Longitudinal Traction Control for Electric Vehicles - IEEE Xplore

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 3, MAY 2006

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“Single Wheel” Longitudinal Traction Control for Electric Vehicles Vincenzo Delli Colli, Giovanni Tomassi, and Maurizio Scarano

Abstract—The traction control is a tool to increase stability and safety and it has a greater performance potential in electrical vehicles (EVs) than in internal combustions vehicles. Moreover, the traction control allows the EV to operate more efficiently preventing slippage in acceleration and permitting the use of use high-efficiency low-drag tires. The presented approach can compete with the well-recognized techniques, but it offers a lighter tuning procedure. This paper presents an approach to the longitudinal control of a single wheel adopting a configuration based on an adherence estimator and a controller of the adherence gradient. Two adherence gradient controllers are examined in the paper: a fuzzy controller and a sliding mode controller. In both cases, the presented approach allows for tracking a value of the adherence derivative in a wide operating range without any knowledge of the road conditions. The work is based on numerical simulations as well as experimental tests. The test bench computes in real-time the vehicle dynamic and loads accordingly, the drive under test. Both controllers were experimentally verified showing good behavior and good response to a sudden change in the road characteristics, whereas the best overall performance was recorded with the sliding mode control. Index Terms—Electric vehicle (EV).

I. INTRODUCTION NVIRONMENTAL concerns are more alive than ever. Advanced technical literature warns that “the need for zero emission vehicles remains critical, and responsible researchers and manufacturers are continuing their work to achieve this goal.” Although tremendous progress has been made during the last decade in battery technology and electric drive systems, allowing for extended driving range and reduced cost, the battery is still the critical component of the pure electric vehicle (EV). The most recent advancements in battery technologies are: nickel metal hydride (NiMH), lithium-ion (Li-ion), lithium metal polymer (Li MP), sodium metal chloride (Zebra), and nickel zinc (NiZn). Currently, the major automakers in Europe, Japan, and the United States, have shifted their development efforts to hybrid concepts so hybrid electric vehicles (HEVs) have now evolved into mature, practical designs. As a matter of fact, they currently are the only option of a fullfledged vehicle with an electric motor offered by the major automakers. In fact, Toyota foresaw a 300 000 car per year HEV market by 2005–2006. Commercially available HEV cars are, to name a few, Toyota Prius, Honda Civic Hybrid, Renault Kangoo Elect’road. Details about battery technology as well as about EV

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Manuscript received March 9, 2005; revised October 26, 2005. Recommended by Associate Editor J. Shen. The authors are with the DAEIMI, University of Cassino, Cassino 03043, Italy (e-mail: [email protected]). Digital Object Identifier 10.1109/TPEL.2006.872363

Fig. 1. Speeds and forces in the tire-road contact.

and HEV configurations can be found in the technical literature [1], [2]. The traction control of road vehicles improves the safety in difficult weather or trafic conditions as well as the stability during high performance driving. Moreover, the limitation of the slip between road and tire reduces the wear of the tires. Nevertheless, a key point is the efficiency benefit produced by the traction control. This benefit lays on the slip reduction and on the possibility of mounting high-efficiency low-drag tires, often ill-advised without control. The efficiency influences the emission of any vehicle, but in the EV case, it is a primary concern because it also influences the range. Also, in the HEV case a better efficiency leads to an improvement of the zero emission range. and In the tire-road contact, the vehicle-road speed the tire-road speed differ in magnitude and direction as in Fig. 1; this contact provides two horizontal force components onto the vehicle: the driving or longitudinal force , and the side or lateral force , as shown in Fig. 1. Both components are strongly dependent on the slip, defined as

(1) and on the slip angle , as shown by Fig. 2, where the forces are respectively expressed, as usual, through the normal force and the driving or longitudinal friction coefficient and the side or lateral friction coefficient [8]–[10]. The traction control can realize two tasks: Longitudinal control—the adhesion improvement control to prevent slip. This is achieved by controlling the traction force. The slippage prevention itself improves the lateral stability since it avoids a loss of lateral force in low adherence conditions.

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Fig. 3. Slip control with optimal slip computation. Fig. 2. Driving and side (dotted) friction coefficients as function of slip and slip angle.

Lateral control—the yaw control to keep the yaw motion at zero. This can be achieved, for example, by controlling the steering angle. Reference [3] proved that the independent slippage prevention on each wheel of a 4WD vehicle greatly improves the lateral stability, although this technique reacts indirectly to unwanted yaw movement. As the dynamics of the traction systems are highly nonlinear and time variant, the design of model-based ABS or traction control system (TCS) schemes (along with those designed empirically) tend to be nonlinear and time varying. The key obstacle to the development of robust ABS/TCS has traditionally been the real-time estimation of the wheel-slip versus adhesion-coefficient characteristics for different tire types and road surface conditions. Some studies have investigated the application of observer/estimation schemes to obtain real-time data indirectly, with the extended Kalman filter (EKF) receiving particular attention [8], [11]. Current commercial/passenger vehicles incorporating ABS/TCS systems often impose prefixed values of the slip that are based on the results of experimental trials, and have been shown to provide adequate performance under the more critical driving situations. This technique tends to accommodate worst-case scenarios, for example, traction control in icy conditions with old tires. Consequently, suboptimal slip conditions are imposed for most driving conditions [12]. The fuzzy control offers potential as an important tool for development of robust traction control [12]. Fuzzy ABS/traction control may substantially improve longitudinal performance and offer significant potential for optimal control of driven wheels. The control approach described by [12] is mainly based on fuzzy assessment of the adherence characteristic gradient that seems to require an accurate tuning. Moreover, the test facility used, based on the similarity between the adhesion characteristic and the torque-slip curve of an induction machine, presents some limitations: the simulated vehicle speed is fixed, and the slip producing the maximum adherence appears hard to change on line. Reference [13] offers an effective fuzzy control strategy to control the slip and the yaw rate for 4WD EV/HEV completed by a fuzzy estimation of vehicle speed, representing a critical task in 4WD vehicles. On the other hand, the slip reference used in [13] is prefixed, and therefore is necessarily suboptimal as

stated above for current vehicles. Moreover, this reference does not indicate how to choose a reference for the yaw rate, and it is based on simulations. The variations in the friction coefficient constitute an uncertainty of the system. The sliding mode control is a powerful tool to tackle uncertainty [14]. Although the sliding mode control was applied to longitudinal control, as well as lateral and combined controls [15]–[17], its potential has not yet been fully exploited, especially in the field of longitudinal control. The above cited contributions provide very effective control approaches, but are based only on simulations; [15] fails to show if the system tracks the maximum adherence, and [16] imposes prefixed slip values. Reference [19] proposes a braking longitudinal control using an iterative learning control, but does not show how to chose the reference slip ratios, that anyway seem prefixed, therefore suboptimal. Moreover, the reference does not show how, and if, the learning process triggers and reacts in presence of a sudden change of the road conditions, and if the learning is fast enough in such a case. Reference [20] addresses both longitudinal and lateral control. The proposed longitudinal control effectively avoids high slip operation but one does not know if the system tracks the maximum adherence. Moreover, [20] does not show how the system reacts to changes in the road conditions. According to the authors knowledge, the best available solution for longitudinal control is the slip ratio control with a computation of the optimal slip; this computation requires an estimation of the road conditions. To estimate in real-time the road conditions different algorithms can be considered [3]–[7]. In [3], is the gradient of the adherence-slip characteristic evaluated from samples of slip and adherence by means of an identification algorithm. Slip, adherence, and gradient identify the actual adherence characteristics. A fuzzy interpolation obtains coefficients from the actual characteristic expression. The obtained coefficients to express the actual optimal slip as function of the typical optimal slips presented by four kinds of standard road surface as resumed by Fig. 3. The system operates at a value of the adherence gradient 1. Other choices could be considered for and the maximum adherence would be ideally attained for 0. This paper presents an approach to the longitudinal control of a single driven wheel, adopting a configuration based on an adherence estimator and a controller of the adherence gradient as shown by Fig. 4 [18]–[21]. The proposal aims to offer comparable or competitive performance with respect to the existing

DELLI COLLI et al.: LONGITUDINAL TRACTION CONTROL

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Fig. 5. Driven wheel. Fig. 4. Adherence gradient control.

solutions, while allowing a lighter tuning procedure than the system proposed by [1] and represented in Fig. 3. Two adherence gradient controllers are examined in the paper: a fuzzy controller and a sliding mode controller. In both cases, the presented approach allows tracking a desired target in a wide operating range without any a priori knowledge of the road conditions and in presence of sudden changes of the curve of Fig. 2. The work is based on numerical simulations as well as experimental verifications. The experimental tests are on a test bench allowing the hardware-in-the-loop study of the power train using the real time computation and actuation of the vehicle dynamic, taking into account arbitrary and on-line modifiable road conditions. It is worthwhile to mention that the longitudinal control of a vehicle with two driven wheels can be realized by duplicating the proposed system and sharing the same pedal reference and the same adherence gradient reference [3]; moreover, the duplicated proposed system can be used as a suitable actuator for a possible lateral control distinguishing the pedal references and the adherence gradient references. The outline of the paper is as follows. Section II presents some mathematical background about the driven wheel and the adherence. Section III shows the adherence observer. Section IV contains the presentation of both the fuzzy and the sliding mode adherence gradient controllers. Section V gives numerical results for both controllers. Section VI presents the experimental platform. Finally, Section VII shows experimental results for both controllers. II. MATHEMATICAL MODEL OF THE DRIVEN WHEEL This section briefly presents the mathematical model of the driven wheel of Fig. 5. The dynamic of a driven wheel is given by an equation of forces equilibrium

(2) and by an equation of torques equilibrium

Fig. 6. Typical trends of longitudinal and side friction coefficients.

where is the passive resistance to the vehicle motion, is the vehicle mass, is the motor torque applied on the tire, is the tire radius, is the tire angular speed, is the tire inertia, is assumed as a quarter of the car weight, and in (1)

The above model has to be completed by the road-tire friction characteristic of Fig. 2 that depends strongly on the operating conditions. Namely, the actual law depends on the tire slip angle, on the steering angle, on the road and tire conditions, and on the speed. Fig. 6 reports typical trends of the function for various road conditions, with a zero slip angle. These trends illustrate that some amount of slip is necessary to produce longitudinal tire-road force; on the other hand, the trends show an excessive slip leads to a loss of driving force, with high power losses and wear due to the friction. Moreover, an example of the side friction coefficient is also reported in Fig. 6; its decreasing trend indicates the slips have to be limited to guarantee the lateral guidance of the vehicle. The work considers permanent magnet excited dc motors, therefore, the torque production is ruled by

(3) the traction force is given by the normal force and the friction coefficient

(4)

(5) where is the motor voltage, is the motor current, is the motor e.m.f., , are, respectively, the e.m.f. and torque

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Fig. 8. Observer step response. Fig. 7. Driving friction force observer.

A. Evaluation of the Adherence-Slip Gradient are the motor

The target of this TC is to operate at an assigned value of , thus its correct estimation is critical. In dynamic conditions, may be estimated by means of the ratio

This Section presents the observer used to estimate the actual driving friction coefficient . The actual dynamic gives

(10)

constants of the motor, is the gear ratio and , parameters. III. ADHERENCE ESTIMATION

(6) Let

an estimate of the adherence force, the estimation error

is

This approximation cannot be adopted in real life application because it produces computation singularities in steady state conditions. To compute correctly the gradient, the proposed algorithm updates the ratio just when the amplitude of is appreciable, according to the flowchart of Fig. 9. B. Fuzzy Adherence Gradient Control

(7) The desired error dynamic is

(8) The following equation can be obtained substituting (7) into (8) and supposing piecewise 0

(9) A previous relationship leads to the block scheme of Fig. 7. Fig. 8 reports the simulated observer output responding to a step in the adherence and a step in the motor torque. The data show the observed driving force soon converges to the actual value and it is insensitive to a torque step. IV. TRACTION CONTROL This Section shows how to estimate the adherence gradient , then presents the fuzzy and the sliding mode controllers.

The inputs of the fuzzy traction controller are the pedal reference and the estimated value of . They are fuzzified through the membership functions of Figs. 10 and 11. The input membership functions for the pedal reference of Fig. 10 (Small, Medium-Small, Medium-High, High) are equally spaced along the reference range and do not require tuning. The input membership functions for the adherence derivative (Negative, Zero, Positive-Small, Positive-High) are not equally spaced and they have to be tuned by means of a trial procedure. If the value of belongs mainly to the Negative set, the system is operating in the unstable region, consequently the wheel should decelerate. A mainly Zero value of indicates that the system is close to the optimum and the wheel should maintain its speed. A mainly Positive-Small value of indicates that the wheel can slightly accelerate without passing into the unstable region. If the value of is mainly Positive-High, the wheel is free to accelerate. The fuzzy output is the torque demand , that is imposed by a PI current control loop as shown by Fig. 13. However, if is high, the torque demand is equal to the pedal reference, otherwise, the torque demand is less than the pedal reference. The output functions are reported in Fig. 12; they are equally spaced and do not require tuning. The chosen rules translate the previous considerations and are reported by Table I. A complete block scheme of the fuzzy


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Fig. 11. Input membership functions for the adherence gradient.

Fig. 9. Algorithm for estimation of d=d .

Fig. 12. Output membership functions.

TABLE I RULES

Fig. 10. Input membership functions for the pedal reference.

traction control can be seen in Fig. 13, where the speeds of the driven wheel and of the vehicle are measured, the last by means of an nondriven wheel; both speeds are needed to compute using (1); the current is measured to compute the torque using the third of (5); the block scheme of Fig. 7 is used to compute while the flowchart of Fig. 9 is used to compute .

C. Sliding Mode Adherence Gradient Control The region of the state space where sliding manifold. Based on the typical

0 is the desired curves reported in

Fig. 13. Block scheme of the system with fuzzy adherence gradient control.

Fig. 6 let us suppose that the actual curve presents a maxis a decreasing function of imum; consequently, the

(11)

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Fig. 14. Block scheme of the system with sliding mode adherence gradient control.

at least close to the maximum. If the vehicle speed be considered constant, (1) gives

can

(12) Equations (11) and (12) give (13) Moreover, according to the model of Section II, with, 0 for certain values of the torque if if

0,

(14)

the controlling quantity and Consequently, considering adopting the discontinuous control: if if

(15)

0 will result, enforcing sliding mode on from (13)–(15) the manifold 0 [14]. Because the above discontinuous control is affected by the current control loop dynamic, it would lead the wheel speed to chatter. Instead, the boundary layer technique is adopted to alleviate the chattering [14]. A sliding mode current control loop [14] assists the adherence gradient control loop (see Fig. 14). D. Comparative Issues The proposed approaches are based on the same measure set. All the computations used to obtain are the same. In order to stress the smooth action characteristic of the fuzzy control a PI current control was used with it, while to stress the fast reaction characteristic of the sliding mode control a sliding mode control was used with it. The fuzzy control will be implemented on a low cost fuzzy microcontroller and the sliding mode control will be implemented on an ordinary microcontroller. V. NUMERICAL RESULTS This section reports a numerical verification of both controller performances during the acceleration of the vehicle, in the presence of a sudden change of the adherence-slip curve of the road. The chosen curves would cause an uncontrolled driven wheel to attain the unstable region of the curves. The is 0.1, while the maximum driving friction coefficient

Fig. 15. Simulated fuzzy control with a sudden change of the ( ) curve: (a) inear speeds of tire and vehicle, (b) adherence gradient, and (c) dynamic locus with road curves = f ( ) and = f ( ).

0

slip of maximum driving friction coefficient steps from 1 s. Fig. 15 reports the fuzzy control while 0.2 to 0.4 when Fig. 16 reports the sliding mode control. Figs. 15(a) and 16(a) report and , Figs. 15(b) and 16(b) show the estimate of , and Figs. 15(c) and 16(c) show the dynamic locus of the system during the test and , curves imposed before and after the step in 1 s. The data show good, almost equivalent, response for both controllers. The oscillations visible in the low slip region of the diagram in Figs. 15(c) and 16(c) can be tolerated, because they occur at very low speeds, as evidenced by the speed diagrams of Figs. 15(a) and 16(a). The data about presented in Figs. 15(b) and 16(b) highlight the system approaches its references. The comparison between the results achieved by both methods should be based on Figs. 15(a), 16(a), and 15(b), and 16(b) since Figs. 15(c) and 16(c) are quite similar. The actual oscillations visible in Figs. 15(a) and 16(a) are also quite similar in both cases. Figs. 15(b) and 16(b) illustrate that the sliding-mode control presents a better steady-state estimated response, because the obtained value is closer to the reference.


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Fig. 16. Simulated sliding mode control with a sudden change of the ( ) curve: (a) linear speeds of tire and vehicle, (b) adherence gradient, and (c) dynamic locus with road curves = f ( ) and = f ( ).

0

Fig. 17. Block scheme of the test bench.

This data is confirmed by the vehicle speed at the end of the test, [Figs. 15(a) and 16(a)] that is, 0.7 m/s for the fuzzy and 0.75 m/s for the the sliding mode, thus the the sliding mode performs better in simulation, although considerations of Section VI-D apply. VI. TEST BENCH To tune and verify both antiskid traction controllers, the authors predisposed a test bench in the “Giovanni D’Angelo” Lab-

Fig. 18. Fuzzy control with fixed ( ): (a) linear speeds of tire and vehicle, (b) torque C , (c) slip ratio and , (d) driving friction coefficient and , (e) adherence gradient d=d , and (e) , locus.

oratory of Industrial Electronics, The University of Cassino. The test bench is based on the real time computation and actuation of the wheel dynamic, and consists of the following items as also shown by the block scheme of Fig. 17. • Items under test. — Actual control hardware.

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Fig. 19. Fuzzy control with stepping ( ): (a) linear speeds of tire and vehicle, , (d) driving friction coefficient and (b) torque C , (c) slip ratio and , (e) adherence gradient d=d , and (f) , locus.

— Actual dc/dc power converter. — Actual dc motor. • Wheel real-time power simulator. — Control hardware for the real-time computation of the wheel dynamic, including the adherence.


Fig. 20. Sliding Mode control with fixed ( ): (a) linear speeds of tire and vehicle, (b) torque C , (c) slip ratio and , (d) driving friction coefficient , (e) adherence gradient d=d , and (f) , locus. and

— Power inverter. — AC machine loading the actual dc motor above. This bench can reproduce arbitrary adherence-slip curves and can modify them in running. The simulator determines in real-


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VII. EXPERIMENTAL RESULTS This section presents the performance of both controllers recorded by means of the test bench. As in Section V, the test considers an acceleration of the vehicle consequent to a step pedal command A reference value 0.5 was adopted. Figs. 18 and 19 relate to the fuzzy control while Figs. 20 and 21 curves relate to the sliding mode control. The considered imposed through the test bench would cause slippage of the uncontrolled system. Two tests have been conducted for each controller: one with a fixed curve (Figs. 18 and 20) and one with a sudden change in the curve (Figs. 19 and 21). In all the tests, the maximum driving friction coefficient is 0.1. In the second test of each controller (Figs. 19 and 21) steps the slip of maximum driving friction coefficient from 0.4 to 0.2. Each of the above said Figs. 18–21 reports the linear speeds of tire and vehicle [Figs. 18–21(a)], the motor torque applied on the tire [Figs. 18–21(b)], the slip ratio and of the considered curve [Figs. 18–21(c)], the driving friction coefficient and of the considered curve [Figs. 18–21(d)], the adherence gradient , [Figs. 18–21(e)], and finally the locus of the system during the test [Figs. 18–21(f)]. The experimental data evidence a good agreement with the simulation as well as a good response of the controller. The trend of Figs. 12(e) and 13(e) highlights the system the reference 0.5. (see Figs. 18 and 20), In the test with a fixed road curve the final speed of the vheicle is the same, 10 m/s, but in the case of sliding mode control (Fig. 20), the speed of the wheel is subject to obscillations. Moreover, the trend of and is noisy in the sliding mode case. In the test with a sudden change in the road curve (Figs. 19 and 21), although the wheel speed with the sliding mode control is noisier, the final speed of the vehicle is much higher in the sliding mode case. The sliding mode control also performs better in the experimental case, although considerations of Section IV-D should be taken into account. VIII. DISCUSSION On the basis of the obtained results, one can say that the proposed approach has longitudinal control performance as good as, e.g., [3]–[7]; on the other hand, the approach proposed by [3]–[7] requires a heavier tuning campaign of the system. The predisposed laboratory set-up allowed an experimental verification in presence of sudden changes in the road, that was not provided by [12]. References [13], [15], [17], [19], and [20] work at prefixed (or unknown) slip ratios, and therefore do not exploit (or do not prove they do) the available adherence offered by the road as well as the proposed approach. IX. CONCLUSION

Fig. 21. Sliding mode with stepping ( ): (a) linear speeds of tire and vehicle, , (d) driving friction coefficient and (b) torque C , (c) slip ratio and , (e) adherence gradient d=d , and (f) , locus.

time the motor speed as the vehicle equations foresee. The simulator can set the axle speed in any likely operating condition, thanks to its torque and bandwidth performances.

The paper presented an approach to the longitudinal control of a single wheel adopting a configuration based on an adherence estimator and a controller of the adherence gradient. Two adherence gradient controllers are examined in the paper: a fuzzy controller and a sliding mode controller. After a numerical investigation, both controllers were verified by means of experimental tests and showed that they track a requested value of adherence gradient in a very wide operating range without any knowledge of the road conditions. Moreover, the experimental tests proved both controllers have a good response to a sudden

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change in the road characteristics, whereas the best overall performance was recorded with the sliding mode control. The proposal can also be applied as it is to avoid high slip skid during electrical braking.

[17] H. Pham, K. Hedrick, and M. Tomizuka, “Combined lateral and longitudinal control of vehicles for IVHS,” in Proc. Amer. Contr. Conf., Jun. 29–Jul. 1 1994, vol. 2, pp. 1205–1206. [18] E. de Santis, ““VED” EV Torque Control: Design and Test of a Fuzzy Antiskid Control,” (in Italian) Laurea dissertation, Fac. Elect. Eng., Univ. of Cassino, Cassino, Italy, 2005. [19] C. Mi, H. Lin, and Y. Zhang, “Iterative learning control of antilock braking of electric and hybrid vehicles,” IEEE Trans. Veh. Technol., vol. 54, no. 2, pp. 486–494, Mar. 2005. [20] H. Fujimoto, T. Saito, A. Tsumasaka, and T. Noguchi, “Motion control and road condition estimation of electric vehicles with two in-wheel motors,” in Proc. IEEE Int. Conf. Contr. Appl., Sep. 2–4, 2004, vol. 2, pp. 1266–1271, vol. 2. [21] V. Delli Colli, G. Tomassi, and M. Scarano, “Fuzzy longitudinal traction control,” in Proc. IEEE/ASME Int. Conf. Adv. Intell. Mechatron., Jul. 24–28, 2005, pp. 289–294.

ACKNOWLEDGMENT The authors wish to thank E. de Santis for contributing to the realization of the traction controller while working in the project as the laurea degree student, and Dr. Gianluca Antonelli for his helpful contribution about the observer dynamic.

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Vincenzo Delli Colli was born in Cassino, Italy, in 1970. He received the Laurea degree in electrical engineering from The University of Cassino, Cassino, Italy, in 1996, and the Ph.D. degree in conversion of electrical energy from The Second University of Naples, Naples, Italy, in 2000. Since 2001, he has been Research Assistant with the Electrical Machine Research Group, The University of Cassino. His past research interests were mainly modeling and control of linear induction machines, and he was committed with the industrial design of arc welding machines. He is currently engaged in the fields of the control of current source and resonant converters, traction control, and the control of tubular and axial-flux PM machines.

Giovanni Tomassi was born in Cassino, Italy, in 1971. He received the Laurea degree in electrical engineering from The University of Cassino, Cassino, Italy, in 2002, and the Ph.D. degree in conversion of electrical energy from The Second University of Naples, Naples, Italy, in 2005. His main Ph.D. activities were the design of axial-flux permanent magnet machines, traction control, and the use of DSP for drive control. He is currently committed to developomg a brakeless and speed sensorless automatic test system for induction machines.

Maurizio Scarano received the Laurea degree in electrotechnical engineering from the “Federico II” University of Naples, Naples, Italy, in 1979. He was Assistant Professor of Electromagnetic Fields and Circuits Theory at the “Federico II” University, from 1983 to 1992. While there, he was mainly involved in research on mathematical modeling of electrical machines. From 1992 to 1999, he was an Associate Professor of Electrical Machines at the University of Cassino, Cassino, Italy, becoming Full Professor in November 1999. He was a Scientific Coordinator with the Industrial Electronic Laboratory of this university from 1992 to 1999. He has been Scientific Coordinator of several research contracts with public agencies and industrial companies in the field of electrical machines and power electronics. Since 2001, he has been the Director of the Department of Automation, Electromagnetism, Computer Science and Mathematics, University of Cassino and Scientific Coordinator of a local Scientific Public-Industrial Consortium. He is author of about 160 papers and notes in the field of electrical machines and drives. He has specialized his scientific production in the field of nontraditional actuators (linear machines, transverse flux machines, micromachines) both by developing novel machine configurations and proposing original mathematical analysis and control algorithms. His experimental activity is often devoted to design, prototyping, and test of these actuators and control algorithms.