NivaarExam Prep

17-Phys-B5 Systems and Control

Worked solutions to 5 past sittings (2016–2018), 40 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

May 2018

  1. Question 1: Servo-Positioning Signal-Flow Graph — Closed-Loop and Disturbance TFs, Stability Range
  2. Question 2: Error Constants, DC Gain and 2nd-Order Dominant-Pole Model at $K_{op}=3.0$
  3. Question 3: Steady-State Error Design, Gain Margin, and Superposed Ramp Disturbance
  4. Question 4: State-Space Model — Eigenvalues, TF, Controllability/Observability, Pole Placement
  5. Question 5: Lead Controller Design in the Frequency Domain
  6. Question 6: Root Locus of a System with a Right-Half-Plane Pole — Conditional Stability
  7. Question 7: Rate-Feedback vs. PD Control — Same $K_p,T_d$, Very Different Outcomes
  8. Question 8: Three 2nd-Order Dominant-Pole Models — s-Domain, Open-Loop and Closed-Loop Frequency Response

December 2017

  1. Question 1: Root Locus Crossovers, Magnitude Criterion and Routh–Hurwitz Confirmation
  2. Question 2: Lag Controller Design from a Steady-State-Error and Overshoot Specification
  3. Question 3: Lead Controller Design from a Steady-State-Error, Overshoot and Settling-Time Specification
  4. Question 4: Polar Plot and Nyquist Stability with an Unstable Open-Loop Pole
  5. Question 5: State Space Model from a Transfer Function, Pole Placement by State Feedback
  6. Question 6: Second-Order Dominant-Pole Models from Three Different Sources
  7. Question 7: Root Locus Construction, Gain Selection for a Target Damping Ratio, and Gain Margin
  8. Question 8: PID Controller Design by Pole Placement with Pole–Zero Cancellation

May 2017

  1. Question 1: Servo-Positioning System under PI Control — Closed-Loop TF, Stability Range, Operating Gain
  2. Question 2: Open-Loop Type, Error Constants and 2nd-Order Dominant-Pole Model
  3. Question 3: Analytical Step Response by Partial Fractions
  4. Question 4: Polar Plot and Nyquist Stability with an Unstable Open-Loop Pole
  5. Question 5: Controller Canonical Form and Pole Placement by State Feedback
  6. Question 6: Controllability/Observability vs. Parameter α, and the Transfer Function by Mason's Gain Formula
  7. Question 7: Root Locus, Critical Gain, and a 5% Overshoot Design
  8. Question 8: Series-Configuration PID Design by Pole Placement

May 2016

  1. Question 1: Basic Definitions and Concepts of Control
  2. Question 2: Stability via Root Locus, Bode and Routh–Hurwitz
  3. Question 3: State Space, Controllability/Observability, Steady-State Error
  4. Question 4: Root Locus, Gain Selection and Second-Order Model
  5. Question 5: PID Controller Design by Pole Placement
  6. Question 6: Lead/Lag Controller Design by Pole Placement
  7. Question 7: Lead Controller Design in the Frequency Domain
  8. Question 8: Nyquist Criterion and State-Space Step Response

Undated paper

  1. Question 1: PID + Hydraulic Process — Closed-Loop TF and Routh–Hurwitz Stability Range
  2. Question 2: Frequency Response and Root Locus — Verifying Question 1
  3. Question 3: Signal-Flow Graph — Mason's Gain Formula
  4. Question 4: Second-Order Dominant-Poles Models — s-Domain, Step, and Frequency Response
  5. Question 5: Lead Controller Design in Frequency Domain
  6. Question 6: Root Locus, Gain Selection and Dominant-Pole Validity
  7. Question 7: Controller Design by Pole Placement — PI + Dynamic Rate Feedback
  8. Question 8: State-Space Model — Pole Placement by State Feedback