Block diagram
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This document discusses block diagram representation in control system engineering. It introduces block diagrams as a pictorial representation of a system using blocks and arrows to show inputs, outputs, and signal flow. Examples are provided to illustrate how to represent mathematical equations using block diagrams and techniques for reducing complex block diagrams, such as combining blocks in series or parallel and moving summing and pickoff points. The goal of reduction is to transform the block diagram into canonical form to determine the system's characteristic equation.
Block diagram
- 1. Control System Engineering Kuntumal Sagar M. B.TECH (E.E) UID-U41000000484 [email protected] Mno. +917600941450 TOPIC BLOCK DIAGRAM REPRESENTATION
- 2. Introduction • A Block Diagram is a shorthand pictorial representation of the cause-and-effect relationship of a system. • The interior of the rectangle representing the block usually contains a description of or the name of the element, or the symbol for the mathematical operation to be performed on the input to yield the output. • The arrows represent the direction of information or signal flow. dt d x y
- 3. Introduction • The output is the algebraic sum of the inputs. • Any number of inputs may enter a summing point. • Some books put a cross in the circle.
- 4. Introduction • Take Off point permits the signal to proceed unaltered along several different paths to several destinations.
- 5. Example-1 • Consider the following equations in which x1, x2, x3, are variables, and a1, a2 are general coefficients or mathematical operators. 522113 xaxax
- 6. Example-1 • Consider the following equations in which x1, x2, x3, are variables, and a1, a2 are general coefficients or mathematical operators. 522113 xaxax
- 7. Canonical Form of A Feedback Control System
- 8. Characteristic Equation • The control ratio is the closed loop transfer function of the system. • The denominator of closed loop transfer function determines the characteristic equation of the system. • Which is usually determined as: )()( )( )( )( sHsG sG sR sC 1 01 )()( sHsG
- 9. Example-4 1. Open loop transfer function 2. Feed Forward Transfer function 3. control ratio 4. feedback ratio 5. error ratio 6. closed loop transfer function 7. characteristic equation 8. closed loop poles and zeros if K=10. )()( )( )( sHsG sE sB )( )( )( sG sE sC )()( )( )( )( sHsG sG sR sC 1 )()( )()( )( )( sHsG sHsG sR sB 1 )()()( )( sHsGsR sE 1 1 )()( )( )( )( sHsG sG sR sC 1 01 )()( sHsG )(sG )(sH
- 10. Reduction techniques 2G1G 21GG 1. Combining blocks in cascade 1G 2G 21 GG 2. Combining blocks in parallel
- 11. Example-5: Reduce the Block Diagram to Canonical Form.
- 12. Example-5: Continue. However in this example step-4 does not apply. However in this example step-6 does not apply.
- 13. Reduction techniques 3. Moving a summing point behind a block G G G
- 14. 5. Moving a pickoff point ahead of a block G G G G G 1 G 3. Moving a summing point ahead of a block G G G 1 4. Moving a pickoff point behind a block
- 15. 6. Eliminating a feedback loop G H GH G 1 7. Swap with two neighboring summing points A B AB G 1H G G 1
- 17. Example-8 R _+ _ + 1G 2G 3G 1H 1 2 G H + + C
- 20. block diagram: reduction example R _+ _ + 121 21 1 HGG GG 3G 1 2 G H C
- 21. block diagram: reduction example R _+ _ + 121 321 1 HGG GGG 1 2 G H C
- 22. block diagram: reduction example R _+ 232121 321 1 HGGHGG GGG C