1. Motion control 主題 : Observer-Based Speed Tracking Control for Sensorless Permanent Magnet Synchronous Motors With Unknown Load Torque 作者 : Patrizio Tomei and Cristiano Maria Verrelli 出處 : IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 56, NO. 6, JUNE 2011 p.1484~p.1488 報告人 :4972C063 謝元耀 老師 : 王明賢教授

2. 大綱 1-Abstract 2-Introduction 3-Dynamic Model 4-Nonlinear Adaptive Design 5-Simulation Results 6-Conclusion 7-References

3. Abstract Abstract—Assuming that only stator currents and voltages are available for feedback, a novel sixth order nonlinear adaptive control algorithm is designed

4. Introduction 1-Permanent magnet synchronous motors have the following advantages over typically used electric motors 2-motor mechanical variables (rotor position or speed) are available from measurements, high performance can be achieved in rotor position or speed tracking applications even in the presence of uncertain model parameters (see for instance [2]–[5], [7], [9], [12] and ref-erences therein).

5. Introduction? 3-A problem is rather difficult to be solved since: motor dynamics are nonlinear and multivariable; measured outputs (stator currents) do not coincide with one of the controlled outputs (rotor speed) which are required to track smooth bounded reference signals; the load torque depends on applications and is a typically uncertain model parameter.

6. Introduction 4-In this letter we extend the result presented in [11] by designing a novel nonlinear adaptive control for sensorless The control algorithm, which is based on stator current and voltage measurements only, incorporates two closed loop observers

7. Dynamic Model

12. Simulation Results

14. with =45rad/s. The necessary first and second order derivatives were obtained from the state space realization of the filter. The load torque (2Nm,the rated value) was applied at t=0.05s. The reference for rotor speed and the applied torque are reported in Fig. 1.

15. Simulation Results

16. Figs. 2–4, which show the tracking and estimation errors along with the(a; b)-components of stator current and voltage vectors, demonstrate the effectiveness of the proposed nonlinear adaptive control algorithm:exponential rotor speed tracking is achieved along with exponential estimation of the unmeasured and of the unknownTL.

17. Simulation Results

20. A second simulation, whose results are reported In Fig. 5, was carried out in order to illustrate the robustness of the proposed controller with respect to: i) stator current sensor bias errors (0.05 A) ; ii) a variation in stator resistance R (a 3% increase at t = 0:3 s). A small residual rotor speed tracking error (of about 2%) appears at steady-state, due to system uncertainties and model inaccuracies.

21. Simulation Results

22. Conclusion On the basis of stator current and voltage measurements only, an innovative nonlinear adaptive speed tracking control algorithm (3), (4)has been proposed for a permanent magnet synchronous motor (1): it relies on the new theoretical result (not based on motor friction) stated in Theorem 1. Simulation results illustrate the closed loop performance and show the effectiveness of the proposed solution even in the presence of current sensor noise and stator resistance variations.

23. References [1] D. Basic, F. Malrait, and P. Rouchon, “Euler-Lagrange models withcomplex currents of three-phase electrical machines and observabilityissues,” IEEE Trans. Autom. Control, vol. 55, no. 1, pp. 212– 217, Jan.2010. [2] M. Bodson, J. N. Chiasson, R. T. Novotnak, and R. B. Rekowski,“High- performance nonlinear feedback control of a permanent magnet stepper motor,” IEEE Trans. Control Syst. Technol., vol. 1, no. 1, pp.5–14, Mar. 1993. [3] J. Chiasson, Modeling and High-Performance Control of Electric Machines. Hoboken, NJ: Wiley-IEEE Press, 2005. [4] D. M. Dawson, J. Hu, and T. C. Burg, Nonlinear Control of ElectricMachinery. New York: Marcel Dekker, 1998. [5] S. Di Gennaro, “Adaptive output feedback control of synchronous motors,” Int. J. Control, vol. 73, no. 16, pp. 1475–1490, 2000. [6] H. K. Khalil, Nonlinear Systems. Upper Saddle River, NJ: PrenticeHall, 2002. [7] F. Khorrami, P. Krishnamurthy, and H. Melkote, Modeling andAdaptive Nonlinear Control of Electric Motors. Berlin, Germany:Springer-Verlag, 2003.

24. References [8] J. Lee, J. Hong, K. Nam, R. Ortega, L. Praly, and A. Astolfi, “Sensorless control of surface-mount permanent magnet synchronous motors basedon a nonlinear observer,” IEEE Trans. Power Electron., vol. 25, no. 2,pp. 290–297, Feb. 2010. [9] R. Marino, S. Peresada, and P. Tomei, “Nonlinear adaptive control of permanent magnet step motors,” Automatica, vol. 31, no. 11, pp.1595–1604, 1995. [10] R. H. Park, “Two-reaction theory of synchronous machines – Generalized method of analysis – Part I,” AIEE Trans., vol. 48, pp. 716–727,1929. [11] P. Tomei and C. M. Verrelli, “A nonlinear adaptive speed tracking control for sensorless permanent magnet step motors with unknown loadtorque,” Int. J. Adaptive Control Signal Processing, vol. 22, no. 3, pp.266–288, 2008. [12] M. Zribi and J. N. Chiasson, “Position control of a PM stepper motorby exact linearization,” IEEE Trans. Autom. Control, vol. 36, no. 5, pp.620–625, May 1991.