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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

Mechatronics

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