptive so to enable an automatic and online identification of the friction. Experimental tests validate the controller and compensator design. Keywords: Mechatronic Systems, Automotive Control, Cost Oriented Automation, Adaptive and Learning Systems.. INTRODUCTION The number of electronic control systems in four-wheeled vehicles has been increasing for at least a decade now. At first, the two-wheeled vehicles world was reluctant to adopt these technologies. This happened mainly for economic and romantic reasons. In the past few years this tendency has changed; high-end motorcycles are now being equipped with performance-oriented electronic control systems (like racing ABS (Corno et al. (9b)), traction control (Tanelli et al. (9)) and semi-active suspensions (Savaresi et al. ())). The change of attitude is mainly due to the success of these systems on the racing track. Performance-oriented systems should be regarded as a bridge head to encourage the diffusion of systems that would eventually improve the overall vehicle safety. Among the several electronic control systems being developed, traction control represents one of the first that has hit mass production. In most cases traction control is implemented via ignition and spark control; in a previous work (Corno and Savaresi ()) it was shown how electronic control of the throttle represents a viable (and easier)alternative controlvariable. Ingasolineengines,the throttle controls the air path to the engine and thus the engine torque. Electronic throttle bodies (ETB) are mechanically and electronically simple systems composed of one or more butterfly valves actuated by an electrical motor through a reduction. These systems are completely electronically actuated. Despite their apparent simplicity the problem of controlling such systems is made difficult by cost, reliability and packaging constraints. The cost-driven mechanical design often leads to high friction. The problem of electronic throttle actuation in cars has been studied by many This work has been partially supported by FIRB project Highly innovative motorbikes with ultra-low emission engines, active suspensions, electronic brakes and new materials and MIUR project New methods for Identification and Adaptive Control for Industrial Systems. authors, see for example Rossi et al. (), Pavkovic et al. (6), Vasak et al. (6), Deur et al. (4). Althoughthecontrolproblemsinthefourandtwo-wheeled casesaresimilar;stricterrequirementsmustbesatisfiedfor two-wheeled vehicles. This is mainly due to more stringent packaging constraints and higher static and dynamic performance requirements due to the higher power-to-mass ratio typical of two-wheeled vehicles. For two-wheeled specific results in ETB control one can refer to Beghi et al. (6) where a sliding-mode controller is presented or Corno et al. (to appear) where a gain-scheduled controller is designed for a single-stage throttle and Corno et al. (9a). The first approach is not viable for racing applications because the high frequency switching of the control variable due to the sliding mode controller yields an excessive power usage. In the cited second work, this problem is solved by designing a classical controller. The controller is first designed on a linear model of the throttle and then its scheduling law experimentally tuned; the fine tuning of the classical control is time-consuming. A better solution is presented in the third paper where a method to design and tune a friction compensator is described. The structured approach yields the same performance level as the other controllers with considerably reduced design and tuning costs. The present work builds on the results presented in Corno et al. (9a) by proposing an automated and online identification of the friction compensator. The improvements are two-fold: on one hand the design and tuning costs are further reduced and on the other hand the system is now able to adapt to changing friction characteristic, thus making the overall system more cost effective, reliable and able to deliver consistent performance through the life of the components. This paper is organized as follows: in the second section the system and the experimental set-up are described, the model is briefly recalled and identified. In Section 3 the control architecture is derived; Section 4 is devoted to Copyright by the International Federation of Automatic Control (IFAC) 4785

2 Preprints of the 8th IFAC World Congress Milano (Italy) August 8 - September, the discussion of the online friction adaptation algorithm. Finally, the paper is concluded with some remarks.. SYSTEM DESCRIPTION AND MODELING The electronic throttle body is depicted in Figure. It is a dual-stage throttle and is composed of the series of two valves. The first valve is a classical throttle which is mechanically connected to the handle grip of the motorcycle; the second valve is servo-actuated. Although developed and validated for this architecture, the method presented in this paper is applicable also to the more traditional single-stage throttles.. Model Identification Thanks to the presence of the current control loop, the system can be divided into three parts: the return spring, the friction effect and the mechanical dynamics (inertia and viscous friction). Friction is one of the most important phenomena affecting the throttle dynamics. It does not only make the design of the control system difficult, but it also renders openloop system identification impossible. If a zero mean high frequency current excitation is applied to the throttle, it will not respond with a zero mean position; rather, the throttle plate will drift away reaching either the fully closed or fully open configuration. It is then clear that closed-loop identification techniques (Forsell and Ljung (999)) are required. It is therefore necessary to design a low bandwidth servo loop controller. As it only needs to stabilize the response, the design can be easily done by trial and error. Once this temporary control system is implemented, the spring, friction and linear dynamics can be sequentially identified. At first the return spring is identified via quasi-static testing constituted of ramp from fully closed to fully open. The results of such identification are shown in Figure 3. In analyzing the figure, one should consider that the Fig.. The electronic throttle body. The servo actuated throttle is made of a DC motor, a planetary reduction gear (gearbox ratio η) and a linkage that connects the shaft of the motor to the shaft of four valves. The linkage is required for packaging reasons. An angular potentiometer is mounted on the valve shaft..5 Estimate Current [A].5 The ECU motorcycle (with a sample time of ms) is used to control the throttle Position [ ] Fig. 3. Return spring characteristic. hysteresis is caused by stiction. The second aspect of the system that is considered is the friction. The friction effects are modeled according to the Stribeck model (Guran et al. (996)). The model. /s Fig.. Schematic Representation of the ETB architecture..5 /s It is common practice in servo-control to implement an inner current control loop as it helps decoupling the electric and mechanical dynamics. Further, if the bandwidth of the current loop is high enough, the system can be assumed torque controlled. The design and tuning of such a system is trivial; details on how to approach the problem can be found in any mechatronics textbook (see e.g. Ferretti et al. ()). In the considered system a Hz is achieved. current [A] Figure shows the block diagram of the throttle control system. The following elements are shown: the DC motor dynamics Gel (s), the mechanical part of the ETB modeled as the planetary gear, the return spring, the friction nonlinearity and the linear throttle dynamics Gth (s). The system is completed by the current and position control loops which regulate the throttle position θ to a desired set-point θ. optimal interpolation.5 /s.5 /s speed [( )/s] Fig. 4. Stribeck friction identified model and experimental data. characteristic is shown in Figure 4 and can be synthetically described as: 4786

3 Preprints of the 8th IFAC World Congress Milano (Italy) August 8 - September, where F s if θ = and I > F s F f ( θ) = I if θ = and I < F s F( θ) if θ ( F( θ) = +(F s )e θ θs) sign( θ). The model depends on three parameters (α = [F s,, ]). Theaboveparameterscanbeidentifiedfromdatacollected from ad hoc experiments. In the following, it will be assumed that the overall mechanical dynamics of the system can be described by: () J θ +R θ +K(θ)θ +F f ( θ)+ = I () where J is the equivalent (as the system is written with the current as an input) inertia, R is the equivalent viscous friction, K and are respectively the spring equivalent stiffness and the preload and F f is the static friction. By running experiments at small velocity and acceleration, the terms due to J and R can be neglected and by compensating for the known K it is possible to estimate F f ( θ). Inparticular experiments with constant acceleration (both positive and negative) are run. The results are plotted in Figure 4. The figure clearly confirms the characteristic Stribeck shape and a numerical optimization algorithm returns the optimal parameters ˆα = [.45,35,.7]. Once both the friction and the spring characteristics are identified, the remaining dynamics can be identified with a black-box approach. The closed loop system is fed with a reference signal constituted by a multi-frequency sinusoidal signal (from. to 5Hz) of amplitude 5% centered around the reference position θ = 5%. In order to estimate the frequency-response of the overall system G th (s), the intermediate I signal and the output position θ are employed according to the following expression proposed in Wellstead (98): G th (jω) = Ŝ θθ(jω) Ŝ θu (jω) The experimental frequency response is the basis for the frequency based black-box linear model identification. The intent is that of capturing the linear part of the system; in order to do so the following optimization problem is posed: min p (3) l w f (k) h(k) G th (ω(k)) (4) k= where l is the number of available frequencies, w f (k) is a weight that is used to drive the fitting toward the frequency range [5 5] Hz, h(k) is the experimental frequency response. The choice of focusing the optimization at relatively high frequency is dictated by the need of identifying the linear part of the response. At high frequency (and therefore at high velocity and high acceleration) the effects of static friction can be neglected with respect to inertialandviscouseffects.thesameoptimizationmethod described in Corno et al. (9a) has been employed resulting in a second order system: b G th = s (5) +a s+a 3. Model Validation Previously the three main parts of the system have been described and identified; to validate the model the closedloop system is simulated and the time-domain results are compared with the experimental ones. Note that being a closed-loop validation it is interesting to compare both the measured output and the control variable. Figure 5 and 6 show the validation results for two different frequencies. current [A] Fig. 5. Validation at.5- Hz. current [A] Fig. 6. Validation at Hz. position [ ] position [ ] The figures show that the model is capable of accurately describing the strongly nonlinear behavior of the overall system. 3. CONTROL LAW DESIGN The availability of an accurate model considerably simplifies the servo-controller design. The proposed controller is composed of a linear part and a friction compensator (see Figure 7). Under the hypothesis of perfect compensation, Fig. 7. Complete controller system architecture. the controller can be tuned on the linear part of the system. A classical PID structure has been implemented; the two zeros of the controller are tuned in order to cancel the two poles of the linear part of the system and the gain of the PID controller has been set to obtain a bandwidth of 5Hz and a phase margin of 75. Figure 8 shows tracking performances for different setpoint; without the friction compensation the response is not statically nor dynamically accurate. Sinewave setpoint shows stick-slip phenomena if friction is not compensated, occurring each time the throttle changes its movement direction. Thanks to friction compensation no loss of time is needed to overwhelm static friction and the response of the system is optimal. The second panel shows a dinamically demanding step reference: without friction compensation the response is slower and no static precision is guaranteed. Again the introduction of the compensation solves these problems. Although with the proposed method it is possible to identify Stribeck friction parameters, it is interesting to analyze controller performances with respect to friction 4787

4 Preprints of the 8th IFAC World Congress Milano (Italy) August 8 - September, Position [ ] 5.5. Setpoint w compensator w/o compensator Time [s] Position [ ] Setpoint w compensator w/o compensator Time [s] Fig. 8. Improvement of tracking performances given by friction compensation. Sinewave and step setpoint. compensation changes. In particular Figure 9 is depicts a comparison between the complete model compensator and a simplified one, in which F( θ) = sign( θ) thus neglecting Stribeck effects. This solution is expected to yield worse performance but is computationally less demanding. Tracking signals are shown for a real race-track throttle setpoint: differences between controllers are negligible. first part that estimates the term I f = F f + and the second part that, from the value of I f, estimates the actual friction parameters. 4. I f estimation From equation () I f = F f ( θ)+ = I J θ R θ K(θ)θ (6) which, taking the Laplace transform, becomes I f (s) = I G th (s) θ(s). (7) NotethatthespringpreloadisnowpartofI f anditwillbe estimated online. G th (s) is the linear part of the system; it cannot be inverted as the inverse transfer function would not be causal. A filer Q(s) is used to make the filter causal. To avoid phase shift also the measured current is filtered with the same low pass filter. 4. Friction coefficients and spring preload estimation Position [ ]. Setpoint Stribeck model Simplified model Time [s] Fig. 9. Comparison between complete and simplified friction model. Figure summarizes the results showing the RMS of the tracking error for different reference signals: both friction compensators consistently enhances performances. 4. ONLINE FRICTION COMPENSATION Friction compensation notably improve the reference tracking; however, offline identification of the friction parameters is time consuming; moreover friction depends on the component wear and lubrication. The friction characteristic will likely be time-varying. It would therefore be useful to automatically identify the friction model and keep it updated as the lubrication status changes. This is achieved via the online friction observer outlined in Figure 7; the friction observer is composed of two main parts: the RMS error W/o compensator Stribeck model Simplified model Sweep Steps Random noise Sine wave Real Throttle Fig.. RMS tracking error for different setpoint: summary with different friction compensators. Once I f is known, the friction and spring preload parameters can be estimated using a least square approach. In fact [ ( Î f (t)= +(F s )e θ ) ] θs sign( θ)+ +ǫ(t) =φ(t) T ρ+ǫ(t) (8) where [ ( φ T = e ( θ ( θs) sign( θ), e θ ) ) ] θs sign( θ), [ ] Fs ρ= c The ǫ term accounts for modeling errors. If the Stribeck velocity is assumed known, the estimation can be carried out through a recursive least square approach by minimizing the following cost function: J = N λ n (. Î a (i) φ(i) ρ) T (9) N i= The estimation of the Stribeck velocity requires accurate measurements,thereforeitwillbesurelyaffectedbyerrors. Figure studies the effect of those estimation errors. The plots show the convergence of the three parameters resulting from a sinusoidal excitation test (at.5 Hz). In presence of errors in the estimated Stribeck velocity, estimationoff s and arebiased;thisiseasilyunderstoodby recalling that F s and are intimately bound to, as the Stribeck velocity appears in the corresponding regressors. On the other hand, the estimation of the preload is not affected by a wrong estimate of the Stribeck velocity. This is due to the fact that the preload is independent on the velocity and, if it is assumed that during the test the average velocity is (meaning that the throttle is opened and closed with the same dynamics, reasonable assumption), the average value of I f provides a good estimate of. To better understand the estimation bias let consider first the case limit of : φ and phi ; this means that the estimation is forced to fit the nonlinear Stribeck function with the constant value. Same reasoning holds when : in this case F s is the constant value that is estimated. It is clear that in both cases, the value that is assumed by the estimated parameter is bounded 4788

5 Preprints of the 8th IFAC World Congress Milano (Italy) August 8 - September, F s.8 θ *3 s / *3 / /3 simplified model * simplified model Fig.. Estimated F s, and resulting from a sinusoidal excitation test for different values of the assumed Stribeck Velocity. between the real friction F s and. It is more difficult to provide estimation bounds when {,, }, since both friction parameters play a role in the estimation: as it is shown in Figure estimated values are not necessarily bounded between real F s and. Based on the above considerations, it is thus concluded that in absence of an accurate estimation of the most conservative choice is to use a simplified version of the model in wich. In this way F s is not estimated and will be slightly overestimated. This choice corresponds to using the simplified compensator discussed in Section 3: it s important to underline that, from a control system point of view, tracking performances are preserved even when the simplified model is used for friction compensation. In conclusion the RLS approach estimate friction parameters according to model () 4.3 Simulation Validation φ T = [ sign( θ), ] ρ=[ Fc c ] () Simulation data can be used to better understand the propertiesandfeaturesoftheproposedestimationmethod. Inparticulartheeffectsofmeasurementnoiseanddifferent excitation signals will be discussed. Figure plots the behavior of the estimated preload and parameters as a function of time in a sinusoidal experiment for different noise levels. Whereas the preload measurement noise 3*measurement noise no noise 6*measurement noise 4 6 Fig.. Estimated and resulting from a sinusoidal excitation test for different values of the measurement and velocity estimation noise. force converges to the right estimate, high levels of noise introduce a bias in the estimation of : this is caused by chattering induced in the first regressor of () when the velocity is small due to the presence of the sign nonlinearity. This effect can be reduced by introducing a dead-band to around the zero velocity, however it is noted that with realistic level of noise the bias can be neglected and the estimate converges to a value that is comprised between the real F s and. In Section it was pointed out that the best signal to identifythefrictioncharacteristicisalowfrequencysignal; during normal usage of the throttle the signal may not have the desired frequency characteristics. The sensitivity of the identification method to different reference signals is now verified. Figure 3 compares the effects of different excitation signals: sinusoidal input, band limited white noise and the data collected during real track laps. Eventually the estimated parameters converge in all cases;.6.4 sine filtered noise sine. filtered noise Fig. 3. Estimated friction and preload parameters trajectories for different kind of excitations. in the test track data the convergence is slower (it takes an average of 6 s). Further note the small bias in the estimation of the spring preload caused by the non-zero mean ofthereferencesignal intheconsideredwindow; also in this case is comprised between F s and. The slower convergenceinthecaseofrealusageprofilesdoesnotaffect the controller overall performance. Note that as the goal of the system is that to adapt to changes of friction due to wear and tear a convergence time of minute is more than adequate. 4.4 Experimental Validation The validation of the friction coefficient estimator on real dataisshowninfigure4wheretheresultsforasinusoidal test are shown along with the results for a. The.6.4 sine sine 4 6 Fig. 4. Estimated friction and preload parameters trajectories in the case of sine and racing track excitation signal - simplified friction model. same conclusions drawn in simulation apply. In case of a sinusoidal excitation the convergence is faster, but equally accurate in both cases. Ithasbeenshownhowitispossibletoestimatethefriction coefficient and thus simplify the friction identification procedureandatthesametimehaveanadaptivefrictioncompensator. The previous analysis was focused only on the 4789

6 Preprints of the 8th IFAC World Congress Milano (Italy) August 8 - September, estimation of the compensator parameters. The tests were run with a fixed compensator. When the output is used to adaptively change the compensator then it is important to guarantee that the estimated parameters dynamics does not fall within the bandwidth of the controller, as this would invalidate the linear design and analysis carried out in Section 3. The dynamical decoupling is guaranteed by low pass filtering the parameter estimator output. The experimental results of the complete closed loop system are shown in Figure 5. As it can be seen from figure, position [ ] measured set point Fig. 5. Reference tracking of the complete adaptive system. provided that the output of the estimation is low pass filtered, the two control loops are decoupled in frequency and a good tracking performance is achieved. 5. CONCLUSIONS In this paper a complete procedure to design a electronic throttle control system has been proposed. The procedure starts with the derivation and identification of a model of the system. The LTI part of the identified model is used to design a PID controller while the nonlinear friction model is used to design a friction compensator that is shown to improve the tracking performance of the system. In order to speed up the control design phase and to ensure that consistent performances are achieved also in case of wear and tear of the components, an online identification of the friction coefficients is presented. It is shown that only a simplified model of the friction can be consistently estimated. However the simplified compensator yields the same tracking performance as the complete one. It is further shown that by running an ad-hoc experiment, the identification of the friction model is faster and more accurate; whereas with regular usage data convergence takes longer. One could envision an automated end-ofline tuning of the compensator and a slow adaptation to varying friction condition during normal usage..4. Systems and Control Conference (DSCC9).Hollywood, CA, USA. Corno, M. and Savaresi, S. (). Experimental Identification of Engine-to-Slip Dynamics for Traction Control Applications. European Journal of Control, 6(). Corno, M., S.M., S., and Balas, G. (9b). On linear parameter varying (lpv) slip-controller design for twowheeled vehicles. International Journal of Robust and Nonlinear Control, 9(), Corno, M., Tanelli, M., Savaresi, S.M., Fabbri, L., and Nardo, L. (to appear). Analysis and Design of a Throttle Control System for Ride-by-Wire in Sport Motorcycles. In IEEE Multi-conference on Systems and Control (MSC). Deur, J., Pavkovic, D., Nedjeljko, P., Jansz, M., and Hrovat, D. (4). An electronic throttle control strategy including compensation of friction and limp-home effects. IEEE Transactions on Industrial Electronics, 4, Ferretti,G.,Magnani,G.,andRocco,P.(). Modelling and Control of Servomechanisms. Ramsete, Forsell, U. and Ljung, L. (999). Closed loop identification revisited. Automatica, 35(7). Guran, A., Pfeiffer, F., and Popp, K. (996). Dynamics with friction: modeling, analysis and experiment. World Scientific Publishing Company. Pavkovic,D.,Deur,J.,Jansz,M.,andNedjeljko,P.(6). Adaptive control of automotive electronic throttle. Control Engineering Practice, 4, 36. Rossi, C., Tilli, A., and Tonielli, A. (). Robust control of a throttle body for drive by wire operation of automotive engines. IEEE Transactions on Control Systems Technology, 8, 993. Savaresi, S., Poussot-Vassal, C., Spelta, C., Dugard, L., andsename,o.(). Semi-Active Suspension Control Design for Vehicles. Butterworth-Heinemann. Tanelli, M., Vecchio, C., Corno, M., Ferrara, A., and Savaresi, S. (9). Traction control for ride-by-wire sport motorcycles: a second order sliding mode approach. IEEE Transactions on Industrial Electronics, 56(9), Vasak, M., Baotic, M., Morari, M., Petrovic, I., and Peric, N. (6). Constrained optimal control of an electronic throttle. International Journal of Control, 79, Wellstead, P.E. (98). Non-Parametric Methods of System Identification. Automatica, 7, ACKNOWLEDGEMENTS The authors would like to thank Marco Cauchi and Ezequiel Tisminetzky REFERENCES Beghi, A., Nardo, L., and Stevanato, M. (6). Observerbased discrete-time sliding mode throttle control for drive-by-wire operation of a racing motorcycle engine. IEEE Transactions on Control Systems Technology, 4, Corno, M., Panzani, G., Maggio, G., Mazzocchi, P., and Goggi, G., S.S. (9a). Nonlinear modeling and control of a dual-stage hybrid ride-by-wire throttle body for a sport motorbike. In nd ASME Annual Dynamic 479