2016 Kappa Electronics Motor Control Training Series 2016 Kappa Electronics LLC. -V th. Dave Wilson Co-Owner Kappa Electronics.

Transcription

1 2016 Kappa Electronics Motor Control Training Series 2016 Kappa Electronics LLC V th CoOwner Kappa Electronics

2 Speed Sensorless FOC P Commanded Rotor Speed Commanded i d = 0 Commanded i q (torque) P I P V d V q Reverse ClarkePark Transform θ d V a V b V c PMSM Dave s Motor Control Center Rotor Speed I I i d i q Forward ClarkePark Transform i a i b i c Phase C Current Calculation Observer θ d θ d Shaft position sensors are VERY expensive ($1,500 in some cases). Many applications cannot afford the cost of a shaft sensor.

3 Model Based Filtering Noise Process Σ Measurement Error feedback Σ Mathematical Model of Process Estimate

4 Tracking Filters y n 1 yn yn yn yn yˆ( n) yˆ( n 1) y n y n ^ y correction y ^ correction β α yn errorn Σ y n Z 1 Z 1 y n Σ Σ Σ Integrator Integrator y n 1 Better tracking is obtained when α and β are high Better filtering is obtained when α and β are low

5 The Tracking Filter Unmasked! The tracking filter is revealed to be a simple 2 nd order IIR filter as shown below. Accumulator X(n) Y(n1) Delay Delay X(n1) 2 Y(n) Delay 1 Y(n1)

6 Cascaded Representation This form of the filter reveals the derivatives of the tracked variable. β α Measured Position Error Σ Z 1 Z 1 Σ Σ Σ Integrator Integrator Estimated Position Estimated Velocity Estimated Acceleration

7 Tracking Filters have Phase Delay CHICAGO Feedforward input fixes this problem

8 Parameter Estimation with Observers By providing an additional feedforward input, the tracking filter can make better output estimates. It then takes the form of an OBSERVER. Can be designed to have zero (or near zero) estimation lag. β α Source: Motion Controller Employs DSP Technology, Robert van der Kruk and John Scannell, Phillips Centre for Manufacturing Technology, PCIM September, 1988 Model of H(z) Integrator Integrator Observers are used to observe a quantity which is difficult to measure by mathematically modeling the system. Observers literally recreate the desired signal mathematically (great noise decoupling). The guess is corrected by comparison with an observable signal.

9 Observer with PI Frontend PI Controller (Beta) (Alpha)

10 Servo Performance with Velocity Directly from Encoder vs. Observer

11 V b PMSM Rs Lls L s Lm V k E syn V a Clarke Rs Lls L s Lm V c V k E syn Applied voltage v v R Resistance voltage s i i L s Inductance voltage d dt i i k syn E BackEMF voltage sin cos emf emf

12 Phase Current Model V in alpha EMF alpha Current Estimator Block 1/L s R s i alpha V in beta Current Estimator Block 1/L s i beta EMF beta R s

13 Compare to Actual Phase Current V in alpha EMF alpha Current Estimator Block 1/L s (0) R s i alpha i alpha (measured) error V in beta EMF beta Current Estimator Block 1/L s (0) R s i beta i beta (measured) error

14 BackEMF Observer V in alpha EMF alpha Current Estimator Block 1/L s R s i alpha i alpha (measured) error PI V in beta EMF beta Current Estimator Block 1/L s R s i beta i beta (measured) error PI Use observable parameter (current) to estimate unobservable parameter (backemf).

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16 Actual BackEMF Estimated BackEMF LTSpice Sampling frequency = 10 KHz

17 Finding the Angle tan 1 EMF EMF beta alpha ( t) ( t) Requires floating point math Must take inverse tangent function Singularity when EMF alpla (t) = 0 Takes a long time to calculate

18 V in alpha EMF alpha Current Estimator Block i alpha error PI k E syn cos( ) i alpha (measured) x x sin sin( est ) cos k1 k2 Angle Demodulator sin()cos( est )cos()sin( est ) = sin( est ) k E syn sin( ) EMF beta V in beta Current Estimator Block i beta error PI i beta (measured)

19 Sliding Mode EMF Observer I α V α 1/L s ^ I α I α error SGN Kslide Z α R s /L s Z α LPF EMF α A Position and Velocity Sensorless Control of Brushless DC Motors Using an Adaptive Sliding Observer, Takeshi Furuashi, Somboon Sangwongwanich, Shigeru Okuma, 1990 IEEE Proceedings, /90/ , pp

20 ZeroSpeed Saliency Tracking Observer err = 0 High Frequency Current Measurement i q VmZ 2 Z Z hf d Demodulator L P F High Frequency Voltage Injection (about 500 Hz) q sin 2 err P I regulator results in steady state value servoing to zero P I Z q Z d 1 s n L P F n θ err Disadvantages: 2 Z Only works on motors with a strong saliency signal. Saliency graph shifts when the motor is loaded. Works at low speeds, but falls apart at high speeds.