# Dynamic Behavior of Ideal Systems

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Dynamic Behavior of Ideal Systems
Chapter 6 Dynamic Behavior of Ideal Systems

Overall Course Objectives
Develop the skills necessary to function as an industrial process control engineer. Skills Tuning loops Control loop design Control loop troubleshooting Command of the terminology Fundamental understanding Process dynamics Feedback control

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.

Inputs

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

First Order Process

Determine the Process Gain and Process Time Constant from Gp(s)

Estimate of First-Order Model from Process Response

In-Class Exercise By observing a process, an operator indicates that an increase of 1,000 lb/h of feed (input) to a tank produces a 8% increase in a self-regulating tank level (output). In addition, when a change in the feed rate is made, it takes approximately 20 minutes for the full effect on the tank to be observed. Using this process information, develop a first-order model for this process.

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.

Underdamped vs Overdamped

Effect of z on Overdamped Response

Effect of z on Underdamped Response

Effect of z on Underdamped Response

Characteristics of an Underdamped Response
Rise time Overshoot (B) Decay ratio (C/B) Settling or response time Period (T)

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.

Determining the Parameters of a 2nd Order System from its Gp(s)

Second-Order Model Parameters from Process Response

High Order Processes The larger n, the more sluggish the process response (i.e., the larger the effective deadtime) Transfer function:

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

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

Deadtime Transport delay from reactor to analyzer: Transfer function:

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.

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:

Determination of t1/3 and t2/3

In-Class Exercise Determine a FOPDT model for the data given in Problem 5.51 page 208 of the text.

Inverse Acting Processes
Results from competing factors. Example: Thermometer Example of two first order factors:

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.

Mass Recycle Example

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