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ENEE 252Bachelor in Mechanical Engineering · Semester 63 Papers Available

Control System

Past examination question papers and complete curriculum syllabus for Control System (ENEE 252), Bachelor in Mechanical Engineering Semester 6 under Institute of Engineering (IOE), Tribhuvan University.

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Note: This question paper file (3rd sem) was archived from an IOE exam session for the common Control System curriculum.

3rd-sem_Control System.pdf

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Most Frequently Asked Questions

Top recurring IOE board exam questions for Control System with verified mark schemes, formula notation, and recurrence frequency.

Showing 30 of 30 top repeated questions

Control System Background

1 Question
#1Repeated 5 Times[8 Marks]Control System Background
What is control system? "When feedback is added on a control system, its response is faster." Illustrate this statement mathematically.
Appeared in:2083 Baishakh2082 Shrawan2082 Baishakh2078 Bhadra2076 Chaitra

Component Modeling

2 Questions
#1Repeated 4 Times[8 Marks]Component Modeling
Find the transfer function $\frac{X_2(s)}{F(s)}$ of the mechanical system by constructing the free body diagram and writing necessary mathematical equations. Also develop the Force-Voltage ($F-V$) and Force-Current ($F-I$) analogous circuits.
Appeared in:2082 Shrawan2082 Baishakh2081 Bhadra2078 Kartik
#2Repeated 2 Times[4 Marks]Component Modeling
A servomechanism is designed to keep a radar antenna pointed at a flying aeroplane. If the aeroplane is flying with a velocity of $600\text{ km/hr}$ at a range of $2\text{ km}$ and the maximum tracking error is to be within $0.1^\circ$, determine the required velocity error coefficient.
Appeared in:2083 Baishakh2078 Bhadra

System Transfer Function and Responses

5 Questions
#1Repeated 3 Times[8 Marks]System Transfer Function and Responses
Explain Mason's Gain Formula $T = \frac{1}{\Delta}\sum P_k \Delta_k$. For a given signal flow graph with multiple forward paths and feedback loops, determine the overall closed-loop transfer function $\frac{C(s)}{R(s)}$.
Appeared in:2083 Baishakh2082 Shrawan2080 Chaitra
#2Repeated 3 Times[8 Marks]System Transfer Function and Responses
Derive the unit step response of a standard second-order underdamped control system $c(t) = 1 - \frac{e^{-\zeta \omega_n t}}{\sqrt{1 - \zeta^2}}\sin(\omega_d t + \phi)$. Formulate expressions for Rise Time ($t_r$), Peak Time ($t_p$), Maximum Percentage Overshoot ($M_p$), and Settling Time ($t_s$).
Appeared in:2082 Shrawan2081 Bhadra2079 Chaitra
#3Repeated 2 Times[8 Marks]System Transfer Function and Responses
The open loop transfer function of a unity feedback system is given by $G(s) = \frac{K}{s(1+sT)}$, where $K$ is gain constant and $T$ is time constant. With the gain multiplied by a factor $K_1$, the maximum overshoot of the system is increased from $25\%$ to $50\%$. Determine $K_1$.
Appeared in:2081 Bhadra2077 Magh
#4Repeated 2 Times[4 Marks]System Transfer Function and Responses
A system has $25\%$ overshoot and settling time of $6$ seconds, for a unit step input. Determine the transfer function and calculate peak time. Assume $t_s$ as $2\%$.
Appeared in:2083 Baishakh2078 Bhadra
#5Repeated 2 Times[6 Marks]System Transfer Function and Responses
The open loop transfer function of a unity feedback system is given by $G(s) = \frac{108}{s^2(s+1)(s+2)(s+3)}$. Find the static error coefficients and steady state error of the system when subjected to input given by $r(t) = 2 + 5t + 8t^2$.
Appeared in:2082 Shrawan2079 Chaitra

Stability

4 Questions
#1Repeated 3 Times[8 Marks]Stability
State the Routh-Hurwitz Stability Criterion. Determine the stability of a closed-loop system having characteristic equation $s^6 + 2s^5 + 8s^4 + 12s^3 + 20s^2 + 16s + 16 = 0$. Explain how special cases (first column element zero, entire row zero) are handled using auxiliary polynomials.
Appeared in:2083 Baishakh2081 Bhadra2078 Kartik
#2Repeated 2 Times[8 Marks]Stability
What is relative and absolute stability? Check the stability of system with characteristic equation: $s^5 + s^4 + 2s^3 + 2s^2 + 3s + 5 = 0$ using R-H criteria.
Appeared in:2081 Bhadra2078 Bhadra
#3Repeated 2 Times[6 Marks]Stability
Construct Routh array and determine the stability of the system whose characteristic equation is $s^6 + 3s^5 + 4s^4 + 6s^3 + 5s^2 + 3s + 2 = 0$. Comment on the location of the roots of characteristic equation.
Appeared in:2082 Shrawan2081 Baishakh
#4Repeated 2 Times[8 Marks]Stability
The characteristic equation of a feedback control system is $s^4 + 20s^3 + 15s^2 + 2s + K = 0$. (i) Determine the range of $K$ for the system to be stable. (ii) Can the system be marginally stable? If so, find the required value of $K$ and the frequency of sustained oscillation.
Appeared in:2082 Baishakh2078 Kartik

Root Locus Technique

3 Questions
#1Repeated 3 Times[10 Marks]Root Locus Technique
The open loop transfer function of a control system is given by $G(s)H(s) = \frac{K}{s(s+4)(s^2+4s+20)}$. Sketch the root locus for $0 \le K < \infty$ and determine the breakaway point, the angle of departure from complex poles and the stability conditions.
Appeared in:2083 Baishakh2078 Kartik2076 Chaitra
#2Repeated 3 Times[10 Marks]Root Locus Technique
For a unity feedback system, the open loop transfer function is given by $G(s) = \frac{K}{s(s+1)(s+2)}$. Sketch the root locus for the system when $K$ is varied from $0$ to $\infty$. Indicate frequency of sustained oscillation at marginal stability and gain at critical damping.
Appeared in:2082 Baishakh2080 Chaitra2078 Bhadra
#3Repeated 3 Times[8 Marks]Root Locus Technique
Explain the construction rules of the Root Locus: real-axis segments, asymptotes centroid $\sigma_a = \frac{\sum P - \sum Z}{n - m}$, angle $\theta_a = \frac{(2q+1)180^\circ}{n - m}$, breakaway/break-in points, and $j\omega$-axis crossing. Sketch the root locus for $G(s)H(s) = \frac{K}{s(s+2)(s+4)}$.
Appeared in:2082 Shrawan2080 Chaitra2078 Bhadra

Frequency Response Techniques

5 Questions
#1Repeated 3 Times[8 Marks]Frequency Response Techniques
The open loop transfer function of a system is $G(s)H(s) = \frac{1}{s(1+s)(1+2s)}$. Sketch polar plot and determine the stability of open and closed loop system using Nyquist criterion.
Appeared in:2083 Baishakh2082 Shrawan2076 Chaitra
#2Repeated 3 Times[8 Marks]Frequency Response Techniques
Define Gain Margin ($GM$) and Phase Margin ($PM$). Sketch the asymptotic Bode magnitude and phase plots for open-loop transfer function $G(s) = \frac{200}{s(s+2)(s+10)}$, and determine gain crossover frequency $\omega_{gc}$, phase crossover frequency $\omega_{pc}$, $GM$, and $PM$.
Appeared in:2083 Baishakh2082 Shrawan2079 Chaitra
#3Repeated 3 Times[8 Marks]Frequency Response Techniques
State and explain the Nyquist Stability Criterion $Z = N + P$. Sketch the Nyquist plot for open-loop transfer function $G(s)H(s) = \frac{K}{s(s+1)(s+2)}$ and find the range of $K$ for closed-loop stability.
Appeared in:2082 Baishakh2081 Bhadra2077 Magh
#4Repeated 2 Times[8 Marks]Frequency Response Techniques
Draw the Bode Plot of the unity feedback system with an open loop transfer function $G(s) = \frac{1000}{s(1+0.1s)(1+0.001s)}$. Also comment on stability.
Appeared in:2083 Baishakh2081 Bhadra
#5Repeated 2 Times[10 Marks]Frequency Response Techniques
For open loop transfer function of closed loop system as $G(s) = \frac{K}{s(s+1)(s+2)}$, determine restriction on $K$ for stability as per Nyquist criterion for stability. Will the system be stable if gain margin is $3\text{ dB}$?
Appeared in:2082 Baishakh2079 Chaitra

Performance Specifications and Compensation Design

5 Questions
#1Repeated 3 Times[12 Marks]Performance Specifications and Compensation Design
Design a suitable lead compensating network for $G(s) = \frac{K}{s^2(1+0.25s)}$ to meet the following specifications: $K_a = 10\text{ sec}^{-2}$, Phase Margin $\text{PM} \ge 35^\circ$.
Appeared in:2082 Shrawan2078 Bhadra2076 Chaitra
#2Repeated 3 Times[8 Marks]Performance Specifications and Compensation Design
Explain Lead, Lag, and Lag-Lead Compensators. Compare their transfer functions, pole-zero placements on the s-plane, and their relative effects on transient response speed and steady-state accuracy.
Appeared in:2082 Shrawan2080 Chaitra2078 Kartik
#3Repeated 3 Times[8 Marks]Performance Specifications and Compensation Design
Explain the Proportional-Integral-Derivative (PID) Controller: $u(t) = K_p e(t) + K_i \int e(t) dt + K_d \frac{de(t)}{dt}$. Describe the operational impact of P, I, and D terms on rise time, peak overshoot, settling time, and steady-state error. Explain Ziegler-Nichols frequency response tuning method.
Appeared in:2083 Baishakh2081 Bhadra2076 Chaitra
#4Repeated 2 Times[12 Marks]Performance Specifications and Compensation Design
Design a suitable phase lead compensating network for $G(s) = \frac{K}{s(1+0.1s)(1+0.001s)}$ to meet the following specifications: $K_v = 1000\text{ sec}^{-1}$, Phase Margin $\text{PM} \ge 45^\circ$.
Appeared in:2083 Baishakh2082 Baishakh
#5Repeated 2 Times[12 Marks]Performance Specifications and Compensation Design
Design a lag compensator for a unity feedback system with open loop transfer function $G(s) = \frac{K}{s(1+s)(1+0.5s)}$ such that velocity error constant would become $5\text{ s}^{-1}$ without significant change in transient properties.
Appeared in:2081 Bhadra2078 Kartik

State Space Analysis

5 Questions
#1Repeated 3 Times[8 Marks]State Space Analysis
A system is described by the following equations: $\dot{x}(t) = \begin{bmatrix} 0 & 1 \\ -2 & -3 \end{bmatrix} x(t) + \begin{bmatrix} 0 \\ 1 \end{bmatrix} u(t)$ and $y(t) = \begin{bmatrix} 1 & 0 \end{bmatrix} x(t)$. Find the transfer function of the system and identify if the system is stable.
Appeared in:2083 Baishakh2082 Shrawan2078 Bhadra
#2Repeated 3 Times[8 Marks]State Space Analysis
Define State, State Variables, State Vector, and State Space Representation. Obtain the state space model ($\dot{x} = Ax + Bu, y = Cx + Du$) in Controllable Canonical Form and Observable Canonical Form for transfer function $T(s) = \frac{s + 3}{s^3 + 5s^2 + 8s + 6}$.
Appeared in:2082 Shrawan2080 Chaitra2078 Bhadra
#3Repeated 3 Times[8 Marks]State Space Analysis
Define the State Transition Matrix $\Phi(t) = e^{At} = \mathcal{L}^{-1}\{(sI - A)^{-1}\}$. Derive its mathematical properties and compute $\Phi(t)$ for system matrix $A = \begin{bmatrix} 0 & 1 \\ -2 & -3 \end{bmatrix}$.
Appeared in:2082 Baishakh2081 Bhadra2077 Magh
#4Repeated 3 Times[8 Marks]State Space Analysis
Define Controllability and Observability of LTI systems. State Kalman's Rank Conditions for Controllability matrix $U = [B \ AB \ A^2B \dots A^{n-1}B]$ and Observability matrix $V = [C^T \ A^T C^T \ \dots \ (A^T)^{n-1} C^T]$. Test controllability and observability for a given system.
Appeared in:2083 Baishakh2082 Shrawan2079 Chaitra
#5Repeated 2 Times[6 Marks]State Space Analysis
For a system having transfer function $\frac{Y(s)}{U(s)} = \frac{s^2+3s+4}{s^3+6s^2+11s+6}$, determine the state model and output equation for the system in matrix form.
Appeared in:2083 Baishakh2082 Baishakh

Curriculum Syllabus & Course Topics

Sourced from TU curriculum portal
Full Syllabus (PDF)
Chapter-wise Units & Micro-Syllabus Topics (8 Units)

  1. 1. Control System Background

    • 1.1History of control system and its importance
    • 1.2Control system: Definition, Characteristics and basic features, Components and variables
    • 1.3Types of control system and their comparison

  2. 2. Component Modeling

    • 2.1Differential equation and transfer function, Characteristics equation, concept of pole and zero
    • 2.2Modeling of mechanical system (linear and rotational)
    • 2.3Modeling of electrical components: Inductance, capacitance, resistance, DC and AC motor, transducers and operational amplifiers, electric circuit and transfer function
    • 2.4Mechanical to electrical analogy: Force-voltage and force- current
    • 2.5Linearized approximations of non-linear characteristics

  3. 3. System Transfer Function and Responses

    • 3.1Block diagram modelling and reduction techniques
    • 3.2Signal flow graphs and mason’s gain formula
    • 3.3Time response analysis
    • 3.3.1Types of test signals: Impulse, step, ramp, parabolic
    • 3.3.2Time response analysis of first order system
    • 3.3.3Time response analysis of second order system (Step)
    • 3.3.4Time response specifications: Rise time, peak time, delay time, settling time and maximum overshoot and steady state error
    • 3.4Static error coefficients and steady state error
    • 3.5P, PI, PD, PID controller and derivative feedback controller

  4. 4. Stability

    • 4.1Introduction of stability and causes of instability
    • 4.2Characteristic equation, root location and stability
    • 4.3R-H stability criterion and application
    • 4.4Relative stability analysis from complex plane axis shifting

  5. 5. Root Locus Technique

    • 5.1Introduction of root locus
    • 5.2Relationship between root loci and time response of systems
    • 5.3Rules for manual calculation and construction of root locus
    • 5.4Stability concept from Root Locus

  6. 6. Frequency Response Techniques

    • 6.1Frequency domain characterization of the system
    • 6.2Relationship between real and complex frequency response
    • 6.3Polar Plot
    • 6.4Stability analysis in Frequency Domain: Gain Margin, Phase Margin
    • 6.5Nyquist Plot and Criterion for stability analysis
    • 6.6Bode Plot: Significance of Bode Plot, Magnitude and Phase Plot
    • 6.7Stability analysis from Bode plot

  7. 7. Performance Specifications and Compensation Design

    • 7.1Compensation technique and compensators
    • 7.2Application of root locus and frequency response on control system design
    • 7.3Lead compensator and lag compensator design from:
    • 7.3.1Root locus method
    • 7.3.2Bode plot method
    • 7.4Concept of Lead-lag compensator

  8. 8. State Space Analysis

    • 8.1Definition of state-space, state variables and state vector
    • 8.2State space representation of electrical and mechanical system
    • 8.3State space from differential equations
    • 8.4Conversion from transfer function to state space
    • 8.5Conversion from state space to a transfer function
    • 8.6State-transition matrix

Examination Scheme & Marks Distribution

Evaluation Structure

  • Final Board Theory Exam: 60 Marks (Pass mark: 24)
  • Internal Assessment: 40 Marks (Pass mark: 16)
  • Practical / Lab Exam: 25 or 50 Marks (Continuous lab evaluation + viva, where applicable)

* This is the general current IOE 60/40 scheme; verify course-specific details in the syllabus above.

Exam Preparation Guidelines

  • Review the 3 available past examination papers to identify recurring patterns, core problem types, and chapter weightage.
  • Cross-reference key answers with official syllabus units, standard textbooks, and lecture notes.
  • Structure answers with labeled diagrams, concise bullet points, and highlight final answers in numerical solutions.

Frequently Asked Questions (Control System)

Q: How can I download Control System past question papers?

You can preview or download the Control System question papers (PDF) directly using the built-in viewer on this page with zero redirects or paywalls.

Q: What is the pass mark for Control System?

The general current scheme is a 60-mark final theory exam and a 40-mark internal assessment, with pass marks of 24 and 16. Verify the course-specific syllabus above.

Q: Where can I find the complete syllabus for this subject?

The available chapter-wise syllabus and topic breakdown is indexed in the Syllabus section above, with links to the curriculum PDF source.

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