This paper focuses on the control at the power-zero condition of a power-split continuously variable transmission (CVT) used in agricultural tractors. The power-zero condition requires the controller to regulate the transmission ratio to zero, independently of the input engine speed. This is particularly useful when the tractor is operated uphill or downhill, in order to keep the vehicle still without using brakes. As the considered CVT is tailored to low-power tractors used in orchards and vineyards, this is indeed a very important functioning mode. Specifically, it is shown how the control problem is deeply interleaved with the choice of the appropriate angular speed sensors used for computing the transmission ratio and the algorithm used to process their output for computing the angular speed. An innovative analysis on the estimation error and the time delay of the two main speed estimation algorithms is developed. In particular, it is proven that the delay introduced by the speed sensor can cause an undesired limit-cycle behaviour in the closed-loop system. The existence and stability properties of such a limit cycle are assessed with a describing-function approach, and a strategy to suppress the limit cycle is proposed.
KienckeU.NielsenL.Automotive control systems for engine, driveline, and vehicle, 2000 (Springer-Verlag, Berlin).
3.
SavaresiS. M.TanelliM.BittantiS.MangiliA.TaroniF.PrevidiF.Control of a powershuttle motion inverter. In Proceedings of the 2005 American Control Conference, Portland, Oregon, USA, 2005, vol. 2, pp. 1010–1015 (IEEE, New York).
4.
SavaresiS. M.TaroniF.PrevidiF.BittantiS.Control system design on a power-split CVT for high-power agricultural tractors. IEEE/ASME Trans. Mechatronics, 2004, 9(3), 569–579.
5.
SetlurP.WagnerJ. R.DawsonD. M.SamuelsB.Nonlinear control of a continuously variable transmission (CVT) for hybrid vehicle powertrains. In Proceedings of the IEEE/ASME American Control Conference, 2001, pp. 1304–1309 (IEEE, New York).
ChanC.YangD.VolzT.BreitweiserD.JamzadehF. S.FrankA.OmitsuT.System design and control considerations on automotive continuously variable transmissions. SAE paper 840048, 1984.
8.
ScarlettA. J.Integrated control of agricultural tractors and implements: A review of potential opportunities relating to cultivation and crop establishment machinery. Int. J. Computers Electronics Agriculture, 2001, 30(1–3), 167–191.
9.
SchwabM.Electronically-controlled transmission systems - current position and future developments. In Vehicle Electronics in the 90's, Proceedings of the International Congress on Transportation electronics, 1990, pp. 335–342 (IEEE, New York).
10.
ZouZ.ZhangY.ZhangX.ToblerW.Ratio control of traction drive continuously variable transmissions. In Proceedings of the 2000 American Control Conference, 2000, pp. 1525–1529 (IEEE, New York).
11.
ChengY.De MoorB. L. R.Robustness analysis and control system design for a hydraulic servo system. IEEE Trans. Control Systems Technol., 1994, 2(3), 183–197.
12.
HebbaleK.CarpenterM.Control of the geared neutral point in a traction drive CVT. In Proceedings of the 2003 American Control Conference, Denver, Colorado, USA, 2003, vol. 3, pp. 2572–2576 (IEEE, New York).
13.
KhalilH. K.Nonlinear systems, 2nd edition, 1996 (Prentice-Hall, Upper Saddle River, New Jersey).
14.
SavaresiS. M.BitmeadR.DunstanW.Nonlinear system identification using closed-loop data with no external excitation: The case of a lean combustion process. Int. J. Control, 2001, 74, 1796–1806.
15.
AttaineseC.TomassoG.Position measurement in industrial drives by means of low-cost resolver-to-digital converter, IEEE Trans. Instrumn Measmt, 2007, 56(6), 2155–2159.
16.
BaehrA.MutschlerP.Comparison of speed acquisition methods based on sinusoidal encoder signals. In Proceedings of the Eighth International Conference on Optimization of Electrical and Electronic Equipment (OPTIM 2002), Brasov, Romania, 2002, in JEE J. Electl Engng, 2002, 2(1), 16.05–17.05.
17.
BrownR. H.SchneiderS. C.MulliganM. G.Analysis of algorithms for velocity estimation from discrete position versus time data. IEEE Trans. Ind. Electronics, 1992, 39(1), 11–19.
18.
BunteA.BeinekeS.High-performance speed measurement by suppression of systematic resolver and encoder errors. IEEE Trans. Ind. Electronics, 2004, 51(1), 49–53.
19.
CarpenterP. S.BrownR. H.HeinenJ. A.SchneiderS. C.On algorithms for velocity estimation using discrete position encoders. In Proceedings of the IEEE 21st International Conference on Industrial electronics, control and instrumentation (IECON), 1995, vol. 2(6-10), pp. 844–849 (IEEE, New York).
20.
KavanaghR. C.Shaft encoder characterization via theoretical model of differentiator with both differential and integral nonlinearities. IEEE Trans. Instrumn Measmts, 2000, 49(4), 795–801.
21.
KavanaghR. C.Performance analysis and compensation of M/T-type digital tachometers. IEEE Trans. Instrumn Measmts, 2001, 50(4), 965–970.
22.
LemkinM.YangP. H.WuangA. C.JonesJ.AuslanderD. M.Velocity estimation from widely spaced encoder pulses. In Proceedings of the 1995 American Control Conference, Seattle, Washington, USA, 1995, pp. 998–1002 (IEEE, New York).
23.
YienC.Incremental encoder errors: causes and ways to reduce them. In Proceedings of the International Conference on Power conversion and intelligent motion (PCIM 1992), Nürnberg, Germany, April 1992, pp. 110–121 (ZM Communications, Gmbh, Nürnberg, Germany).
24.
MañèR.Ergodic theory and differentiable dynamics, 1987 (Springer-Verlag, Berlin).
25.
BittantiS.PicciG. (Eds) Identification, adaptation, learning - the science of learning models from data, Computer and Systems Sciences Series, 1996 (Springer-Verlag, Berlin)s.
26.
BittantiS.SavaresiS. M.On the parametrization and design of an extended Kalman filter frequency tracker. IEEE Trans. on Autom. Control, 2000, 45(9), 1718–1724.
27.
PintelonR.SchoukensJ.System identification: a frequency domain approach, 2001 (IEEE, New York).
28.
SavaresiS. M.TanelliM.TaroniF.PrevidiF.BittantiS.Analysis and design of an automatic motion inverter. IEEE/ASME Trans. Mechatronics, 2006, 11(3), 346–357.
29.
KailathT.Linear systems, 1980 (Prentice Hall, Englewood Cliffs, New Jersey).
30.
GuardabassiG. O.SavaresiS. M.Approximate linearization via feedback - an overview. Automatica, 2001, 27, 1–15.
