How to Simplify a Block Diagram to Obtain Y/R?

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SUMMARY

The discussion focuses on simplifying a block diagram to derive the expression for Y/R. The feedback loop in the bottom right is identified as 1/(s+a1), and the left summation combines b3R and a3Y, resulting in the equation (1/s)(b3R + a3Y). Participants are encouraged to trace signals R and Y to complete the expression leading to Y. The goal is to establish a clear relationship between Y and R through systematic analysis of the block diagram.

PREREQUISITES
  • Understanding of control systems and block diagram representation
  • Familiarity with feedback loops in system dynamics
  • Knowledge of signal flow and summation in control theory
  • Proficiency in Laplace transforms and their application in system analysis
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  • Study the principles of block diagram reduction techniques
  • Learn about signal flow graphs and their applications in control systems
  • Explore the concept of transfer functions in system dynamics
  • Investigate the use of MATLAB for simulating block diagrams and analyzing feedback systems
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Control system engineers, students studying system dynamics, and anyone involved in the design and analysis of feedback control systems will benefit from this discussion.

magnifik
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I am having trouble trying to obtain Y/R from the block diagram below:
xf56cz.png


the only thing i understand so far is that the bottom right loop is a feedback loop and can be simplified to 1/(s+a1). i know b1s can be obtained from the right loop, but i am having trouble getting to that point. i know it has to do with moving the summer
 
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Hi magnifik! :smile:

Trace the signals R and Y and construct an equation from them.

For instance, the left summation sums b3R and a3Y, which is then multiplied by 1/s.
This yields:
$$\frac 1 s (b_3 R + a_3 Y)$$

Can you complete the expression tracing it up to the right side, where it must be equal to Y?
 

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