1. Dynamic Behavior of Ideal Systems
Chapter 6
Dynamic Behavior of Ideal Systems

2. 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

3. 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.

4. Inputs

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

6. First Order Process

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

8. Estimate of First-Order Model from Process Response

9. 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.

10. 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.

11. Underdamped vs Overdamped

12. Effect of z on Overdamped Response

13. Effect of z on Underdamped Response

14. Effect of z on Underdamped Response

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

16. 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.

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

18. Second-Order Model Parameters from Process Response

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

20. 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

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

22. Deadtime
Transport delay from reactor to analyzer:
Transfer function:

23. 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.

24. 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:

25. Determination of t1/3 and t2/3

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

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

28. Lead-Lag Element

29. 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.

30. Mass Recycle Example

31. 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