List of top Control Systems Questions on Lead and Lead‐Lag compensators asked in GATE EE

Consider a continuous-time signal \[ x(t) = -t^2 \left[ u(t+4) - u(t-4) \right] \] where \( u(t) \) is the continuous-time unit step function. Let \( \delta(t) \) be the continuous-time unit impulse function. The value of \[ \int_{-\infty}^{\infty} x(t) \delta(t+3) \, dt \text{ is:} \]

Consider a lead compensator of the form \[ K(s) = \frac{1 + \tfrac{s}{a}}{1 + \tfrac{s}{\beta a}}, \beta > 1, \, a > 0 \] The frequency at which this compensator produces maximum phase lead is \(4 \, \text{rad/s}\). At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of \(K(s)\), is \(6 \, \text{dB}\). The values of \(a, \beta\), respectively, are: