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Control System Design on a Power-Split CVT for High-Power Agricultural Tractors Sergio M. Savaresi, Member, IEEE, Francesco L. Taroni, Fabio Previdi, and Sergio Bittanti, Fellow, IEEE
Abstract—The problem considered in this paper is the design and tuning of the control system of a power-split continuously variable transmission (CVT) used in high-power tractors. Power-split CVTs are characterized by the combination of a traditional mechanical transmission and by a continuously-variable transmission. This guarantees, at the same time, smooth variations of the transmission-ratio and high efficiency of the overall transmission system. The control architecture of an hydrostatic power-split CVT is constituted by three main parts: 1) servo-controller on the current of the valve which drives the hydraulic transmission; 2) a servo-controller on the hydraulic transmission-ratio; and 3) a synchronizer which coordinates the hydraulic and the mechanical parts of the CVT. In this work, these three controllers are fully developed, including: design, implementation, and evaluation on an experimental system. Index Terms—Agricultural tractors, automotive, continuously variable transmission (CVT), hybrid control.
I. PROBLEM STATEMENT AND CONTROL OBJECTIVES
T
HE problem considered in this paper is the design and tuning of the control system of a power-split continuously variable transmission (CVT) used in high-power tractors. The material presented here is based on a joint work made by the Politecnico di Milano, Milano, Italy, and the Research and Development Department of the SAME Deutz-Fahr Group, (SAME, Lamborghini, Deutz-Fahr, Hürlimann, and Adim Diesel and Deutz AG) developed on a test CVT prototype built for research purposes. This CVT is a hydrostatic power-split transmission system, designed for top-power (up to 300 HP) agricultural tractors, see Fig. 1. Power-split CVTs are a very special type of CVT ([4], [12], [23]); they are characterized by the combination of a traditional mechanical transmission, and by a continuously-variable transmission (Fig. 2). They are used in very demanding applications, which require high-power transmission. Power-spilt transmissions are appealing since they provide a good compromise between traditional mechanical transmissions (highly efficient but discontinuous) and standard CVTs without torque-split widely
Manuscript received September 11, 2002; revised April 2, 2003, August 22, 2003. This work was supported in part by the Rearch and Developement Department of the SAME Deutz-Fahr Group, and in part by the MIUR project “New methods for Identification and Adaptive Control for Industrial Systems.” S. M. Savaresi and S. Bittanti are with the Dipartimento di Elettronica e Informazione, Politecnico di Milano, 20133 Milano, Italy (e-mail:
[email protected]). F. L. Taroni is with SAME Deutz-Fahr Group, 24047 Treviglio, Bergamo, Italy. F. Previdi is with Università degli Studi di Bergamo, Dipartimento di Ingegneria, 24044 Dalmine, Bergamo, Italy. Digital Object Identifier 10.1109/TMECH.2004.835334
Fig. 1.
One of the agricultural tractors used for the testing of the CVT.
used for automotive applications ([5], [15], [20], [21], [25]), which are very smooth but they are characterized by modest efficiency and are unsuited to deliver high torque. The CVT considered in this work uses a hydrostatic system (note that other power-split configurations are possible, see e.g., [6], [12], [22], [24]). Power-split hydrostatic CVTs inherently need a sophisticated electronic control architecture, since the control and the coordination of the hydraulic and the mechanic parts of the CVT cannot be obtained by mechanical elements only. The control architecture considered in this work is summarized—using a top-down approach—in Fig. 3. In Fig. 3(a), the top-level control problem of a modern electronically-controlled transmission system is represented. The final goal of a CVT in an agricultural tractor is to track the required forward speed in a very smooth and regular way. As a matter of fact, due to the huge inertias and loads experienced by a tractor, the speed can suffer abrupt variations and bumps. Hence, a supervising control unit receives as inputs the actual and desired forward speeds, and sends a speed requireto the engine, and a transmission-ratio requirement ment to the CVT (the transmission-ratio of a transmission unit is the ratio between the output and the input rotation speeds, namely ). Fig. 3(b) represents the internal structure of the overall powersplit CVT system [shaded box of Fig. 3(a)]. The input torque is split and redirected into the hydraulic transmission and into the mechanic transmission. These two branches are recombined at the output of the system. The transmission controller is a synchronizer, which receives as input the desired total transmissionratio ; its outputs are the desired hydraulic transmission-ratio , and the switch commands which trigger the mode changes in the mechanic transmission.
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Fig. 2.
Schematic of a power-split hydrostatic CVT.
Fig. 3. (a) High-level view of speed control in a tractor. (b) General architecture of the power-split CVT control system. (c) Controller structure of the hydrostatic part of the power-split CVT.
Fig. 3(c) represents the internal structure of the hydrostatic transmission [shaded box of Fig. 3(b)]. The hydrostatic transmission is mainly constituted by a motor/pump system, driven by a proportional electro-hydraulic valve. The control architecture typically used for the regulation of this system is a cascade-control system: the inner loop is a servo-loop to a desired having the aim of regulating the valve current
over a large bandwidth. The outer loop (using as value control variable) regulates the hydraulic transmission ratio to the desired value requested by the synchronizer. This work focuses on the design of the CVT control system. The final goal of the control problem addressed, hence, is to achieve a good tracking of the desired transmission ratio .
SAVARESI et al.: CONTROL SYSTEM DESIGN ON A POWER-SPLIT CVT FOR HIGH-POWER AGRICULTURAL TRACTORS
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TABLE I DETAILS ON THE SET OF FRICTIONS AND ON THE TRANSMISSION-RATIO RANGES IN FORWARD AND REVERSE MODE
The main contribution and originality of this work is the description of the complete design procedure for the entire control architecture of an hydrostatic power-split CVT (as already observed, this is a very special type of CVT, which has received less attention in the literature than CVTs used in automotive applications). The results obtained at the end of this design process are satisfactory and fulfill the requirements of a modern agricultural tractor. Some final hints for the further improvement of the overall CVT performance are also given. II. SYSTEM DESCRIPTION
Fig. 4. Transmission-ratio controllers).
tracking
experiment
(empirically-tuned
The starting point of this work is a simple and empiricallytuned set of controllers, which provides unsatisfactory performance. This is revealed by the simple -tracking experiment displayed in Fig. 4, where (at the engine rotation speed, rpm) the CVT is required to track a transmission-ratio to in about 10 s. Note that the ramp, ranging from measured transmission-ratio is characterized by a large phase lag and by bumps and oscillations. This behavior is mainly due to the narrow bandwidth of the servo-loops of the hydraulic transmission, and to the unsatisfactory synchronization of the hydraulic and the mechanic branches of the CVT. The final goal of this work was to improve the tracking performance illustrated in Fig. 4. This has been done by redesign and tuning the current servo-loop (Section III), by redesign and tuning the hydraulic transmission-ratio servo-loop (Section IV), and by improving the synchronization of the mode-switching signals (Section V). Section II will be devoted to a preliminary brief description of the CVT system this work focuses on.
The hydrostatic power-split CVT system considered in this work is constituted by the combination of: 1) a Sauer hydraulic system driven by a proportional electro-hydraulic valve ([16]): 2) a mechanical unit characterized by a set of 10 frictions labeled CF, CR, CL, BLM, CHH, CH, CP, BW, CTR, and CVHH. These frictions are driven by on–off electrohydraulic valves. The activation (or deactivation) of the frictions determines the mode-changes of the mechanic part of the CVT. The admissible range of the transmission-ratio of this CVT . Within this range, the mechanical part is of the CVT has six forward modes and six reverse modes. In Table I, the details of the forward and reverse modes are given. Note that: the frictions CF and CR determine the direction of movement; in order to switch from a mode to the next one, one friction must be turned-off and one must be turned-on; in the L mode, the direction of movement is determined by the hydrostatic transmission only. All the controllers used for the regulation and management of the transmission are implemented on an ECU based on the Intel Microcontroller 80C196KR ([8]).The I/O signals of the ECU are ; 1) measure of the rotation speeds 2) measure of the current of the proportional electro-hydraulic valve which drives the hydrostatic transmission; 3) input [pulse–width–modulated (PWM)] of the proportional electro-hydraulic valve; 4) on–off triggers to the electro valves of the frictions of the mechanical part of the transmission.
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Fig. 5. Control system for the current regulation.
The ECU is also connected at 250 Kb/s to the CAN bus of the vehicle. The ECU can be programmed by uploading on a flash EPROM the control algorithm code via a RS232 connection to a laptop PC. For prototyping purposes, a replica of the entire CVT is available on a laboratory test bench. III. CONTROLLER TUNING: THE CURRENT LOOP The first control loop, which must be considered in the CVT control system design, is the servo-loop on the output current of the proportional electro-hydraulic valve which drives the hydraulic transmission [see Fig. 3(c)]. A high-bandwidth current control system is mandatory for the subsequent design of the hydraulic transmission-ratio control-loop. The control scheme for the current regulation is depicted in Fig. 5, where is the valve current, is the PWM input signal of the valve, is the is the transfer funcdesired value of the valve current, tion which models the I/O dynamics of the valve from to (linear and time-invariant dynamics are assumed), and is the transfer function of the controller. The first step in the design of this control system is the development of a mathematical model of the plant. A black-box approach has been chosen. The estimation procedure of the has been done as follows (see e.g., [3] transfer function and references cited therein) 1) The plant (electro-hydraulic valve) has been fed with a , for 9 different freset of 9 pure-tone signals , where quencies rad/s and . 2) The corresponding outputs have been measured. Since the plant is linear, the output signals are pure tones at the same input frequency. Using the estimated magnitude and phase of the output signals (see e.g., [1], [2], [17]), an estimated frequency response can be computed. 3) A parametric model has been chosen, by direct inspection of the measured frequency response. The selected model is constituted by a pole and a pure time delay, namely . 4) The parameters of the model have been identified by minimizing a frequency-domain performance index as follows [3]:
Fig. 6. Measured and estimated frequency response of the valve I/O dynamics.
Fig. 7.
Closed-loop frequency responses (experimentally measured).
Fig. 8.
Control system for the hydrostatic transmission-ratio
regulation.
Using this procedure, the estimated model parameters are: . The quality of the model can be evaluated by Fig. 6, where the measured and the estimated frequency responses are plotted. Note that the estimated model, in spite of its simplicity, provides a good fitting of the data (especially on the phase, which is the most critical for control system design). On the basis of the estimated model, a PI controller has been designed with the objectives of a large bandwidth and a good phase margin ([9], [11]). The estimated parameters of the controller are .
SAVARESI et al.: CONTROL SYSTEM DESIGN ON A POWER-SPLIT CVT FOR HIGH-POWER AGRICULTURAL TRACTORS
Fig. 9.
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Measured frequency responses of the hydraulic transmission I/O dynamics at different engine speeds.
Finally, the closed-loop performance have been experimentally tested by measuring the closed-loop frequency response (from to ). The results are displayed in Fig. 7. The following conclusions can be drawn: 1) The closed-loop bandwidth is almost 10 Hz. This large bandwidth allows a significant performance improvement to the outer loop on the hydraulic transmissionratio. 2) The redesign of the control loop increased the inner-loop bandwidth by about one order of magnitude. Note that the narrow bandwidth of the empirically-tuned control system was an intrinsic limit to the overall performance of the CVT.
IV. CONTROLLER TUNING: THE TORQUE LOOP The second control loop considered in this work is the . This servo-loop on the hydrostatic transmission-ratio control loop is crucial, since good synchronization of the hydrostatic and the mechanic transmission branches can be requested by the achieved only if the transmission-ratio synchronizer is well-tracked over a large bandwidth. The control scheme for the hydrostatic transmission-ratio regulais the actual hydrostatic tion is depicted in Fig. 8, where transmission-ratio, is the desired value of the valve current, is the desired hydrostatic which is used as control input, is the transfer function which models transmission-ratio, to ) of the hydraulic transmisthe I/O dynamics (from sion (linear and time-invariant dynamics are assumed—see is the transfer function of the following discussion), and controller. Note that the plant in this control scheme is constituted by the cascade of the inner current-loop and of the motor/pump dynamics. The mathematical model of the plant has been developed with the same black-box parametric identification in the frequency-domain approach used for the inner loop. The set of harmonic signals used for identification purposes is a subset of the
Fig. 10. Measured frequency responses of the hydraulic transmission I/O dynamics at different load levels.
frequency-set used for the inner loop: rad/s, where . For the hydraulic transmission a crucial issue, however, is the possible dependence of its dynamics on the input rotation speed , and the transmitted torque. To this end, two sets of have been estimated in 7-point frequency-responses the following conditions: • three input rotation speeds have been tested: rpm, rpm, and rpm; in all cases, the transmission is unloaded (zero torque transmitted). The results of these three experiments are displayed in Fig. 9; • three load conditions have been tested: null load, medium load, and maximum load. In all cases, the input rotation rpm. The results of these three speed was experiments are displayed in Fig. 10. The analyses of Figs. 9 and 10 clearly show that the dependence of the hydraulic transmission dynamics on engine speed and load is negligible. Hence, the plant can be well-approximated with a unique linear time-invariant transfer function. Even in this case, the selected model is constituted by a pole , whose and a pure time delay,
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Fig. 11.
Measured and estimated frequency response of the hydraulic transmission I/O dynamics.
Fig. 12.
Closed-loop frequency responses (experimentally measured).
parameters have been identified by minimizing the following frequency-domain performance index
being the measured frequency-responses averaged on the six experiments described above). The estimated model . The parameters are: frequency-domain fitting of the model to the data is displayed in Fig. 11. On the basis of the estimated model a PI controller has been designed, with the objective of a large bandwidth and a good phase margin. The parameters of . the controller are
Fig. 13.
0.05 Hertz sinusoid tracking experiment.
The closed-loop performance have been experimentally tested by measuring the closed-loop frequency response (from to ). The results are displayed in Fig. 12. The following conclusions can be drawn. • The closed loop bandwidth is about 1 Hz. Note that, the fact that the outer loop is about a decade slower than the
SAVARESI et al.: CONTROL SYSTEM DESIGN ON A POWER-SPLIT CVT FOR HIGH-POWER AGRICULTURAL TRACTORS
Fig. 14.
Relationship between the total transmission-ratio and the hydraulic transmission-ratio
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.
V. CONTROLLERS TUNING: THE SYNCHRONIZER
Fig. 15. Time-domain behavior of the internal valve pressure during activation and de-activation.
inner loop guarantees an almost perfect dynamic decoupling between the two loops (this confirms the soundness of the cascade-control architecture—[9], [11]). Dynamic decoupling here means that in the design of the outer loop the inner loop can be treated as a pure algebraic system with unitary gain. • The redesign of the control loop increased the outer-loop bandwidth by almost one order of magnitude. -tracking control Finally, it is worth observing that this system exhibits an unexpected undesired behavior in the neigh(i.e., when ). This is clearly borhood of shown in Fig. 13, where the results of an experiment performed on the real plant are displayed. The experiment consists in the tracking of a 0.05-Hz sinusoid signal of amplitude 1.2 . Note that the tracking of this signal is very accurate (as expected, since the frequency of the input signal is within the close-loop bandwidth of the control system), but the zero-crossing exhibits a bad behavior (jumps and overshoots—see shadowed areas in Fig. 13). An accurate analysis of this behavior has revealed that this is due to the (a complete shaft rough quantization of the sensor of rotation is quantized and encoded using 24 levels only). The drawback of this rough quantization is that, at very low rotation speeds, the sensor delivers a very noisy speed measurement. This problem could be easily solved by replacing this sensor with a continuous-type (see e.g., [14]) speed sensor, which does not suffer of low-speed quantization problems. It is interesting to observe that a completely different way of dealing with this problem (see e.g., [7]) is to use torque sensors in addition to speed sensors.
The last control problem considered in this work is the design and tuning of the synchronizer. The synchronizer is a hybrid ([18]) supervising control unit, which mainly performs the following two tasks: (namely the desired hydraulic 1) generates the signal transmission-ratio, fed into the outer control-loop of the hydraulic transmission); 2) activates and de-activates the set of frictions, by means of triggering commands to the electro-hydraulic valves. In an ideal setting, these two tasks are simple and well defined. 1) Using the algebraic relationship (Fig. 14) between the overall transmission ratio and the hydraulic transmis(note that the diagram in Fig. 14 is the picsion ratio torial representation of Table I), the synchronizer must dewhich joins the actual and the liver a ramp-signal target transmission ratio. It is easy to see, that if the attainment of the target transmission ratio requires a mode change, a sequence of increasing ramps followed by decreasing ramps (or vice-versa) must be generated. Moreover, in the time domain, the slope of the ramp depends on the rate of the speed variation requested by the driver. 2) The triggering command of the mode change should be activated exactly in correspondence of a peak of the piece. In correspondence to the peak, wise ramp signal a friction must be switched-off and a friction must be switched-on, according to Table I. However, due to the nonideal behavior of the on–off valves, the actual task of the synchronizer is more complicated, and requires some additional insight and tuning. The actual behavior of a nonideal on–off valve can be easily and fully understood from Fig. 15, where the internal pressures of the electro-hydraulic valves driving the frictions CH and CHH (during the mode-change from HH to H) are displayed in the time domain. The internal pressure of the valves gives an indirect indication of the valve activation status: the valve is on when the pressure reaches 20 bar (the pressure of the hydraulic circuit which drives the valves); the valve is off
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Fig. 18. current.
Scheme of the open-loop compensation on the proportional-valve
Fig. 16. Activation and de-activation time taken by the electro-hydraulic on–off valves.
Fig. 19. Time-domain profile of the current compensation (absolute value).
Fig. 17.
Mode change M
! H without open-loop compensations.
when the pressure is null. By inspecting Fig. 15, the following observations are due. 1) After the activation command is sent to CH, the pressure of the valve does not jump instantaneously to the 20 bar target pressure; it increases following a well-defined path. First, the pressure is subject to a small pure time delay of about 20 ms; after the time-delay, the pressure rapidly increases, until the pressure of about 15 bar is reached (at this time the valve is not activated yet); the pressure remains almost constant for about 130 ms, due to process of oil-filling of the valve; finally, the pressure restart increasing until the target pressure is reached. The overall activation time of CH is about 250 ms. 2) After the de-activation command is sent to CHH, the valve pressure follows this simple path (note that the pressure in CHH is slightly influenced by the activation command to CH, since they are driven by the same hydraulic circuit): after the activation command is given, the pressure remains unchanged for about 50 ms; the pressure quickly decreases until the null pressure is reached. The overall de-activation time of CHH is about 100 ms. Since the activation time is always larger than the de-activation time (see Fig. 16, where the entire set of activation and de-activations times is displayed), the mode-change is done in a time equal to the activation-time of the up-coming friction. The mode-change procedure performed by the synchronizer hence is as follows: the up-coming friction is activated; a time-lag equal to the difference between the activation-time of the up-coming
friction and the de-activation time of the out-coming friction is waited for; the out-coming friction is de-activated. The overall mode-change time takes, on average, about 250 ms (it only depends on the type of the up-coming friction, and ranges from 170 to 400 ms; see Fig. 16). The simplest and most intuitive way of managing a mode change is to start the routine in correspondence to the peak of the . In Fig. 17, an example of a piecewise ramp on mode change (activation of CH and de-activation of BLM) performed using this simple rationale is displayed. The accurate inspection of the behavior of the total and of the hydraulic transmission-ratio shows many interesting characteristics of this control system. is inherently affected by 1) The transmission-ratio a phase-lag, with respect to the desired reference-signal . This lag obviously propagates on the total transas well. This is due to the finite bandmission-ratio -tracking servo-loop. In Fig. 17 this width of the time-lag is about 70 ms. This time-lag can be reduced only by enlarging the bandwidth of the servo-loop on the hydraulic transmission-ratio. exhibits a long 2) The hydraulic transmission-ratio overshoot (shaded area in Fig. 17) just after the peak . This also affects the of the piecewise ramp on total transmission ratio (note the two under-tracking and over-tracking bumps in the neighborhood of the modechange). This behavior of the synchronizer has been significantly improved using an open-loop compensation approach. Two modifications have been proposed (Fig. 19). 1) The mode-change routine has been anticipated of an amount of time exactly equal to the activation-time of the up-coming friction. If the peak of the piecewise ramp occurs at time , and the activation-time of on
SAVARESI et al.: CONTROL SYSTEM DESIGN ON A POWER-SPLIT CVT FOR HIGH-POWER AGRICULTURAL TRACTORS
Fig. 20.
Mode change M
577
! H with open-loop compensations.
the up-coming friction is , the mode-change routine is started at time . Note that the prediction of can be easily made since the slope of the peak-time the ramp is known in advance. 2) The reference signal of the proportional valve current has been added with an impulse-like correction signal, , in order to remove the just after the peak on . A fine-tuning procedure on the real overshoot on plant has shown that the best results can be achieved if the impulse-like compensation signal has the triangular shape illustrated in Fig. 19. The height of the optimal impulse-like triangular compensation signal slightly depend on the type of mode change. mode change, using the In Fig. 20, the results of the modified synchronizer, are displayed. Note that the total transmission-ratio tracking is almost perfect; also the fitting of the actual hydraulic transmission ratio to the reference signal has been strongly improved. Finally, in Fig. 21 the results of a -tracking experiment over a large range of transmission-ratio (involving three mode-changes) is plotted. Note the remarkable improvements achieved by the redesign and retuning of the three controllers of the CVT. The results displayed in Fig. 21 are very satisfactory, and fulfill the requirements of a modern top-range agricultural tractor. Regarding the performance achievable with the proposed control architecture two final remarks are due. Remark 1. Robustness of the Open-Loop Compensation: The synchronization approach proposed and implemented in this work is based on a classical open-loop framework. It is well known that this approach inherently provides poor robustness performances, and requires a lot of tuning to obtain near-optimal performance. The open-loop compensation proposed herein cannot overcome this problem: it is expected that, due to wearing phenomena, temperature drifts, construction tolerances, the performance of the synchronization law can
Fig. 21.
Transmission-ratio tracking experiment.
decrease. This problem could be, in principle, overcome with two different approaches. The first approach is the online estimation and tuning of the slowly-varying parameters of the transmission (adaptive control); this approach in practice can be over-demanding in terms of design effort and computational power. The second approach can be the feedback control of the overall transmission ratio: one can imagine measuring, online, the actual value of and to drive the on–off valves accordingly. This approach would result in a much more robust control system; the main obstacle, along this path, can be given by the valve dynamics (which might be too slow for a genuinely feedback-control architecture). A mixed feedback-feedforward approach could be the best solution, but goes beyond the scope of this work. Remark 2. Tracking Delay: The residual tracking time lag, clearly visible in Fig. 20, is simply due to the limited bandwidth
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of the servo-loop on the hydrostatic transmission-ratio . This bandwidth is about 1 Hz for the hydrostatic transmission used on this test bench, see Section IV, and this limit is due to the intrinsic dynamic behavior of the hydrostatic transmission and to its input limitations. This phase-lag clearly depends on the : variation rate of the required hydrostatic transmission-ratio the higher is the variation rate, the more visible and obnoxious is the corresponding phase-lag. In principle this effect could be reduced if a good prediction of the required transmission ratio is available. This assumption has not been made in this work is slowly-varying and a good even if, in practice, the signal short-range prediction might be figured out and used to reduce the tracking lag. Finally, it is worth observing that, apart from the small time window around a mode change, the relationship between the hydrostatic and total transmission-ratio is purely algebraic since the mechanical branch (clutches) of the transmission has a negligible dynamic behavior when the mode-change is terminated. This can be easily appreciated by the fact (see, e.g., Fig. 20) that the tracking-lag is the same in the hydrostatic and in the total transmission ratio. VI. CONCLUSIONS AND FUTURE WORK In this paper, the complete procedure of design and tuning of the entire set of controllers in a power-split hydrostatic CVT used in high-power tractors has been proposed. The final results (in terms of smoothness of the transmission variation) obtained on the prototype used for testing are satisfactory and fulfill the requirements of a modern agricultural tractor. The analysis developed in this work has shown that further improvements could be obtained by improving the signal-to-noise ratio of the speed sensors in the neighborhood of zero forward speed, and by enlarging the bandwidth of the tracking servo-loop on the hydraulic transmission ratio. Given the near-optimal performance achieved with the control system proposed in this work on the test prototype, these improvements could be obtained only by replacing the currently-used speed sensors and hydraulic motor/pump.
[6] Y. Cheng and B. L. R. De Moor, “Robustness analysis and control system design for a hydraulic servo system,” IEEE Trans. Contr. Syst. Technol., vol. 2, pp. 183–197, Sept. 1994. [7] K. M. C. Hebbale, “Control of the geared neutral point in a traction drive CVT,” in Proc. American Control Conf., Denver, CO, 2003, pp. 2572–2577. [8] 8XC196Kx, 8XC196Jx, 87C196CA Microcontroller Family User’s Manual, 1995. [9] T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980. [10] U. Kiencke and L. Nielsen, Automotive Control Systems for Engine, Driveline, and Vehicle. New York: Springer Verlag, 2000. [11] The Control Handbook, W. S. Levine, Ed., IEEE , Piscataway, NJ, 1996. [12] S. Liu and B. Paden, “A survey of today’s CVT controls,” in Proc. 36th IEEE Decision Control Conf., 1997, pp. 4738–4743. [13] K. Nevala, J. Penttinen, and P. Saavalainen, “Developing of the anti-slip control of hydrostatic power transmission for forest tractor and optimization of the power of diesel engine,” in Proc. 5th Int. Workshop on Advanced Motion Control, 1998, pp. 475–480. [14] R. Ohba, Intelligent Sensor Technology. New York: Wiley, 1992. [15] M. Paul, “CVT’s driving the future of transmission technology,” in Proc. Int. Congress Continuously Variable Power Transmission, Eindhover, The Netherlands, 1999. [16] G. Sauer, Continuously Variable Transmissions for Tractor Drive Line, Milan, Italy: Ag. Eng., 1994. Internal Report 94-D-020. [17] S. M. Savaresi, R. Bitmead, and W. Dunstan, “Nonlinear system identification using closed-loop data with no external excitation: The case of a lean combustion process,” Int. J. Contr., vol. 74, pp. 1796–1806, 2001. [18] A. V. Savkin and R. J. Evans, Hybrid Dynamical Systems: Birkhauser, 2002. [19] A. J. Scarlett, “Integrated control of agricultural tractors and implements: A review of potential opportunities relating to cultivation and crop establishment machinery,” Int. J. Comput. Electron. Agriculture, vol. 30, no. 1–3, pp. 167–191, 2001. [20] M. Schwab, “Electronically-controlled transmission systems—Current position and future developments,” Int. Congress Transportation Electron., pp. 335–342, 1990. [21] P. Setlur, J. R. Wagner, D. M. Dawson, and B. Samuels, “Nonlinear control of a continuously variable transmission (CVT) for hybrid vehicle powertrains,” in IEEE American Control Conf., 2001, pp. 1304–1309. [22] H. Tanaka, “Speed ratio control of a parallel layout double cavity halftoroidal CVT for four-wheel drive,” J. Soc. Automotive Eng. Jpn., vol. 23, no. 3, pp. 213–217, 2002. [23] H. Vahabzadeh and S. M. Linzell, “Modeling, Simulation, and Control Implementation for a Split-Torque, Geared Neutral, Infinitely Variable Transmission,”, SAE paper n.910 409, 1991. [24] K. Wonoh and G. Vachtsevanos, “Fuzzy logic ratio control for a CVT hydraulic module,” in Proc. IEEE Int. Symp. Intelligent Control, 2000, pp. 151–156. [25] Z. Zou, Y. Zhang, X. Zhang, and W. Tobler, “Ratio control of traction drive continuously variable transmissions,” in Proc. IEEE American Control Conf., 2000, pp. 1525–1529.
ACKNOWLEDGMENT The authors would like to thank P. Rottigni for his help in the implementation and analysis of the identification and control algorithms presented in this work. REFERENCES [1] S. Bittanti, M. Campi, and S. M. Savaresi, “Unbiased estimation of a sinusoid in noise via adapted notch filters,” Automatica, vol. 33, no. 2, pp. 209–215, 1997. [2] S. Bittanti and S. M. Savaresi, “On the parametrization and design of an extended Kalman filter frequency tracker,” IEEE Trans. Automatic Contr., vol. 45, pp. 1718–1724, Sept. 2000. [3] S. Bittanti and G. Picci, Eds., Identification, Adaptation, Learning—The Science of Learning Models from Data. ser. Computer and Systems Sciences Series, Berlin, Germany: Springer-Verlag, 1996. [4] Automotive Handbook, 5th ed., Bosch, BOSCH Gmbh, Germany, 2000. [5] C. Chan, D. Yang, T. Volz, D. Breitweiser, F. S. Jamzadeh, A. Frank, and T. Omitsu, “System Design and Control Considerations on Automotive Continuously Variable Transmissions,” SAE paper n.840 048, 1984.
Sergio M. Savaresi (M’02) was born in Manerbio, Italy, on September 21, 1968. He received the M.Sc. degree in electrical engineering and the Ph.D. degree in systems and control engineering from the Politecnico di Milano, Milan, Italy, in 1992 and 1997, and the M.Sc. degree in applied mathematics from the Universitá Cattolica, Brescia, Italy, in 2000. In 1998, he worked at McKinsey&Company. Since 1999, he has been with the Politecnico di Milano, where he is currently an Associate Professor teaching courses in automatic control. He has been a Visiting Researcher at Lund University, Sweden, at the University of Twente, The Netherlands, at the Canberra National University, Australia, and at the University of Minnesota at Minneapolis. His main research interests are in the areas of vehicle control, automotive systems, data analysis and system identification, nonlinear control theory, and control applications. Dr. Savaresi is an Associate Editor of the European Journal of Control.
SAVARESI et al.: CONTROL SYSTEM DESIGN ON A POWER-SPLIT CVT FOR HIGH-POWER AGRICULTURAL TRACTORS
Francesco L. Taroni was born in Milan, Italy, on September 26, 1964. He received the M.Sc. in electronic engineering from the Politecnico di Milano, Milan, Italy, in 1992. In 1992, he joined Esaote S.p.a., Research and Development Group, as a designer of HW and SW for ultrasound digital ecographic systems. Since 1997, he has been with SAME Deutz Fahr Group, Treviglio, Bergamo, Italy, and is currently working in the Electric and Electronic Department where his focus is on the design of the control of powertrains in tractor applications.
Fabio Previdi was born in Milan, Italy, on August 22, 1968. He received the “Laurea” degree (M.Sc.) in electronic engineering and the Ph.D. in computer science and automatic control, from the Politecnico di Milano, Milan, Italy, in 1993 and 1999, respectively. From 1999 to 2001, he was Research Assistant in Automatic Control, Department of Electronics and Information Sciences, Politecnico di Milano, where he was also a Teaching Assistant for courses on automatic control. During winter 1999 to 2000, he was a Visiting Scientist at the Center for Systems and Control, University of Glasgow, U.K. From 1999 to 2001, he was a Contract Professor of Automatic Control, University of Bergamo, Italy. Since 2002, he has been a Researcher at the University of Bergamo, where he teaches Automatic Control and Industrial Automation. In recent years he has been involved in many national and international research projects developed by universities and industrial companies. He has published more than 40 papers in international journals and international conference proceedings. His research interests include fault diagnosis, nonlinear identification and control, linear parameter varying (LPV) systems, application of control in biomedical engineering, and marine systems.
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Sergio Bittanti (F’01) is a Professor on the Faculty of Engineering, Politecnico di Milano, Milan, Italy. Besides being active on various theoretical topics of system identification and control, he has developed a number of advanced application studies in cooperation with industries. The outcomes of this intense research activity are summarized in a hundred of refereed papers in the best international journals. He is the author of a number of textbooks in Italian and the editor or co-editor of four volumes in English (all published by Springer-Verlag). In particular, he is the co-editor of Identification, adaptation, learning—The science of learning models from data (New York: Springer-Verlag, 1996), which contains a collection of selected lectures given at the NATO ASI From Identification to Learning (Como, Italy, 1994). From 1988 to 1995, he acted as Project Manager of the Italian Research Network Model Identification, System Control, and Signal Processing, which connected about 70 Italian professors and researchers from in different universities. At the Politecnico, he coordinated the Ph.D. Program in computer and control engineering from 1993 to 1998. Prof. Bittanti served as Editor for a number of journals and is currently Editor in Chief of the European Journal of Control. He is a member of the IFAC Council. He organized a number of conferences, the latest one being the IFAC Symposium on Robust Control, held in Milan, Italy, in 2003.
