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Block diagram reduction: Problems
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Questions on Block Diagram Reduction

Anil Pal
PhD Research Scholar in Control Systems at IIT-BHU l M.Tech in Control Systems from IIT-BHU l B.E. in E&TC from BIT,Durg l

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1. Basics of Control Systems 9.Block Diagram Reduction: Problems Anil Kumar Pal Anil Kumar Pal (IT-BHU) Basics of Control Systems

2. About Me o Currently pursuing Ph.D. in Control Systems(Deptt. of Electrical Engg.) from IIT-BHU o Teaching experience of 5 years o Qualified gate in 2011,2012,2013,2015,2016 and 2017 o Interest: Mathematics, Control Theory Anil Kumar Pal o B.E. in Electronics & TelecommunicationPassion: Teaching and Learning from Bhilai Institute of Technology,Durg in 2008 o Believe that" Not only good teachers make good students but better students make better teacher" o M.Tech in Control Systems(Deptt. of Electrical Engg.) from IIT-BHU in 2013 Anil Kumar Pal (IT-BHU) Basics of Control Systems 2 16

3. For Whom ?? o Gate/IES Aspirants of EE, ECE and Instrumentation. o B.Tech students of EE,ECE,Instrumentation and Mechanical o Research students of EE,ECE and Interdisciplinary streams. o Students doing masters in Control Systems. Anil Kumar Pal (IT-BHU) Basics of Control Systems 3 16

4. Detenmine Tran 00 C/, G3 R + G1 G2 Fig. 3.2.1. Block diagram for example 3.2.1. Solution. Shift the take off point after block G2 to a position before block G2 R + G2 Anil Kumar Pal (IT-BHU) Basics of Control Systems 4 16

5. R + 2 93 G2H, Fig. 3.2.1. (b) Block diagram reduction of system in Fig.3.2.1 (a) Eliminate the summing point after block G2 Shift the take off point before block (G2+G3) to a position after block (G+G3) G2H1 Anil Kumar Pal (IT-BHU) Basics of Control Systems 5 16

6. 1G2 G + (G2+ G3) R + G2H1 Fig. 3.2.1 (d) Block diagram reduction of system in Fig. 3.2.1 (c). Anil Kumar Pal (IT-BHU) Basics of Control Systems 6 16

7. Eliminate the summing point before block (G2+G) According to Fig. 3.2.1 (d) the overall transfer function determined below G1 (G2 +G3) 1G2+Ga G,Q,-GG, Ans. 12:403:-01 06 10 Anil Kumar Pal (IT-BHU) Basics of Control Systems 7 16

8. Example 3.2.2. Reduce the block diagram shown in Fig. 3.2.2 into (G) a form having one block in the forward path and one in feedback path ( ) single block representation form. G1 H1 Fig. 3.2.2. Block diagram for example 3.2.2. Anil Kumar Pal (IT-BHU) Basics of Control Systems 8 16

9. Solution. Shift the summing point before block Gi to a position after block G 3 Fig. 3.2.2 (a) Block diagram reduction of system in Fig. 3.2.2 Interchange consecutive summing points after block G1 G1 G3 H1 Anil Kumar Pal (IT-BHU) Basics of Control Systems 9 16

10. Eliminate summing point after block G1, GH1 Fig. 3.22 (c)Block diagram reduction of system in Fig. 3.2.2(b) 10 16 Basics of Control Systems Anil Kumar Pal (IT-BHU)

11. The overall transfer function is determined below G+G2)G G, H According to equation (1) the single block diagram representation is shown in Fig. 3.2.2 (e). Ans. (i) Anil Kumar Pal (IT-BHU) Basics of Control Systems 12 16

12. Fig. 3.2.6. (a) Block diagram of Fig. 3.2.6 redrawn. Solution. The block diagram of Fig. 3.2.6 can be redrawn as shown in Fig. 3.2.6 (a) 1+G2H Eliminate two summing points According to Fig. 3.2.6 (b) the overall Fig. 3.2.6 (b) Block diagram reduction of system in Fig. 3.2.6 (a). transfer function is determined below Ans. Anil Kumar Pal (IT-BHU) Basics of Control Systems 14 16