Adaptive sliding mode control of a chaotic nonsmooth-air-gap permanent magnet synchronous motor with uncertainties. (English) Zbl 1279.34075
Summary: Using the sliding mode control approach, a simple adaptive controller design method is proposed for a chaotic nonsmooth-air-gap permanent magnet synchronous motor (PMSM). The proposed method does not require the restrictive assumption that accurate information on the PMSM parameter and load torque values is available, thus it has robustness to model uncertainties. This paper analyzes the stability and convergence of the closed-loop control system, and this paper gives a discretized control algorithm for DSP implementation. Finally, this paper presents some simulation results to illuminate that the proposed method can effectively handle the controller design problem for a chaotic nonsmooth-air-gap PMSM under inaccurate information on the PMSM parameter and load torque values.
MSC:
| 34H10 | Chaos control for problems involving ordinary differential equations |
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C40 | Adaptive control/observation systems |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
Keywords:
chaos; adaptive control; sliding mode control; permanent magnet synchronous motor (PMSM); uncertaintyReferences:
| [1] | Siewe, M.S., Yamgoue, S.B., Kakmeni, F.M.M., Tchawoua, C.: Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory. Nonlinear Dyn. 62, 379-389 (2010) · Zbl 1209.93068 · doi:10.1007/s11071-010-9725-3 |
| [2] | Yang, T., Chua, L.O.: Impulsive stabilization for control and synchronization of chaotic systems: theory and applications to secure communication. IEEE Trans. Circuits Syst. I 44, 976-988 (1997) · doi:10.1109/81.633887 |
| [3] | Wang, Y., Hao, J., Zuo, Z.: A new method for exponential synchronization of chaotic delayed systems via intermittent control. Phys. Lett. A 374, 2024-2029 (2010) · Zbl 1236.34073 · doi:10.1016/j.physleta.2010.02.069 |
| [4] | Faieghi, M., Kuntanapreeda, S., Delavari, H., Baleanu, D.: LMI-based stabilization of a class of fractional-order chaotic systems. Nonlinear Dyn. 72, 301-309 (2013) · Zbl 1268.93121 · doi:10.1007/s11071-012-0714-6 |
| [5] | Zhang, R., Yang, S.: Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach. Nonlinear Dyn. 72, 269-278 (2013) · doi:10.1007/s11071-012-0659-9 |
| [6] | Cai, L., Zhou, J.: Impulsive stabilization and synchronization of electro-mechanical gyrostat systems. Nonlinear Dyn. 70, 541-549 (2012) · Zbl 1267.34118 · doi:10.1007/s11071-012-0474-3 |
| [7] | Kwuimy, C.A.K., Woafo, P.: Dynamics, chaos and synchronization of self-sustained electromechanical systems with clamped-free flexible arm. Nonlinear Dyn. 53, 201-213 (2008) · Zbl 1170.74349 · doi:10.1007/s11071-007-9308-0 |
| [8] | Fradkov, A.L., Evans, R.J.: Control of chaos: methods and applications in engineering. Annu. Rev. Control 29, 33-56 (2005) · doi:10.1016/j.arcontrol.2005.01.001 |
| [9] | Kwuimy, C.A.K., Nataraj, C.: Modeling and dynamic analysis of a magnetically actuated butterfly valve. Nonlinear Dyn. 70, 435-451 (2012) · doi:10.1007/s11071-012-0466-3 |
| [10] | Pennacchi, P.: Nonlinear effects due to electromechanical interaction in generators with smooth poles. Nonlinear Dyn. 57, 607-622 (2009) · Zbl 1176.74064 · doi:10.1007/s11071-009-9496-x |
| [11] | Mu, C., Zhang, F., Shu, Y., Zhou, S.: On the boundedness of solutions to the Lorenz-like family of chaotic systems. Nonlinear Dyn. 67, 987-996 (2012) · Zbl 1245.34055 · doi:10.1007/s11071-011-0041-3 |
| [12] | Aghababa, M.P., Aghababa, H.P.: Chaos suppression of rotational machine systems via finite-time control method. Nonlinear Dyn. 69, 1881-1888 (2012) · Zbl 1263.93110 · doi:10.1007/s11071-012-0393-3 |
| [13] | Li, Z., Park, J.B., Joo, Y.H., Zhang, B., Chen, G.: Bifurcations and chaos in a permanent-magnet synchronous motor. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 49, 383-387 (2002) · Zbl 1368.93519 · doi:10.1109/TCSI.2002.801242 |
| [14] | Jing, Z., Yu, C., Chen, G.: Complex dynamics in a permanent-magnet synchronous motor model. Chaos Solitons Fractals 22, 831-848 (2004) · Zbl 1129.70329 · doi:10.1016/j.chaos.2004.02.054 |
| [15] | Ren, H., Liu, D.: Nonlinear feedback control of chaos in permanent magnet synchronous motor. IEEE Trans. Circuits Syst. II, Express Briefs 53, 45-50 (2006) · doi:10.1109/TCSII.2005.854592 |
| [16] | Zribi, M., Oteafy, A., Smaoui, N.: Controlling chaos in the permanent magnet synchronous motor. Chaos Solitons Fractals 41, 1266-1276 (2009) · doi:10.1016/j.chaos.2008.05.019 |
| [17] | Yu, J., Chen, B., Yu, H.: Fuzzy-approximation-based adaptive control of the chaotic permanent magnet synchronous motor. Nonlinear Dyn. 69, 1479-1488 (2012) · Zbl 1253.93070 · doi:10.1007/s11071-012-0363-9 |
| [18] | Yu, J., Yu, H., Chen, B., Gao, J., Qin, Y.: Direct adaptive neural control of chaos in the permanent magnet synchronous motor. Nonlinear Dyn. 70, 1879-1887 (2012) · doi:10.1007/s11071-012-0580-2 |
| [19] | Choi, H.H., Vu, N.T.T., Jung, J.-W.: Digital implementation of an adaptive speed regulator for a PMSM. IEEE Trans. Power Electron. 26, 3-8 (2011) · doi:10.1109/TPEL.2010.2055890 |
| [20] | Leu, V.Q., Choi, H.H., Jung, J.-W.: Fuzzy sliding mode speed controller for PM synchronous motors with a load torque observer. IEEE Trans. Power Electron. 27, 1530-1539 (2012) · doi:10.1109/TPEL.2011.2161488 |
| [21] | Do, T.D., Choi, H.H., Jung, J.-W.: SDRE-based near optimal control system design for PM synchronous motor. IEEE Trans. Ind. Electron. 59, 4063-4074 (2012) · doi:10.1109/TIE.2011.2174540 |
| [22] | Choi, H.H., Jung, J.-W.: Discrete-time fuzzy speed regulator design for PM synchronous motor. IEEE Trans. Ind. Electron. 60, 600-607 (2013) · doi:10.1109/TIE.2012.2205361 |
| [23] | Vu, N.T.T., Yu, D.-Y., Choi, H.H., Jung, J.-W.: T-S fuzzy-model-based sliding-mode control for surface-mounted permanent-magnet synchronous motors considering uncertainties. IEEE Trans. Ind. Electron. 60, 4281-4291 (2013) · doi:10.1109/TIE.2012.2213554 |
| [24] | Loria, A.: Robust linear control of (chaotic) permanent-magnet synchronous motors with uncertainties. IEEE Trans. Circuits Syst. I, Regul. Pap. 56, 2109-2122 (2009) · doi:10.1109/TCSI.2008.2011587 |
| [25] | Slotine, J.-J., Li, W.: Applied Nonlinear Control. Prentice Hall, New York (1991) · Zbl 0753.93036 |
| [26] | DeCarlo, R.A., Zak, S.H., Matthews, G.P.: Variable structure control of nonlinear multivariable systems—a tutorial. Proc. IEEE 76, 212-232 (1988) · doi:10.1109/5.4400 |
| [27] | Bartolini, G., Ferrara, A., Usai, E., Utkin, V.I.: On multi-input chattering-free-second order sliding mode control. IEEE Trans. Autom. Control 45, 1711-1717 (2000) · Zbl 0990.93012 · doi:10.1109/9.880629 |
| [28] | Kachroo, P., Tomizuka, M.: Chattering reduction and error convergence in the sliding-mode control of a class of nonlinear systems. IEEE Trans. Autom. Control 41, 1063-1068 (1996) · Zbl 0858.93022 · doi:10.1109/9.508917 |
| [29] | Lee, H., Utkin, V.I.: Chattering suppression methods in sliding mode control systems. Annu. Rev. Control 31, 179-188 (2007) · doi:10.1016/j.arcontrol.2007.08.001 |
| [30] | Bartolini, G., Ferrara, A., Usai, E.: Chattering avoidance by second order sliding mode control. IEEE Trans. Autom. Control 43, 241-246 (1998) · Zbl 0904.93003 · doi:10.1109/9.661074 |
| [31] | Utkin, V.I.: Variable structure systems with sliding modes. IEEE Trans. Autom. Control 22, 212-222 (1977) · Zbl 0382.93036 · doi:10.1109/TAC.1977.1101446 |
| [32] | Choi, H.H.: Sliding-mode output feedback control design. IEEE Trans. Ind. Electron. 55, 4047-4054 (2008) · doi:10.1109/TIE.2008.2004386 |
| [33] | Boyd, S., ElGhaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994) · Zbl 0816.93004 · doi:10.1137/1.9781611970777 |
| [34] | Astrom, K.J., Witternmark, B.: Computer-Controlled Systems—Theory and Design. Prentice Hall, Philadelphia (1990) |
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