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GATE EC 2019 Set 1 — Question 42

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MCQ+2 / -0.67MediumBlock Diagram ReductionSystem ModellingControl Systems

Control Systems → System Modelling → Block Diagram Reduction

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Question

The block diagram of a system is illustrated in the figure shown, where X(s)X(s) is the input and Y(s)Y(s) is the output. The transfer function H(s)=Y(s)X(s)H(s) = \frac{Y(s)}{X(s)} is
A block diagram showing an input X(s) entering a summing junction. The output of the junction goes to two parallel paths: one with gain 's' and another with gain '1/s'. These paths are summed at a second junction. The output of the second junction goes to an integrator '1/s' to produce Y(s). There are two negative feedback loops: one from Y(s) back to the first summing junction, and another from the output of the second summing junction back to the first summing junction.
In the diagram, the first summing junction is E=X−Z−YE = X - Z - Y, where ZZ is the output of the second summing junction (fed back from the top) and YY is the output of the final 1s\frac{1}{s} block (fed back from the bottom). EE feeds the parallel blocks ss and 1s\frac{1}{s}, whose outputs are added to give ZZ, and Y=1sZY = \frac{1}{s}Z.
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