CHEN90032 · Process Simulation and Control
Feedback Control & P&IDs
Feedback Control & P&IDs is the Week-1 foundation of University of Melbourne CHEN90032 Process Simulation and Control: it introduces the measure–compare–act loop that the whole subject is built to analyse. You learn the sign convention e = SP − c (error = set point minus measured controlled variable), how a controller, final control element (valve), process and sensor combine into a closed-loop transfer function, and how to lay feedback loops over real unit operations such as a flash drum or distillation column. You also learn to read and draw a Piping & Instrumentation Diagram (P&ID) — the instrument tags, sensors, controllers and control valves that encode a control scheme — the skill the exam tests first and heaviest.
What this chapter covers
- 01The feedback principle: measure the controlled variable c, compare with set point SP, act on a manipulated variable m
- 02The error sign convention e = SP − c and why it gives negative feedback
- 03Naming loop variables: set point SP (R), controlled variable c, manipulated variable m, disturbance/load d
- 04The closed-loop block diagram and its servo C/R = GcGvGp/(1 + GcGvGpGm) and regulator C/QL transfer functions
- 05The characteristic equation 1 + GcGvGpGm = 0 as the root of all stability analysis
- 06The PID control law m(t) = m̅ + Kc[e + (1/TI)∫e dt + TD de/dt] with correct units on Kc, TI, TD
- 07Reverse-acting vs direct-acting controllers, and why P-only control leaves a permanent offset
- 08Designing a control scheme by pairing each controlled variable with one manipulated valve (degrees of freedom)
- 09Control schemes for common unit operations: the flash-drum P, L and T loops, extended to distillation
- 10Reading and drawing P&IDs: ISA instrument tags, sensors/transmitters, controllers and final control elements
Feedback error and proportional-controller output on a heater loop
- +1Error, e = SP − c. In % of range SP = 80.0% and c = 77.5%, so e = 80.0 − 77.5 = +2.5% (equivalently +2.5 °C). The measurement is below set point, so the error is positive and the heater should open further.
- +1Valve signal, m = m̅ + Kc·e = 50% + 4 × (2.5%) = 50% + 10% = 60% valve opening. Direction check: too cold → e > 0 → m rises → more steam → temperature rises back toward SP, which is correct negative feedback.
- +1Proportional band, PB = 100%/Kc = 100%/4 = 25%: an error of 25% of range drives the valve across its full travel. Because a proportional controller only moves off its bias in proportion to a non-zero error, it settles with a permanent offset; removing it needs the integral term (add TI).
Key terms
- Feedback control
- A control strategy that measures the controlled variable, compares it with the set point to form an error, and adjusts a manipulated variable to drive that error toward zero. It reacts to the effect of any disturbance without needing to measure the disturbance itself.
- Error, e = SP − c
- The set point minus the measured controlled variable, in the engineering units of c (or in % of range once signals are scaled). A measurement below set point gives a positive error; this sign convention is what makes the loop negative feedback.
- Controlled / manipulated / disturbance variable
- The controlled variable c is what you regulate (level, temperature, pressure, composition); the manipulated variable m is what the valve changes (a flow or duty) to move c; the disturbance (load) d is an uncontrolled input that upsets c.
- Closed-loop (servo & regulator) transfer function
- The servo response to a set-point change is C/R = GcGvGp/(1 + GcGvGpGm); the regulator response to a load is C/QL = Gd/(1 + GcGvGpGm). Both share the same denominator, which contains every element of the loop including the sensor Gm.
- Characteristic equation
- The equation 1 + GcGvGpGm = 0 (that is, 1 + G_OL = 0), formed by setting the closed-loop denominator to zero. Its roots are the closed-loop poles; the loop is stable only if every root has a negative real part.
- PID controller
- The control law m(t) = m̅ + Kc[e + (1/TI)∫e dt + TD de/dt], or Gc(s) = Kc(1 + 1/(TI s) + TD s). Kc is the gain (dimensionless when scaled), TI the integral (reset) time and TD the derivative time, both in units of time; integral action removes offset.
- Final control element (control valve)
- The device that actually changes the manipulated variable, almost always a control valve with a pneumatic actuator. Its fail-safe action is chosen for safety: air-to-open (fails closed) or air-to-close (fails open).
- P&ID (Piping & Instrumentation Diagram) / ISA tag
- A drawing showing process lines and instrument loops. Each instrument is a balloon with an ISA tag whose first letter is the measured variable (F, L, P, T, A) and whose succeeding letters give the function (T transmitter, C controller, V valve), e.g. LC = level controller.
Feedback Control & P&IDs FAQ
What is the difference between the controlled variable, the manipulated variable and the set point?
The controlled variable c is the quantity you want to hold steady — a level, temperature, pressure or composition that a sensor measures. The set point SP (also written R) is the target value you want c to reach. The manipulated variable m is what the controller actually changes — usually a flow or a duty adjusted through a valve — to push c toward SP. The loop works on the error e = SP − c: when c drifts from SP the controller moves m until the error returns to (or near) zero.
Why does a proportional-only controller leave an offset, and how do you remove it?
A P-only controller sets its output as m = m̅ + Kc·e, so it can only sit away from its bias m̅ while the error e is non-zero. After a load change the loop settles at a new steady state that still needs a small standing error to hold the valve in its new position — that residual error is the offset, equal to 1/(1 + KcKp) of a unit set-point step. Increasing Kc shrinks the offset but never removes it. The integral term keeps accumulating error until e = 0, so adding integral action (a finite TI) is what eliminates offset entirely.
Can AI help me with feedback control and P&IDs in CHEN90032?
Yes, as a study aid. Sia can explain the loop step by step — how to write e = SP − c, form the closed-loop transfer function, decide reverse- versus direct-acting, and read the ISA tags on a P&ID — and can check your variable pairings and unit work on practice problems. Treat it as a tutor that walks you through method and reasoning, not a source of ready-made assessment answers: it does not sit your exam or guarantee a mark, and drawing the schemes and deriving the loops yourself is what earns credit and clears the exam hurdle.
Studying with AI? Sia — free AI chemical engineering tutor works through CHEN90032 step by step.
Exam move
Make the loop automatic: for any process, name c, SP, m and the disturbance, then write e = SP − c before anything else. Practise drawing the block diagram (controller, valve, process, sensor + comparator) and reading off the servo and regulator transfer functions, and rehearse P&ID sketching until you can pair every controlled variable with exactly one valve — that pairing is the heart of the exam's first question. The written final is 4 questions and 100 marks over 3 hours, about 1.8 minutes per mark, so a 35-mark control-design question is roughly 63 minutes; budget the first several minutes labelling the P&ID and justifying each pairing rather than rushing. On every practice loop, check the sign of the feedback (is it really negative?), state units on Kc, TI and TD, and note whether P-only would leave an offset.
