NivaarExam Prep

22-Mec-A3 System Analysis and Control

Worked solutions to 13 past sittings (2013–2019), 79 questions. Pick a sitting, or start from a topic below.

Topics across the sittings

Topics that come up in more than one sitting, taken from the headings of our worked solutions. A topic counts once per sitting.

Questions by sitting

December 2019

  1. Question 1: Direct Laplace Transforms of Differential and Integral Equations
  2. Question 2: Two-Phase AC Servomotor Positioning System
  3. Question 3: Steady-State Error of a Type-2 Loop
  4. Question 4: Routh–Hurwitz Stability of Three Feedback Loops
  5. Question 5: Bode Diagram and Unconditional Stability of a Second-Order Servomechanism
  6. Question 6: Root Locus and Critical Gain of a Three-Pole Loop

December 2018

  1. Question 1: DC Gain and Final Value of an Unstable Second-Order System
  2. Question 2: Routh Stability Range for a Tape-Drive Servo
  3. Question 3: Root Locus of $k/[s(s^{2}+6s+12)]$
  4. Question 4: Bode Plots and the Gain Margin at 45° Phase Margin
  5. Question 5: Laplace Solution of Two Differential Equations
  6. Question 6: Step Response from a Pole–Zero Description, and an Inverse Transform
  7. Question 7: Error Constants and Steady-State Errors

May 2018

  1. Question 1: Closed-loop transfer function, poles and zeros, step response
  2. Question 2: Steady-state error with a pre-loop gain
  3. Question 3: Routh–Hurwitz test with a vanishing row
  4. Question 4: Root locus — breakaway and break-in points
  5. Question 5: Gain for a specified damping ratio
  6. Question 6: Bode diagrams of two loop transfer functions

December 2017

  1. Question 1: Impulse and Step Response; Free Response of a Second-Order ODE
  2. Question 2: Routh Stability — Range of Gain and an Open-Loop Unstable Plant
  3. Question 3: Steady-State Error — Recovering G ( s ) and the Effect of Gain and Damping
  4. Question 4: Root Locus of a Four-Pole Plant and its Imaginary-Axis Crossings
  5. Question 5: Lead-Compensator Design for Specified Damping and Natural Frequency
  6. Question 6: Bode Diagram of a Resonant Plant; Gain Design for a Specified Phase Margin

May 2017

  1. Question 1: DC Gain and Final Value of an Unstable Second-Order System
  2. Question 2: Routh’s Criterion Applied to Two Unity-Feedback Loops
  3. Question 3: Compensator Constraints for Type 1 Behaviour and Robust Stability
  4. Question 4: Motor Position Control — Velocity Constant, Damping Ratio and Ramp Error
  5. Question 5: Root Locus of a Third-Order Loop — Segments, Asymptotes and the Imaginary-Axis Crossing
  6. Question 6: Bode Magnitude and Phase Asymptotes for Two Open-Loop Transfer Functions

December 2016

  1. Question 1: Impulse Response of a Repeated-Pole and of an Underdamped System
  2. Question 2: Steady-State Level of a Proportional Liquid-Level Loop
  3. Question 3: Bode Diagrams — a Lag Network and a Three-Pole Loop
  4. Question 4: Root-Locus Design for a Damping Ratio of 0.5
  5. Question 5: Routh–Hurwitz Stability, Step Response and Gain Tolerance
  6. Question 6: Error Constants and Steady-State Errors

May 2016

  1. Question 1: DC Gain and Final Value of a Second-Order System
  2. Question 2: Inverse Laplace Transforms by Partial-Fraction Expansion
  3. Question 3: Routh Stability Range and Root Locus for System 1.0
  4. Question 4: Bode Magnitude and Phase Asymptotes
  5. Question 5: Steady-State Error Specifications for a Position Control System
  6. Question 6: Counting Right-Half-Plane Roots with Routh's Criterion

May 2015

  1. Question 1: Asymptotic Bode Magnitude Plots
  2. Question 2: Unit Step Responses by Partial Fractions
  3. Question 3: Proportional Temperature Control — Type Number, Gain and Steady-State Error
  4. Question 4: Root Locus and Steady-State Error with Rate Feedback
  5. Question 5: Routh–Hurwitz Stability Determination
  6. Question 6: Effect of Loop Gain on Step Response and Steady-State Error

December 2014

  1. Question 1: Root Locus and Range of Stabilising Gain
  2. Question 2: Bode Diagrams of Two Transfer Functions
  3. Question 3: Sinusoidal Steady-State Response of a First-Order System
  4. Question 4: Routh–Hurwitz Root Counts
  5. Question 5: Transient Terms of a Two-Input Servo with Rate Feedback
  6. Question 6: Steady-State Errors of a Motor Position Servo

May 2014

  1. Question 1: Bode plot, gain margin and phase margin
  2. Question 2: Routh–Hurwitz ranges of a parameter
  3. Question 3: Root locus for positive and negative gain
  4. Question 4: Transient-response terms under proportional control
  5. Question 5: Steady-state errors for step and ramp inputs
  6. Question 6: Sinusoidal steady-state response of a first-order system

December 2013

  1. Question 1: Unit step response, and the time constants of a transient
  2. Question 2: Routh–Hurwitz gain limit and the poles at that limit
  3. Question 3: System type, loop gain and steady-state errors
  4. Question 4: Motor position servo with and without rate feedback
  5. Question 5: Root locus of an unstable plant and the gain range for stability
  6. Question 6: Asymptotic Bode magnitude plot, phase margin and gain margin

May 2013

  1. Question 1: Unity-feedback system — real-pole range, step response, steady-state error
  2. Question 2: Type-1 system — gain for a ramp-error spec, then step/ramp errors
  3. Question 3: Routh–Hurwitz stability range of a fourth-order loop
  4. Question 4: Stability range, and the stabilising effect of a feedback zero
  5. Question 5: Root locus and the gain for $\zeta=0.5$
  6. Question 6: Bode design of a plant zero location for a target gain-crossover

Undated paper

  1. Question 1: Routh–Hurwitz stability of two characteristic equations
  2. Question 2: Impulse response of two transfer functions
  3. Question 3: Steady-state response of a proportional liquid-level loop
  4. Question 4: Absolute stability of a hydraulic servo by Routh’s criterion
  5. Question 5: Bode diagrams of two open-loop transfer functions
  6. Question 6: Root-locus plots for two open-loop transfer functions