Prepare for ISRO ICRB examinations with worked engineering solutions across Control Systems, Electrical Machines, Power Systems, Power Electronics, Signals & Systems, and Network Theory.
Marking scheme: +3.00 positive, -0.75 negative (ICRB Standard).
A linear time-invariant continuous dynamical system is governed by the state and input matrices:
$$\mathbf{A} = \begin{bmatrix} 0 & 1 \\ -2 & -3 \end{bmatrix}, \quad \mathbf{B} = \begin{bmatrix} 0 \\ 1 \end{bmatrix}$$What is the rank of the controllability matrix $\mathcal{C} = \begin{bmatrix} \mathbf{B} & \mathbf{AB} \end{bmatrix}$, and is the system completely state controllable?
A $3\text{-phase}$, star-connected non-salient pole synchronous generator with negligible armature resistance ($R_a \approx 0$) is connected to an infinite bus of voltage $V = 1.0\text{ p.u.}$. The synchronous reactance is $X_s = 0.8\text{ p.u.}$ and the excitation EMF is $E = 1.2\text{ p.u.}$. What is the steady-state maximum power output ($P_{\max}$) per phase that can be delivered before synchronism is lost?
Neglecting magnetic saturation, if the armature current taken by a DC series motor is increased from $10\text{ A}$ to $12\text{ A}$, the percentage increase in developed torque will be:
In a DC chopper circuit operating from a DC source, an SCR (Silicon Controlled Rectifier) is switched OFF at regular intervals by employing: