A Coriolis flow meter is distinctive because it measures

mass flow directly, rather than inferring it from a volumetric measurement

volumetric flow only, never mass flow

mass flow directly, rather than inferring it from a volumetric measurement

only the flow of conducting liquids

Linearizing a nonlinear process model near an operating point is done by

a first-order Taylor expansion, dropping higher-order terms

replacing all variables with their steady-state values

assuming the process has no dead time

converting the model to state-space form only

A process showing inverse response, after a step change in input, has an output that

first moves opposite to its eventual direction, then turns and heads the correct way

immediately jumps to its final steady-state value

first moves opposite to its eventual direction, then turns and heads the correct way

oscillates forever with no steady state

never reaches a new steady state

Which of the following are true of P, PI and PID controller modes?

A pure proportional (P) controller leaves a permanent offset that never fully closes.

Adding integral action (PI) removes steady-state offset for a step change.

Adding derivative action (PID) anticipates the rate of error change, at the cost of noise sensitivity.

A pure proportional (P) controller leaves a permanent offset that never fully closes.

Adding integral action (PI) removes steady-state offset for a step change.

Adding derivative action (PID) anticipates the rate of error change, at the cost of noise sensitivity.

PI control is always faster than PID control for the same process.

Equal-percentage valve trim is the usual default choice for a control valve chiefly because it

offsets a process's own falling gain, keeping overall loop gain roughly constant across the range

is simpler to manufacture than linear trim

offsets a process's own falling gain, keeping overall loop gain roughly constant across the range

gives the highest possible maximum flow capacity

eliminates the need for a positioner

PID tuning rules such as Ziegler-Nichols or Cohen-Coon exist chiefly to

compute reasonable starting controller settings from a small amount of test data, without solving the full closed-loop transfer function

eliminate the need for any process model

compute reasonable starting controller settings from a small amount of test data, without solving the full closed-loop transfer function

guarantee zero steady-state error for any process

replace the need for a control valve

Cascade control's inner (secondary) loop is set up so that

it acts on the final control element while the outer controller sets its setpoint

it ignores the outer loop entirely

it is always slower than the outer loop

it replaces the need for the outer controller

Process Measurement, Modelling, Control Modes and Loop Stability

Section 8 of the GATE Chemical Engineering (CH) paper. A chemical plant is a network of loops, and this section asks how each one is measured, modelled, and kept under control. Start with the sensors that measure a process variable in the first place and the P&ID symbols that record where they sit; then process modelling — linearization, state-space, transfer functions, and the special cases (inverse response, the process reaction curve) that a real plant actually produces; then the controller modes P, PI, PID and the control valve that turns their output into action; and finally closed-loop analysis — stability, frequency response, tuning, and the cascade and feedforward structures built on top of a single loop.

1. Measurement of process variables, sensors and P&ID symbols

Temperature is measured by thermocouples (a small voltage generated across dissimilar-metal junctions at different temperatures, the Seebeck effect), RTDs (a metal's resistance rising predictably with temperature) or thermistors (a semiconductor whose resistance falls sharply with temperature, more sensitive but over a narrower range); pressure by Bourdon tubes, diaphragms or strain-gauge transducers; flow by orifice plates, venturi meters, magnetic flow meters (for conducting liquids only) and Coriolis meters (which measure mass flow directly, not volumetric); and level by differential pressure, capacitance or ultrasonic devices, chosen by the fluid's own properties (conductivity, dielectric constant, foaming tendency).

ℹ️ P&ID tags encode what a symbol measures and does

A P&ID (piping and instrumentation diagram) instrument bubble carries a letter code read left to right: the first letter is the measured variable (T temperature, P pressure, F flow, L level), and the following letters are the function (I indicator, C controller, T transmitter, R recorder, A alarm) — so 'TIC' reads as a temperature indicating controller, and 'FT' as a flow transmitter. This vocabulary is what actually lets an engineer read an unfamiliar flowsheet's control philosophy at a glance.

2. Process modelling, linearization, state-space and dynamic response

Most real process models are nonlinear (a valve's flow depends on the square root of pressure drop, a reaction rate on an exponential of temperature), and linearization approximates such a model near a chosen operating point with a first-order Taylor expansion, dropping all higher-order terms — this is what makes classical transfer-function and Laplace-domain analysis applicable at all, at the cost of accuracy far from that operating point. A first-order process (a stirred tank's temperature, say) responds to a step input with an exponential approach to a new steady state, characterised by a gain (final change per unit input change) and a time constant (how fast it gets there); a second-order (or higher) process can show overshoot and oscillation the way a first-order process structurally cannot.

⚠️ An inverse response dips before it turns — do not read the dip as the wrong-direction final answer

A system with a right-half-plane zero in its transfer function shows an inverse response: after a step input, the output initially moves in the OPPOSITE direction to its eventual steady-state change before turning around and heading the correct way — a classic example is a boiler drum level that first drops when feedwater is increased, because the added cold water briefly collapses steam bubbles, before rising as the mass balance catches up. Reading the initial dip as the process's real direction (and adjusting the controller to fight it) is exactly the trap this behaviour sets, and it is why an inverse-response process is notoriously hard to tune with a simple PID.

3. Controller modes (P, PI, PID) and control valves

What each controller mode adds
Mode	Acts on	Leaves behind
P (proportional)	The error itself	A permanent offset that never fully closes
PI (proportional-integral)	Error plus its accumulated (integrated) history	No steady-state offset, but slower and can overshoot more
PID (proportional-integral-derivative)	Error, its history, and its rate of change	Faster, better-damped response, at the cost of noise sensitivity

A control valve's inherent characteristic (how its flow coefficient Cv varies with stem position at constant pressure drop) is chosen to match the process it serves: linear for a process whose gain is already roughly constant, and equal-percentage (flow rises exponentially with opening) for a process whose gain drops as flow rises, because the two characteristics combine to keep the LOOP gain roughly constant across the operating range — this is the real reason equal-percentage trim is the default choice for most control loops rather than linear trim, despite 'linear' sounding like the simpler, more natural option.

4. Closed-loop stability, frequency response, tuning, cascade and feedforward

Closed-loop stability is checked the same three ways as in general control theory — the Routh array on the characteristic equation's coefficients, the Bode plot's gain and phase margins, and the Nyquist criterion's encirclement count — and PID tuning rules (Ziegler-Nichols, Cohen-Coon, and others) exist specifically because a process reaction curve or an ultimate-gain test gives just enough information (process gain, time constant, dead time; or ultimate gain and period) to compute reasonable starting controller settings without solving the full closed-loop transfer function by hand.

Cascade control nests a fast inner (secondary) loop inside a slower outer (primary) loop — the outer controller sets the inner controller's setpoint rather than acting on the final control element directly — so a disturbance entering the inner loop is corrected before it ever reaches, or significantly upsets, the outer, more important variable.
Feedforward control measures a disturbance directly and acts on it before it ever shows up as an error in the controlled variable, unlike feedback control which can only react after the error has already appeared — feedforward's whole value is speed, at the cost of needing an accurate process model and a measurable disturbance, and it is almost always used alongside feedback (feedback trim) rather than alone, to correct for whatever the feedforward model gets wrong.

Key takeaways

P&ID tag letters encode variable then function, read left to right — TIC is a temperature indicating controller, FT a flow transmitter — and this vocabulary is what makes an unfamiliar flowsheet's control philosophy legible at a glance.
Linearization is a first-order Taylor expansion around an operating point, which is what makes transfer-function analysis applicable, at the cost of accuracy far from that point.
A right-half-plane zero produces inverse response — the output first moves opposite to its eventual direction — which is exactly why such processes are hard to tune with a simple PID.
Equal-percentage valve trim is the default choice because it offsets a process's own falling gain, keeping overall loop gain roughly constant across the operating range — not because it is simpler than linear trim.
Cascade control corrects an inner-loop disturbance before it reaches the outer variable; feedforward acts on a measured disturbance before it becomes an error, but is almost always paired with feedback trim rather than used alone.

Practice questions (9)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

A Coriolis flow meter is distinctive because it measures
1. volumetric flow only, never mass flow
2. mass flow directly, rather than inferring it from a volumetric measurement
3. only the flow of conducting liquids
4. temperature rather than flow
Show answer
Answer: B — mass flow directly, rather than inferring it from a volumetric measurement
A Coriolis meter senses the Coriolis force on fluid moving through a vibrating tube, which is directly proportional to mass flow rate — unlike orifice or venturi meters, which measure a pressure drop related to volumetric flow and then need the fluid's density to back out mass flow.
In P&ID tagging, the instrument bubble labelled 'FIC' represents a
1. flow indicating controller
2. fluid isolation control valve
3. final indicator of composition
4. field instrument controller
Show answer
Answer: A — flow indicating controller
Read left to right, F is the measured variable (flow), I is a function letter (indicating) and C is another function letter (controller) — so FIC reads as a flow indicating controller, following the same variable-then-function convention as TIC for temperature.
Linearizing a nonlinear process model near an operating point is done by
1. a first-order Taylor expansion, dropping higher-order terms
2. replacing all variables with their steady-state values
3. assuming the process has no dead time
4. converting the model to state-space form only
Show answer
Answer: A — a first-order Taylor expansion, dropping higher-order terms
Linearization keeps only the first-order (linear) term of a Taylor series expansion around the chosen operating point and discards all higher-order terms, which is exactly what makes classical transfer-function and Laplace-domain tools applicable, at the cost of accuracy away from that point.
A process showing inverse response, after a step change in input, has an output that
1. immediately jumps to its final steady-state value
2. first moves opposite to its eventual direction, then turns and heads the correct way
3. oscillates forever with no steady state
4. never reaches a new steady state
Show answer
Answer: B — first moves opposite to its eventual direction, then turns and heads the correct way
Inverse response is exactly this signature: caused by a right-half-plane zero in the transfer function, the output dips (or rises) the wrong way first before eventually turning to approach its correct final steady state — the classic example being a boiler drum level dropping before it rises after a feedwater increase.
Which of the following are true of P, PI and PID controller modes?
1. A pure proportional (P) controller leaves a permanent offset that never fully closes.
2. Adding integral action (PI) removes steady-state offset for a step change.
3. Adding derivative action (PID) anticipates the rate of error change, at the cost of noise sensitivity.
4. PI control is always faster than PID control for the same process.
Show answer
Answer: A — A pure proportional (P) controller leaves a permanent offset that never fully closes.; B — Adding integral action (PI) removes steady-state offset for a step change.; C — Adding derivative action (PID) anticipates the rate of error change, at the cost of noise sensitivity.
The fourth statement is false: derivative action in PID is added specifically to anticipate and damp the response, generally making PID FASTER and better-damped than PI alone for a well-tuned loop, not slower. The first three correctly describe what each mode contributes and costs.
Equal-percentage valve trim is the usual default choice for a control valve chiefly because it
1. is simpler to manufacture than linear trim
2. offsets a process's own falling gain, keeping overall loop gain roughly constant across the range
3. gives the highest possible maximum flow capacity
4. eliminates the need for a positioner
Show answer
Answer: B — offsets a process's own falling gain, keeping overall loop gain roughly constant across the range
Many processes' gain falls as flow rises; an equal-percentage valve's own gain rises as it opens, and pairing the two keeps the product (overall loop gain) roughly constant across the operating range — which is the real engineering reason for the choice, not manufacturing simplicity.
PID tuning rules such as Ziegler-Nichols or Cohen-Coon exist chiefly to
1. eliminate the need for any process model
2. compute reasonable starting controller settings from a small amount of test data, without solving the full closed-loop transfer function
3. guarantee zero steady-state error for any process
4. replace the need for a control valve
Show answer
Answer: B — compute reasonable starting controller settings from a small amount of test data, without solving the full closed-loop transfer function
A process reaction curve (open-loop step test) or an ultimate-gain test gives just a few numbers — process gain, time constant, dead time, or ultimate gain and period — and the tuning rules turn those directly into starting P, I and D settings, sparing the engineer from deriving and solving the full closed-loop characteristic equation by hand.
Cascade control's inner (secondary) loop is set up so that
1. it acts on the final control element while the outer controller sets its setpoint
2. it ignores the outer loop entirely
3. it is always slower than the outer loop
4. it replaces the need for the outer controller
Show answer
Answer: A — it acts on the final control element while the outer controller sets its setpoint
The outer (primary) controller does not act on the final control element directly; it sets the setpoint of the faster inner (secondary) controller, which does act on the valve or final element — this nesting is exactly what lets a disturbance entering the inner loop get corrected before it disturbs the outer, more important variable.
A first-order process has time constant tau = 5 minutes. After how many minutes does its step response reach approximately 63.2% of its total final change (one time constant)?
Numerical answer — type the value.
Show answer
Answer: 5
A first-order step response is y(t) = final-change*(1 - exp(-t/tau)); at t = tau, this equals (1 - exp(-1)) = 1 - 0.368 = 0.632, or 63.2% of the total change, regardless of the process's gain or the size of the input step — exactly one time constant, 5 minutes here.