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Servo Motor Drive Velocity Tracking
                                  Reducing tracking error




                                      www.controltrix.com



copyright 2011 controltrix corp                             www. controltrix.com
Framework
     PMSM vector control drive

     Velocity Feedback:

     • Encoder with finite pulses/rev (e.g. 10000)

     Current feedback:

     • LEM sensor + onchip 12 bit ADC +/-15A full range

     Voltage feedback:

     • DC Voltage sense + onchip 12 bit ADC 800 V full range


copyright 2011 controltrix corp                                www. controltrix.com
Framework…
     Application:

     • Machine tool industry



     Objective:

     • Control motor velocity as precisely (from 0 to 100 % or more
            rated speed)

     • Under external disturbances



copyright 2011 controltrix corp                                www. controltrix.com
Challenges at low speed operation
     • Limit abs. err. @ Slow velocities (small value  large % err)

     • Limit Rel. err. @ faster velocities (small %  large err)

     • Rel. and Abs velocity tracking error

     • Abs err. required approx 10 rev/day




copyright 2011 controltrix corp                                    www. controltrix.com
Limit factors
   1.         ADC current resolution
   2.         Velocity feedback resolution
   3.         Dead time
   4.         Inductance
   5.         Back emf distortion
   6.         Residual encoder offset




copyright 2011 controltrix corp              www. controltrix.com
Limit factors.
   ADC Current feedback res  limits torque impulse res.
   • Kt = torque constant = 0.75 Nm/A
   • Ts = sampling time = 1 ms
   • J = inertia = 0.00017 Kgm2
   •          I = ADC current resolution = 10 mA


                T = Kt. I
             Min abs velocity resolution = Ts. T / J approx 20 -50 rev/day


copyright 2011 controltrix corp                                       www. controltrix.com
Limit factors..
   Mitigation :

   • Oversampling and averaging to reduce quantization noise

   Disadvantage :

   • ADC sampling frequency and triggering limitations




copyright 2011 controltrix corp                                www. controltrix.com
Limit factors…
   Velocity feedback resolution
   • Fixed time sampling (# pulses in 1 sample period)
   • 1 pulse/1ms = 6 rev per min
   • @ High velocities less troublesome
   • @ Low velocities major problem




copyright 2011 controltrix corp                          www. controltrix.com
Limit factors….
   Mitigation :
   •       Fixed angular distance/measured time
   •       Limited by processor timer resolution
   •       @ High velocities more trouble some
   •       @ Low velocity is OK
   Disadvantage :
   • Non linear / non time invariant dynamics
     (LTI analysis not valid)




copyright 2011 controltrix corp                    www. controltrix.com
Limit factors…..
   Deadtime
   • 2 - 5% duty is wasted in deadtime
   • Leads to 6 step voltage to be applied @ electrical freq.
   • Non linear dynamics
   • Distorts dynamics @ 6X electrical frequency + harmonics
         ( open loop ripple torque)




copyright 2011 controltrix corp                                 www. controltrix.com
Limit factors……
   Inductance
   • Inductance varies with current due to saturation
   • Distorts dynamics @ 6X electrical frequency + harmonics
           ( open loop ripple torque)




copyright 2011 controltrix corp                                www. controltrix.com
Limit factors…….
   Back emf distortion
   • Back emf waveform is never ideal sine wave.
   • Some distortion always present
   • Distorts dynamics @ 6X electrical frequency + harmonics
           ( open loop ripple torque)




copyright 2011 controltrix corp                                www. controltrix.com
Limit factors……..
   Residual encoder offset
   • Leads to direction dependent performance
   • The angular offset between encoder 0 and motor 0 position is
           always an estimate. Some residual always remain




copyright 2011 controltrix corp                              www. controltrix.com
Limit factors………
   Static friction
   • Non linear direction dependent component near zero velocity




     Note: 3 – 4 – 5 – 6 – 7 are not easy to mitigate unless using
     repetitive control techniques




copyright 2011 controltrix corp                                      www. controltrix.com
Other considerations:
   • Non linear dynamics with fixed distance variable time sampling
   • Dynamics change with velocity




copyright 2011 controltrix corp                               www. controltrix.com
Proposed method
   • Kalman filter based data fusion
   • Motor Current and encoder data combined to estimate
           instantaneous velocity
   • Estimate velocity @ current sampling freq. approx (20KHz)
   • No gain changes




copyright 2011 controltrix corp                                  www. controltrix.com
Proposed method.
   • No change in sampling freq. based on velocity
           (only pulses per sampling period measurement used)
   • Zero velocity control
   • Abs velocity resolution limited by current feedback
   • Relative resolution can be arbitrarily reduced (subject to
           abs limit) trade off against dynamic performance
   • Other limit factors automatically taken care




copyright 2011 controltrix corp                                   www. controltrix.com
Simulation results
   • Typ. velocity ripple @ 300 rad/s
   • Abs err = 0.004 rad/s = 57 rev/day
   • Rel. err. = 13ppm




copyright 2011 controltrix corp           www. controltrix.com
copyright 2011 controltrix corp   www. controltrix.com
Extrapolated estimated results
   (simulation time is very long at slow speeds)

   • @ low rpm (6 rpm)
           (abs error/ripple estimate based on current quantization)
            = 0.0002 rad/s = 3 rev/day
   • Rel. err. = 100 ppm




copyright 2011 controltrix corp                                        www. controltrix.com
Thank You
                                  consulting@controltrix.com




copyright 2011 controltrix corp                                www. controltrix.com

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Filtering servo motor- Reducing velocity tracking error

  • 1. Servo Motor Drive Velocity Tracking Reducing tracking error www.controltrix.com copyright 2011 controltrix corp www. controltrix.com
  • 2. Framework PMSM vector control drive Velocity Feedback: • Encoder with finite pulses/rev (e.g. 10000) Current feedback: • LEM sensor + onchip 12 bit ADC +/-15A full range Voltage feedback: • DC Voltage sense + onchip 12 bit ADC 800 V full range copyright 2011 controltrix corp www. controltrix.com
  • 3. Framework… Application: • Machine tool industry Objective: • Control motor velocity as precisely (from 0 to 100 % or more rated speed) • Under external disturbances copyright 2011 controltrix corp www. controltrix.com
  • 4. Challenges at low speed operation • Limit abs. err. @ Slow velocities (small value  large % err) • Limit Rel. err. @ faster velocities (small %  large err) • Rel. and Abs velocity tracking error • Abs err. required approx 10 rev/day copyright 2011 controltrix corp www. controltrix.com
  • 5. Limit factors 1. ADC current resolution 2. Velocity feedback resolution 3. Dead time 4. Inductance 5. Back emf distortion 6. Residual encoder offset copyright 2011 controltrix corp www. controltrix.com
  • 6. Limit factors. ADC Current feedback res  limits torque impulse res. • Kt = torque constant = 0.75 Nm/A • Ts = sampling time = 1 ms • J = inertia = 0.00017 Kgm2 • I = ADC current resolution = 10 mA T = Kt. I Min abs velocity resolution = Ts. T / J approx 20 -50 rev/day copyright 2011 controltrix corp www. controltrix.com
  • 7. Limit factors.. Mitigation : • Oversampling and averaging to reduce quantization noise Disadvantage : • ADC sampling frequency and triggering limitations copyright 2011 controltrix corp www. controltrix.com
  • 8. Limit factors… Velocity feedback resolution • Fixed time sampling (# pulses in 1 sample period) • 1 pulse/1ms = 6 rev per min • @ High velocities less troublesome • @ Low velocities major problem copyright 2011 controltrix corp www. controltrix.com
  • 9. Limit factors…. Mitigation : • Fixed angular distance/measured time • Limited by processor timer resolution • @ High velocities more trouble some • @ Low velocity is OK Disadvantage : • Non linear / non time invariant dynamics (LTI analysis not valid) copyright 2011 controltrix corp www. controltrix.com
  • 10. Limit factors….. Deadtime • 2 - 5% duty is wasted in deadtime • Leads to 6 step voltage to be applied @ electrical freq. • Non linear dynamics • Distorts dynamics @ 6X electrical frequency + harmonics ( open loop ripple torque) copyright 2011 controltrix corp www. controltrix.com
  • 11. Limit factors…… Inductance • Inductance varies with current due to saturation • Distorts dynamics @ 6X electrical frequency + harmonics ( open loop ripple torque) copyright 2011 controltrix corp www. controltrix.com
  • 12. Limit factors……. Back emf distortion • Back emf waveform is never ideal sine wave. • Some distortion always present • Distorts dynamics @ 6X electrical frequency + harmonics ( open loop ripple torque) copyright 2011 controltrix corp www. controltrix.com
  • 13. Limit factors…….. Residual encoder offset • Leads to direction dependent performance • The angular offset between encoder 0 and motor 0 position is always an estimate. Some residual always remain copyright 2011 controltrix corp www. controltrix.com
  • 14. Limit factors……… Static friction • Non linear direction dependent component near zero velocity Note: 3 – 4 – 5 – 6 – 7 are not easy to mitigate unless using repetitive control techniques copyright 2011 controltrix corp www. controltrix.com
  • 15. Other considerations: • Non linear dynamics with fixed distance variable time sampling • Dynamics change with velocity copyright 2011 controltrix corp www. controltrix.com
  • 16. Proposed method • Kalman filter based data fusion • Motor Current and encoder data combined to estimate instantaneous velocity • Estimate velocity @ current sampling freq. approx (20KHz) • No gain changes copyright 2011 controltrix corp www. controltrix.com
  • 17. Proposed method. • No change in sampling freq. based on velocity (only pulses per sampling period measurement used) • Zero velocity control • Abs velocity resolution limited by current feedback • Relative resolution can be arbitrarily reduced (subject to abs limit) trade off against dynamic performance • Other limit factors automatically taken care copyright 2011 controltrix corp www. controltrix.com
  • 18. Simulation results • Typ. velocity ripple @ 300 rad/s • Abs err = 0.004 rad/s = 57 rev/day • Rel. err. = 13ppm copyright 2011 controltrix corp www. controltrix.com
  • 19. copyright 2011 controltrix corp www. controltrix.com
  • 20. Extrapolated estimated results (simulation time is very long at slow speeds) • @ low rpm (6 rpm) (abs error/ripple estimate based on current quantization) = 0.0002 rad/s = 3 rev/day • Rel. err. = 100 ppm copyright 2011 controltrix corp www. controltrix.com
  • 21. Thank You consulting@controltrix.com copyright 2011 controltrix corp www. controltrix.com