Self-sustaining Strategy for a Hybrid Electric Bike

Transcription

1 American Control Conference (ACC) Washington, DC, USA, June 7-9, Self-sustaining Strategy for a Hybrid Electric Bike Pierfrancesco Spagnol, Matteo Corno, Roberto Mura and Sergio M. Savaresi Abstract Electrically Power Assisted Cycles (EPACs) have been gaining attention as an efficient and clean means of transportation. In this work, the concept of full hybrid bike presented in previous research is further developed by introducing a charge sustaining strategy. The main idea is to consider the load-dependent efficiency of the cyclist and let the electric motor assist the cyclist in low efficiency regions while letting the cyclist recharge the battery in high efficiency regions. To this end a State-of-Charge (SoC) controller is designed. Its tuning is analyzed and compared in terms of efficiency and feeling against the acausal strategy available in the literature. I. INTRODUCTION Energy prices and environmental considerations have increased the interest on Light Electric Vehicle (LEV). Strict regulations and new paradigms for urban mobility (e.g. bike and car sharing) have been developed in urban areas in order to tackle traffic issues and pollution. In this urban context, Electrically Power Assisted Cycles (EPACs) are receiving a great deal of attention. EPACs have great potential to improve urban mobility. EPACs reduce the physical fatigue associated with cycling and thus enlarge the use basin. However, as all electric vehicles, they still suffer from some disadvantages []: limited range, increased weight compared to a normal bicycle and long recharging time. This work further develops the concept of the novel full hybrid electric bike (HEB), already presented in [], by developing a charge sustaining strategy. The HEB is configured as a parallel hybrid vehicle [] and its main characteristics are: Self-sustenance (the bike is grid-independent and does not need to be recharged); Small added weight (the HEB needs a smaller battery pack); The HEB helps cyclists during power peaks and is recharged by pedaling during cruising. This work stems from previous research. In [] the rationale has been presented and validated on a cycling track following a specific protocol, i.e. speed profile, showing a reduction of % of the consumed oxygen (an indication of metabolic efficiency). In that case - given the knowledge of the protocol - a proper offline tuning of the parameters guaranteed that the SoC was maintained during Manuscript received September 4,. P. Spagnol, M. Corno, R. Mura S. M. Savaresi are with Politecnico di Milano, Dipartimento di Elettronica e Informazione, Via Ponzio 4/5 - Milano Italy (phone: +9994; spagnol@elet.polimi.it; corno@elet.polimi.it; roberto.rob.mura@gmail.com; savaresi@elet.polimi.it). the whole ride. In this work a casual charge sustaining strategy that does not require a priori knowledge of the speed profile is designed and validated. The proposed SoC control only requires an estimation of the SoC [4]. The effects of the proposed strategy are discussed using an acausal charge sustaining strategy as benchmark and available results on the load-dependent efficiency of cyclists. In Section II a brief vehicle description is provided. In Section III the principles of how the hybrid bike works is recalled and the energy fluxes and the implemented algorithm are detailed. Section IV presents the charge sustaining strategy: control variable choice, model equations and simulation protocol are explained. Simulation results are shown in Section V. II. VEHICLE DESCRIPTION The hybrid bike is based on a Bianchi Camaleonte carbon frame (see Fig. ). The bike is configured as a light city bike. The added electric components are: Brushless hub motor (5W nominal power and 6V nominal voltage). ECU and motor driver. The control strategy runs on the ECU. Battery pack (ten batteries in series of ASystem Nano-phosphate, 99W nominal power, 6.Wh nominal capacity) and its Battery Management System (BMS). Integrated pedaling sensor (measuring pedaling cadence and torque). A user interface running on an Android OS smartphone; the application displays energy flows, cyclist and motor power and SoC of the battery. The total weight of added electric components is about.5kg. III. HEB ALGORITHM The requirement for a full hybrid electric bike is its complete independence from the electric grid. As the cyclist is the only external source, the electric energy balance requires a proper management of human and electric power. By helping the cyclist when his/her metabolic efficiency is low and taking energy when his/her efficiency is high, the full hybrid electric bike is capable of ensuring grid independence and of reducing the perceived physical fatigue. In order to understand the power assist strategy all the possible energy fluxes modes have to be considered /$. AACC 479

2 (a) (b) (c) (d) Fig. The integrated hybrid electric bike Possible fluxes for an EPAC are: No assistance during traction The power to overcome inertia and friction is given by the user. The motor is in idle and rotates at the same speed of the front wheel Fig. a. Electric assistance during traction Both user and motor provide power (see Fig. b). Cycling regeneration during traction The cyclist provides mechanical power to the bike and at the same time to the generator in order to recharge the battery pack as shown in Fig. c. Regenerative braking During braking (or downgrade) power is partially regenerated and partially dissipated by brakes (Fig. d). The algorithm that modulates the motor current setpoint (thus the assistance or recovery levels) is shown in Fig. 4 and presented in detail in []. From stop condition, the boost state is activated when the cyclist starts pedaling for the first pedal revolution ( _ >). In this state an electric power surplus is provided to the system. The pedaling state (that is detailed later on) is reached if the estimated gear ratio [m/rev] (ratio between bicycle speed and pedaling speed) is equal to the actual ( [m/rev]). If is lower than (the minimum speed in order to stop any electric assistance) and the cyclist is not pedaling ( is the pedaling speed [rev/min]) the control strategy gets back in the boost state. If the estimated ratio is greater than the actual and is greater than or a braking is detected, the braking state is activated, recovering energy. If the estimated and actual gear ratios are the same and is greater than, the control enters again in the pedaling state. The remaining two transitions between braking and boost states are similar. In the pedaling state the motor current setpoint increases linearly from to, with bike speed [km/h] ( to, [km/h]). From, to [km/h] the current setpoint has a linear decrease and is positive. For speed higher than [km/h], the current setpoint decreases linearly, becoming negative (recovery during pedaling), until it reaches the saturation value, (see Fig. 5). Fig. Operation modes: (a) no assistance (b) electric assistance during traction (c) cycling regeneration during traction (d) regenerative braking Fig. Algorithm scheme Fig. 4 Current setpoint generating function for different states IV. CHARGE SUSTAINING STRATEGY The charge sustaining requirement in terms of power depleted and stored into the battery during a long run is: (()() / ) = () where: is the time at the beginning of the ride [s]; is the time at the end of the ride [s]; () is the voltage of the battery [V]; () is the current depleted from/stored into the battery [A]; / () is the charge/discharge efficiency of the battery [-]; 48

3 In designing a causal charge sustaining strategy, a suitable control variable must be chosen. Section III showed that the power assist strategy depends on numerous parameters; is found to be the most suitable as a control variable because of three main motivations. First, using guarantees a single input single output structure, thus simplifying the control design. Next, can be modulated without affecting the basic rationale of the bike. In [] it was shown that human efficiency is low during acceleration and at slow speed. Thus, for example,, and, are not a good choice for control variable: in fact a decrease of SoC would lead to a decrease of the current level during the boost state and low speeds in the pedaling state. This behavior would lower the electric aid as well as human efficiency when it is most needed, i.e. during transients. Finally, increasing,, i.e the extra-power that cyclist should store in the battery at very high speed, affects the efficiency and the perception of fatigue. At the same time changing, and the current level during braking could negatively affect the riding feeling. On the other hand, smooth changing has low impact on cycling feeling. where (>) is the power developed by pedaling [W]; is the power developed (>) or regenerated (<) by the motor/generator [W]; (>) is the power dissipated thermally by the friction brakes [W]. Fig. 6 Hybrid electric bicycle model [W] is the friction power modeled as: = ( + + ) () where is the and,, are coefficients identified during a coasting-down test [5] [Nm /s ],[Nm/s],[N]. is the total inertial power [W]: = (4) is the mass of the system (cyclist and HEV are 95kg); is the acceleration of the bike [m/s ]. The electric motor power is: Fig. 5 Pedaling state Thus during the pedaling state a Proportional-Integral controller is designed in order to vary and maintain the SoC around a desired value. The pedaling state scheme is shown in Fig. 6. The bandwidth of the PI controller will determine how much the SoC is free to fluctuate. As the SoC variability strongly depends on the velocity profile a Monte Carlo approach is implemented to help design the controller. A. Bicycle model In order to compare performance for different tunings a longitudinal model of electric bicycle has been developed (assuming no slope during ride). The scheme is shown in Fig. 7. The longitudinal model of the bike is based on power balance: + = + () = (5) where is the motor current selected by the hybrid strategy (see Fig. 5) [A], is the torque constant of the motor [Nm/A], is the mechanical motor efficiency during traction and re-generation [-] and is the angular speed of the motor [rad/s]. In order to calculate the battery current, it is necessary to calculate the PWM duty cycle as follows: = + = < < = = / where, are motor parameters [] [Vs/rad]. is the duty cycle [..] and is calculated as the ratio between (motor voltage [V]) and (the battery voltage [V]). is the battery current [A], positive in discharge, negative in charge. Also the battery-motor-generator energy conversion is characterized by losses: is the charge/discharge battery efficiency [-].The SoC can simply be calculated as varies considering the different motor/generator and inverter working points. For sake of simplicity, in the model is considered constant with a value of.65 if the electric actuator is behaving as a motor and /.65 if it is behaving as a generator. varies considering the SoC of the battery pack, its temperature and the inverter working point. However, in the model it has been (6) 48

4 = () 6 (7) where is the state of charge of the battery at the beginning of the run [%..%] and S is the capacity of the battery [Ah]. The cyclist that generates is modeled as a fast Proportional-Integral speed controller. B. Human Metabolic Efficiency In order to compute the overall gain (or losses) in terms of efficiency a way to quantify the cyclist s metabolic efficiency is needed. The study of human efficiency is a vast area and, in the sport medicine literature, different approaches are found; they are often based on O /CO consumption/production and/or lactate production [6], [7], [8], [9]. In particular, the pedaling gross efficiency is defined as the ratio of the work accomplished per minute to energy expended per minute calculated starting from O consumption and lactate production. RPM Contour efficiency lines [%] Fig. 7 Static Human Gross Efficiency Map In the following we refer to the results of [6] where the gross efficiency is computed for several pedaling rates and loads for semi-professional cyclists. Interpolating the available points, the steady state efficiency map shown in Fig. 8 is obtained. The map shows a considerable spread of efficiency. The body is most efficient at relatively mid power and low rates (%), while pedaling at low load and high RPM yields a % gross efficiency. As we will see, the proposed strategy exploits these differences. Note that it is a static efficiency map: it is computed for constant velocity. In [], it is shown that the strategy is mainly effective because it helps the cyclist during transients. The main goal of the present work is to show how the introduction of a causal strategy affects the results of []; for this objective a static map suffices as the choice of the control variable guarantees that the charge sustaing strategy only affects the low frequency behavior of the system. Furthermore one should be aware that this map is not used to design the controller (that is map-independent), but only to evaluate its considered.9 when discharging and /.9 when charging the pack given the Li-Fe battery characteristics used in the real prototype Power [W] performance; every cyclist has its own efficiency map that can differ from the one proposed, thus the result proposed should be considered as an average evaluation, based on data available from sport medicine literature, which shows that the actual gross efficiency may vary but the trend is consistent and repeatable. C. SoC controller tuning Two different controller tunings have been tested: a fast and slow tuning. Each tuning corresponds to a different use of the battery. The Slow controller is tuned to let the SoC oscillate in the %-8% SoC range, while the fast controller allows only smaller variation of the SoC around 4%-6%. As a matter of fact, the SoC behavior, given the same tuning, is cycle dependent. Thus, in order to compare different tuning, random cycles have been created and tested. Starting from different real urban cycles, seven basic speed profiles have been identified: slow, mild and fast acceleration and braking and slow, mild and fast constant speed profiles. These basic blocks are then randomly shuffled, stretched in time and amplitude in order to create random urban profiles of roughly one hour and fifteen minutes. An example of a random speed profile is shown in Fig Time [min] Fig. 8 Random speed profile It is important to compare the performance of the novel causal strategy against the already used acausal strategy similar to the one implemented in []. The acausal strategy is obtained by setting a different such that the SoC at the end of the cycle is equal to the one at the beginning. Fig. shows the SoC profile resulting from the speed profile of Fig. 9 with the optimized static parameters and the two PI controllers. As one can see, depending on the strategy, the SoC has a different behavior and so the control variable. The acausal strategy has a strong dependence on the speed profile: it is possible to calculate the static value of the parameter only knowing a priori the profile: in this particular example SoC is in the range of 4%-6%. However for particular speed profiles it could be not possible to find a feasible value in order to maintain SoC in the -% range: in these cases simulations have been discarded. On the other hand, when the acausal strategy is feasible, it has an advantage in terms of cycling feeling: for a defined speed and acceleration, the cycling power is completely defined by the bicycle 48

5 characteristics and parameters of the strategy that are not time-varying. In other words, a cyclist does not feel any difference in the bicycle response given the same conditions (velocity and accelerations) and inputs (cycling force). The lets the system oscillate in a wider SoC range, while the fast PI as expected tends to keep the SoC near the setpoint (5%). As a consequence, the slow PI control variable has an erratic behavior. This clearly affects the cycling feeling: cycling power requirements vary given the same speed and acceleration. SOC [%] SOC [%] SOC [%] Time [min] Fig. 9 Charge sustaining strategy SoC control: acausal Fast PI v ped [km/h] v ped [km/h] v ped [km/h] 4 acausal acausal Time [min] Fig. Charge sustaining strategy control variable: acausal V. RESULTS To validate the proposed strategies 5 different random cycles have been simulated using the acasual, the fast and slow PI strategies and a traditional bike (accounting for the reduced mass and only mechanical losses). The results have been compared in terms of: Cycling power distribution Cycling power levels Relative efficiency loss A. Cycling power distribution The results for the whole set of random cycles have firstly been compared in terms of cycling power distribution. Basically, for all cycles the occurrences of the power (with a step of W) have been computed. Fig. plots the power distribution along with the average value of the cyclist s total energy. Some comments are in place: The total mechanical energy required by the acausal and the slow PI cases is similar, respectively 555 kj, 55 kj and 57 kj. The fast PI requires % more energy. The hybrid strategies affect the cyclist power distribution. Generally speaking, the hybrid strategies uniform the power distribution. They increase the occurrences over W and under 5 W and completely remove the occurrences over 8 W. The increase of low power occurrences and the removal of high power are due to the boost feature of the strategy. The medium-high power increase is instead due to cycling regeneration (high speed in the pedaling state). The slow PI shows a more uniform cyclist power distribution, while the shows a more concentrated power around (W) Traditional Acausal SoC sustaining Power [W] Fig. Cycling power distribution. B. Cycling power levels The previous analysis provides quantitative result on the power distribution in a -dimentional perspective. Plotting the average power as a function of velocity and acceleration provides a more complete picture on how the system assists the cyclist, as shown in Fig.. In the traditional and acausal cases, being time-invariant, it is easy to calculate the cycling power as a function of velocity and acceleration. On the other hand the slow and fast PI controllers yield a timevarying behavior and thus the average cyclist power is reported. 48

6 .5 Traditional.5 Acausal charge sustaining 8 7 reasons: (a) it yields a better efficiency and (b) it yields a smoother control action and therefore a more consistent bike behavior. acceleration [m/s ] acceleration [m/s ] Note that the above method only allows to perform a relative comparison among different strategies as the gross efficiency map is static and using it to account for dynamical effect (as the effect of the boost state tuning) would lead to a considerable underestimation of the efficiency as discussed in []. Moreover, in the relative comparison of interest, possible variations of the gross efficiency among different cyclists do not affect the conclusion that the causal strategies do not considerably affect the performance of the HEB. acceleration [m/s ] Fig. Cycling power levels C. Efficiency The last analysis takes into account the map shown in Fig. 8. From all the considered cycles the cycling efficiency is computed as follows: () = () ( (), ()) is the punctual human gross efficiency described as a function of () calculated as already mentioned in () and pedaling revolution rate (Fig. 8). Note that () already includes the electric/mechanic energy conversion efficiency. The efficiency is then calculated as the ratio between the energy developed by the cyclist during the cycle and the human metabolic energy during the same cycle. This value represents the amount of mechanical energy developed by the cyclist over the energy burnt by the human body. is then averaged considering all the cycles simulated using a particular configuration (acausal, slow PI, fast PI). The average efficiency enables a relative assessment of the causal strategies against the reference acausal for different strategies. The results are shown in Table. TABLE EFFICIENCY RESULTS Strategy Acausal Relative increase of Efficiency acceleration [m/s ] % -.6% -.8% These results show that the introduction of the causal strategies proposed in Section IV brings only a marginal loss of performance with respect to the acausal strategy. In particular the tuning has to be preferred for two (8) VI. CONCLUSION A novel concept of charge sustaining hybrid electric bike has been presented starting from the results of []. In this work two tunings of a causal charge sustaining strategy have been presented and compared to an acausal strategy in terms of efficiency and cycling feeling. The acausal strategy yields the best performance; the slow PI strategy has characteristics that are close to the acausal in terms of control variable oscillations, range of SoC usage and increased efficiency. Moreover the slow tuning outperforms the fast control in terms of cycling feeling. Future research will involve the experimental validation and further investigations on metabolic human during transients. REFERENCES [] J. Capelle, K. Sint-Lieven, G. Maggetto and et al., "Electrically Assisted Cycling around the World," in Proceedings of the th international battery, hybrid and fuel cell Electric Vehicle Symposium, Long Beach,. [] P. Spagnol, G. Alli, C. Spelta, P. Lisanti, C. Todeschini, S. Savaresi and A. Morelli, "A full hybrid electric bike: how to increase human efficiency," in American Control Conference, Montreal, (to appear). [] J. H. H. a. R. K. Walters, "Comparative Study of Hybrid Powertrain Strategies," SAE Technical Paper, no. --5,. [4] P. Spagnol, S. Rossi and S. M. Savaresi, "Kalman Filter SoC estimation for Li-Ion batteries," in IEEE Multi-Conference on Systems and Control, Denver (CO),. [5] G. Alli, S. Formentin and S. Savaresi, "On the suitability of EPACs in urban use," in IFAC Mechatronics, Boston,. [6] J. Chavarren and J. Calbet, "Cycling efficiency and pedalling frequency in road cyclists," European Journal of Applied Physiology, vol. 8, pp , 999. [7] J. Coast and H. Welch, "Linear increase in optimal pedal rate with increased power output in cycle ergometry," European Journal of Applied Physiology, vol. 5, pp. 9-4, 985. [8] E. Fox, The Physiological Basis for Exercise and Sport, 5th ed. Madison ed., Brown & Benchmark, 99. [9] K. Isaac, C. Glen and e. al., "Modeling energy expenditure and oxygen consumption in human exposure models: accounting for fatigue and EPOC," Journal of exposure science and environmental epidemiology, vol. 8, pp , September 7. [] S. Savaresi, G. Alli, C. Spelta, P. Spagnol, M. Vanzulli, G. Biesuz, Politecnico di Milano, SEMS srl and FNM spa, "Bicicletta a pedalata assistita elettricamente". Italy Patent MIA5,. 484