GATE EC 2014 Question Paper (15-Feb-2014) (Shift 1)

Consider the state – space model

≤ft[ {*20c {x_1}\\ {x_2}\\ {x_3} } ] = ≤ft[ {*20c - 1&1&0\\ 0& - 1&0\\ 0&0& - 2 } ]≤ft[ {*20c x_1\\ x_2\\ x_3 } ] + ≤ft[ {*20c 0\\ 4\\ 0 } ]u

y = ≤ft[ {*20c 1&1&1 } ]≤ft[ {*20c x_1\\ x_2\\ x_3 } ]

System is

Phase margin in degree of $G\left(s\right)=\frac{10}{\left(s+0.1\right)\left(s+1\right)\left(s+10\right)}$ Using asymptotic Bode plot is _____

For the following system $G\left(s\right)=\frac{1}{\left(s+1\right)\left(s+2\right)}$

The 2% settling time of the step response is required to be less than 2 sec.



Which one the following compensator C(s) can achieve this

Let X be a real-valued random variable with E[X] and E[X²] denoting the mean values of X and X², respectively. The relation which always holds is

Consider a random process X(𝑡) = √2 sin(2𝜋t + 𝜑), where the random phase 𝜑 is uniformly distributed in the interval [0,2𝜋]. The auto-correlation R[𝑡₁ , 𝑡₂] is