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The system represents a robotic arm actuated at the elbow joint. The overall system is represented as a block diagram below.
Procedure
To begin, we assumed that Gp(s) was equal to 1 and our gain, K, was also equal to 1. With this assumption, we found the transfer function to be:
OVERALL TRANSFER FUNCTION WHEN Gp(s)=1:
T = GpG1G2/[1+G1G2H]
0.3009 s^3 + 2.708 s^2 + 8.424 s + 6.017
----------------------------------------
s^4 + 12 s^3 + 52 s^2 + 86 s + 6
With the aid of Matlab, we then created a Root-locus plot to find the values of gain, K.
PLOT OF ROOT LOCUS FOR K>=0;
STEADY STATE ERROR:
We needed to select the input controller Gp so we could get a steady state error equal to zero for a step input so this required T(0) = 1...
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