Match the transfer functions of the second-order systems with the nature of the systems given below. P: \(\frac{{15}}{{{s^2} + 5s + 15}}\) Q: \(\frac{{25}}{{{s^2} + 10s + 25}}\) R: \(\frac{{35}}{{{s^2} + 18s + 35}}\) I: Overdamped II: Critically damped III: UnderdampedTransfer functions Nature of system
P-III, Q-II, R-I
Compare \(s^2+2\zeta\omega_ns+\omega_n^2\). P has \(\zeta=5/(2\sqrt{15})<1\) and is underdamped. Q has ζ = 10/(2×5) = 1 and is critically damped. R has \(\zeta=18/(2\sqrt{35})>1\) and is overdamped. Thus P–III, Q–II, R–I.
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:
