Use block diagram reduction technique and obtain the following transfer functions for the system shown in Fig.
Question:
Use block diagram reduction technique and obtain the following transfer functions for the system shown in Fig. D3.3:
(i) \(\frac{\mathrm{C}(s)}{\mathrm{R}(s)}\)
(ii) \(\frac{\mathrm{C}(s)}{\mathrm{X}(s)}\)
(iii) \(\frac{\mathrm{C}(s)}{\mathrm{Y}(s)}\)
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Step by Step Answer:
To apply the block diagram reduction technique we analyze the flow of the signals through the systems blocks and summing points reducing the system step by step to obtain the desired transfer functions Stepbystep reduction for Transfer Function fracCsRs 1 Initial setup Based on your diagram we have G1s directly after the input Rs Then the output of G1s goes into G2s We can combine these two in series Gtextcombineds G1s cdot G2s 2 Feedback loops There are two feedback loops one with H1s enclosing G2s and the other one with H3s enclosing the whole system The first feedback loop can be simplified to a single block since it only affects the G2s block G2textclosedloops fracG2s1 H1s cdot G2s 3 Further reduction Combine the modified G2s block with the initial G1s block Gtextcombineds G1s cdot G2textclosedloops 4 This combined block then goes into G3s and we have the second feedback loop around the whole thing with H2s Then the final transfer function ...View the full answer
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