In this paper, chaos control and anticontrol of a tachometer system by Ge—Yao—Chen (GYC) partial region stability are proposed. The Lyapunov function becomes a simple linear homogeneous function and the controllers become simpler by using the GYC partial region stability theory. The simulation results are more precise because the controllers are in lower degree than that of traditional controllers. Finally, chaos control and anticontrol of the tachometer system by GYC partial region stability are obtained and verified by numerical simulations.
OttE.GrebogiC.YorkeJ. A., Controlling chaosPhys. Rev. Lett.64 (1990): 1196–1199.
2.
ChenG.DongX., From chaos to order: perspectives, methodologies and applications (Singapore: World Scientific1998).
3.
ChenG.DongX., On feedback control of chaotic continuous time systemsIEEE Trans. Circuits Syst.40 (1993): 591–601.
4.
YassenM. T., Chaos control of Chen chaotic dynamical systemChaos Solitons Fractals15 (2003): 271–283.
5.
YassenM. T., Controlling chaos and synchronization for new chaotic system using linear feedbackChaos Solitons Fractals26 (2005): 913–920.
6.
AgizaH. N., Controlling chaos for the dynamical system of coupled dynamicsChaos Solitons Fractals12 (2002): 341–352.
7.
YassenM. T., Adaptive control and synchronization of a modified Chua's circuit systemAppl. Math. Comput.135 (2001): 113–128.
8.
LiaoT. L.LinS. H., Adaptive control and synchronization of Lorenz systemJ. Franklin Inst.336 (1999): 925–937.
9.
YangX. S.ChenG., Some observer-based criteria for discrete-time generalized chaos synchronizationChaos Solitons Fractals13 (2002): 1303–1308.
10.
SanchezE. N.PerezJ. P.MartinezM.ChenG., Chaos stabilization: An inverse optimal control approachLat. Amer. Appl. Res. Int. J.32 (2002): 111–114.
11.
BaiE. W.LonngrenK. E., Sequential synchronization of two Lorenz systems using active controlChaos Solitons Fractals11 (2000): 1041–1044.
12.
ChenH. K.LeeC. I., Anti-control of chaos in rigid body motionChaos Solitons Fractals21 (2004): 957–965.
13.
GeZ. M.WuH. W., Chaos synchronization and chaos anticontrol of a suspended track with moving loadsJ. Sound Vibr.270 (2004): 685–712.
14.
GeZ. M.YuC. Y.ChenY. S., Chaos synchronization and chaos anticontrol of a rotational supported simple pendulumJSME Int. J. Ser. C47 (2004): 233–241.
15.
GeZ. M.LeuW. Y., Anti-control of chaos of two-degree-of-freedom louderspeaker system and chaos system of different order systemChaos Solitons Fractals20 (2004): 503–521.
16.
GeZ. M.ChengJ. W.ChenY. S., Chaos anticontrol and synchronization of three time scales brushless DC motor systemChaos Solitons Fractals22 (2004): 1165–1182.
17.
GeZ. M.LeeC. I., Anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governorChaos Solitons Fractals282 (2005): 635–648.
18.
GeZ. M.LeeC. I., Control anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delayChaos Solitons Fractals23 (2005): 1855–1864.
19.
GeZ. M.YaoC. W.ChenH. K., Stability on partial region in dynamicsJ. Chin. Soc. Mech. Eng.15 (1994): 140–151.
20.
GeZ. M.ChenH. K., Three asymptotical stability theorems on partial region with applicationsJpn. J. Appl. Phys.37 (1998): 2762–2773.
21.
GeZ. M., Necessary and sufficient conditions for the stability of a sleeping top described by three forms of dynamic equationsPhys. Rev. E77 (2008): 046606-1046606-8.
22.
GeZ. M.YangC. H.ChenH. H.LeeS. C., Non-linear dynamics and chaos control of a physical pendulum with vibrating and rotation supportJ. Sound Vibr.242 (2001): 247–264.
23.
GeZ. M.ChangC. M., Chaos synchronization and parameters identification of single time scale brushless DC motorsChaos Solitons Fractals20 (2004): 883–903.
24.
LiuF.RenY.ShanX.QiuZ., A linear feedback synchronization theorem for a class of chaotic systemsChaos Solitons Fractals13 (2002): 723–730.
25.
GeZ. M.ShiueJ. S., Nonlinear dynamics and control of chaos for tachometerJ. Sound Vibr.253 (2002): 773–793.
26.
MalkinI. G., Theory of stability of motion (Oak Ridge, Tennessee, USA: Moscow—Leningrad, United States Atomic Energy Commission, Technical Information Service Extension1952) translated from a publication of the state publishing house of Technical-Theoretical Literature.
27.
ChetayevN. G., The stability of motion (New York: Pergamon Press1961).
28.
KhalilK. H., Nonlinear systems (New Jersey: Prentice Hall2002).
