1 / 34

Fundamentals of Control Systems Technology for Engineers

Understand block diagrams, control signals, signal flow graphs, transfer functions in control systems technology. Learn feedback systems, error signals, signal flow graph development, Mason's rule.

gdunton
Download Presentation

Fundamentals of Control Systems Technology for Engineers

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. UNIVERSITI MALAYSIA PERLIS fakultiteknologikejuruteraan Jabatankejuruteraanelektrik (kuasaindustri) CHAPTER 2 PLT305 -The Basic of Control Theory PLT 305 : CONTROL SYSTEMS TECHNOLOGY

  2. Chapter Objective. • Block Diagram. • Control Signal • Signal Flow Graph. • .

  3. Block Diagram Transfer Function G(s) Input Output A block diagram of a system is a practical representation of the functions performed by each component and of the flow of signals. Cascaded sub-systems:

  4. Block Diagram. • Transfer function is the ratio of the output over the input variables. • The output signal can then be derived as; C = GR (a) Multi-variables. Figure 2.0: Block Diagram. Figure 2.1: Block Diagram of Summing Point.

  5. Cont’d… (b) Block Diagram Summing point. Figure 2.3: Block Diagram of Summing Point.

  6. Cont’d… (c) Linear Time Invariant System. Figure 2.4: Components of a Block Diagram for a Linear, Time-Invariant System.

  7. (d) Cascade System. Figure 2.5: Cascade System and the Equivalent Transfer Function. Figure 2.6: Parallel System and the Equivalent Transfer Function.

  8. (e) Summing Junction. (f) Pickoff Points. Figure 1.12: Block diagram algebra for pickoff points— equivalent forms for moving a block (a) to the left past a pickoff point; (b) to the right past a pickoff point.

  9. Reduction Rules

  10. Reduction Rules

  11. Block Diagram Feedback Control System

  12. Block Diagram The negative feedback of the control system is given by: Ea(s) = R(s) – H(s)Y(s) Y(s) = G(s)Ea(s) Feedback Control System Therefore,

  13. Block Diagram Problem:

  14. + + + - + - Block Diagram H2/G4 Y(s) U(s) G4 G1 G2 G3 H1 H3 Problem:

  15. Block Diagram Y(s) U(s) G1 G2 G4 G3 + + - - H1/G2 H2/G4 H3 G1 Problem:

  16. Block Diagram Y(s) U(s) G1 G2G3G4 + + H1/G2- H2/ G4- H3 G1 Problem:

  17. Block Diagram Y(s) U(s) G1 Problem:

  18. Block Diagram Y(s) U(s) Y(s) U(s) Problem:

  19. Block Diagram Problem:

  20. Control Signal. • E(s) error signal R(s) reference signal Y(s) output signal C(s) output signal B(s) output signal from feedback • Feed forward transfer function, • Feedbacktransfer function, • Error, E(s)transfer function, B(s)

  21. Cont’d… • Characteristic equation, • Close-Loop transfer function,

  22. 2.6 Signal Flow Graph. • Multiple subsystem can be represented in two ways; (a) Block Diagram. (b) Signal Flow Graph. • The block diagram. • The signal flow graph,

  23. Cont’d… • Signal flow graph consists only branches which represent system and nodes which represents signals. • Variables are represented as nodes. • Transmittance with directed branch. • Source node: node that has only outgoing branches. • Sink node: node that has only incoming branches.

  24. Cont’d… • Parallel connection, • Signal-flow graph components: (a) system; (b) signal; (c) interconnection of systems and signals

  25. Cont’d… Cascade Parallel Feedback Signal-flow graph development: (a) signal nodes; (b) signal-flow graph; (c) simplified signal-flow graph

  26. Example 2.13: Signal Flow Graph. Given the block diagram, find the signal flow graph.

  27. Solution:

  28. Mason’s rule where  Total transmittence for every single loop.  Total transmittence for every 2 non-touching loops.  Total transmittence for every 3 non-touching loops.  Total transmittence for every m non-touching loops.  Total transmittence for k paths from source to sink nodes.

  29. Mason’s rule where:  Total transmittence for every single non-touching loop of ks’ paths.  Total transmittence for every 2 non-touching loop of ks’ paths.  Total transmittence for every 3 non-touching loop of ks’ paths.  Total transmittence for every n non-touching loop of ks’ paths.

  30. G1(s) G2(s) G3(s) G4(s) G5(s) R(s) C(s) V4(s) V3(s) V2(s) V1(s) H2(s) H1(s) G6(s) G8(s) G7(s) V6(s) V5(s) H4(s) Example 2.14: Mason’s Rule Given the block diagram, find the transfers function (C(s)/R(s)).

  31. The forward-path gains: T1=G1(s)G2(s)G3(s)G4(s)G5(s) • The loop gains: • G2(s)H1(s) • G4(s)H2(s) • G7(s)H4(s) • G2(s)G3(s)G4(s)G5(s)G6(s) G7(s) G8(s) • The non-touching taken two at a time: • G2(s)H1(s) G4(s)H2(s) • G2(s)H1(s) G7(s)H4(s) • G4(s)H2(s) G7(s)H4(s)

  32. The non-touching taken three at a time: • G2(s)H1(s) G4(s)H2(s) G7(s)H4(s) • Compute : =1-[G2(s)H1(s)+ G4(s)H2(s)+ G7(s)H4(s)+ G2(s)G3(s)G4(s)G5(s)G6(s) G7(s) G8(s) ]+[G2(s)H1(s) G4(s)H2(s)+ G2(s)H1(s) G7(s)H4(s)+ G4(s)H2(s) G7(s)H4(s)]- [G2(s)H1(s) G4(s)H2(s) G7(s)H4(s)] • Compute k: 1=1- G7(s)H4(s) • Compute G(s):

  33. Cont’d…

  34. Cont’d…

More Related