All the problems in this set are represented with the following diagram, without considering the measurement noise (that is N(s) = 0).
1. Consider the problem of controlling the position of a system with loop transfer function G(s) = 1/s(s+5) with a proportional controller Gc(s) = K. The transfer function of the sensor is H(s) = 1/s/2+1
2. Consider the problem of controlling an unstable system, whose transfer function is obtained as G(s) = 0.1/s2+2s-8. A controller in the form of Gc(s) = K s+6/s+10 with a unity feedback H(s) =1 has been selected for the problem. One of the design objectives is to maintain the output y(t) ≈ 0 when r(t) = 0 in the presence of disturbance. The design specifications, based on a step disturbance, are as follows:
Select the value of K (K > 0) to meet all the specifications and describe your approach used in your selection process. Plot the results based on your final selection of K value.
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