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GATE CH: Instrumentation and Process Control

GATE CH · Work through your exam, one topic at a time.

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Instrumentation and Process Control

This domain pairs measurement hardware with dynamic analysis and controller tuning. Marks come from sensors (thermocouple, RTD, orifice, DP cell), from first- and second-order dynamics, and from stability tools (Routh, Bode, root locus) applied to closed loops.

Core rules

  • Temperature. A thermocouple measures an emf that needs cold-junction compensation; an RTD is more linear and stable but slower; a pyrometer is for non-contact high temperature.
  • Flow. Orifice and venturi meters are square-root devices: flow ∝ √ΔP, so a 25% drop in flow halves the differential. Rotameters give a linear visual scale; Coriolis meters measure mass flow directly.
  • Process dynamics. First order: τ(dy/dt) + y = Kx, giving 63.2% of the final change in one time constant. Second order is described by the damping factor ζ and natural frequency ω_n.
  • Closed loop. For a loop with G_c G_v G_p G_m, the characteristic equation is 1 + G_OL = 0; use Routh for the limiting gain. Gain margin and phase margin read from a Bode plot (phase margin measured at the gain crossover).
  • Controller action. Proportional control leaves offset; integral removes offset but adds lag; derivative speeds response but amplifies noise.
  • Valves. Air-to-open valves fail closed; equal-percentage trim suits a wide range of pressure drop.

Worked example

A loop has G_c = K_c, G_p = 1/(s+1)³, with unity valve and transmitter. The characteristic equation is 1 + K_c/(s+1)³ = 0, i.e. s³ + 3s² + 3s + (1 + K_c) = 0. The Routh array gives the s¹ row as (9 − 1 − K_c)/3, so stability requires K_c > −1 and K_c < 8. The ultimate gain is therefore K_u = 8, which with the ultimate period is exactly what Ziegler–Nichols tuning needs.

Traps

  • Using the orifice's linear flow assumption (flow ∝ ΔP) instead of √ΔP.
  • Forgetting cold-junction compensation in a thermocouple reading.
  • Reading phase margin at the phase crossover rather than the gain crossover.
  • Applying derivative action to a noisy flow signal.
  • Confusing valve fail-safe direction with the controller's reverse action.