Control Systems & Signal Processing
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📘 Comprehensive Syllabus & Examination Guide
Control Systems & Signal Processing
Official curriculum roadmap, subject/topic distribution, negative marking rules, pacing guidelines, and solved sample questions.
🎯 Mapped Subjects & Topic Question Distribution
Total Question Pool
100%
35 MCQs
Combined Active Syllabus
Control Systems & Signal Processing
35 MCQs
Topic Pool
📊 Question Pool Structure
35 MCQs across fundamental, intermediate, and advanced concept tiers.
⚡ Recommended Pacing
45 to 60 seconds per MCQ. Flag complex problems and preserve 10 minutes for final revision.
⚖️ Scoring & Negative Marking
+1 mark per correct answer. In competitive tests with negative marking, -0.25 applies for incorrect guesses.
💡 Strategic Preparation & Exam Hall Guidelines
To maximize your score on Control Systems & Signal Processing, candidates are advised to follow a structured three-pass approach. In the First Pass, solve all direct recall and formula-based questions within 30 seconds each to secure foundational marks. In the Second Pass, tackle multi-step analytical and quantitative reasoning problems. In the Third Pass, review marked questions and verify calculations.
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📝 Pre-Rendered Solved Sample Questions & Detailed Solutions
Review the solved problems below to understand question phrasing, answer choices, and step-by-step solution logic prior to starting the full interactive practice drill:
Sample Question 1
Control Systems & Signal Processing
Easy • Electronics Engineering
A linear time-invariant (LTI) continuous-time system is BIBO (Bounded-Input Bounded-Output) stable if and only if:
A
All closed-loop poles lie strictly in the left half of the s-plane (LHP)
B
All poles lie on the imaginary axis
C
All zeros lie in the right half of the s-plane
D
The system impulse response diverges to infinity as t approaches infinity
✓ Correct Answer: A - All closed-loop poles lie strictly in the left half of the s-plane (LHP)
📖 Step-by-Step Solution & Conceptual Rationale:
For an LTI continuous system to be BIBO stable, all poles of the transfer function must have negative real parts, meaning they must lie strictly in the open left-half of the s-plane.
Sample Question 2
Control Systems & Signal Processing
Easy • Electronics Engineering
In a discrete-time LTI system with transfer function H(z), BIBO stability requires that all system poles lie:
A
Strictly inside the unit circle (|z| < 1) in the z-plane
B
Strictly outside the unit circle (|z| > 1)
C
On the real axis only
D
Along the imaginary axis
✓ Correct Answer: A - Strictly inside the unit circle (|z| < 1) in the z-plane
📖 Step-by-Step Solution & Conceptual Rationale:
In discrete-time systems, the stable region in the s-plane (Re(s) < 0) maps into the interior of the unit circle in the z-plane (|z| < 1).
Sample Question 3
Control Systems & Signal Processing
Medium • Electronics Engineering
In the Routh-Hurwitz stability criterion, the number of sign changes in the first column of the Routh array equals:
A
The number of closed-loop poles in the left-half s-plane
B
The number of closed-loop poles with positive real parts (in the right-half s-plane)
C
The total number of system zeros
D
The system damping ratio
✓ Correct Answer: B - The number of closed-loop poles with positive real parts (in the right-half s-plane)
📖 Step-by-Step Solution & Conceptual Rationale:
According to the Routh-Hurwitz theorem, the number of roots of the characteristic equation with positive real parts (RHP poles) is exactly equal to the number of sign changes in the first column of the Routh array.
Sample Question 4
Control Systems & Signal Processing
Easy • Electronics Engineering
For a standard second-order system with transfer function G(s) = omega_n^2 / (s^2 + 2*zeta*omega_n*s + omega_n^2), what is the system response when damping ratio zeta = 0?
A
Overdamped (non-oscillatory)
B
Critically damped
C
Undamped with sustained sinusoidal oscillations at frequency omega_n
D
Exponentially decaying with zero overshoot
✓ Correct Answer: C - Undamped with sustained sinusoidal oscillations at frequency omega_n
📖 Step-by-Step Solution & Conceptual Rationale:
When zeta = 0, the roots are s = +-j*omega_n (purely imaginary), causing undamped, perpetual sinusoidal oscillation at the natural frequency omega_n.
Sample Question 5
Control Systems & Signal Processing
Easy • Electronics Engineering
A standard second-order control system is critically damped when the damping ratio zeta is equal to:
A
zeta = 0
B
0 < zeta < 1
C
zeta = 1
D
zeta > 1
✓ Correct Answer: C - zeta = 1
📖 Step-by-Step Solution & Conceptual Rationale:
When zeta = 1, the system is critically damped: two repeated real roots at s = -omega_n, giving the fastest response possible without overshoot.
Sample Question 6
Control Systems & Signal Processing
Medium • Electronics Engineering
What is the steady-state error of a Type-1 control system subjected to a unit step input?
A
Zero
B
Constant finite value 1 / (1 + Kp)
C
Infinity
D
Undetermined
✓ Correct Answer: A - Zero
📖 Step-by-Step Solution & Conceptual Rationale:
A Type-1 system has one integrator (pole at origin) in open loop, giving an infinite position error constant (Kp = infinity). Therefore, ess = 1 / (1 + Kp) = 0.
Sample Question 7
Control Systems & Signal Processing
Medium • Electronics Engineering
In a Bode plot, Phase Margin (PM) is defined as:
A
180 degrees + Phase angle at the gain crossover frequency (where |G(j*omega)| = 1)
B
Gain at the phase crossover frequency
C
Phase angle at omega = 0
D
180 degrees - Gain crossover frequency
✓ Correct Answer: A - 180 degrees + Phase angle at the gain crossover frequency (where |G(j*omega)| = 1)
📖 Step-by-Step Solution & Conceptual Rationale:
Phase Margin PM = 180° + phi_gc, where phi_gc is the phase of the open-loop frequency response at the gain crossover frequency (where |G(j*omega)| = 1 or 0 dB).
Sample Question 8
Control Systems & Signal Processing
Medium • Electronics Engineering
Gain Margin (GM) in decibels is measured at which frequency on a Bode diagram?
A
At the gain crossover frequency
B
At the phase crossover frequency (where phase angle is -180 degrees)
C
At resonance peak frequency
D
At the origin (omega = 0)
✓ Correct Answer: B - At the phase crossover frequency (where phase angle is -180 degrees)
📖 Step-by-Step Solution & Conceptual Rationale:
Gain Margin GM = -20 * log10|G(j*omega_pc)|, measured at the phase crossover frequency omega_pc where the phase crosses -180 degrees.
Sample Question 9
Control Systems & Signal Processing
Hard • Electronics Engineering
According to the Nyquist stability criterion, the number of unstable closed-loop poles Z in the RHP is given by:
A
Z = N + P (where N is clockwise encirclements of -1+j0, P is open-loop RHP poles)
B
Z = N - P
C
Z = P - N
D
Z = N * P
✓ Correct Answer: A - Z = N + P (where N is clockwise encirclements of -1+j0, P is open-loop RHP poles)
📖 Step-by-Step Solution & Conceptual Rationale:
Nyquist criterion: N = Z - P, where N is the number of clockwise encirclements of the critical point (-1+j0). Therefore, the number of unstable closed-loop poles is Z = N + P. For stability, Z must be 0, requiring N = -P (P counter-clockwise encirclements).
Sample Question 10
Control Systems & Signal Processing
Medium • Electronics Engineering
A lead compensator is primarily used in control system design to:
A
Improve steady-state accuracy by adding open-loop gain at low frequencies
B
Improve transient response, increase phase margin, and enhance system stability/speed
C
Filter out high-frequency sensor noise
D
Eliminate DC offset voltage
✓ Correct Answer: B - Improve transient response, increase phase margin, and enhance system stability/speed
📖 Step-by-Step Solution & Conceptual Rationale:
A lead compensator adds positive phase (lead angle) near the gain crossover frequency, increasing the phase margin and bandwidth, which speeds up transient response and improves stability.
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