closed loop control
DESCRIPTION
Closed Loop Control. Why 2 nd Order Control?. 3 Challenges implementing a Second order controller Challenge 2. Second Order Motion Profile - Higher Order PID. Higher Order Target Generator. First Order Model . Second Order Model . Hydraulic Design Guide. - PowerPoint PPT PresentationTRANSCRIPT
ADVANCED MOTION CONTROL
First and Second Order Motion
byPeter Nachtwey
Pressure/Force Only
Position-Speed
Position-ForcePressure/Force LimitPosition-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 mathMotion
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
Velo
city
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 0.2482011
0.002651 377.177281G 3.095512
Second Order Model
G 2.99991 0.10225 C 5.935563 10 6 ERR 0.009074 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
Velo
city
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
byPeter Nachtwey