Discover the Transfer Functions of Block Diagrams for Optimal Performance

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To determine the transfer functions of the specified block diagrams, one must analyze each block's input-output relationship. For the first diagram, the transfer function is derived from the ratio of the output to the input, resulting in [K(s+a)/(s+1)] leading to [1/s(s+2)(s+3)]. The second diagram combines the components to yield a transfer function of [4+(40/s)] resulting in [s^2/(s+100)(4s^2+5s+4)]. The third diagram's transfer function is derived similarly, where [a+(B/s)] leads to [1/(s+1)]. Understanding the multiplication of cascaded transfer functions is crucial for optimal performance in control systems.
kwbake01
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How do I get the transfer functions of the following block diagrams

a) [K(s+a)/(s+1)]--->[1/s(s+2)(s+3)]
...BLOCK 1....BLOCK 2

b) [4+(40/s)]--->[s^2/(s+100)(4s^2+5s+4)]
...BLOCK 1.....BLOCK 2

c) [a+(B/s)]---->[1/(s+1)]
...BLOCK 1...BLOCK 2
 
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Cascaded transfer functions can be combined through multiplication.
 

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