Asked Dec 17, 2019

1. Write down a transfer function of a stable system for which pure proportional feedback could drive the system unstable.


answer and explanation please!


Expert Answer

Step 1

A system is said to be a stable system if the poles of the system lie on the negative real axis.

Let’s write the transfer system for a stable system. All the poles of this system will lie on the distinct points of the negative real axis. Such systems are stable in nature because they give a decaying oscillating signal in the output.


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G(s)=- (s + 2)(s+1)(s+3)

Step 2

Design a naegative feedback loop for the system and with the pure proportional feedback Kp as shown in the figure.


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Ru) es) Ge) Kp Gu) си) 1 + Kplne) RIS)

Step 3

The characteristic equation of th...


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1+G(s)H(s)=(s+ 2)(s +1)(s+3)+K, = s° + 6s? +11s +(6+K,) Construct the Routh array as shown below. 11 (6+Kp)


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