Optimizing Performance Using Slotless Motors Mark Holcomb, Celera Motion
Agenda 1. How PWM drives interact with motor resistance and inductance 2. Ways to reduce motor heating 3. Locked rotor test vs. drive manufacturer 4. Tuning to optimize performance 5. Example of frequency domain current loop tuning for maximum integrator gain
Introduction My Career Path - 25 Years in the Motion Industry University of Buffalo, MS ME CSA\Moog, Active Systems - Product Development Piezo motors Active isolation Active damping Dynamic Systems Engineering, Owner Supported KLA-Tencor with Servo modeling/tuning Vibration characterization Data acquisition 1994 1997 2009 2011 2016 Today AeroJet Corp, Systems Engineer Modeling control of thrust actuation devices onboard kinetic warheads Celera Motion, Senior Engineer - Motion Control Specialist Automation software and hardware Motor modeling/analysis software Supporting customers with motion control applications
Motor Types Un-slotted vs. Slotted Slotless rotary motors do not have protruding poles (salient iron teeth), making them physically look and perform different than a typical Slotted motor Lack of iron teeth in a Slotless motor makes it have no naturally occurring torque cogging positions, unlike a slotted motor where the rotor s magnetic poles are attracted to the steel teeth In linear motors, the ironless linear motor is analogous to the rotary slotless and the linear iron-core motor is analogous to the slotted rotary Slotless Slotted
Comparison of Slotless verses Slotted Slotless Zero cogging Very attractive feature when ultra smooth motion is needed Smooth motion is critical for certain types of robotic applications Less core losses (Eddy current + hysteresis) for the same bus voltage and same Ke value Higher, no load speed Linear torque vs. current curve (no saturation in iron) Slotted High torque vs. weight General purpose (lower cost) Easier to manufacture 50-75% of torque vs. similar size slotted* Skewed stack of rotor can reduce cogging *This is becoming less true as new magnetic formulas for ring magnets are producing higher and higher magnetic fields
Cogging and Inductance Cogging Cogging Position - The stable location where a slotted brushless dc (BLDC) motor s rotor aligns with the stator teeth The servo system must push its way through cogging positions in order to rotate the motor. For this reason, zero cogging slotless motors are the preferred choice when smooth motion is critical Inductance Slotless motors have no iron teeth. The lack of iron inside the coils of wire creates a significantly lower inductance When driven with a PWM drive, this characteristic of slotless motors creates a unique engineering challenge a primary focus of this discussion
PWM Drives and Low Inductance Motors A PWM drive creates the desired dc current by varying the on-off time (duty cycle) of the applied voltage Using PWM to drive a motor creates a dynamic current waveform based on the time constant of the RL circuit Figure A shows how current will rise and fall as the PWM voltage is applied across an RL circuit In this case, the PWM is at 50% duty cycle and the RL time constant is less than the half period of the PWM rate so the current is reaching its maximum and minimum before the next voltage transition The average current shown is about 4 amps with 7.5 amp peak to peak of ripple
PWM Drives & Motors Lowest current Highest current 50% 0.1% 99% In order to create more or less average current, the PWM duty cycle is altered Maximum current duty cycle at 99.9% Minimal current duty cycle is at 0.1%
PWM and Motor Heating Current ripple created from PWM drives and low inductance motors can be a major contributor to motor heating Example: For a motor with 1 amp of average current, and 0.6 amps of peak to peak This is a 17% increase over the average current and power dissipation increases by 37% 37% increase in dissipated power will equate to a 37% increase in temperature of the motor coil RMS of the total current is 1 + 1/sqrt(3)*0.3 = 1.17 amps (using triangle waveform RMS calculation) Motor power dissipation uses the current squared, therefore 1.17 amps squared becomes 1.37 amps Thermal resistance (Rth) = Temperature rise (C)/watt DeltaT (C) = watts*rth
Reducing Motor Heating 1. Increase PWM rate Not all drive manufactures will suggest this, as it puts more thermal load on drive devices which has likely not been evaluated at the proposed PWM rate and motor load Always recommend discussing these issues with drive company s Applications Engineers and inform them of any motor power dissipation concerns when driving a low inductance motor 2. Add inductance Additive inductance has undesirable consequence of more resistance and creates a less efficient motor Size the inductor correctly for its power dissipation
Evaluating Current Ripple- Locked Rotor Test Locked rotor test - rotor is not allowed to spin while a constant current is being commanded to the drive The rotor was rotated manually to find electrical angle such that the phase current for the probe was at its maximum 15-20 KHz is a typical PWM rate found on most drives 30-40 KHz is available from several manufacturers often requires discussion with application engineer 60-100 KHz is available from a small number of suppliers and can dramatically reduce current ripple
Locked Rotor Test vs. Drive Manufacturer The data shows three key points 1. Higher PWM rates result in lower amounts of current ripple 2. All three drive companies have similar performance 3. One of the three drive companies did not offer an 80 KHz PWM rate
Adding Inductors Generally, this is only an option with low current drives inductor sizes can quickly exceed motor sizes as the required current levels increase Pro - Doubling the inductance achieves the same ripple as doubling the PWM rate Con - Often requires new current loop tuning, as the RL pole in the plant will have shifted Con - Requires additional cabling for connecting to each motor phase, and in many applications this option is simply too complicated due to space limitations
Tuning For Optimized Performance
Performance Optimization- Current Loop Tuning As PI gains increase response gets closer to the commanded step in current Medium PI best combination of response time and overshoot Some overshoot, without oscillation, is a stable gain set and is the highest gain possible for the system CAUTION - higher gains can lead to interaction with structural resonances and create an audible tone or worst case, an instability Higher I gain values yield better disturbance rejection
Maximizing I Gain - Frequency Domain Tuning Position and integral control are represented in the LaPlace domain as Gain s+a where A = Ki/Kp and Gain = Kp s Why Frequency Domain Tuning? Bode plots show how P and I gains affect the gains versus frequency curve. Increasing low frequency gain and not high frequency gain achieves stability and increased performance when there are high frequency resonances
I Gain Tradeoffs In control design, we often make tradeoffs based on the applications needs The benefit from increasing low frequency gain causes lost phase near the targeted servo bandwidth At the targeted bandwidth (the green circle), there is about 15 degrees of phase loss from the 10*Ki case versus the Ki gain case Lower phase margin can lead to the overshoot, shown in the Step Response plots
Increasing I Gain - Improving Disturbance Rejection Example: Varying magnetic field strength causes motor s Kf to vary in strength as a function of position Other contributors to position dependent force variability are: Magnet spacing, motor coil to coil spacing, and motor coil turn spacing All of these combine to create a disturbance force as a function of position Note: Kf Kt for rotary motors and ironless linear motors rotary Slotless motors
Modeling Voltage Disturbance Across Motor Coil Ke is numerically the same as the Kf* - as the coil moves through the varying magnetic field, Ke also fluctuates, thereby creating a fluctuating back emf voltage This model is creating a voltage disturbance simulating the effect of varying Ke Creates a sinusoidal scaling factor to represent how Ke fluctuates * SI units only
Modeling Voltage Disturbance Across Motor Coil Current loop s job is to keep the desired current correct while any voltage disturbances are taking place As the coil moves through the varying magnetic fields, there is a voltage disturbance (in the form of back emf) that the current loop must correct for Voltage command Voltage Disturbance From varying Ke
Disturbance Frequency Slow speed means voltage disturbance has low frequency Frequency = linear speed (mm/sec) / magnetic pitch (mm/pole pair or electrical cycle) electrical cycles per second = Hz Sub Hz regions difficult to measure any benefit of optimal integrator tuning because loop gain is already high At higher speeds (and frequencies of 5-500Hz) maximizing I gain leads to improvement in current ripple from varying Kf
Simulation Input A 200 Hz sine wave was used to represent voltage fluctuation Using a Ke value of 10 volts per m/sec, at a speed of 0.5 m/sec and a variation of 10% Kf (or Ke) will vary +/- 10% at a frequency of 200 Hz Varying Ke will cause a fluctuation at 200 Hz of the back emf component of coil voltage This fluctuation acts as a disturbance to voltage being applied to the coil that current loop must correct
Simulation Results Loop Transfer Function (slide 21) displays the two gain sets that were simulated Both have a 0 db cross over frequency of approximately 2 KHz (bandwidth), but have different low frequency gains due to the different I gain used At 200 Hz, the gain difference is about 10 db, which is a factor of 3 The net benefit of 3 times gain is shown in the figure above, where the higher Ki is clearly performing better by more than 2 to 1
Summary A fundamental difference between a slotless and slotted rotary motor is slotless motors typically have low inductance (<1mH) Fast RL time constant of a slotless motor, in combination with a PWM drive, creates current ripple that can be a significant contributor to motor heating Different approaches to reduce current ripple are increasing PWM rate and adding inductance Current ripple was tested from three common PWM drive manufactures, and all were found to be similar in their performance, but not all offered an 80 KHz PWM rate
Summary Time domain current loop tuning was discussed and it was shown that current loop P and I gains affect rise time and overshoot Advanced frequency domain tuning was simulated and showed how P and I gain shaped the gain and phase verses frequency curves The concept of maximizing I gain was taken to a simple motor example voltage disturbance from magnetic field variation was an input to the commanded voltage across a resistive and inductive load (motor) It was shown that the current error was reduced by a factor of 2 with optimizing I gain tuning
Conclusion 1. Optimizing performance of a slotless motor driven by a PWM voltage drive requires knowledge of how a resistive and inductive load behaves under varying applied voltage 2. PWM rate, additive inductance, and current loop tuning are all tools one can use to optimize performance of slotless motors with PWM drives Using these techniques will enhance the inherent smooth motion benefit of a slotless motor 3. Understanding how proportional and integral gains shape the current loop s gain and phase versus frequency curves is essential for getting the most out of a slotless motor system