servo motor drive velocity tracking-reducing tracking error
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copyright 2011 controltrix corp www. controltrix.com
www.controltrix.com
Servo Motor Drive Velocity Tracking
Reducing tracking error
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 factors1. ADC current resolution2. Velocity feedback resolution3. Dead time4. Inductance5. Back emf distortion6. Residual encoder offset
copyright 2011 controltrix corp www. controltrix.com
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
• dI = ADC current resolution = 10 mA
dT = Kt. dI
Min abs velocity resolution = Ts. dT / J approx 20 -50 rev/day
Limit factors.
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
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
Limit factors…
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
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)
Limit factors…..
copyright 2011 controltrix corp www. controltrix.com
Inductance
• Inductance varies with current due to saturation
• Distorts dynamics @ 6X electrical frequency + harmonics
( open loop ripple torque)
Limit factors……
copyright 2011 controltrix corp www. controltrix.com
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)
Limit factors…….
copyright 2011 controltrix corp www. controltrix.com
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
Limit factors……..
copyright 2011 controltrix corp www. controltrix.com
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
Limit factors………
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
• 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
Proposed method
copyright 2011 controltrix corp www. controltrix.com
• 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
Proposed method.
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
• @ low rpm (6 rpm)
(abs error/ripple estimate based on current quantization)
= 0.0002 rad/s = 3 rev/day
• Rel. err. = 100 ppm
Extrapolated estimated results (simulation time is very long at slow speeds)
copyright 2011 controltrix corp www. controltrix.com
Thank Youconsulting@controltrix.com
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