Controlled Operations Limited Design COLD, Inc.

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Controlled Operations Limited Design (COLD, Inc.)

• Owner Dr. V. G. J. Rodgers

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Budget Cut Announcement
Dear Engineers. Our Company will be merging
with the Japanese Company, Imaginary Control
Enterprises (ICE) to form a new global control
dynasty. We will become ICE-COLD Inc.
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Budget Cut Announcement
We are now faced with a need to remove all dead
weight as we establish the worlds number one
control company. ICE executives will flying in
next week to review your work Thursday afternoon.
Your next presentation on PID control aspects of
your particular projects will be used to
determine who will remain in our dynamic control
engineering design dynasty. In other words..
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Budget Cut Announcement
Only the Baddest of the Bad will remain.
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Weight of Effort Adjustment
Given the great weight on the final work all
written material will now be due on December 13,
215 p.m.
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December 13, 2005 Schedule
All activities will be in room 3321 and everyone
must be there at 215 p.m.Each group will be
given only 15 minutes total.
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December 13, 2005 Schedule
215 Andrew, Lexie Bret230 James, Tyler
Chad245 Leigh, Dane Robert300 Katie, Drew
Sandra315 Ryan, Kendra David330 Brett,
Peter Aaron345 Mike, Jason Dustin
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Presentation Preparation
Dr. V. G. J. Rodgers has asked that we prepare
you for the level of intensity of ICEs visit.
The remaining presentation, based on the work of
Seborg et al. will be used to guide you.
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Got Control?

• It is your control analysis that will carry the
  greatest weight in your evaluation.
• Think globally! In the end how is your system
  handling disturbance and setpoint changes.
• Stability analysis compare methods but know the
  limitations. With approximation methods, do not
  expect exact answers.
• Tuning methods. These are only getting you in the
  ballpark. Are fine tuned results better? By how
  much. Remember, decimal place accuracy is not
  that important.

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Overview System Description

• We want our control system to handle disturbances
  and setpoint changes nicely.

disturbance
manipulated variable
Develop the open loop model for the system
process variable
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Getting There 1) Open Loop

• We want our control system to handle disturbances
  and setpoint changes nicely.

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Getting There 2) Closed- Loop
Now its all about control Gc
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Closed Loop Behavior Examples

• Change the Setpoint (Servo Problem)

Setpoint changed from 0 to 1 here. Offset in this
case because P-only control.
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Closed Loop Behavior Examples

• Disturbances Occur (Regulator Problem)

Setpoint remains at 0.
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Overview 3) Its All About Gc

• We will be using PID control.
• Ideal PID

P PI PD PID
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Overview 3) Its All About Gc

• Oh great one. But what values of Kc, tI, tD shall
  we use for our controller?
• Stability Analysis. Look at P-only control
• Find your range in which you are limited
• Use basic tuning techniques to get approximate
  controller parameters
• Model closed-loop controller system
• Fine tune and analyze

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Stability 4) Overview

• Closed-Loop
• Find your range in which you are limited
• Use basic tuning techniques to get approximate
  controller parameters
• Model closed-loop controller system
• Fine tune and analyze

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Stability 5) Closed-Loop Methods
Closed-Loop Methods Use the Characteristic
Equation
Set Equal to zero is the characteristic equation
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Stability 5) Closed-Loop Methods
Figure 11.25 Stability regions in the complex
plane for roots of the charact-eristic equation.
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Stability 5) Closed-Loop Methods

• Closed-Loop Methods
• Direct Substitution
• Routh-Horowitz Stability Criterion
• Root Locus
• Need to Approximate Dead time with Pade

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Stability 5) Closed-Loop Methods
Root Locus
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Stability 6) Open-Loop Methods
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Stability 6) Open-Loop Methods

• Open-Loop Methods Frequency Response
• Bode Diagram
• Nyquist Diagram
• No Need to Approximate Dead time
• Model behavior of

input
output
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Stability 6) Open-Loop Methods
Get these from
Step 1. Set sjw in G(s) to obtain
. Step 2. Rationalize G(jw) We want to express
it in the form. G(jw)R jI where R and
I are functions of w.
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Stability 6) Open-Loop Methods
Unstable Kc
Critical Kc
Stable Kc
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Stability 6) Open-Loop Methods
Unstable if encircles -1
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Tuning 7) Reaction Curve Methods
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Tuning 7) Reaction Curve Methods
q
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Tuning 7) Reaction Curve Methods
Use model to get values of Kc, tI, tD from
appropriate tables in Chapter 12.
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Tuning 7) Reaction Curve Methods

• Introduce into PID controller

P PI PD PID
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Tuning 7) Reaction Curve Methods
Use These Gcs in the Closed-Loop System
Take Inverse Laplace for Step or Impulse Changes
in setpoint or disturbances
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Tuning 7) Reaction Curve Methods

• Change the Setpoint (Servo Problem)

Setpoint changed from 0 to 1 here. Offset in this
case because P-only control.
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Tuning 7) Reaction Curve Methods

• Disturbances Occur (Regulator Problem)

Setpoint remains at 0.
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Tuning 7) Reaction Curve Methods

• Fine Tune to Your Liking!

Setpoint remains at 0.
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Tuning 8) Ziegler Nichols Method

• Continuous Cycling Method

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Tuning 8) Ziegler Nichols Method
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Tuning 8) Ziegler Nichols Method

• But Can Get Kcu and Pu from Nyquist (Bode, Root
  Locus, Routh Stability)!

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Tuning 8) Ziegler Nichols Method

• Introduce into PID controller

P PI PD PID
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Tuning 8) Ziegler Nichols Method
Use These Gcs in the Closed-Loop System
Take Inverse Laplace for Step or Impulse Changes
in setpoint or disturbances
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Tuning 8) Ziegler Nichols Method

• Change the Setpoint (Servo Problem)

Setpoint changed from 0 to 1 here. Offset in this
case because P-only control.
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Tuning 8) Ziegler Nichols Method

• Disturbances Occur (Regulator Problem)

Setpoint remains at 0.
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Tuning 8) Ziegler Nichols Method

• Fine Tune to Your Liking!

Setpoint remains at 0.
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Final Thoughts

• ICE COLD is expecting only the best from you.
• Good luck to all of you!