GATE Chemical Engineering Instrumentation and Process Control Syllabus

Instrumentation and Process Control syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Instrumentation and Process Control in GATE Chemical Engineering, not a summary of it.

1. 1

   Measurement of Process Variables

   1 topic

   • Sensors and Transducers
2. 2

   P&ID Equipment Symbols

   1 topic

   • Process Modeling and Linearization
3. 3

   Transfer Functions and Dynamic Responses of Various Systems

   1 topic

   • Systems with Inverse Response
4. 4

   Process Reaction Curve

   overview

   Examined as a single unit within Instrumentation and Process Control — no further topic split in the official outline.

5. 5

   Controller Modes (P, PI, and PID)

   overview

   Examined as a single unit within Instrumentation and Process Control — no further topic split in the official outline.

6. 6

   Control Valves

   1 topic

   • Transducer Dynamics
7. 7

   Analysis of Closed Loop Systems

   4 topics

   • Stability
   • Frequency Response
   • Controller Tuning
   • Cascade and Feed Forward Control

Instrumentation and Process Control flashcards for GATE Chemical Engineering

25 of 50 cards from the Instrumentation and Process Control deck — real questions with worked answers.

1. What is the difference between a sensor and a transducer?

   A sensor detects a physical/chemical quantity (e.g., temperature, pressure). A transducer converts that measured quantity into a different (usually electrical) signal that can be processed. Every transducer contains a sensing element, but adds signal conversion.

2. Classify transducers based on their energy requirement, with examples.

   Active (self-generating) transducers produce an output without external power, e.g., thermocouple, piezoelectric crystal. Passive transducers require external excitation to produce output, e.g., RTD, strain gauge, capacitive/LVDT sensors.

3. State the working principle of a thermocouple and the relevant effect.

   A thermocouple works on the Seebeck effect: a junction of two dissimilar metals generates an EMF proportional to the temperature difference between the measuring (hot) and reference (cold) junctions. It is an active transducer.

4. What is the resistance-temperature relationship for an RTD (linearized form)?

   $$R_T = R_0\,(1 + \alpha\,\Delta T)$$ where $R_0$ is the resistance at the reference temperature, $\alpha$ is the temperature coefficient of resistance, and $\Delta T$ is the temperature change. Platinum (Pt-100) is the common RTD material.

5. Define static sensitivity (gain) of a measuring instrument.

   Static sensitivity is the ratio of the change in output to the change in input at steady state: $$K = \frac{\Delta(\text{output})}{\Delta(\text{input})}$$ It is the slope of the calibration (input-output) curve.

6. Distinguish between accuracy and precision of an instrument.

   Accuracy is closeness of a measured value to the true value (small systematic error). Precision is repeatability — closeness of repeated measurements to one another (small random scatter). An instrument can be precise but inaccurate.

7. What is the transfer function of a general first-order (transducer) system?

   $$G(s) = \frac{Y(s)}{X(s)} = \frac{K}{\tau s + 1}$$ where $K$ is the steady-state gain and $\tau$ is the time constant. Many transducers (e.g., thermometer in a well) behave as first-order systems.

8. For a first-order system subjected to a step input of magnitude $A$, write the time response.

   $$y(t) = K A\left(1 - e^{-t/\tau}\right)$$ The response reaches 63.2% of its final value at $t=\tau$ and is essentially complete ($\approx 98.2\%$) at $t=4\tau$.

9. What fraction of the final value does a first-order system reach at $t = \tau$, $2\tau$, $3\tau$ and $4\tau$?

   At $\tau$: 63.2%, at $2\tau$: 86.5%, at $3\tau$: 95.0%, at $4\tau$: 98.2%. Settling is conventionally taken at about $4\tau$ (within 2%).

10. Define the time constant of a first-order thermal transducer physically.

    For a temperature sensor, $$\tau = \frac{m\,C_p}{h\,A}$$ where $m$ is mass, $C_p$ specific heat, $h$ heat-transfer coefficient, and $A$ surface area. A smaller mass or larger $hA$ gives a faster (smaller $\tau$) sensor.

11. What is the standard form of a second-order system transfer function?

    $$G(s) = \frac{K\,\omega_n^{2}}{s^{2} + 2\zeta\omega_n s + \omega_n^{2}} = \frac{K}{\tau^{2}s^{2} + 2\zeta\tau s + 1}$$ where $\zeta$ is the damping ratio, $\omega_n = 1/\tau$ the natural frequency, and $\tau$ the characteristic time.

12. Classify the response of a second-order system by its damping ratio $\zeta$.

    $\zeta = 0$: undamped (sustained oscillation); $0<\zeta<1$: underdamped (decaying oscillation); $\zeta = 1$: critically damped (fastest non-oscillatory); $\zeta > 1$: overdamped (sluggish, no overshoot).

13. Give the formula for percent overshoot of an underdamped second-order system to a step input.

    $$\text{Overshoot} = \exp\!\left(-\frac{\pi\zeta}{\sqrt{1-\zeta^{2}}}\right)$$ Percent overshoot $= 100\times$ this value. It depends only on $\zeta$, decreasing as $\zeta$ increases.

14. Write the expressions for decay ratio and period of oscillation of an underdamped second-order system.

    Decay ratio $= (\text{overshoot})^{2} = \exp\!\left(-\dfrac{2\pi\zeta}{\sqrt{1-\zeta^{2}}}\right)$. Period of oscillation $$T = \frac{2\pi\tau}{\sqrt{1-\zeta^{2}}}$$ The 'quarter decay ratio' design corresponds to $\zeta \approx 0.215$.

15. What is the rise time and what is its qualitative dependence on damping?

    Rise time is the time for the response to first reach its final value (for underdamped systems). It decreases as $\zeta$ decreases (less damping = faster rise), but smaller $\zeta$ also increases overshoot — a fundamental trade-off.

16. What is process modeling, and what are the two broad approaches?

    Process modeling is deriving mathematical equations (mass, energy, momentum balances) describing process dynamics. Two approaches: (1) theoretical/first-principles (white-box) models from conservation laws, and (2) empirical (black-box) models fitted from input-output data.

17. State the general unsteady-state mass balance used in process modeling.

    $$\frac{dm}{dt} = \dot{m}_{in} - \dot{m}_{out}$$ Rate of accumulation = rate in $-$ rate out ($+$ generation $-$ consumption for component balances with reaction).

18. Why is linearization needed in process control?

    Most process models are nonlinear, but linear control theory (Laplace transforms, transfer functions, stability criteria) requires linear ODEs. Linearization approximates the nonlinear model around a steady-state operating point so linear tools apply.

19. State the Taylor-series linearization of a one-variable nonlinear function $f(x)$ about $x_s$.

    $$f(x) \approx f(x_s) + \left.\frac{df}{dx}\right|_{x_s}(x - x_s)$$ Higher-order terms are neglected. In deviation variable $x' = x - x_s$, this becomes linear in $x'$.

20. Linearize a two-variable function $f(x,y)$ about the steady state $(x_s, y_s)$.

    $$f(x,y) \approx f(x_s,y_s) + \left.\frac{\partial f}{\partial x}\right|_{s}(x-x_s) + \left.\frac{\partial f}{\partial y}\right|_{s}(y-y_s)$$ using first-order partial derivatives evaluated at the operating point.

21. What is a deviation (perturbation) variable and why is it used?

    A deviation variable is the difference between a variable and its steady-state value, e.g., $x' = x - x_s$. It is used because at steady state the deviation and its derivatives are zero, eliminating constant terms and giving transfer functions with zero initial conditions.

22. As an example, linearize the efflux term $F = c\sqrt{h}$ (tank outflow) about $h_s$.

    $$F \approx c\sqrt{h_s} + \frac{c}{2\sqrt{h_s}}(h - h_s)$$ The linearized resistance/slope is $\dfrac{c}{2\sqrt{h_s}}$, valid for small deviations of $h$ about $h_s$.

23. What is inverse response in a process system?

    Inverse response occurs when the process output initially moves in the opposite direction to its eventual steady-state direction following an input change. It is caused by competing fast and slow effects of opposite sign.

24. What feature in the transfer function causes inverse response?

    Inverse response is caused by a right-half-plane (positive) zero in the transfer function, i.e., a numerator zero with positive real part. Example: $$G(s) = \frac{-\tau_a s + 1}{(\tau_1 s + 1)(\tau_2 s + 1)}, \quad \tau_a > 0.$$

25. For two opposing first-order responses $G(s)=\frac{K_1}{\tau_1 s+1}-\frac{K_2}{\tau_2 s+1}$, what condition gives inverse response?

    Inverse response occurs when the steady-state gains satisfy $K_1 - K_2 > 0$ but the initial slope is negative, which requires $$\frac{K_1}{\tau_1} < \frac{K_2}{\tau_2}.$$ The faster (smaller $\tau$) effect dominates initially and acts opposite to the steady state.

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