A second-order system with a constant numerator has damping ratio 0.5, undamped natural frequency 10 rad/s, and final output 1.02 for a unit-step input under zero initial conditions. What is its transfer function?
\(\frac{{102}}{{{s^2} + 10s + 100}}\)
The denominator is \(s^2+2(0.5)(10)s+10^2=s^2+10s+100\). Unit-step final value equals DC gain, so the numerator must be 1.02×100 = 102. Thus \(G(s)=102/(s^2+10s+100)\).
Important Questions from Time Response Analysis
Which of the following is correct for over-damped and under-damped system, respectively?
What will be the time response expression for a standard first order system having unit step function \(\frac{1}{s}\) as the input
A second order system has natural frequency 3rad/sec and unity damping ratio. Identify its transfer function.
Statement (I): All the systems which exhibit overshoot in transient response will also exhibit resonance peak in frequency response.
Statement (II): A large resonance peak in frequency response corresponds to a large overshoot in transient response.
The steady state error of a control system can be minimized by:
