Sensorless Control on Super High Speed Motors Yang Hu and Prof. Thomas Wu Department of Electrical Enginnering and Computer Science University of Central Florida, Orlando 32816

Outline „

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Super High Speed Permanent Magnet Synchronous Motors (PMSM) Sensorless Control Simulation Results Conclusion

High Speed PMSM „

Advantages „ High efficiency „ Small volume „ High power density

L. Zheng (2005), “Super High-speed Miniaturized Permanent Magnet Synchronous Motor” (Doctoral dissertation)

Challenges of High Speed „

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Super high speed (50,000 rpm or higher) makes the system highly dynamic, and requires very fast response from the controller. Position sensors are not available at very high speed due to reliability and precision issues. Other non electrical challenges, such as bearings, cooling, etc.

Sensorless Control „

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Motor control needs feedback information like rotor position and speed, etc. Mechanical sensors increases instability and cost of the system Sensorless control – no mechanical sensors „ Simplicity „ Lower cost More important for high speed motors where mechanical sensors are often unavailable

Open Loop Control „

Constant V/f Control „ No feedback required, therefore do not need sensors. „ Simple and easy to realize. „ Robustness is bad because of no feedback. Could lose synchronization because of any wrong settings. „ Can run the PMSM to a very high speed.

Longya Xu; Changjiang Wang; , "Implementation and experimental investigation of sensorless control schemes for PMSM in super-high variable speed operation," Industry Applications Conference, 1998. Thirty-Third IAS Annual Meeting. The 1998 IEEE , vol.1, no., pp.483-489 vol.1, 12-15 Oct 1998

Closed-Loop Control – Field Oriented Control (Vector Control)

D. Woodburn, T. Wu, L. Chow, Q. Leland, J. Bindl, Y. Hu, L. Zhou, Y. Lin, N. Rolinski, W. Brokaw, B. Tran, B. Jordan, E. Gregory, S. Lin and S. Iden, “Integrated Nonlinear Dynamic Modeling and Field Oriented Control of Permanent Magnet (PM) Motor for High Performance EMA,” SAE Paper No. 2010-01-1742, SAE Power Systems Conference, Ft. Worth,, TX, Nov. 2-4, 2010.

Dynamical Equations of PM Motor in dq Frame did dt diq dt dωm dt dθ m dt

where

=

(1 / L d )( − R s id + ω m e L q iq + u d )

=

(1 / L q )( − R s iq − ω m e L d id − ω m e λ PM + u q )

=

(1 / I )(τ M − τ L − c ω m )

=

ωm

τM

ω me

3p = i q ⎡⎣ λ P M + i d ( L d − L q ) ⎤⎦ 4

p = ωm 2

Current Control Derivation τ M = τ L + Iα m + cωm iq

τM iq

αm

dωm = dt

⎛ eωm ⎞ * c τ M − Iα m + I ⎜ k p ( ω + ⎟ m − ωm ) Δt ⎠ ⎝ * iq =

τM

= τ L + Iα m + cωm

τ L + Iα m + cωm iq = τM iq ⎛ eωm ⎞ * τL + I ⎜ kp c ω + ⎟ m t Δ ⎝ ⎠ iq* =

τM iq

iq

⎞ 1 ⎡ ⎛ eωm − α m ⎟ + c k p eωm iq = iq + I ⎜ kp ⎢ τ M ⎢⎣ ⎝ Δt ⎠ iq

(

*

iq = iq + ki *

2 iq 1 p τM

eθme Δt

+

⎡ ⎛ eωme ⎞ − αme ⎟ + c k p eωme ⎢I ⎜ k p ⎢⎣ ⎝ Δt ⎠

(

)

⎤ ⎥ ⎥⎦

)

⎤ ⎥ ⎥⎦

Voltage Control Equations

* di * * * ud * = Rs id * + L*d d − ωme Lq iq dt 2 * di q * * * * uq* = Rs iq* + L*q Ld id + ωme + ωme λPM dt 3

Position Estimation Techniques „

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Back EMF „ The rotating rotor will induce a voltage in the winding, which can be detected and used to estimate the rotor position „ Suitable for mid-high speed. At low speed, back EMF voltage is too small that the signal to noise ratio is too low. Signal injection „ Inject some voltage or current signals (usually high frequency) into the motor and using correspondent signals to detect rotor position

Back EMF • The induced voltage is dependent on the rotor speed • By measuring current and voltage of the stator windings, the back EMF information can be obtained

http://www.acroname.com/robotics/info/articles/back-emf/back-emf.html

Model Reference Adaptive System

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Two models, one is for estimation, one is the real model Every state variable in the first model is observable Only current and voltages of the real motor model is observable Compare the two models and adjust the estimation model Highly dependent on parameter accuracy

⎡ R − ⎢ i ' ⎡ ⎤ d d L = ⎢ ⎥ ⎢ dt ⎣ iq ' ⎦ ⎢ −ω ⎢⎣ ⎡ R − d ⎡iˆd ' ⎤ ⎢ L ⎢ ⎥=⎢ dt ⎢⎣ iˆq ' ⎥⎦ ⎢ −ωˆ ⎢⎣

⎤

ω ⎥ i ' ⎡d ⎤

1 ⎡ud ' ⎤ ⎥⎢ ⎥+ ⎢ ⎥ R i ' L ⎣ uq ' ⎦ − ⎥⎣ q ⎦ L ⎥⎦

ωˆ ⎤⎥ ⎡iˆ ' ⎤ d

1 ⎡ud ' ⎤ ⎥ ⎢ˆ ⎥ + ⎢ ⎥ R i ' L ⎣ uq ' ⎦ − ⎥ ⎢⎣ q ⎥⎦ L ⎥⎦

Yan Liang; Yongdong Li; , "Sensorless control of PM synchronous motors based on MRAS method and initial position estimation," Electrical Machines and Systems, 2003. ICEMS 2003. Sixth International Conference on , vol.1, no., pp. 96- 99 vol.1, 9-11 Nov. 2003

State Observer or Kalman Filter „

Dynamic equation of state variables and output equation ⎧ x& = Ax + Bu ⎨ ⎩ y = Cx

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Use some iteration to approach the real position/speed Controller & Observer Redesign

Parameter Estimator

Velocity Controller

Current Controller

Inverter Observer AC Motor

Signal Injection

Ji-Hoon Jang; Seung-Ki Sul; Jung-Ik Ha; Ide, K.; Sawamura, M.; , "Sensorless drive of surface-mounted permanent-magnet motor by highfrequency signal injection based on magnetic saliency," Industry Applications, IEEE Transactions on , vol.39, no.4, pp. 1031- 1039, July-Aug. 2003

Simulation System

Dynamic Equation „

State variables and PMSM dynamic equation

x& = g ( x )

⎧ did ud id ⎪ dt = L − τ + ωiq ⎪ ⎪ diq = uq − iq − ωi − λPM ω d ⎪ dt L τ L ⎪ c p ⎪ d ω p 2λPM ω τL I = − − ⎨ q J J J ⎪ dt ⎪ dθ ⎪ dt = ω ⎪ ⎪ dτ L = 0 ⎪⎩ dt L τ = , Ld = Lq = L R

System „

Observable variables are d-q currents. Use them as output vector

y = ⎡⎣id

T

iq ⎤⎦ = Cx

iq ω θ τ L ⎤⎦ ⎡1 0 0 0 0⎤ C=⎢ ⎥ 0 1 0 0 0 ⎣ ⎦ With x = ⎡⎣id

T

Extended Kalman Filter „

Estimate state variables of next time step, then calculate the error covariance matrix, and also the error of estimation, use them to correct the estimation and update the coefficients 1.Compute state ahead and error covariance ahead xˆk |k −1 = xˆk −1|k −1 + g ( xˆk −1|k −1 )Te Pk |k −1 = Fk −1Pk −1|k −1FkT−1 + Qk −1 2.Compute the Kalman gain. K k = Pk |k −1C

T

(CP

C + Rk −1 )

k |k −1

T

3.Update estimate with measurement

−1

Traditional observer: xˆk = xˆk −1 + g ( xˆk −1 ) Te + K ( y − Cxˆk |k −1 )

xˆk |k = xˆk |k −1 + K k ( yk − Cxˆk |k −1 ) 4.Update the error covariance matrix Pk |k = [ I − K k C ] Pk |k −1 Zedong Zheng; Fadel, M.; Yongdong Li; , "High Performance PMSM Sensorless Control with Load Torque Observation," EUROCON, 2007. The International Conference on "Computer as a Tool" , vol., no., pp.1851-1855, 9-12 Sept. 2007

Extended Kalman Filter

Controller

Motor and Drive

Simulation Results Stroke and speed curves

Conclusions „

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Sensorless Control is useful and important for high speed PMSM systems. Open loop control can be used for high speed PMSM systems, but it has limitations and drawbacks. Closed-loop sensorless vector control is tested through simulation. Hardware experiment is underway.

References on Sensorless Control ‰

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Zedong Zheng; Fadel, M.; Yongdong Li; , "High Performance PMSM Sensorless Control with Load Torque Observation," EUROCON, 2007. The International Conference on "Computer as a Tool" , vol., no., pp.1851-1855, 9-12 Sept. 2007 Kye-Lyong Kang; Jang-Mok Kim; Keun-Bae Hwang; Kyung-Hoon Kim; , "Sensorless control of PMSM in high speed range with iterative sliding mode observer," Applied Power Electronics Conference and Exposition, 2004. APEC '04. Nineteenth Annual IEEE , vol.2, no., pp. 1111- 1116 vol.2, 2004 Sakamoto, K.; Iwaji, Y.; Endo, T.; Takakura, T.; , "Position and speed sensorless control for PMSM drive using direct position error estimation," Industrial Electronics Society, 2001. IECON '01. The 27th Annual Conference of the IEEE , vol.3, no., pp.1680-1685 vol.3, 2001 Hung-Chi Chen; Wei-Shun Huang; Jhen-Yu Liao; , "PMSM sensorless control with Coordinate Rotation Digital Computer," IECON 2010 - 36th Annual Conference on IEEE Industrial Electronics Society , vol., no., pp.951-955, 7-10 Nov. 2010 Yan Liang; Yongdong Li; , "Sensorless control of PM synchronous motors based on MRAS method and initial position estimation," Electrical Machines and Systems, 2003. ICEMS 2003. Sixth International Conference on , vol.1, no., pp. 96- 99 vol.1, 9-11 Nov. 2003 Ji-Hoon Jang; Seung-Ki Sul; Jung-Ik Ha; Ide, K.; Sawamura, M.; , "Sensorless drive of surface-mounted permanent-magnet motor by high-frequency signal injection based on magnetic saliency," Industry Applications, IEEE Transactions on , vol.39, no.4, pp. 1031- 1039, July-Aug. 2003 Sepe, R.B.; Lang, J.H.; , "Real-time observer-based (adaptive) control of a permanent-magnet synchronous motor without mechanical sensors," Industry Applications Society Annual Meeting, 1991., Conference Record of the 1991 IEEE , vol., no., pp.475-481 vol.1, 28 Sep-4 Oct 1991 Andreescu, G.-D.; Pitic, C.I.; Blaabjerg, F.; Boldea, I.; , "Combined Flux Observer With Signal Injection Enhancement for Wide Speed Range Sensorless Direct Torque Control of IPMSM Drives," Energy Conversion, IEEE Transactions on , vol.23, no.2, pp.393-402, June 2008 Ji-Hoon Jang; Jung-Ik Ha; Ohto, M.; Ide, K.; Seung-Ki Sul; , "Analysis of permanent-magnet machine for sensorless control based on high-frequency signal injection," Industry Applications, IEEE Transactions on , vol.40, no.6, pp. 1595- 1604, Nov.Dec. 2004 Longya Xu; Changjiang Wang; , "Implementation and experimental investigation of sensorless control schemes for PMSM in super-high variable speed operation," Industry Applications Conference, 1998. Thirty-Third IAS Annual Meeting. The 1998 IEEE , vol.1, no., pp.483-489 vol.1, 12-15 Oct 1998