ADVANCED MOTION CONTROL First and Second Order Motion by Peter Nachtwey

ADVANCED MOTION CONTROL

First and Second Order Motion

byPeter 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 0.2482011

0.002651 377.177281G 3.095512

Second Order Model

G 2.99991 0.10225 C 5.935563 106 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

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

byPeter Nachtwey