Dynamic Behavior of Ideal Systems

1
Chapter 5

• Dynamic Behavior of Ideal Systems

2
Ideal Dynamic Behavior

• Idealized dynamic behavior can be effectively
  used to qualitatively describe the behavior of
  industrial processes.
• Certain aspects of second order dynamics (e.g.,
  decay ratio, settling time) are used as criteria
  for tuning feedback control loops.
• This material is not, in general, directly
  applied to industrial control.

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Inputs
4
First Order Process

• Differential equation
• Transfer function
• Note that gain and time constant define the
  behavior of a first order process.

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First Order Process
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Determine the Process Gain and Process Time
Constant from Gp(s)
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Estimate of First-Order Model from Process
Response
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Second Order Process

• Differential equation
• Transfer function
• Note that the gain, time constant, and the
  damping factor define the dynamic behavior of 2nd
  order process.

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Underdamped vs Overdamped
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Effect of z on Underdamped Response
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Effect of z on Overdamped Response
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Characteristics of an Underdamped Response

• Rise time
• Overshoot (B)
• Decay ratio (C/B)
• Settling or response time
• Period (T)

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Example of a 2nd Order Process

• The closed loop performance of a process with a
  PI controller can behave as a second order
  process.
• When the aggressiveness of the controller is very
  low, the response will be overdamped.
• As the aggressiveness of the controller is
  increased, the response will become underdamped.

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Determining the Parameters of a 2nd Order System
from its Gp(s)
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Second-Order Model Parameters from Process
Response
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High Order Processes

• The larger n, the more sluggish the process
  response (i.e., the larger the effective
  deadtime)
• Transfer function

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Example of Overdamped Process

• Distillation columns are made-up of a large
  number of trays stacked on top of each other.
• The order of the process is approximately equal
  to the number of trays in the column

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Integrating Processes

• In flow and out flow are set independent of level
• Non-self-regulating process
• Example Level in a tank.
• Transfer function

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Deadtime

• Transport delay from reactor to analyzer
• Transfer function

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FOPDT Model

• High order processes are well represented by
  FOPDT models. As a result, FOPDT models do a
  better job of approximating industrial processes
  than other idealized dynamic models.

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Determining FOPDT Parameters

• Determine time to one-third of total change and
  time to two-thirds of total change after an input
  change.
• FOPDT parameters

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Determination of t1/3 and t2/3
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Inverse Acting Processes

• Results from competing factors.
• Example Thermometer
• Example of two first order factors

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Lead-Lag Element
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Recycle Processes

• Recycle processes recycle mass and/or energy.
• Recycle results in larger time constants and
  larger process gains.
• Recycles (process integration) are used more
  today in order to improve the economics of
  process designs.

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Mass Recycle Example
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Overview

• It is important to understand terms such as
• Overdamped and underdamped response
• Decay ratio and settling time
• Rectangular pulse and ramp input
• FOPDT model
• Inverse acting process
• Lead-Lag element
• Process integration and recycle processes