Measurements, Instrumentation and Controls is 5-8 questions on the FE Mechanical exam. Along with Electricity and Magnetism it is the area mechanical candidates most often skip, usually because controls was one course taken once and never revisited.
Skipping it is expensive. Five to eight questions is a similar block to electricity, and much of the content overlaps with statistics and dynamics you are already studying.
Exam weight: NCEES lists Measurements, Instrumentation, and Controls at 5-8 questions of the 110-question FE Mechanical exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Measurements, Instrumentation, and Controls
The specification covers sensors and measurement devices, measurement uncertainty, control systems and their components, and dynamic system response. Expect a strain gauge or thermocouple question, a propagation-of-uncertainty calculation, a block-diagram reduction, and identification of first- or second-order system behaviour from a response curve.
Dynamic response items ask for a time constant, a settling behaviour, or the effect of damping ratio on overshoot. These are the same second-order relationships that appear in the vibrations part of Dynamics, expressed in control language.
5 Free Measurements, Instrumentation, and Controls Practice Problems
Each measurements instrumentation controls problem below comes from the FEExamClick FE Mechanical question bank, with worked solutions, and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1 — C. Dynamic system response
A first-order system has a transfer function \(G(s) = \frac{5}{2s + 1}\). The time constant of this system is most nearly:
Answer: B) 2.0 s
Refer to the Dynamic Response section in the Instrumentation, Measurement, and Control chapter of the FE Reference Handbook.
A first-order system has the standard form:
$$G(s) = \frac{K}{\tau s + 1}$$
Comparing with \(G(s) = \frac{5}{2s + 1}\):
\(K = 5\) (static gain)
\(\tau = 2\) s (time constant)
The time constant determines how quickly the system responds. After one time constant (\(t = \tau\)), the system reaches 63.2% of its final value.
Problem 2 — B. Control systems (e.g., feedback, block diagrams)
For the negative unity feedback system shown, with forward path transfer function \( G(s) \), the closed-loop transfer function \( Y(s)/R(s) \) is:
Answer: D) G(s)/[1 + G(s)]
Step 1 – Write the signal at the summing junction.
The feedback is subtracted, and the feedback path has \( H(s) = 1 \), so the error signal is
\( E(s) = R(s) - H(s)\,Y(s) = R(s) - Y(s) \)
Step 2 – Write the output of the forward path.
The block \( G(s) \) acts on the error, not on the input:
\( Y(s) = G(s)\,E(s) \)
Step 3 – Substitute and collect \( Y(s) \).
\( Y(s) = G(s)\left[R(s) - Y(s)\right] \)
\( Y(s) + G(s)\,Y(s) = G(s)\,R(s) \)
\( Y(s)\left[1 + G(s)\right] = G(s)\,R(s) \)
Step 4 – Solve.
\( \dfrac{Y(s)}{R(s)} = \dfrac{G(s)}{1 + G(s)} \)
Why the other options fail:
• \( 1/[1 + G(s)] \) is \( E(s)/R(s) \) — the transfer function to the error, not to the output. Substituting \( Y = GE \) into Step 1 gives \( E = R - GE \), hence this ratio. It is a real transfer function of the loop, just not the one asked for.
• \( G(s)/[1 - G(s)] \) is the positive feedback result — it comes from adding the feedback at the summing junction instead of subtracting it.
• \( G(s) + 1 \) is not a closed-loop form at all.
General form: for feedback \( H(s) \) the closed-loop transfer function is \( G(s)/[1 + G(s)H(s)] \); unity feedback is the case \( H(s) = 1 \). Setting the denominator to zero gives the characteristic equation \( 1 + G(s) = 0 \), whose roots are the closed-loop poles.
Correct answer: (D)
Problem 3 — D. Measurement uncertainty
The result of 2.54 \(\times\) 1.2 should be reported as:
Answer: A) 3.0
Rules for significant figures in multiplication/division:
The result should have the same number of significant figures as the factor with the fewest significant figures.
- 2.54 has 3 significant figures
- 1.2 has 2 significant figures
$$2.54 \times 1.2 = 3.048$$
Rounded to 2 significant figures: 3.0
Note: 3.0 has 2 sig figs; "3" alone has only 1 sig fig.
Problem 4 — A. Sensors and transducers
An 8-bit A/D converter has a voltage range of 0-10 V. The voltage resolution is:
Answer: C) 0.039 V
Voltage resolution of an A/D converter:
$$\varepsilon_V = \frac{V_H - V_L}{2^n}$$
where \(n\) = number of bits
$$\varepsilon_V = \frac{10 - 0}{2^8} = \frac{10}{256}$$
$$\boxed{\varepsilon_V = 0.039 \text{ V}}$$
This is the smallest voltage change the converter can detect.
Problem 5 — B. Control systems (feedback, block diagrams)
Two transfer function blocks are connected in parallel: \(G_1(s) = \frac{3}{s + 2}\) and \(G_2(s) = \frac{5}{s + 2}\). The combined transfer function is:
Answer: C) \(\frac{8}{s + 2}\)
Refer to the Control Systems section in the Instrumentation, Measurement, and Control chapter of the FE Reference Handbook.
For blocks in parallel, the overall transfer function is the sum:
$$G(s) = G_1(s) + G_2(s) = \frac{3}{s + 2} + \frac{5}{s + 2} = \frac{3 + 5}{s + 2} = \frac{8}{s + 2}$$
Note: For parallel blocks, outputs are summed. For series blocks, transfer functions are multiplied.
Using the FE Reference Handbook for Measurements, Instrumentation, and Controls
The Measurement and Controls material is spread rather than concentrated, so know the two anchors: the uncertainty propagation expression and the standard second-order response parameters. Search the handbook for uncertainty and for damping ratio during practice, because hunting for these while the clock runs is what makes candidates abandon the area.
Four Mistakes That Cost Points
- Adding uncertainties linearly. Independent random uncertainties combine in quadrature, as the square root of the sum of squares. Straight addition overstates the result and is always offered as an option.
- Confusing accuracy with precision. A systematically biased instrument can be highly repeatable and consistently wrong. Concept questions in this area turn on exactly that distinction, and calibration corrects bias rather than scatter.
- Reducing a block diagram without the feedback sign. A negative feedback loop gives forward gain over one plus loop gain; positive feedback gives one minus. Getting the sign wrong changes stability conclusions entirely.
- Reading a time constant as the time to reach final value. One time constant brings a first-order system to about 63 percent of its final change, not to completion. Practical settling takes roughly four to five time constants.
Frequently Asked Questions
How many measurements and controls questions are on the FE Mechanical exam?
NCEES specifies 5-8 questions from Measurements, Instrumentation and Controls out of 110. It carries the same weight as Electricity and Magnetism.
How much control theory is required?
Substantially less than a controls course. You need block-diagram reduction, the behaviour of first- and second-order systems, and the roles of proportional, integral and derivative action. Root locus, Bode design and state-space methods are outside the usual scope.
What sensors should I know?
Strain gauges, thermocouples, RTDs, pressure transducers and encoders cover most of what appears. Know the physical principle behind each and its typical output signal rather than manufacturer specifications.
Is measurement uncertainty the same as the statistics area?
It draws on it. Uncertainty propagation is applied statistics, so studying Probability and Statistics first makes this area substantially shorter. The two together are worth 9-14 questions, which is why treating them as one study block is efficient.
Keep Going
These topics feed into each other on the exam:
- FE Mechanical Electricity and Magnetism practice problems — 5-8 questions on the exam
- FE Mechanical Probability and Statistics practice problems — 4-6 questions on the exam
- FE Mechanical Dynamics, Kinematics, and Vibrations practice problems — 10-15 questions on the exam
Done with measurements instrumentation controls? Browse every knowledge area from the free FE Mechanical practice problem hub, see what the full bank covers on the FE Mechanical exam prep page, or plan your schedule with the FE study timeline. Or test yourself against the clock with the free FE Mechanical practice exam: 20 timed questions in the CBT format.