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Robotics
Course 6. Robot control technology
Bernard BayleTélécom Physique Strasbourg
TI Santé, DTMI, master IRIV
1 / 49
This course. . .
Course objectiveThis course deals with the technology of robot controllers.Prerequisites: basics of electrical engineering, ideally course 5.
Open access references:http://www.maxonmotor.com/maxon/view/content/academy
http://www.adept.com/products/controls/
2 / 49
Robot control system
SynopticPower: adjustable power supplyControl: references, supervision, communication
Control system of a robot Adept Viper s650 3 / 49
4 / 49
Robot supervision
Adept SmartController CX moduleMotion planning, control and supervisionDedicated operating system, programming languageInterfaces, I/O
5 / 49
Robot programming
; Define a simple transformationSET loc_a = TRANS(300,50,350,0,180,0)
; Move to the locationMOVE loc_aBREAK
; Move to a location offset -50mm in X, 20mm in Y,; and 30mm in Z relative to "loc_a"
MOVE loc_a:TRANS(-50, 20, 30)BREAK
; Define "loc_b" to be the current location relative; to "loc_a"
HERE loc_a:loc_b ;loc_b = -50, 20, 30, 0, 0, 0BREAK
; Define "loc_c" as the vector sum of "loc_a" and "loc_b"SET loc_c = loc_a:loc_b ;loc_c = 350, 70, 320, 0, 180, 0
; Once this code has run, loc_b exists as a; transformation that is completely independent; of loc_a. The following instruction moves the; robot another -50mm in the x, 20mm in the y,; and 30mm in the z direction (relative to loc_c):
MOVE loc_c:loc_b
6 / 49
Robot communication
Adept SmartController CX interfacesIEEE 1394 (FireWire): high-rate transfers (800 Mb/s),sampled at 8kHz, real-timeFast Ethernet, DeviceNet=fieldbus CAN, serial busRS-232, XDIO=on-off input/output, etc.Special functionalities: visual servoing, programmablelogic controller (PLC) drive
7 / 49
Robot pendent
Adept SmartController CX interfacesXMPC connector: manual control pendentLearning of variables to be used for robot programmingSafety: emergency stop/power switch
8 / 49
9 / 49
Robot controller / variable speed drive
Main functionalities of the robot controller MotionBlox-60RAdjustable voltage supplyCurrent/angular velocity and position feedback control
Other functionalities:communications with the robot supervision→ at 1kHz: references, encoder measurements, statusmotor supervision: status, tracking error, over-heatingwhen applies, electrical/manual axes brake controlemergency stop to switch off the robot power
PowerVariable loads: the power depends on masses and geometry,but also on velocities and accelerations.
Viper s650: 2kW max for 5 kg maximal payload.10 / 49
Outline
1 Robot control systems
2 TechnologyActuationAngular position measurementVariable speed drives
11 / 49
Actuation
ActuatorMechanical transmission + (electric) motorAngular position/velocity sensorsPower electronics: variable speed drive
Motors in roboticsUsual choice: DC brushed (or brushless) motors.
Some special choices include: AC motors, pneumatic andhydraulic actuators, piezoelectric and stepper motors.
12 / 49
(Brushed) DC motors
13 / 49
(Brushed) DC motors
Advantages
Simple and very commonEasy controlCheap electronic drive
DrawbacksBrush wearLimited velocitySparks
14 / 49
(Brushed) DC motors
15 / 49
Brusless DC motors
PrincipleSynchronous motor with permanent magnet at the rotor, controlbased on the analogy with DC motor.
Advantages
Better efficiency, better mechanical characteristicsBetter torque-to-weight ratioHigher maximal angular velocityLess commutation electronic noise, no sparks
DrawbacksMore expensiveMore complex digital driveTorque cogging at low speed
16 / 49
Transmission
AdvantageElectric motors adapted to high rotation speed: reductionVelocity decrease and torque increase
DrawbacksIncrease axis inertia and friction
17 / 49
Conventional and epicyclic gear trains
Straight cut (spur) gears or helical gears
Multi stage and epicyclic gear trains
18 / 49
Epicyclic gear
PrincipleTwo gears mounted so that the center of one gear revolvesaround the center of the other. A carrier connects the centers ofthe two gears and rotates to carry one gear (planet gear,revolving) around the other (sun gear, fixed).
https://en.wikipedia.org/wiki/Epicyclic_gearing
19 / 49
Harmonic Drive
PrincipleStrain wave gearing has 3 components: an elliptical wavegenerator (WG), a flex spline (FS), and a circular spline (CS).
As the WG rotates, the FS teeth move, meshed with those ofthe CS. With fewer teeth on the FS than on the CS, the WGrotation results in a much slower rotation of the FS.
https://www.youtube.com/watch?v=bzRh672peNk20 / 49
Outline
1 Robot control systems
2 TechnologyActuationAngular position measurementVariable speed drives
21 / 49
Sensors
Advantage
Measure the linear/angular position/velocity of each jointUsed for feedback control
DrawbacksA lot of potential drawbacks to be discussed for each type. . .
22 / 49
Encoders
PrincipleLight from a photodiode sensed by receivers are converted intologic quadrature signals A and B, and an index signal I (or Z).
23 / 49
Encoders
Advantages
Good resolution, by far the most usual solutionSignals A and B: redundancy for robustnessVery compact casingNegligible inertia, no friction
DrawbacksQuantization (low speeds, differentiation)No absolute position measurement
24 / 49
max
on s
enso
r
401
RE 25 179/181 75.3RE 25 179/181 GP 26/GP 32 336/338 •RE 25 179/181 KD 32, 1.0 - 4.5 Nm 347 •RE 25 179/181 GP 32, 0.75 - 6.0 Nm 339/342 •RE 25 179/181 GP 32 S 370-372 •RE 25, 20 W 180 63.8RE 25, 20 W 180 GP 26/GP 32 336/338 •RE 25, 20 W 180 KD 32, 1.0 - 4.5 Nm 347 •RE 25, 20 W 180 GP 32, 0.75 - 6.0 Nm 339/342 •RE 25, 20 W 180 GP 32 S 370-372 •RE 25, 20 W 180 AB 28 446 94.3RE 25, 20 W 180 GP 26/GP 32 336/338 AB 28 446 •RE 25, 20 W 180 KD 32, 1.0 - 4.5 Nm 347 AB 28 446 •RE 25, 20 W 180 GP 32, 0.75 - 6.0 Nm 339/342 AB 28 446 •RE 25, 20 W 180 GP 32 S 370-372 AB 28 446 •RE 25, 20 W 181 AB 28 446 105.8RE 25, 20 W 181 GP 26/GP 32 336/338 AB 28 446 •RE 25, 20 W 181 KD 32, 1.0 - 4.5 Nm 347 AB 28 446 •RE 25, 20 W 181 GP 32, 0.75 - 6.0 Nm 339/342 AB 28 446 •RE 25, 20 W 181 GP 32 S 370-372 AB 28 446 •RE 30, 15 W 182 88.8RE 30, 15 W 182 GP 32, 0.75 - 4.5 Nm 340 •RE 30, 60 W 183 88.8RE 30, 60 W 183 GP 32, 0.75 - 6.0 Nm 338-344 •RE 30, 60 W 183 KD 32, 1.0 - 4.5 Nm 347 •RE 30, 60 W 183 GP 32 S 370-372 •RE 35, 90 W 184 91.7RE 35, 90 W 184 GP 32, 0.75 - 8.0 Nm 338-345 •RE 35, 90 W 184 GP 42, 3.0 - 15 Nm 349 •RE 35, 90 W 184 GP 32 S 370-372 •RE 35, 90 W 184 AB 28 446 124.3RE 35, 90 W 184 GP 32, 0.75 - 8.0 Nm 338-345 AB 28 446 •RE 35, 90 W 184 GP 42, 3.0 - 15 Nm 349 AB 28 446 •RE 35, 90 W 184 GP 32 S 370-372 AB 28 446 •
1
9
2
10
110512 110514 110516
500 500 5003 3 3
100 100 100 12 000 12 000 12 000
3 4 6
s 45°es2 s = 90°e1..4s1s4s3
U
U
U
U
U
U
High
High
High
Low
Low
Low
90°e
R
R
R
May 2016 edition / subject to change maxon sensor
Stock programStandard programSpecial program (on request)
Encoder HEDL 5540 500 CPT, 3 Channels, with Line Driver RS 422
maxon Modular System+ Motor Page + Gearhead Page + Brake Page Overall length [mm] / • see Gearhead
Part Numbers
TypeCounts per turnNumber of channelsMax. operating frequency (kHz)Max. speed (rpm)Shaft diameter (mm)
Direction of rotation cw (definition cw p. 150)
Technical Data Pin Allocation Connection exampleSupply voltage VCC 5 V ± 10%Output signal EIA Standard RS 422 driver used: DS26LS31Phase shift ) 90°e ± 45°eSignal rise time (typically, at CL = 25 pF, RL = 2.7 k:, 25 °C) 180 nsSignal fall time (typically, at CL = 25 pF, RL = 2.7 k:, 25 °C) 40 nsIndex pulse width 90°eOperating temperature range -40…+100 °CMoment of inertia of code wheel d 0.6 gcm2
Max. angular acceleration 250 000 rad s-2
Output current per channel min. -20 mA, max. 20 mAOption 1000 Counts per turn, 2 Channels
The index signal , is synchronized with channel A or B. Terminal resistance R = typical 120 :
1 N.C. 2 VCC
3 GND 4 N.C. 5 Channel A 6 Channel A 7 Channel B 8 Channel B 9 Channel I (Index)10 Channel I (Index)
Pin type DIN 41651/EN 60603-13flat band cable AWG 28
Line receiverRecommended IC's:- MC 3486- SN 75175- AM 26 LS 32
Channel B
Channel B
Channel A
Channel A
Channel I
Channel I
GND
VCC
Enc
oder
, Lin
e D
river
, DS
26LS
31
Channel A
Channel B
Channel I
Cycle C = 360°ePulse P = 180°e
Phase shift
overall length overall length
Tachymetric generators
Tachymeter = (small) DC machine used as a generator:analog voltage, continuous measurementdirect angular velocity (no differentiation)more bulky, much more pricey
max
on s
enso
r
411
RE 25 179/181 76.8RE 25 179/181 GP 26, 0.75 - 2.0 Nm 336 •RE 25 179/181 GP 32, 0.75 - 4.5 Nm 338/339 •RE 25 179/181 GP 32, 0.75 - 6.0 Nm 342 •RE 25 179/181 GP 32, 1.0 - 4.5 Nm 347 •RE 25 179/181 GP 32 S 370-372 •RE 25, 20 W 180 65.3RE 25, 20 W 180 GP 22, 0.5 Nm 329 •RE 25, 20 W 180 GP 26, 0.75 - 2.0 Nm 336 •RE 25, 20 W 180 GP 32, 0.75 - 4.5 Nm 338/339 •RE 25, 20 W 180 GP 32, 0.75 - 6.0 Nm 342 •RE 25, 20 W 180 GP 32, 1.0 - 4.5 Nm 347 •RE 25, 20 W 180 GP 32 S 370-372 •RE 35, 90 W 184 89.1RE 35, 90 W 184 GP 32, 0.75 - 6.0 Nm 338-344 •RE 35, 90 W 184 GP 32, 8 Nm 345 •RE 35, 90 W 184 GP 42, 3.0 - 15 Nm 349 •RE 35, 90 W 184 GP 32 S 370-372 •
118909 118910
3 4
May 2016 edition / subject to change maxon sensor
Stock programStandard programSpecial program (on request)
DC Tacho DCT 22 0.52 Volt
maxon Modular System+ Motor Page + Gearhead Page Overall length [mm] / • see Gearhead
Part Numbers
TypeShaft diameter (mm)
Technical Data Connection exampleOutput voltage per 1000 rpm 0.52 V Max. current 10 mATerminal resistance tacho 37.7 W Tolerance of the output voltage ± 15 %Typical peak to peak ripple ≤ 6 % Rotor inertia (tacho only) < 3 gcm²Ripple frequency per turn 14 Resonance frequency with motors on p. 179 – 181 > 2 kHzLinear voltage tolerance, 500 to 5000 rpm ± 0.2 % with motors on p. 184 > 4.5 kHzLinear voltage tolerance with 10 kΩ load resistance ± 0.7 % Temperature range -20 ... +65 °CPolarity error ± 0.1 %Temperature coefficient of EMF (magnet) -0.02 % /°C Option: Pigtails in place of solder terminals.Temperature coefficient of coil resistance +0.4 % /°C
Important Information• Tacho with moving coil, maxon system.• Tacho with precious metal commutation.• To establish total inertia add motor and
tacho inertias.• With the output shaft turning CW as seen from
the mounting surface, the tacho output voltage will be positive at the + terminal.
• A high impedance load is recommended at tacho terminals.
• The tacho current should be kept low.• The indicated resonance frequency refers to the
motor-tacho rotor system.
Ripple = x 100 (%)
T
180 W
Resonance frequency Motor winding-Tacho winding fR 4 kHz
1 kW
UAC
0.1 mF
UDC
overall length overall length
26 / 49
Outline
1 Robot control systems
2 TechnologyActuationAngular position measurementVariable speed drives
27 / 49
Variable speed drives
Objectives and hypothesesPrinciple of Variable Speed Drive
DC motor case only
DefinitionVariable speed drive (VSD): device that simultaneouslyprovides a motor with its power supply and input control.
28 / 49
Variable speed drives
Objectives and hypothesesPrinciple of Variable Speed DriveDC motor case only
DefinitionVariable speed drive (VSD): device that simultaneouslyprovides a motor with its power supply and input control.
28 / 49
Variable speed drives
Objectives and hypothesesPrinciple of Variable Speed DriveDC motor case only
DefinitionVariable speed drive (VSD): device that simultaneouslyprovides a motor with its power supply and input control.
28 / 49
Static conversion
Conversion chainPower supply from the electric AC network:
rectifier (AC/DC conversion)chopper (DC/DC conversion)different cases:
energy supply: single-phase, tri-phase voltagesstatic converters technology:
full wave diode bridge rectifier, or fully controlled rectifier1, 2 or 4 quadrants chopper
Power supply from a battery (embedded systems): requiresonly a chopper.
29 / 49
Static conversion
Conversion chainPower supply from the electric AC network:
rectifier (AC/DC conversion)
chopper (DC/DC conversion)different cases:
energy supply: single-phase, tri-phase voltagesstatic converters technology:
full wave diode bridge rectifier, or fully controlled rectifier1, 2 or 4 quadrants chopper
Power supply from a battery (embedded systems): requiresonly a chopper.
29 / 49
Static conversion
Conversion chainPower supply from the electric AC network:
rectifier (AC/DC conversion)chopper (DC/DC conversion)
different cases:
energy supply: single-phase, tri-phase voltagesstatic converters technology:
full wave diode bridge rectifier, or fully controlled rectifier1, 2 or 4 quadrants chopper
Power supply from a battery (embedded systems): requiresonly a chopper.
29 / 49
Static conversion
Conversion chainPower supply from the electric AC network:
rectifier (AC/DC conversion)chopper (DC/DC conversion)different cases:
energy supply: single-phase, tri-phase voltagesstatic converters technology:
full wave diode bridge rectifier, or fully controlled rectifier1, 2 or 4 quadrants chopper
Power supply from a battery (embedded systems): requiresonly a chopper.
29 / 49
Static conversion
Conversion chainPower supply from the electric AC network:
rectifier (AC/DC conversion)chopper (DC/DC conversion)different cases:
energy supply: single-phase, tri-phase voltages
static converters technology:
full wave diode bridge rectifier, or fully controlled rectifier1, 2 or 4 quadrants chopper
Power supply from a battery (embedded systems): requiresonly a chopper.
29 / 49
Static conversion
Conversion chainPower supply from the electric AC network:
rectifier (AC/DC conversion)chopper (DC/DC conversion)different cases:
energy supply: single-phase, tri-phase voltagesstatic converters technology:
full wave diode bridge rectifier, or fully controlled rectifier1, 2 or 4 quadrants chopper
Power supply from a battery (embedded systems): requiresonly a chopper.
29 / 49
Static conversion
Conversion chainPower supply from the electric AC network:
rectifier (AC/DC conversion)chopper (DC/DC conversion)different cases:
energy supply: single-phase, tri-phase voltagesstatic converters technology:
full wave diode bridge rectifier, or fully controlled rectifier1, 2 or 4 quadrants chopper
Power supply from a battery (embedded systems): requiresonly a chopper.
29 / 49
Tri-phase, full wave rectifier, 4Q chopper
Static converter example [adapted from Louis2002]
i : currentΩ: rotational velocity
4 quadrants operation [adapted from Louis2002]
i : currentc= motor torqueΩ: rotational velocityγ= motor acceleration
Static converter modeling
Discrete timeThe chopper provides a voltage adjusted by its duty cycleα ∈ [0 1]: it is a sampled system.
High frequency commutation (50 kHz for P < 1kW ).
Continuous model→ As a first approximate, it is a continuous system: adjustablevoltage source modeled by a simple gain, the ratio between thePWM duty cycle and the output voltage.
32 / 49
Static converter modeling
Discrete timeThe chopper provides a voltage adjusted by its duty cycleα ∈ [0 1]: it is a sampled system.
High frequency commutation (50 kHz for P < 1kW ).
Continuous model→ As a first approximate, it is a continuous system: adjustablevoltage source modeled by a simple gain, the ratio between thePWM duty cycle and the output voltage.
32 / 49
DC motor modelling
v
f
R Li
e
i
Ω
cv
Equations
v = Ri + L didt + e
e = Ke Ω
J dΩdt = c − f Ω (−c0)c = Kmi
Remark: c0 is any additional modeled torque, friction or load33 / 49
DC motor modelling
v
f
R Li
e
i
Ω
cv
Equations
V (s) = (R + Ls)I(s) + E(s)E(s) = Ke Ω(s)
JsΩ(s) = C(s)− f Ω(s) (−C0(s))C(s) = KmI(s)
Remark: Ke ' Km = Kem in the following34 / 49
DC motor modelling
Combining the previous equations:
RKem
(f Ω(s) + JsΩ(s))+L
Kem
(fsΩ(s) + Js2Ω(s)
)+KemΩ(s) = V (s)
Transfer function voltage→ angular velocity
G(s) =Ω(s)
V (s)=
KemLJ
s2 + (RL + f
J )s + Rf +K 2em
LJ
→ order 2, no integration
35 / 49
DC motor modelling: first order approximate
ApproximateLet us neglect the motor armature (motor winding) inductance.
Transfer function voltage→ angular velocity
G(s) =Ω(s)
V (s)=
K1 + τems
where the electromechanical time constant of the system and thestatic gain are written:
τem =RJ
Rf + K 2em
and K =Kem
Rf + K 2em
→ order 1, one stable pole p = −1/τem
36 / 49
Second order model
Second expression
G(s) =K
1 + (τem + µτel)s + τelτems2
with the electrical time constant: τel = LR
As µ = RfRf +K 2
em<< 1, then τem + µτel ' τem ' τem + τel , and:
G(s) =Ω(s)
V (s)=
K(1 + τels)(1 + τems)
→ order 2, poles in p1 = −1/τel and p2 = −1/τem
Remark: transfer function voltage→ position by integration:
G(s) =Θ(s)
V (s)=
Ks(1 + τels)(1 + τems)
37 / 49
Second order model
Second expression
G(s) =K
1 + (τem + µτel)s + τelτems2
with the electrical time constant: τel = LR
As µ = RfRf +K 2
em<< 1, then τem + µτel ' τem ' τem + τel , and:
G(s) =Ω(s)
V (s)=
K(1 + τels)(1 + τems)
→ order 2, poles in p1 = −1/τel and p2 = −1/τem
Remark: transfer function voltage→ position by integration:
G(s) =Θ(s)
V (s)=
Ks(1 + τels)(1 + τems)
37 / 49
Second order model
Second expression
G(s) =K
1 + (τem + µτel)s + τelτems2
with the electrical time constant: τel = LR
As µ = RfRf +K 2
em<< 1, then τem + µτel ' τem ' τem + τel , and:
G(s) =Ω(s)
V (s)=
K(1 + τels)(1 + τems)
→ order 2, poles in p1 = −1/τel and p2 = −1/τem
Remark: transfer function voltage→ position by integration:
G(s) =Θ(s)
V (s)=
Ks(1 + τels)(1 + τems)
37 / 49
Operating Range Comments
Continuous operationIn observation of above listed thermal resistance(lines 17 and 18) the maximum permissible windingtemperature will be reached during continuousoperation at 25°C ambient.= Thermal limit.
Short term operationThe motor may be briefly overloaded (recurring).
Assigned power rating
n [rpm]
max
onD
Cm
otor
Specifications
Stock programStandard programSpecial program (on request)
Order Number
May 2008 edition / subject to change maxon DC motor 83
maxon Modular System Overview on page 16 - 21
RE 36 !36 mm, Graphite Brushes, 70 Watt
Thermal data17 Thermal resistance housing-ambient 6.4 K / W18 Thermal resistance winding-housing 3.4 K / W19 Thermal time constant winding 44.2 s20 Thermal time constant motor 1120 s21 Ambient temperature -30 ... +100°C22 Max. permissible winding temperature +125°C
Mechanical data (ball bearings)23 Max. permissible speed 12000 rpm24 Axial play 0.05 - 0.15 mm25 Radial play 0.025 mm26 Max. axial load (dynamic) 5.6 N27 Max. force for press fits (static) 5.6 N
(static, shaft supported) 1200 N28 Max. radial loading, 5 mm from flange 28 N
Other specifications29 Number of pole pairs 130 Number of commutator segments 1331 Weight of motor 350 g
Values listed in the table are nominal.Explanation of the figures on page 49.
Tolerances may vary from the standardspecification.
OptionPreloaded ball bearings
Planetary Gearhead!32 mm0.75 - 4.5 NmPage 239
Planetary Gearhead!32 mm0.4 - 2.0 NmPage 237
Planetary Gearhead!42 mm3 - 15 NmPage 244
DC-Tacho DCT!22 mm0.52 VPage 271
Encoder HEDS 5540500 CPT,3 channelsPage 262Encoder HEDL 5540500 CPT,3 channelsPage 264
118797 118798 118799 118800 118801 118802 118803 118804 118805 118806 118807 118808 118809 118810Motor Data
Values at nominal voltage1 Nominal voltage V 18.0 24.0 32.0 42.0 42.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0 48.02 No load speed rpm 6610 6210 6790 7020 6340 6420 5220 4320 3450 2830 2280 1780 1420 11803 No load current mA 153 105 88.6 70.4 61.4 54.6 41.6 32.6 24.7 19.5 15.2 11.5 8.97 7.314 Nominal speed rpm 5880 5530 6120 6350 5660 5740 4520 3600 2720 2090 1530 1010 651 3905 Nominal torque (max. continuous torque) mNm 70.2 78.2 77.1 77.9 79.9 79.5 81.5 82.2 83.6 84.1 84.1 83.8 84.1 83.16 Nominal current (max. continuous current) A 2.90 2.25 1.82 1.45 1.33 1.18 0.978 0.813 0.660 0.545 0.439 0.343 0.275 0.2267 Stall torque mNm 730 783 832 866 786 785 627 504 403 326 258 198 158 1278 Starting current A 28.6 21.5 18.7 15.3 12.6 11.1 7.22 4.80 3.06 2.04 1.30 0.784 0.501 0.3349 Max. efficiency % 84 85 86 86 86 86 85 84 82 81 79 77 75 72
Characteristics10 Terminal resistance " 0.628 1.11 1.71 2.74 3.35 4.32 6.65 10.0 15.7 23.5 36.8 61.3 95.8 14411 Terminal inductance mH 0.0988 0.201 0.300 0.487 0.597 0.760 1.15 1.68 2.62 3.87 5.96 9.70 15.1 21.912 Torque constant mNm / A 25.5 36.4 44.5 56.6 62.6 70.7 86.9 105 131 160 198 253 315 38013 Speed constant rpm / V 375 263 215 169 152 135 110 90.9 72.7 59.8 48.2 37.8 30.3 25.114 Speed / torque gradient rpm / mNm 9.23 8.05 8.27 8.18 8.14 8.25 8.41 8.65 8.67 8.80 8.96 9.17 9.21 9.5115 Mechanical time constant ms 6.00 5.89 5.84 5.81 5.81 5.80 5.81 5.81 5.82 5.83 5.84 5.86 5.85 5.8816 Rotor inertia gcm2 62.0 69.9 67.5 67.8 68.1 67.2 66.0 64.2 64.1 63.3 62.2 61.1 60.7 59.0
Planetary Gearhead!32 mm1.0 - 6.0 NmPage 240
Encoder MR256 - 1024 CPT,3 channelsPage 259
M 1:2
Recommended Electronics:ADS 50/5 Page 276ADS 50/10 277ADS_E 50/5 277ADS_E 50/10 277EPOS 24/5 294EPOS2 50/5 295EPOS P 24/5 297Notes 18
Need to control current
Current transfer function
GI(s) =I(s)
V (s)=
Js + fLJs2 + (RJ + Lf )s + Rf + K 2
em
→ 2 poles, 1 zero
Angular velocity/current step response: Maxon RE36, 11880039 / 49
Need to control current
Current transfer function
GI(s) =I(s)
V (s)=
Js + fLJs2 + (RJ + Lf )s + Rf + K 2
em
→ 2 poles, 1 zero
RiskCurrent overshoot in the chopper power components, and inthe DC motor winding = potential damage.
As a result, there is a need to:control current overshootinglimit maximal current in order to protect the motor
40 / 49
Current control synthesis
Approach
either use GI(s)
or (better): as the motor electromotive force changesslowly, it is considered as a disturbance in the equationV (s) = (R + Ls)I(s) + E(s).
Hence:GI(s) =
1R + Ls
=1R
11 + τes
→ order 1, no integral→ PI control: CI(s) = Kp(1 + 1τi s
)
41 / 49
Current control synthesis
Approach
either use GI(s)
or (better): as the motor electromotive force changesslowly, it is considered as a disturbance in the equationV (s) = (R + Ls)I(s) + E(s).
Hence:GI(s) =
1R + Ls
=1R
11 + τes
→ order 1, no integral→ PI control: CI(s) = Kp(1 + 1τi s
)
41 / 49
Current control synthesis
Open loop with PI control: CI(s)GI(s) =KpRτi
1+τi ss(1+τes)
TuningElectrical pole compensation:
→ open loop transfer: CI(s)GI(s) =Kp
Rτi s
→ closed loop transfer:
GIBF (s) =1ki
11 + Rτi
Kpkis
with ki the gain of the current sensor
The 5% settling time of the current feedback loop is a functionof Kp that could decrease infinitely: of course it is nonsenseand Kp has to be tuned to avoid control saturation in realimplementations!
42 / 49
Angular velocity and position control
Control structure: analog implementation
Once the current is controlled, angular velocity and position canbe controlled using a cascade architecture
kiI(s)
−
+Ω(s)
kΩVΩ(s) = kΩΩ(s)
Vr (s) +
CΩ(s) CI(s) DC motor
−
V (s)
DC motor angular velocity analog servoing
It is necessary to saturate the current servo loop reference(corresponding voltage ±ki IM ).
43 / 49
Synthesis
Velocity control synthesisWrite the DC motors equation considering that the current isnow controlled (with a time constant that is much faster than theone of the velocity).
→ order 1 model, no integration: PI controller
Position servoing
Same remarks.
→ order 2 model, one integration: phase lead (PD) control
44 / 49
Maxon 4-Q-DC Servoamplifier ADS 50/5
45 / 49
maxon motor 4-Q-DC Servoamplifier ADS 50/5 Operating Instructions
3 Minimum External Wiring for Different Modes of Operation
4 maxon motor control July 2009 Edition / Doc. No. 538837-07 / Subject to change
maxon motor 4-Q-DC Servoamplifier ADS 50/5 Operating Instructions
4.3 Adjustment of the Potentiometers 4.3.1 Pre-adjustment
With the pre-adjustment, the potentiometers are set in a preferred position. ADS units in original packing are already pre-adjusted.
Pre-adjustment of potentiometers
P1 IxR 0 %
P2 Offset 50 %
P3 nmax 50 %
P4 Imax 50 %
P5 gain 10 %
4.3.2 Adjustment Encoder mode
DC-Tacho mode 1. Adjust set value to maximum (e.g. 10 V) and turn potentiometer P3 nmax
so far that the required speed is achieved. IxR compensation 2. Set potentiometer P4 Imax at the limiting value desired.
Maximum current in the 0 ... 10 A range can be adjusted in linear fashionwith potentiometer P4. Important: The limiting value lmax should be below the nominal current (max. continuous current) as shown on the motor data sheet and may not exceed 5 A continuously.
3. Increase potentiometer P5 gain slowly until the amplification is set large enough. Caution: If the motor vibrates or becomes loud, the amplification is ad-justed too high.
4. Adjust set value to 0 V, e.g. by short circuiting the set value. Then set the motor speed to 0 rpm with the potentiometer P2 Offset.
In addition, only in the case of lxR compensation: 5. Slowly increase potentiometer P1 IxR until the compensation is set large
enough so that in the case of high motor load the motor speed remains the same or decreases only slightly. Caution: If the motor vibrates or becomes loud, the amplification is ad-justed too high.
Current controller mode 1. Set potentiometer P4 lmax at the limiting value desired.
Maximum current in the 0 ... 10 A range can be adjusted in linear fashionwith potentiometer P4. Important: The limiting value lmax should be below the nominal current (max. continuous current) as shown in the motor data sheet and may not exceed 5 A continuously.
2. Adjust set value to 0 V. Then set the motor current to 0 A with the poten-tiometer P2 Offset.
Note • A set value in the -10 ... +10 V range is equal to a current range of approx.
+Imax ... -Imax • Configured as a current controller, P1, P3 and P5 are not activated.
6 maxon motor control July 2009 Edition / Doc. No. 538837-07 / Subject to change
maxon motor 4-Q-DC Servoamplifier ADS 50/5 Operating Instructions
6 Additional Possible Adjustments Potentiometer Function Position left right
P6 ngain speed gain low high
P7 Igain current gain low high
P8 Icont continuous current limit lower higher
P8 Icont
P7 Igain
P6 ngain
6.1 Adjustments potentiometer P6 ngain and potentiometer P7 Igain In most applications, regulation setting is completely satisfactory using potentio-meters P1 to P5. In special cases the transient response can be optimized by setting the P6 “speed regulation gain” potentiometer. The P7 “current regulator gain” potentiometer can, in addition, be adapted to the dynamics of the current regulator. It is recommend that the success of changes to the settings of P6 ngain and P7 Igain be checked by measuring the transient response with an oscilloscope at the “Monitor n” and “Monitor I” outputs. Pre-adjustment P6 ngain = 25 % and P7 Igain = 40 %.
10 maxon motor control July 2009 Edition / Doc. No. 538837-07 / Subject to change
maxon motor 4-Q-DC Servoamplificateur ADS 50/5 Notice d'utilisation
10 Schéma bloc
ReadyEnable-12V OUT
-12V
+12V
+5V
Supply
DIP6
-12V
+12V
PTC
Current
limitP8 I cont
PWM,
Control &
Protection
Logic
MOSFET
Full-Bridge
Current
Detector
Voltage
Detector
P1 IxR
P4 Imax
Monitor I
-Motor
+Motor
Power Gnd
+Vcc 12-50VDC
+12V OUT
1K +12V 1K
DIP1
P6 n gainP5 gain
DIP2
DIP3
P2 Offset
-12V+12V
Monitor n
P3 n max
DIP4
-Tacho Input
-Set value
+Set value
Encoder B\
Encoder B
Encoder A\
Encoder A
Gnd
+5V/80mA
DIP5
F/V Converter
+5V
P7 I gain
Poly-
fuse
LED
3
Ground
Safety
Earth
earth
optional
3
Case
11
2
4
5
11 Dimensions Dimensions en [mm]
14 maxon motor control Edition Juillet 2009 / Doc. No. 539149-06 / Sous réserve de modification