advanced motion control first and second order motion by peter nachtwey
TRANSCRIPT
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ADVANCED MOTION CONTROL
First and Second Order Motion
byPeter Nachtwey
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Pressure/Force Only
Position-Speed
Position-Force
Pressure/Force Limit
Position-Pressure
Closed Loop Control
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Why Bother Making Another Hydraulic Motion Controller?
Connect. Control.
Optimize.32 bits to interface with 32 bit PLCs
and PCs.
32 or 64 bit
floating point math
Motion Control /
User Programs
off load PLCs.
10/100Mb Full Duplex Ethernet
using EtherNet/IP.
2nd Order Control most
important.
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First order vs. Second order control
Motors look like first order systems
Hydraulic systems look like 2nd order systems• Modeled as a Mass between two springs as a representative, effective, simple models.
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Mass and Two Springs
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First and Second Order Response
0 0.05 0.1 0.15 0.20
1
2
3
4
First Order VelocitySecond Order VelocityOpen Loop Control Output
First Order vs Second Order Response
Time
Vel
ocity
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First and Second Order Controllers
First Order Controllers have a PID and velocity and acceleration feed
forward.
Second order controllers have a PID with a second derivative and velocity,
acceleration and jerk feed forwards.
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It’s costly to design hydraulic systems
• with natural frequencies high enough for higher production rates.
• Response is limited by ξωn/2 without 2nd order motion control
One answer is to control the system with 2nd order motion controllers• quicker accels and
decels (under control) than what 1st order systems permit.
• Lower damping factor & natural frequency, allows greater advantage over 1st order controllers
Compensate for mechanical
cost in the electronic controls
Why 2nd Order Control?
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3 Challenges implementing a Second order controller
Challenge 1.
Must have smooth motion profiles where the jerk changes smoothly for the jerk feed forward. Simple motion or target profile generators aren’t good enough.
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3 Challenges implementing a Second order controller
Challenge 2.Using the double derivative gain is problematic. The derivative gain is difficult enough !• quantizing error due to lack of
resolution.• Sample jitter• Noise.
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3 Challenges implementing a Second order controller Challenge 2.
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3 Challenges implementing a Second order controller
Challenge 3. How does one tune a second order?Use a 5th order motion profile or target generator. Use model based control.
Auto tuning determines the jerk feed forward and second derivative gain.
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Solutions to 2nd order controller implementation problems
Use a 5th order motion profile or target generator.
Use model based control.
Use Auto tuning to determine the jerk feed forward and second derivative
gain.
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Second Order Motion Profile - Higher Order PID
Higher Order Target Generator
)(*2)(*)(*)(*)( 2
2
teKteKdteKpdtteKitudtd
dtd
55
44
33
22000)( tctctcttvsts a
45
34
2300 543)( tctctctavtv
35
2430 20126)( tctctcata
2543 60246)( tctcctj
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Model Based Control
Why Bother?
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Model Based Control
The PID and feed forwards use the positions, velocities, and accelerations generated by the model, not the feedback.
The feedback continuously updates the model to keep the model from going astray.
The advantage is that the PID sees a nearly perfect system virtually free of quantizing errors, sample jitter and noise.
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Model Based Control
The result is a smoother output which allows use of higher gains.
However, one should ask,
• Where does the model come from?
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System Identification and Auto Tuning
The information needed is
in the
plots/graphs
Need time,
control output
and actual
position or
velocity
The result is• Gain and
time constant for a first order model
• Gain, damping factor and natural frequency second order.
Choose the
model for the best fit.
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First Order Model
ERR 0.2482011
0.002651 377.177281G 3.095512
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Second Order Model
G 2.99991 0.10225 C 5.935563 106 ERR 0.009074 125.183235
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Actual vs. Estimated Velocity
0 0.2 0.4 0.6 0.82
0
2
4
6
8
10
10
5
0
5
10
ActVelEstVelControl
Actual vs Estimated Velocity
Time
Vel
ocity
Con
trol
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Actual and Estimated Accelerations
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Estimated State Feedback
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Selecting the Closed Loop Gain.
Closed Loop
Gains are calculated from the model and
the desired bandwidth.
Only one parameter to choose – the desired bandwidth.
Feed-Forward Gains are
calculated from the model only
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Auto Tuning via Tuning Wizard
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Step Response for Different Bandwidths
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Summary
Why Bother?• Machines can be simpler and less costly to manufacture.
• Technology allows advances in machine motion control
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Thank You for Your Time and
Attention!
Questions?
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Hydraulic Design Guide
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ADVANCED MOTION CONTROL
First and Second Order Motion
byPeter Nachtwey