LECTURE TWO BLOCK DIAGRAM REDUCTION
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1 3rd Yearomputer ommunication EngineeringU ontrol Theory LETUE TWO BLOK DIAGAM EDUTION Block diagram is a pictorial representation of a control system showing interrelation between the transfer function of various components. The block diagram is obtained after obtaining the differential and transfer function of all components of a control system. Figure 2.1 shows an element of the block diagram. The arrowhead pointing toward the block indicates the input and the one pointing away from the block indicates the output. Figure 2.1 Single block diagram system may be written as; ( ) ( ) ( ) After obtaining the block diagram for each and every components, all blocks are combined to obtain a complete representation. It is then reduced using some rules to a more simple form with the help of block diagram algebra. Dr. Mohammed Saheb Khesbak Page 7
2 3rd Yearomputer ommunication EngineeringU ontrol Theory 2.1 ules for Block Diagram eduction: Now the following block diagram algebra is often used to describe rules for reduction: ule 1: Blocks in cascade Two or more blocks in cascade may be combined in one block. G 1 (s) G 2 (s) G 1 (s) G 2 (s) ule 2: ombining Blocks in Parallel Two blocks or more in parallel may be combined in one block as the algebraic sum. G 2 (s) G 1 (s) G 1 (s)g 2 (s) Dr. Mohammed Saheb Khesbak Page 8
3 3rd Yearomputer ommunication EngineeringU ontrol Theory ule 3: Eliminating a Feedback Loop Each feedback combination may be replaced by one block with its corresponding beedback equation. H(s) 1 H(s) ule 4: Moving a Summing Point Beyond a Block ule 5: Moving a Summing Point Ahead of a Block 1 Dr. Mohammed Saheb Khesbak Page 9
4 3rd Yearomputer ommunication EngineeringU ontrol Theory ule 6: Moving a Take off Point Beyond a Block X (s) X (s) 1 ule 7: Moving a Take off Point Ahead of a Block Y (s) Y (s) ule 8: earranging Summing point X3(s) X3(s) X3(s) Dr. Mohammed Saheb Khesbak Page 10
5 3rd Yearomputer ommunication EngineeringU ontrol Theory ule 9: Moving a Takeoff point beyond a Summing point X (s) Z(s) Z(s) X (s) Z(s) Example 2.1: Obtain the transfer function of the block diagram control system using block diagram reduction method. Dr. Mohammed Saheb Khesbak Page 11
6 3rd Yearomputer ommunication EngineeringU ontrol Theory The solution of this type of problems will be based on detecting the combinations that match one or more of the rules previously explained. ( ) 1 ( ) 1 ( ) 1 ( ) ( ) ( ) 1 ( ) ( ) 1 ( ) ( ) Dr. Mohammed Saheb Khesbak Page 12
7 3rd Yearomputer ommunication EngineeringU ontrol Theory Example 2.2: Obtain the transfer function of the block diagram control system using block diagram reduction method. Using the previously explained rules: 1 Dr. Mohammed Saheb Khesbak Page 13
8 3rd Yearomputer ommunication EngineeringU ontrol Theory Dr. Mohammed Saheb Khesbak Page 14
9 3rd Yearomputer ommunication EngineeringU ontrol Theory 1 Exercises: Obtain the transfer function of the following block diagram control systems using block diagram reduction method. 1 H3 2 H3 Dr. Mohammed Saheb Khesbak Page 15
10 3rd Yearomputer ommunication EngineeringU ontrol Theory 3 G5 4 G5 G6 Dr. Mohammed Saheb Khesbak Page 16
11 3rd Yearomputer ommunication EngineeringU ontrol Theory 5 6 G5 G6 G7 H8 7 Dr. Mohammed Saheb Khesbak Page 17
12 3rd Yearomputer ommunication EngineeringU ontrol Theory 8 H3 9 H3 10 Dr. Mohammed Saheb Khesbak Page 18
Fourier Series : Dr. Mohammed Saheb Khesbak Page 34
Fourier Series : Dr. Mohammed Saheb Khesbak Page 34 Dr. Mohammed Saheb Khesbak Page 35 Example 1: Dr. Mohammed Saheb Khesbak Page 36 Dr. Mohammed Saheb Khesbak Page 37 Dr. Mohammed Saheb Khesbak Page 38
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