22-Elec-B2 Advanced Control Systems
Worked solutions to 14 past sittings (2013–2019), 77 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.
- Asymptotes (4 sittings): December 2018 Q2 · May 2018 Q2 · May 2017 Q2 · December 2016 Q2
- Controllability (4 sittings): December 2015 Q4 · May 2015 Q2 · December 2013 Q2 · May 2013 Q2
- Observability (4 sittings): December 2015 Q4 · May 2015 Q2 · December 2013 Q2 · May 2013 Q2
- Seventeen items (4 sittings): December 2019 Q1 · December 2018 Q1 · December 2017 Q1 · May 2017 Q1
- State-space realisation (4 sittings): May 2016 Q2 · December 2015 Q2 · May 2014 Q2 · December 2013 Q2
- Phase margin (3 sittings): May 2016 Q1 · May 2014 Q6 · December 2013 Q1
- Root locus (3 sittings): May 2018 Q1 · December 2016 Q1 · December 2014 Q5
- Sampled-data loop (3 sittings): December 2015 Q5 · May 2015 Q5 · December 2014 Q5
- Angle of departure (2 sittings): May 2018 Q2 · December 2016 Q2
- Asymptotic Bode construction (2 sittings): May 2018 Q4 · December 2016 Q4
- Bode diagram (2 sittings): December 2019 Q5 · December 2017 Q5
- Bode plots (2 sittings): December 2018 Q4 · May 2017 Q4
- Break points (2 sittings): December 2018 Q2 · May 2017 Q2
- Break-in point (2 sittings): May 2018 Q2 · December 2016 Q2
- Frequency response (2 sittings): May 2018 Q1 · December 2016 Q1
Questions by sitting
December 2019
- Question 1: Multiple choice — seventeen items
- Question 2: Root locus from a pole-zero map
- Question 3: Partial fractions and the inverse Laplace transform
- Question 4: Servo motor with rate feedback
- Question 5: Bode diagram and stability margins
December 2018
- Question 1: Multiple choice — seventeen items
- Question 2: Root-locus geometry — asymptotes, break points and a \(j\omega\)-axis crossing
- Question 3: Placing the zero of a PD compensator by the angle criterion
- Question 4: Bode plots and stability margins for \(K/[s(s+2)(s+10)]\)
- Question 5: Design on a printed circular locus — and the limits of a PD compensator
May 2018
- Question 1: Nineteen short-answer items on error constants, stability, the root locus and frequency response
- Question 2: Angle of departure, break-in point, asymptotes and the imaginary-axis crossing
- Question 3: Cascade-compensator design for a double-integrator plant
- Question 4: Asymptotic Bode construction and the stability margins of $K/[s(s+1)(s+5)]$
- Question 5: Root-locus design on an open-loop unstable, non-minimum-phase plant
December 2017
- Question 1: Multiple choice — seventeen items
- Question 2: Root locus from a pole-zero map
- Question 3: Partial fractions and the inverse Laplace transform
- Question 4: Servo motor with rate feedback
- Question 5: Bode diagram and stability margins
May 2017
- Question 1: Multiple choice — seventeen items
- Question 2: Root-locus geometry — asymptotes, break points and a \(j\omega\)-axis crossing
- Question 3: Placing the zero of a PD compensator by the angle criterion
- Question 4: Bode plots and stability margins for \(K/[s(s+2)(s+10)]\)
- Question 5: Design on a printed circular locus — and the limits of a PD compensator
December 2016
- Question 1: Nineteen short-answer items on error constants, stability, the root locus and frequency response
- Question 2: Angle of departure, break-in point, asymptotes and the imaginary-axis crossing
- Question 3: Cascade-compensator design for a double-integrator plant
- Question 4: Asymptotic Bode construction and the stability margins of $K/[s(s+1)(s+5)]$
- Question 5: Root-locus design on an open-loop unstable, non-minimum-phase plant
May 2016
- Question 1: Stability limit, phase margin and steady-state errors of a non-minimum-phase loop
- Question 2: State-space realisation, minimality conditions and sampled-data poles
- Question 3: Full state feedback with pole placement and unity DC gain
- Question 4: Deadbeat digital control of an integrator behind a zero-order hold
- Question 5: Identifying a first-order-plus-dead-time plant from a sampled step test
- Question 6: Proportional control of a delayed integrator to a specified gain margin
December 2015
- Question 1: Near-instability, input-disturbance rejection, and a 90° phase-margin design
- Question 2: State-space realisation and pole placement with reference scaling
- Question 3: Least-squares identification of a second-order discrete model
- Question 4: Controllability, observability and BIBO stability of a parametrised system
- Question 5: Sampled-data loop: ZOH equivalent, Jury stability range and a deadbeat redesign
- Question 6: Transport delay under proportional control: margins, step error and redesign
May 2015
- Question 1: Disturbance rejection and phase margin of a cruise-control loop
- Question 2: State-space model, modal response, controllability and observability
- Question 3: Least-squares identification of a first-order discrete model
- Question 4: Pole placement by state feedback with reference scaling
- Question 5: Sampled-data loop — discrete model, Jury stability and ramp error
- Question 6: Feedback around a pure transport delay
December 2014
- Question 1: Proportional-integral design for a double-lag plant
- Question 2: State-space model and pole placement for a satellite attitude loop
- Question 3: Least-squares identification of a first-order discrete model
- Question 4: Transfer functions from step and frequency-response data
- Question 5: Sampled-data loop — closed-loop pulse transfer function, root locus and inter-sample response
- Question 6: Nyquist analysis and margins for a delayed integrator
May 2014
- Question 1: PI control of a double-integrator servo
- Question 2: State-space realisation and pole placement for a non-minimum-phase plant
- Question 3: Model-matching controller design and its stability margins
- Question 4: Identifying a non-minimum-phase plant from three frequency-response points
- Question 5: Proportional control of a discrete plant and its continuous-time origin
- Question 6: Gain limits, phase margin and disturbance error for a delayed integrator
December 2013
- Question 1: Gain limit, phase margin and steady-state tracking of a non-minimum-phase plant
- Question 2: State-space realisation, controllability, observability and the sampled-data poles
- Question 3: Pole placement by state feedback with unity DC gain
- Question 4: Deadbeat design of a digital PI controller for an integrating plant
- Question 5: Identification of a first-order plant with transport delay from step data
- Question 6: Proportional design to a specified gain margin for a plant with transport delay
May 2013
- Question 1: Steady-state error of a cruise-control loop with a road grade
- Question 2: Controllability, observability and stability of a parameter-dependent state model
- Question 3: Algebraic design of a proper, stable controller from a specified sensitivity
- Question 4: Identifying a second-order plant from three experiments
- Question 5: Discrete-time model and deadbeat state feedback for a sampled-data loop
- Question 6: Delay margin, Nyquist plot and the effect of a sensor bias
Undated paper
- Question 1: Multiple choice — fifteen items
- Question 2: Multiple choice — eighteen items
- Question 3: Mason’s rule and PD compensator design
- Question 4: Bode diagram with a stability limit, and a zero-degree root locus
- Question 5: Root locus of a driver–train closed loop