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ADVANCED MOTION CONTROL
First and Second Order Motion
by Peter Nachtwey
Pressure/Force Only
Position-Speed
Position-Force
Pressure/Force Limit
Position-Pressure
Closed Loop Control
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.
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.
Mass and Two Springs
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
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.
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?
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.
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.
3 Challenges implementing a Second order controller Challenge 2.
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.
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.
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 ++=
Model Based Control
Why Bother?
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.
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?
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.
First Order Model
ERR 0.248201=1α
0.002651=α 377.177281=G 3.095512=
Second Order Model
G 2.99991= ζ 0.10225= C 5.935563 10 6−×= ERR 0.009074=ω 125.183235=
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
Actual and Estimated Accelerations
Estimated State Feedback
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
Auto Tuning via Tuning Wizard
Step Response for Different Bandwidths
Summary
Why Bother? • Machines can be simpler
and less costly to manufacture.
• Technology allows advances in machine motion control
Thank You for Your Time and Attention!
Questions?
Hydraulic Design Guide
ADVANCED MOTION CONTROL
First and Second Order Motion
by Peter Nachtwey