mechatronics pid (proportional integral derivative) proportional action (p): makes the system more...
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Mechatronics
PIDPID(Proportional Integral Derivative)(Proportional Integral Derivative)
Proportional Action (P): •Makes the system more reactive (piu’ pronto)•Reduces disturbances on G: goes toward: for high G values
•Can lead to overshoot
Integral Action (I): •Reduces error at regime•Can lead to oscillations•Can move poles to the right (i.e. instability)
Derivative Action (D): •It acts as a damper•It works against high slopes in the controller action•Can move poles to the right (i.e. instability)
GH
G
1 H
1
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PIDNote: with only the proportional gain the control would oscillate around the set point
The transfer function is:
kp
kD
kIt
0
dt
d
+ Plant
H
+-
Set point e
feedback
G
GH
G
1
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Kp low narrow bandwidthf limited poor performances
PID M
E
Set point+
-
Lag error
Kp*Lag error low current peak
Real
profile
bw
Low steepness f low narrow bw
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Kp high wide band widthhigh f good performances
bw
PID M
E
Set point+
-
Lag error
Kp*Lag error high current peak
Real Profile
High steepness high f wide bw
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PID (closed loop)and FeedForward (open
loop)
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PID time response to a step:
Time continuous version:
Proportional Action
Integral Action
Derivative Action (it does derivateonly the feedback to avoid Dirac impulse)
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Motion Profiles
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Socapel Parallel Regulator (position lag proportional to torque)
PositionCommand
PIDVelocity Command
Torque Command
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Rockwell Serial Regulator (position lag proportional to velocity)
PositionLag PI Velocity
CommandPI Torque
Command
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PositionController
PowerStage
Components
Regulator Structure
PI CurrentRegulator
Current Signals to the Motor
• Digital Current (Torque) Regulator
• Safety Value limiting
TorqueLimitation
• Digital PID Position Regulator
+
PIDRegulator
-
FeedbackSignals
+
Set-Points
• Feed-Forward System
+
Feed-Forward
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Parallel PID RegulatorDescription
• For the Proportional Part the Position Lag Value is multiplied with the P-Gain Parameter
• The Input Value for the PID Regulator is the Position Lag (difference between the requested position and the real position)
• The Torque Set-Point is the Output Value of the PID Regulator
• The PID Regulator has three Paths (parts)
– Proportional Part– Integral Part– Derivative Part
• For the Integral Part the Position Lag Value is integrated and then multiplied with the I-Gain Parameter
P
+
PID Regulator
-
Position Feedback
TorqueSet-Point
+
PositionSet-Point
PositionLag
+
I
D
+
• For the Derivative Part the Speed (velocity) Lag Value (same as the first derivative of the Position Lag) is multiplied with the D-Gain Parameter
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Feed-Forward SystemDescription
• Four different Feed-Forward Components are available for the SAM Regulator– External Force– Static / Dry Friction– Viscous Friction– Inertia
• The External Force Component is independent on the Motion and creates a constant Torque value (e.g. Gravity Compensation of a vertical axis)
• The Static or Dry Friction Component uses only the sign of the Speed Set-Point to create a constant Torque value, whenever the speed is not zero
• The Viscous Friction Component is always proportional to the Speed Set-Point
External force
time
speedtorque
time
speedtorque
+
Static/Dry friction Viscous friction
time
speedtorque
++
Inertia
time
speedtorque
TorqueFeed-Forward
=
• The Inertia Component is always proportional to the Acceleration Set-Point and compensates the mechanics Inertia during acceleration and deceleration (M = J *
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Measuring the External Force and Friction Values
speed
Ext.force =|Tp1| -|Tn1|
2
visc =
|Tp10|+|Tn10| - |Tp1|+|Tn1|
2 2
S10 - S1
dry =|Tp1| + |Tn1|
2
- visc * S1
• Run the motor in positive direction with a low speed (S1 = 10%) and measure the mean value of the needed Torque (Tp1) for several samples
S1
Tp1
• Then run the axis with the machine’s nominal speed (S10 = 100%) and measure the Torque as before (Tp10)
viscous friction
torque
+-
dry frictionexternal force
S10
Tp10
Tn10
Tn1
• Do the same in negative rotating direction (Tn1 and Tn10)
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Regulator Tuning•Deactivate the PosLag Error •Clear the Regulator’s Gain and Feed-Forward Parameters
•Start with small but positive P, D-Gains •Enable the Drive (power_on) and run the axis at constant speed
•Increase D-Gain step by step, until vibration starts or the audible noise is too high
•Reduce D-Gain to 50% of the found value•Stop the axis, reset the PosLag (power_off and then power_on)
•Go through the last four steps for P-Gain (instead of R_DGain) trying to improve step response performances
•Set the I-Gain so to reduce the Error At Regime (ear)
•Set Feed Forward GainsNote: Here we refer to a parallel control; the same rule areAnyhow valid for a serial control substituting the word“velocity-P-Gain” to “D-Gain”
TuneLearn link
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Optimise the PD Regulator Step Response
-2000
-1500
-1000
-500
0
500
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Step Response (PosLag) for a critically damped system
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Step Response (PosLag) for an over damped system
-500
-400
-300
-200
-100
0
100
200
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Step Response (PosLag) for an under damped system
Increase P-GainDecrease P-Gain
•Observe (trace) the System’s Step Response (PosLag) while performing a Torque Step Disturbance (with nominal motor torque)
•Modify the D-Gain and P-Gain Parameters until a critically damped system is reached
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-2000
-1000
0
1000
2000
3000
4000
-0.1 0 0.1 0.2 0.3 0.4 0.5
Speed
Adjust the Feed-Forward Parameters
-100
0
100
200
300
400
500
-0.1 0 0.1 0.2 0.3 0.4 0.5
-100
0
100
200
300
400
500
-0.1 0 0.1 0.2 0.3 0.4 0.5-100
0
100
200
300
400
500
-0.1 0 0.1 0.2 0.3 0.4 0.5
Adjust Inertia
Adjust StatFricTorq
Adjust ViscFricTorq
Acceleration proportional PosLag
Speed proportional PosLag
Sign of Speed proportional PosLag
Properly adjusted Feed-Forward Parameters
• Perform positioning movements (relative_move), using the machine’s nominal values for acceleration, deceleration and speed and observe (trace) the resulting PosLag
• Adjust the Inertia, ViscFricTorq, StatFricTorq and ExtTorq parameters until a minimum Range (depending on the application) for PosLag is reached
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I-Gain
-2000
-1500
-1000
-500
0
500
1000
1500
2000
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Step Response (PosLag) for an over damped system -1500
-1000
-500
0
500
1000
1500
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Step Response (PosLag) for an under damped system
-1500
-1000
-500
0
500
1000
1500
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Step Response (PosLag) for a critically damped system
Decrease I-GainIncrease I-Gain
• Observe (trace) the System’s Step Response (PosLag) while performing a Torque Step Disturbance (with nominal motor torque)
• Modify the I-Gain Parameter until a critically damped system is reached
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PD, no FF
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PID, no FF
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PD, with FF