The transfer function of a first-order controller is given as $${G_c}(s) = {{K\left( {s + a} \right)} \over {s + b}}$$

where k, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is

The position control of a DC servo-motor is given in the figure. The values of the parameters are
K_t=1 N-m/A, R_a=$$1\Omega ,$$ L_a=0.1H,
J=5kg-m², B=1 N-m/(rad/sec) and K_b=1V/(rad/sec).
The steady-state position response (in radians) due to unit impulse disturbance torque T_d is ____.

A network is described by the state model as $$$\eqalign{ & {\mathop x\limits^ \bullet _1} = 2{x_1} - {x_2} + 3u, \cr & \mathop {{x_2}}\limits^ \bullet = - 4{x_2} - u, \cr & y = 3{x_1} - 2{x_2} \cr} $$$

the transfer function H(s)$$\left[ { = {{Y\left( s \right)} \over {U\left( s \right)}}} \right]is$$

In the circuit shown, diodes $${D_1}$$ ,$${D_2}$$ and $${D_3}$$ are ideal, and the inputs $${E_1}$$ , $${E_2}$$ and $${E_3}$$ are “0 V” for logic ‘0’ and “10 V” for logic ‘1’. What logic gate does the circuit represent?