22-Elec-A2 Systems and Control
Worked solutions to 14 past sittings (2013–2019), 111 questions. Pick a sitting, or start from a topic below.
- December 2019
- December 2018
- May 2018
- December 2017
- May 2017
- December 2016
- May 2016
- December 2015
- May 2015
- December 2014
- May 2014
- December 2013
- May 2013
- Undated paper
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.
- Routh–Hurwitz (7 sittings): May 2017 Q1 · May 2016 Q2 · December 2015 Q2 · May 2015 Q4 · May 2014 Q2 · December 2013 Q1 · May 2013 Q1
- Controllability (6 sittings): December 2018 Q7 · May 2018 Q4 · May 2017 Q6 · May 2016 Q3 · May 2015 Q7 · December 2014 Q7
- Gain selection (6 sittings): December 2018 Q8 · May 2017 Q7 · December 2016 Q5 · May 2016 Q4 · May 2015 Q2 · Undated paper Q6
- State-space model (6 sittings): December 2018 Q7 · May 2018 Q4 · December 2017 Q5 · May 2017 Q5 · December 2014 Q7 · May 2014 Q7
- Nyquist stability (5 sittings): December 2017 Q4 · May 2017 Q4 · December 2016 Q2 · May 2016 Q8 · May 2015 Q8
- Pole placement (5 sittings): May 2018 Q4 · May 2015 Q7 · December 2014 Q7 · May 2014 Q7 · May 2013 Q7
- Pole Placement by State Feedback (5 sittings): December 2019 Q1 · December 2018 Q7 · December 2017 Q5 · May 2017 Q5 · Undated paper Q8
- State space (5 sittings): May 2016 Q3 · December 2015 Q1 · May 2015 Q7 · December 2013 Q7 · May 2013 Q7
- Transfer function (5 sittings): May 2016 Q3 · December 2015 Q1 · May 2015 Q1 · May 2014 Q3 · May 2013 Q7
- Observability (4 sittings): December 2018 Q7 · May 2018 Q4 · May 2017 Q6 · May 2016 Q3
- Root locus (4 sittings): December 2016 Q5 · December 2015 Q2 · May 2015 Q4 · May 2013 Q3
- Step specs (4 sittings): December 2017 Q7 · May 2017 Q7 · December 2016 Q5 · May 2014 Q3
- Bode (3 sittings): May 2016 Q2 · December 2015 Q2 · May 2013 Q1
- Controllability/observability (3 sittings): December 2015 Q1 · May 2014 Q7 · May 2013 Q7
- Controller Design by Pole Placement (3 sittings): December 2019 Q4 · December 2018 Q1 · Undated paper Q7
Questions by sitting
December 2019
- Question 1: State-Space Analysis and Pole Placement by State Feedback
- Question 2: Lead Controller Design in the Frequency Domain
- Question 3: Root Locus Analysis and Proportional Gain Selection
- Question 4: Controller Design by Pole Placement (PI + Rate Feedback)
- Question 5: Nyquist Stability Criterion for an Open-Loop-Unstable Plant
- Question 6: Routh–Hurwitz Stability of a PID Loop
- Question 7: Analytical Step Response from a State-Space Model
- Question 8: Second-Order Dominant-Poles Models in s- and Frequency Domain
December 2018
- Question 1: Controller Design by Pole Placement
- Question 2: Servo Block Reduction, Disturbance Transfer Function and Routh–Hurwitz Stability
- Question 3: Second Order Dominant Poles Model and Step-Response Specifications
- Question 4: Steady-State Error Analysis with Reference and Disturbance Ramps
- Question 5: Three Second-Order Dominant-Pole Models — s-Domain, Closed Loop and Open Loop Frequency Response
- Question 6: Lag Controller Design in the Frequency Domain
- Question 7: State-Space Model, Controllability, Observability and Pole Placement by State Feedback
- Question 8: Root Locus Analysis, Gain Selection and Response Estimation
May 2018
- Question 1: Servo Transfer Functions, Mason’s Rule and Routh–Hurwitz Stability
- Question 2: Error Constants and the Second-Order Dominant-Poles Model
- Question 3: Steady-State Error by Superposition and the Final Value Theorem
- Question 4: State-Space Model, Controllability, Observability and Pole Placement
- Question 5: Lead Controller Design in the Frequency Domain
- Question 6: Root Locus of a Plant with a Right-Half-Plane Pole
- Question 7: PD Controller Design by Pole Placement — Rate Feedback versus Derivative Control
- Question 8: Three Routes to a Second-Order Dominant-Poles Model
December 2017
- Question 1: Stability by root locus, frequency response and Routh (compulsory)
- Question 2: Lag-controller design in the frequency domain (compulsory)
- Question 3: Lead-controller design in the frequency domain
- Question 4: Polar plot and Nyquist stability, RHP-pole plant
- Question 5: State-space model, pole placement by state feedback
- Question 6: Second-order dominant-pole models from three sources
- Question 7: Root-locus design, gain for $\zeta=0.5$, step specs
- Question 8: PID design by pole placement with pole–zero cancellation
May 2017
- Question 1: Signal flow, Routh–Hurwitz, error analysis (compulsory)
- Question 2: System type, error constants, dominant 2nd-order model (compulsory)
- Question 3: Analytical step response by partial fractions
- Question 4: Polar plot and Nyquist stability, RHP-pole plant
- Question 5: State-space model, pole placement by state feedback
- Question 6: Controllability, observability, transfer function by Mason
- Question 7: Root-locus design, gain selection, step specs
- Question 8: Series-PID design by pole placement
December 2016
- Question 1: Stability of a lag-compensated loop (compulsory)
- Question 2: Nyquist stability, two loops (compulsory)
- Question 3: State space ↔ transfer function, Mason’s rule
- Question 4: Second-order dominant-pole models
- Question 5: Root locus, gain selection, step specs
- Question 6: Identifying a process from its Bode magnitude
- Question 7: Lag-controller design in the frequency domain
- Question 8: Series-PID design by pole placement
May 2016
- Question 1: Basic definitions and concepts of control (compulsory)
- Question 2: Marginal stability by root locus, Bode and Routh–Hurwitz (compulsory)
- Question 3: State space vs. transfer function; controllability, observability, steady-state error
- Question 4: Root-locus analysis, gain selection and dominant model
- Question 5: PID design by pole placement
- Question 6: Lead/Lag controller design by pole placement
- Question 7: Lead controller design in the frequency domain
- Question 8: Nyquist stability (Part A) and state-space response (Part B)
December 2015
- Question 1: State space vs. transfer function, controllability/observability, steady-state error (compulsory)
- Question 2: Stabilising an unstable plant with PID: Bode, root locus, Routh–Hurwitz (compulsory)
- Question 3: Root-locus analysis and gain selection for a RHP-pole plant
- Question 4: Second-order dominant model, system type, transient specs, effect of a zero
- Question 5: Two-port RLC network: transfer function and step response
- Question 6: Nyquist and Routh–Hurwitz stability for a RHP-pole plant
- Question 7: Lead-controller design in the frequency domain
- Question 8: Canonical forms, signal-flow graph, and transfer function by inspection
May 2015
- Question 1: Proportional + rate-feedback design: transfer function, error and overshoot (compulsory)
- Question 2: Root-locus analysis and gain selection (compulsory)
- Question 3: Top-down controller design by pole matching
- Question 4: Stability range from Bode, root locus and Routh–Hurwitz
- Question 5: Second-order dominant model three ways, and step estimates
- Question 6: Lag-controller design in the frequency domain
- Question 7: State space: controllability, pole placement, closed-loop transfer function
- Question 8: Signal-flow state model (Mason) and Nyquist stability
December 2014
- Question 1: Frequency-response & Routh stability of a proportional loop (compulsory)
- Question 2: Root-locus design of a PD controller (compulsory)
- Question 3: Second-order dominant-pole models three ways
- Question 4: PID design by pole placement with rate feedback
- Question 5: Robot-joint servo: Mason reduction & step response
- Question 6: Lead/lag controller design in the frequency domain
- Question 7: State-space model, controllability & pole placement
- Question 8: Mason’s gain formula & second-order derivations
May 2014
- Question 1: Nyquist stability of a proportional loop (compulsory)
- Question 2: Routh–Hurwitz and root locus of the same plant (compulsory)
- Question 3: Second-order RLC two-port: transfer function & step specs
- Question 4: PID with rate feedback by pole–zero cancellation
- Question 5: Signal-flow graph / Mason and proportional-control error
- Question 6: Lag compensator from Bode plots
- Question 7: State-space model, controllability/observability, pole placement
- Question 8: Analytical step response and derivation of the 2nd-order specs
December 2013
- Question 1: Stability by Bode plot and Routh–Hurwitz (compulsory)
- Question 2: Root-locus analysis of an unstable plant (compulsory)
- Question 3: PI-controller design from a dominant-poles model
- Question 4: PD vs. proportional-plus-rate-feedback control
- Question 5: Proportional vs. lead control; margins and dominant model
- Question 6: Additional poles/zeros and step-response specifications
- Question 7: State space, canonical forms, eigenvalues and stability
May 2013
- Question 1: Stability by Root Locus, Bode and Routh–Hurwitz (compulsory)
- Question 2: PID design from a dominant-poles model (compulsory)
- Question 3: Root locus and series-PID settling-time design
- Question 4: Safe operating range under P vs PI control (Routh–Hurwitz)
- Question 5: Lag-controller design from frequency response
- Question 6: Second-order identification and rate-feedback design
- Question 7: State space: transfer function, controllability/observability, pole placement
- Question 8: Nyquist stability of the Q1 system
Undated paper
- Question 1: Routh Array and Routh–Hurwitz Criterion of Stability
- Question 2: Root Locus Analysis; Bode Plots and Gain Margin
- Question 3: Signal Flow Diagrams — Mason’s Gain Formula
- Question 4: Second Order Dominant Poles Model, Step Response Specifications
- Question 5: Controller Design in Frequency Domain — Lead Controller
- Question 6: Root Locus Analysis and Gain Selection, Second Order Model
- Question 7: Controller Design by Pole Placement, Response Specifications
- Question 8: State Space Model, Pole Placement by State Feedback, Steady State Errors