23-Chem-A6 Process Dynamics and Control
Worked solutions to 13 past sittings (2013–2019), 104 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
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.
- Stability (8 sittings): December 2018 Q5 · December 2017 Q1 · May 2017 Q6 · December 2016 Q1 · December 2015 Q4 · May 2015 Q2 · December 2014 Q6 · May 2013 Q6
- Step Response (7 sittings): December 2018 Q5 · December 2017 Q6 · December 2016 Q7 · December 2015 Q3 · May 2015 Q3 · December 2014 Q2 · December 2013 Q3
- Standard Form (6 sittings): December 2018 Q6 · May 2018 Q6 · May 2017 Q6 · May 2015 Q2 · December 2014 Q6 · May 2014 Q6
- Transfer Function (6 sittings): December 2018 Q1 · May 2018 Q1 · May 2017 Q7 · December 2014 Q2 · May 2014 Q7 · May 2013 Q7
- Bode Plot (5 sittings): December 2019 Q8 · December 2018 Q7 · December 2016 Q6 · December 2015 Q2 · December 2014 Q8
- Second-Order ODE (5 sittings): December 2018 Q6 · May 2017 Q6 · May 2015 Q2 · December 2014 Q6 · May 2014 Q6
- Dead Time (4 sittings): December 2019 Q2 · May 2018 Q5 · May 2016 Q5 · December 2014 Q3
- Draining Tank (4 sittings): December 2018 Q8 · May 2016 Q6 · May 2014 Q2 · May 2013 Q2
- Linearising a Radiative Heater (4 sittings): December 2017 Q2 · December 2016 Q2 · December 2015 Q1 · May 2015 Q1
- Model (4 sittings): December 2018 Q1 · May 2017 Q7 · December 2014 Q7 · May 2014 Q7
- Stability Limit (4 sittings): December 2019 Q8 · December 2017 Q3 · December 2016 Q6 · December 2015 Q2
- Step (4 sittings): December 2018 Q8 · May 2016 Q6 · May 2014 Q2 · May 2013 Q2
- Bode Diagram (3 sittings): December 2017 Q7 · May 2017 Q2 · May 2014 Q8
- Damping (3 sittings): May 2017 Q6 · December 2014 Q6 · May 2014 Q6
- First-Order Thermometer (3 sittings): December 2019 Q4 · May 2018 Q4 · May 2016 Q1
Questions by sitting
December 2019
- Question 1: Two Non-Interacting Tanks in Series with a Pump
- Question 2: Internal Model Control of a Process with a RHP Zero and Dead Time
- Question 3: Linearising a Radiation Heater
- Question 4: First-Order Thermometer — Response to a Ramping Bath
- Question 5: PI Controller — Laplace Transform and Output for a Pulse Train
- Question 6: Routh Stability of a Quartic Characteristic Equation
- Question 7: Inverse Laplace Transforms and Time-Response Stability
- Question 8: Closed Loop $1/(s+1)^3$ with Sensor $H$ — Stability Limit, Bode Plot and Margins
December 2018
- Question 1: Stirred Tank with Thermal Solid — Model, Transfer Function, and Large-$UA$ Limit
- Question 2: State-Space Model — Transfer Function and Unit-Step Response
- Question 3: IMC Design for a First-Order-Plus-Dead-Time Process
- Question 4: Nyquist Analysis of an Open-Loop-Unstable Process
- Question 5: PI Control of a First-Order Process — Stability and Step Response
- Question 6: Second-Order ODE — Standard Form and Damping Regimes
- Question 7: Bode Plot and Gain Margin of a First-Order-Plus-Dead-Time Process
- Question 8: Draining Tank — Step and Impulse Response of the Level
May 2018
- Question 1: Integrating Water-Storage Tank — Transfer Function and Overflow Time
- Question 2: Feedback Loop — Closed-Loop Transfer Function and Sensor-Gain Stability Range
- Question 3: Two Interacting Tanks — Nonlinear ODEs and Linear State-Space Model
- Question 4: First-Order Thermometer — Response to a Ramping Bath
- Question 5: IMC Design for a Process with a RHP Zero and Dead Time
- Question 6: Second-Order Transfer Function — Standard Form and Response Regimes
- Question 7: Nyquist Stability of an Open-Loop-Unstable Process
- Question 8: Nyquist Diagram and Gain Margin of $1/(s(s+2)^2)$
December 2017
- Question 1: Inverse Laplace Transform and Stability
- Question 2: Linearising a Radiative Heater
- Question 3: Triple-Lag Loop with a Dead-Time Sensor — Stability Limit and Margins
- Question 4: Thermocouple Lag — Response to a Triangular Input
- Question 5: IMC Design for a First-Order-plus-Dead-Time Process
- Question 6: PI Control of a First-Order Process — Stability and Step Response
- Question 7: Frequency Response of an FOPDT Loop — Bode Diagram and Gain-Margin Design
- Question 8: Nyquist Stability of an Open-Loop-Unstable Process
May 2017
- Question 1: Transport Delay + Integrating Tank — Level Control
- Question 2: Frequency Response of an FOPDT Loop — Bode Diagram and Gain-Margin Design
- Question 3: PI Control of a First-Order Process
- Question 4: Liquid-Level Dynamics — Resistance Valve vs. Exit Pump
- Question 5: IMC Design for an FOPDT Process — Controller Form and Servo Response
- Question 6: Second-Order ODE — Standard Form, Stability and Damping
- Question 7: Second-Order-Reaction CSTR — Model and Transfer Function
- Question 8: Nyquist Stability of an Open-Loop-Unstable First-Order Process
December 2016
- Question 1: Inverse Laplace Transforms and Stability
- Question 2: Linearising a Radiative Heater
- Question 3: Thermocouple Response to a Triangular Pulse
- Question 4: Two Tanks in Series with an Inter-tank Pump
- Question 5: IMC Design for a Process with Dead Time and an RHP Zero
- Question 6: Stability Limit, Bode Plot and Margins with a Sensor Lag
- Question 7: State-Space Model to Transfer Function and Step Response
- Question 8: Nyquist Stability of an Open-Loop-Unstable Process
May 2016
- Question 1: First-Order Thermometer — Response to a Ramping Bath
- Question 2: PI Controller — Laplace Transform and Output for a Pulse Train
- Question 3: Routh Stability of a Quartic Characteristic Equation
- Question 4: Two Concentric Tanks — Second-Order Thermal Response
- Question 5: IMC Design for a Process with a RHP Zero and Dead Time
- Question 6: Draining Tank — Step and Impulse Response
- Question 7: Nyquist Stability of an Open-Loop-Unstable Process
- Question 8: PI Control of a First-Order Process
December 2015
- Question 1: Linearising a Radiative (Calrod) Heater
- Question 2: Stability Limit, Bode Plot and Margins of a Triple-Lag Loop
- Question 3: State-Space Model → Transfer Function and Step Response
- Question 4: PI Control of a First-Order Process — Stability and Step Response
- Question 5: IMC Design, Servo Response and IMC–PID Equivalence (FOPDT)
- Question 6: Transport Delay + Integrating Tank — Level Control
- Question 7: Nyquist Stability of an Open-Loop-Unstable First-Order Process
- Question 8: Bode Plot and Gain-Margin Design for a FOPDT Process
May 2015
- Question 1: Linearising a Radiative (Calrod) Heater
- Question 2: Second-Order ODE — Standard Form and Stability vs. $k$
- Question 3: State-Space Model → Transfer Function and Step Response
- Question 4: Thermocouple Dynamics — Response to a Triangular Input
- Question 5: IMC Design for a First-Order-Plus-Dead-Time Process
- Question 6: Transport Delay + Integrating Tank — Level Control
- Question 7: Nyquist Stability of an Open-Loop-Unstable Process
- Question 8: PI Control of a First-Order Process — Stability and Step Response
December 2014
- Question 1: Stirred Tank with a Solid Thermal Mass
- Question 2: State-Space Model — Transfer Function and Step Response
- Question 3: IMC Design for a Process with a RHP Zero and Dead Time
- Question 4: Nyquist Stability of an Open-Loop-Unstable Process
- Question 5: Ultimate Gain of a Third-Order Loop with Sensor Delay
- Question 6: Second-Order ODE — Standard Form, Stability and Damping
- Question 7: Second-Order-Reaction CSTR — Model and Transfer Function
- Question 8: Bode Plot and Gain Margin of an FOPDT Loop
May 2014
- Question 1: Two Non-Interacting Tanks in Series
- Question 2: Draining Tank — Step and Impulse Response
- Question 3: Internal Model Control (IMC) Design
- Question 4: Nyquist Stability of an Open-Loop-Unstable Process
- Question 5: Thermocouple Dynamics — Response to a Triangular Bath Pulse
- Question 6: Second-Order ODE — Standard Form and Damping
- Question 7: CSTR with a Second-Order Reaction — Model and Transfer Function
- Question 8: Bode Diagram and Gain Margin of a Dead-Time Process
December 2013
- Question 1: Calrod Radiant Heater — Linearisation & Controller Sign
- Question 2: Triple-Lag Loop with a Sensor — Ultimate Gain, Bode, Margins
- Question 3: State-Space Model → Transfer Function & Step Response
- Question 4: Thermocouple Lag — Response to a Triangular Input
- Question 5: IMC Design for a First-Order-plus-Dead-Time Process
- Question 6: Transport Delay in a Pipe Feeding an Integrating Tank
- Question 7: Nyquist Stability of an Open-Loop-Unstable Process
- Question 8: PI Control of a First-Order Process
May 2013
- Question 1: Two Non-Interacting Tanks in Series
- Question 2: Draining Tank — Step and Pulse Response
- Question 3: Internal Model Control (IMC) Design
- Question 4: Nyquist Stability of an Open-Loop-Unstable Process
- Question 5: Routh Test and Closed-Loop Response of a First-Order Process
- Question 6: Dead-Time Process — Stability and Gain Margin
- Question 7: Multivariable Model — Transfer Functions and Response
- Question 8: Block-Diagram Algebra with a Feedforward Path