SECTION–A — Short Questions Testing Core Understanding of Machines & Control Systems (14 Marks)
Section–A contains seven 2-mark conceptual questions designed to test fundamental clarity regarding transformers, control systems, synchronous machines, and servo mechanisms. The opening question asks for the properties of an ideal transformer, requiring students to recall characteristics such as zero losses, infinite permeability, and perfect coupling.
The second question shifts into control theory by asking for the transfer function, along with meaning of poles and zeros, which form the backbone of system stability and dynamic behaviour. Students must then write the rules of block diagram reduction, a crucial method for simplifying complex control systems into manageable forms.
Another key concept tested is the difference between open-loop and closed-loop systems, checking whether students understand feedback mechanism and self-correction. The fifth question requires explaining the term synchronous condenser, a synchronous motor running without mechanical load to supply reactive power to the grid.
The sixth question asks for definitions of static and dynamic systems, focusing on time-dependent behaviour. The final question examines knowledge of AC servo motor features, such as high precision, quick response, and smooth acceleration.
SECTION–B — Analytical, Derivation-Based Questions on Machines & Controllers (21 Marks)
In Section–B, the student must attempt any three out of five 7-mark questions. These are deeper, derivation-oriented topics that evaluate understanding of electromechanical energy conversion and control theory.
One of the main questions asks for deriving the torque equation of a 3-phase induction motor, and then drawing the torque–slip curve, followed by identifying the condition for maximum torque using the standard induction motor equivalent circuit.
Another question demands deriving the EMF equation of a transformer and listing its losses — iron, copper, stray, and dielectric losses — highlighting how real transformers differ from ideal ones.
A comparison-based question contrasts synchronous motors with induction motors, testing understanding of starting methods, speed control, torque production, power factor, and construction differences.
The next question deals with slip in a 3-phase induction motor, requiring the mathematical expression and identification of slip at starting (s = 1) and at synchronous speed (s = 0).
The final option introduces control theory through elaborating PI and PD controllers, explaining how proportional action improves base response, integral action removes steady-state error, and derivative action predicts behaviour for dynamic improvement.
SECTION–C — Transfer Function of RC Network OR Mechanical System Modelling (7 Marks)
Section–C provides two choices. The first asks the student to derive the transfer function of an RC network, which requires forming input–output equations based on Kirchhoff’s laws and converting them into the Laplace domain.
The alternate question shifts to mechanical system modelling, asking students to draw the free-body diagram of a given mass-spring-damper arrangement and write its differential equation. This reinforces the concept of mechanical–electrical analogies used in control system representation.
SECTION–D — Second Order System Time Response OR Single-Phase Induction Motor (7 Marks)
This section examines either control system time response or rotating machine fundamentals.
The first option presents a second-order control system with transfer function
C(s)R(s)=25s2+6s+25\frac{C(s)}{R(s)}=\frac{25}{s^2+6s+25}R(s)C(s)=s2+6s+2525
Students must compute rise time, peak time, maximum overshoot, settling time, and also write the complete step response expression. This assesses understanding of damping ratio, natural frequency, standard response parameters, and Laplace inversion.
The alternative question asks for a detailed explanation of the single-phase induction motor, including its double-revolving field theory and construction, and then list two applications such as fans and domestic appliances.
SECTION–E — Speed Control of DC Motor OR Routh Stability Analysis (7 Marks)
Section–E provides students with two important engineering topics.
The first option asks for the speed control methods of DC motors, including armature voltage control, field flux control, and armature resistance control. Explanations must show how each method affects torque and operating region.
The alternate question involves Routh–Hurwitz Stability Criterion and requires constructing a Routh array for the given polynomial
s5+4s4+8s3+8s2+7s+4=0s^5+4s^4+8s^3+8s^2+7s+4=0s5+4s4+8s3+8s2+7s+4=0
and determining stability based on sign changes in the first column.
SECTION–F — Starting of Induction Motors OR Root Locus Plot (7 Marks)
The first option asks students to list the various starting methods of poly-phase induction motors — such as DOL starter, star-delta, auto-transformer starting, and rotor-resistance starting — and then describe any one method in detail.
The second option moves into classical control, asking students to sketch the root locus of the system with transfer function
G(s)=Ks(s+4)(s+5)G(s)=\frac{K}{s(s+4)(s+5)}G(s)=s(s+4)(s+5)K
as K varies from 0 to ∞. This evaluates understanding of asymptotes, breakaway points, and locus directions.
SECTION–G — Bode Plot OR Polar Plot Construction (7 Marks)
The final section focuses on frequency response analysis.
The first part requires constructing the bode plot for the unity-feedback system with
G(s)=1000s(s+1)(s+100)G(s)=\frac{1000}{s(s+1)(s+100)}G(s)=s(s+1)(s+100)1000
and determining phase margin and gain margin, fundamental indicators of system stability and robustness.
The alternative question asks for the polar plot of
G(s)=6(s+1)(s+2)G(s)=\frac{6}{(s+1)(s+2)}G(s)=(s+1)(s+2)6
which provides insight into system behaviour through magnitude and phase variations in the complex plane.
FINAL SUMMARY — Full Descriptive Overview of the REE-409 Paper
The Electrical Machines and Controls exam paper covers the entire spectrum of rotating machines, transformer theory, and control systems. Section–A evaluates core theoretical understanding of transformers, control fundamentals, synchronous machines, and servo motors. Section–B tests mathematical derivations for induction motors, transformers, slip, and controller design. Sections C–G move across RC transfer functions, mechanical system modelling, second-order time response, DC motor speed control, Routh stability, induction motor starting, root locus, bode plot, and polar plot.
