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Fundamentals of Control Systems Technology for Engineers

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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.

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Fundamentals of Control Systems Technology for Engineers

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  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…

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