# Inverse Nichols Chart

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Question 4:

a) Given P = [s/(-100) + 1]/[(s/4)^2 + 1.4(s/4) + 1], use the Inverse Nichols Chart to design a simple G(s) to achieve the following specifications. Show all design steps and sketch your final loop transfer function on the inverse Nichols Chart.

i) Zero steady state error to a step output disturbance.

ii) |1/(1 + L)| <= -15 dB, w <= 0.3 rad/s

iii) |1/(1 + L)| <= 3 dB, for all w.

b) Using the inverse Nichols chart of the final L(jw) from Question 4a, draw a Bode magnitude plot of the achieved |1/(1+L)|.

c) i) What is the amplitude of the output if there is a sinusoidal output disturbance signal with amplitude 0.5 and frequency 0.3 rad/s?

ii) What is the amplitude of the output if there is a sinusoidal output disturbance signal with amplitude 0.5 and frequency 1 rad/s?

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Given , a proportional and integral (PI) controller G(s) = is to be designed to achieve the specifications.

Solution

and .

Plot and in the Inverse Nichols Chart (A)

a)

Given ,

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