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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 12, NO. 5, SEPTEMBER 2004 645 Analysis and Control of a Flywheel Hybrid Vehicular Powertrain Shuiwen Shen and Frans E. Veldpaus Abstract—Vehicular powertrains with an internal combustion Zero inertia ratio. engine, an electronic throttle valve, and a continuously variable External disturbance torque. transmission (CVT) offer much freedom in controlling the engine Vehicle road load torque. speed and torque. This can be used to improve fuel economy by operating the engine in fuel-optimal operating points. The main Desired engine torque. drawbacks of this approach are the low driveability and, possibly, Induced engine torque. an inverse response of the vehicle acceleration after a kick-down Roll resistance. of the drive pedal. This paper analyzes a concept for a novel pow- Torque in drive shafts. ertrain with an additional flywheel. The flywheel plays a part only Driver pedal angle. in transient situations by (partly) compensating the engine inertia, making it possible to optimize fuel economy in stationary situations Powertrain efficiency. without loosing driveability in transients. Two control strategies Engine speed. are discussed. The first one focuses on the engine and combines Desired engine speed. feedback linearization with proportional control of the CVT ratio. Flywheel speed. The CVT controller has to be combined with an engine torque con- Wheel speed. troller. Three possibilities for this controller are discussed. In the second strategy, focusing on control of the vehicle speed, a bifur- Desired wheel speed. cation occurs whenever a downshift of the CVT to the minimum Throttle opening. ratio is demanded. Some methods to overcome this problem are introduced. All controllers are designed, using a simple model of I. INTRODUCTION the powertrain. They have been evaluated by simulations with an advanced model. ECENT developments in design and control of vehicular Index Terms—Bifurcation, continuously variable transmission R powertrains, combined with ever tightening regulations on (CVT), flywheel hybrid powertrains, fuel economy, I/O lineariza- exhaust emissions, have prompted a renewed interest in the fuel tion, inverse behavior, nonlinear control, powertrain control. consumption of internal combustion engines (see, for instance, [9], [17], [20], [21], [24], [26], [29], [32], [33], [39], and [46]). The fuel mass flow per unit engine power in stationary situa- NOMENCLATURE tions strongly depends on the operating point, i.e., on the en- Air drag coefficient. gine speed and the torque or, alternatively, on and the Moment of inertia of engine, converter, and primary throttle opening . The fuel efficiency in stationary situations pulley. can be improved by operating the engine along the E-line, being Equivalent moment of inertia at engine side. the set of operating points in which a required engine power Moment of inertia of flywheel. is delivered with minimal fuel consumption ([11], Total moment of inertia. [18], [36], [41], [45]). Some papers [30], [33] not only take into Equivalent moment of inertia of wheel and vehicle. account the efficiency of the engine but also of other power- Equivalent moment of inertia at wheel side. train components (torque converter, transmission, etc.). In this Engine power. integrated powertrain control [4], [24], [33], [46], [49], the sta- Desired engine power. tionary operating points lie on the optimal operating line (OOL), Power at the wheels. being the set of operating points in which a required power at Desired power at the wheels. the wheels is delivered with minimal fuel consumption.1 The Overall transmission ratio. OOL will not completely coincide with the E-line. This is trivial Geared neutral ratio. for powertrains with a stepped transmission [17], [40], but is true Maximum transmission ratio. also for powertrains with a continuously variable transmission Minimum transmission ratio. (CVT) because the ratio coverage of current CVTs is fairly lim- ited [24], [35]. Manuscript received October 9, 2001; revised December 18, 2002. Manu- The CVT and throttle controllers [1], [7], [11], [21], [35], script received in final form June 23, 2003. Recommended by Associate Editor [45], [49], aim to operate the engine in stationary situations in M. Jankovic. This work was supported by the Dutch Governmental Program points on or close to the OOL. In general, the engine speed in Economy, Ecology, and Technology (E.E.T.) S. Shen is with University of Leeds, Leeds LS2 9JT, U.K. these points is low (large CVT ratio) and the engine torque is F. E. Veldpaus is with the Dynamics and Control Technology Group, De- high (large throttle opening), meaning that the power reserve partment of Mechanical Engineering, Technische Universiteit Eindhoven, Eind- hoven 5600 MB, The Netherlands (e-mail: [email protected]). Digital Object Identifier 10.1109/TCST.2004.824792 1Sometimes [21], [27] the E-line is also called the optimal operating line. 1063-6536/04$20.00 © 2004 IEEE 646 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 12, NO. 5, SEPTEMBER 2004 (the difference between the power in the chosen operating point and the power at the same engine speed with a wide open throttle) is small. This can result in an unacceptable driveability, where driveability is seen as a measure for the promptness of the vehicle reaction on drive pedal motions. Suppose that, in a stationary situation, the drive pedal is suddenly kicked down completely, meaning that the driver wants the engine to deliver the maximum power as soon as possible. By opening the throttle as fast as possible, a prompt increase of the engine power of magnitude is obtained. However, a further, fast increase is possible only if the engine is speeded up quickly by a fast downshift of the CVT [41]. If is too small to realize the enforced large engine acceleration, power will be withdrawn from the vehicle to accelerate the engine [11], [24], [26], [27], [35], [41] and the vehicle will decelerate, whereas the driver clearly wants an acceleration [1], [7], [11], [24]. This inverse behavior can be avoided by a (much) slower downshift of the CVT. Then, it will take more time before the maximum engine power is delivered and before the driver feels any reaction of Fig. 1. Flywheel assisted power train. the vehicle after the pedal kick-down. Fuel-optimal powertrain controllers, therefore, in general result in an unacceptably slow gine speed increases whereas the flywheel speed decreases. The or even inverse response of the vehicle acceleration [4], [11], resulting decrease of the kinetic energy of the flywheel is partly [27], [36], [41]. This inverse response can be explained by the used to accelerate the engine. From a physical point of view occurrence of a nonminimum phase (NMP) zero in the locally it seems that the engine inertia is (partly) cancelled by the fly- linearized transfer function from the CVT ratio to the vehicle wheel inertia. Therefore, the new powertrain is called zero in- speed. This NMP zero imposes considerable limitations on the ertia (ZI), or ZI powertrain [35]. obtainable performance of the closed-loop system [8], [9], [15], The remainder of this paper is organized as follows. In Sec- [16], [29], [42], [50]. Recently, some authors have suggested tion II, a simple model for the powertrain is given. The tradeoff feedback [27] and feedforward control [4], [41] to overcome between driveability and fuel consumption is discussed in Sec- these limitations. They constrain the stationary operating points tion II-C. There also the objectives of the ZI powertrain con- to the OOL or the E-line but allow operating points outside these trollers are considered in more detail. Section IV focuses on lines in transients. However, the small power reserve then still feedback linearization and robust control with the engine speed implies an often unacceptably low driveability. as the output of interest. In Section V,the output of interest is the The driveability can be improved at the expense of increased vehicle speed. The relative degree of the system with this output fuel consumption by increasing the power reserve, i.e., by gen- is not well defined for all CVT ratios, so straightforward feed- erating the required engine power in high-speed low-torque op- back linearization is not always possible. In Section VI, some erating points (far) below the E-line. The driveability can also be methods to overcome this problem are outlined. These methods improved by incorporating a second power source in the pow- include control gain specification and approximate lineariza- ertrain. Modern hybrid electric vehicles combine a combustion tion. Finally, Section VII gives the main conclusion and some engine with a powerful electric motor and a moderate capacity suggestions for future research. battery. Unlike purely electric vehicles with their inherent draw- backs of large weight, small driving range and large recharging II. ZI SOLUTION OF DRIVEABILITY time, the hybrid electric vehicle is a very attractive concept [25], [32]. In stationary situations, the engine can operate in fuel-op- The essential components of the ZI powertrain (see Fig. 1) timal points whereas the extra power, needed to overcome the are a combustion engine, a CVT (torque converter, drive-neu- inverse response in transients, can be delivered by the electric tral-reverse (DNR) set, metal pushbelt variator, oil pump, final motor [22], [28]. The main drawbacks of hybrid electric vehi- reduction, and differential) and a power assist unit, consisting cles are their increased weight, complexity, and price. of a flywheel and a planetary gear set. The sun gear of this set is The power assist can also be delivered by a flywheel. The connected to the flywheel, the annulus gear is connected to the concepts in [12], [23], [34], [39], and [44] require a large high- primary pulley shaft via a gear box with fixed transmission ratio speed flywheel and extra clutches. Appropriate control of these , and the planet carrier is connected to the secondary pulley clutches is difficult.

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