CMPUT 399 Intro Robotics & Mechatronics: Motor Control Some slides are taken from Northwestern University’s “ME 333 Introduction to Mechatronics” by Kevin Lynch.

DC motors DC motors: cheap, most common DC motor – how it works ? https://www.youtube.com/watch?v=LAtPHANEfQo

Brushed permanent magnet DC motor Lorentz’ law: F = l I x B current flowing through a magnetic field creates a force on the wire carrying the current - use 3 loops - still have torque ripple - insufficient torque > use coil instead of wire - commutators to switch current Torque changes direction - switch direction of current - still torque varies

Model of DC motor Control V I 𝜏,⍵ 𝐼 𝑉=𝜏 𝜔+𝑅 𝐼 2 +𝐿𝐼 𝑑𝐼 𝑑𝑡 +… 𝑉= 𝜏 𝐼 𝜔+𝑅𝐼+𝐿 𝑑𝐼 𝑑𝑡 𝑉= 𝑘 𝑡 𝜔 Electrical power (input) (friction loss, heating, etc.) Mechanical power (output) kt : torque constant : characteristic of motor Open-circuit: I=0 back-emf (electro-motive force) voltage Opposing the driving voltage

Speed-Torque curve 𝑉= 𝑘 𝑡 𝜔+𝑅𝐼+𝐿 𝑑𝐼 𝑑𝑡 𝜔= 𝑉 𝑘 𝑡 − 𝑅 𝑘 𝑡 𝜏 𝑘 𝑡 𝑉= 𝑘 𝑡 𝜔+𝑅𝐼+𝐿 𝑑𝐼 𝑑𝑡 𝜔= 𝑉 𝑘 𝑡 − 𝑅 𝑘 𝑡 𝜏 𝑘 𝑡 𝜔= 𝜔 0 − 𝜔 0 𝜏 𝑠 𝜏 𝜔 0 = 𝑉 𝑘 𝑡 𝜏 𝜔 𝜏 𝑠𝑡𝑎𝑙𝑙 = 𝑘 𝑡 𝑉 𝑅 Speed-Torque curve nominal operating point nominal mechanical power continuous operating region 𝜏 𝑛𝑜𝑚 𝜔 𝑛𝑜𝑚 ⍵0: no-load speed 𝜏s: prevent moving ⇒ large torque (𝜏=kt I) ⇒ large current ⇒ (Power=RI2)⇒ overheating (over long period of time)

Mechanical power in speed-torque curve 𝜔= 𝜔 0 − 𝜔 0 𝜏 𝑠 𝜏 𝜏=( 𝜔 0 −𝜔) 𝜏 𝑠 𝜔 0 𝑃 𝑜𝑢𝑡 =𝜏𝜔 = 𝜏 𝑠 𝜔− 𝜏 𝑠 𝜔 0 𝜔 2 𝜔 0 𝜏 𝜔 𝜏 𝑠 𝑃 𝑜𝑢𝑡 =𝜏𝜔 𝑃 𝑚𝑎𝑥 = 1 4 𝜏 𝑠 𝜔 0 𝜏 𝑠 2 𝜔 0 2 Efficiency = 𝑃 𝑜𝑢𝑡 𝑃 𝑖𝑛 = 𝜏𝜔 𝑉𝐼 x 100 %

Mechanical power in speed-torque curve 𝜔= 𝜔 0 − 𝜔 0 𝜏 𝑠 𝜏 𝜏=( 𝜔 0 −𝜔) 𝜏 𝑠 𝜔 0 𝑃 𝑜𝑢𝑡 =𝜏𝜔 = 𝜏 𝑠 𝜔− 𝜏 𝑠 𝜔 0 𝜔 2 𝜔 0 𝜏 𝜔 𝜏 𝑠 𝑃 𝑜𝑢𝑡 =𝜏𝜔 𝑃 𝑚𝑎𝑥 = 1 4 𝜏 𝑠 𝜔 0 𝜔 0 2 𝜏 𝑠 2 Efficiency = 𝑃 𝑜𝑢𝑡 𝑃 𝑖𝑛 = 𝜏𝜔 𝑉𝐼 x 100 %

Motor specification (datasheet)

DC motor control Goal: drive a DC motor with micro-controller Vm 𝜏,⍵ Add a switch 𝑉 𝑚 = 𝑘 𝑡 𝜔+𝐼𝑅+𝐿 𝑑𝐼 𝑑𝑡 Large change of current ⇒ sparks use diode (flyback diode) current decay to zero exponentially enable us to turn motor on/off +V dig. out M M dig. out Low voltage Low current to control speed we use PWM PWM controls duty cycle of closing/opening the switch 10 KHz < f < 40 KHz enable us to control speed in 1-direction bi-directional >>> H-bridge ⏄

DC motor control H-bridge closed switches: OUT1 OUT2 S1 , S4 : forward S2 , S3 : reverse S1 , S3 : brake S2 , S4 : brake one/none: coast OUT1 OUT2 off off coast H L forward L H reverse shorted brake

Motor Control System Complete motor control system PI 𝝨𝝨 motor counter ref position (θd) Motion controller PI controller H-bridge motor current sensor counter encoder torque / Current command 𝝨𝝨 current error 20 KHz PWM duty measured PID + _ 5 KHz inner loop 200-1000 Hz outer loop

BLDC motors Brushless DC (BLDC) motor – how it works ? https://www.youtube.com/watch?v=bCEiOnuODac