1 / 27

Chapter 5

Chapter 5. Dynamic Behavior of Ideal Systems. Ideal Dynamic Behavior. Idealized dynamic behavior can be effectively used to qualitatively describe the behavior of industrial processes.

Patman
Download Presentation

Chapter 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

  3. Inputs

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

  5. First Order Process

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

  7. Estimate of First-Order Model from Process Response

  8. 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.

  9. Underdamped vs Overdamped

  10. Effect of z on Underdamped Response

  11. Effect of z on Overdamped Response

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

  13. 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.

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

  15. Second-Order Model Parameters from Process Response

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

  17. 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

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

  19. Deadtime • Transport delay from reactor to analyzer: • Transfer function:

  20. 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.

  21. 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:

  22. Determination of t1/3 and t2/3

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

  24. Lead-Lag Element

  25. 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.

  26. Mass Recycle Example

  27. 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

More Related