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PE Control Systems practice questions

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Question 1Measurement and Instrumentation

In a conventional 4–20 mA analog process control loop, what does the 20 mA value represent?

  1. 100 percent of the transmitter span Correct answer.
  2. A fixed alarm level
  3. The minimum measurable process value
  4. The transmitter supply current

Explanation

The standard analog current signal uses 4 mA for the lower range value (0 percent) and 20 mA for the upper range value (100 percent). Any current between the endpoints is a linear fraction of the calibrated span.

Question 2Measurement and Instrumentation

Why is the lower end of a standard analog current loop set at 4 mA rather than 0 mA?

  1. It allows digital HART data to be carried on the same pair.
  2. It eliminates the need for a separate power supply in the loop.
  3. It increases the maximum current that the loop can deliver to a load.
  4. It lets the system tell a failed transmitter from a true zero. Correct answer.

Explanation

A live zero means a genuine 0 percent measurement draws 4 mA, while a broken wire or dead transmitter draws essentially 0 mA. The control system can therefore distinguish a valid zero reading from a failed loop.

Question 3Measurement and Instrumentation

Which element material is most widely used in industrial RTDs for process temperature measurement?

  1. Platinum Correct answer.
  2. Constantan
  3. Chromel
  4. Iron

Explanation

Platinum has a stable, nearly linear resistance–temperature relationship over a wide range and resists contamination and oxidation. The Pt100 element (100 ohms at 0 °C) is the industrial standard.

Question 4Measurement and Instrumentation

A thermocouple produces a measurable voltage because of which effect?

  1. The Seebeck effect at a junction of two dissimilar metals Correct answer.
  2. The change in resistance of a metal element with temperature
  3. The change in capacitance between two plates
  4. The piezoelectric response of two dissimilar crystals

Explanation

Joining two dissimilar metals creates an emf that depends on the junction temperature relative to the reference junction. This is the Seebeck effect, and it is the basis of all thermocouple measurement.

Question 5Measurement and Instrumentation

For a differential-pressure flow element such as an orifice plate, how does volumetric flow rate relate to the measured differential pressure?

  1. As the square of differential pressure
  2. Independently of differential pressure
  3. As the square root of differential pressure Correct answer.
  4. Directly proportional to differential pressure

Explanation

By Bernoulli's relationship, flow through a restriction is proportional to the square root of the differential pressure. This is why square-root extraction is required to obtain a linear flow signal.

Question 6Measurement and Instrumentation

A gauge pressure transmitter reads 40 psig while local atmospheric pressure is 14.7 psia. What is the absolute pressure?

  1. 54.7 psia Correct answer.
  2. 14.7 psia
  3. 40 psia
  4. 25.3 psia

Explanation

Absolute pressure equals gauge pressure plus atmospheric pressure. Adding 40 psig to 14.7 psi of atmosphere gives 54.7 psia.

Question 7Measurement and Instrumentation

Which device is a final control element in a feedback control loop?

  1. Control valve Correct answer.
  2. Current-to-pressure transducer
  3. Orifice plate
  4. RTD

Explanation

The final control element is the device that directly manipulates the process variable, which in most loops is a control valve changing flow. Sensors such as orifice plates and RTDs only measure.

Question 8Measurement and Instrumentation

What is the primary reason for using a three-wire connection with an RTD?

  1. To reduce self-heating in the element
  2. To allow the RTD to be used in hazardous areas
  3. To cancel the resistance of the lead wires Correct answer.
  4. To increase the excitation current through the element

Explanation

In a three-wire hookup the transmitter measures the lead resistance in one leg and subtracts it, so the copper wiring does not add a false temperature offset. This matters when the RTD is far from the transmitter.

Question 9Measurement and Instrumentation

A 4–20 mA transmitter signal is passed through a 250 ohm precision resistor to create an analog voltage input for a PLC. What voltage range results?

  1. 4 to 20 V dc
  2. 0 to 5 V dc
  3. 2 to 10 V dc
  4. 1 to 5 V dc Correct answer.

Explanation

By Ohm's law, 4 mA across 250 ohms gives 1 V and 20 mA gives 5 V. The resulting 1–5 V signal preserves the live zero of the original current loop.

Question 10Measurement and Instrumentation

How is the digital HART signal carried on a standard 4–20 mA loop?

  1. As an amplitude-modulated voltage above 24 V
  2. As a small FSK signal superimposed on the loop current Correct answer.
  3. As brief interruptions of the loop current at 1200 baud
  4. As a separate optical pulse on a fiber pair

Explanation

HART adds a low-amplitude frequency-shift-keyed tone on top of the analog current without disturbing the 4–20 mA measurement. The two frequencies represent binary ones and zeros while the dc level continues to represent the process value.

Question 11Measurement and Instrumentation

A differential-pressure transmitter on an orifice is ranged so 4 mA corresponds to 0 flow and 20 mA to 100 percent flow, with square-root extraction done in the DCS. If the transmitter output is 12 mA and is linear with differential pressure, what flow percentage does the DCS display?

  1. 70.7 percent Correct answer.
  2. 50 percent
  3. 25 percent
  4. 100 percent

Explanation

12 mA is 50 percent of the 4–20 mA span, so the differential pressure is at 50 percent of its range. Flow varies with the square root of differential pressure, and the square root of 0.50 is about 0.707, or 70.7 percent.

Question 12Measurement and Instrumentation

Why must a thermocouple measuring circuit include cold-junction compensation?

  1. To protect the thermocouple from over-temperature damage
  2. Because the emf depends on the reference junction temperature Correct answer.
  3. To linearize the thermocouple output over its entire usable range
  4. To amplify the small thermocouple emf to a usable level

Explanation

A thermocouple emf is generated by the difference between the measuring junction and the terminal where the thermocouple wire meets copper. The transmitter must measure that terminal temperature and correct the reading, which is cold-junction compensation.

Question 13Measurement and Instrumentation

How should the shield of a shielded twisted-pair analog instrument cable normally be grounded?

  1. At every junction box along the run
  2. At both ends to double the shielding effectiveness
  3. It should not be grounded at all
  4. At one point only, normally at the instrument end Correct answer.

Explanation

Grounding the shield at a single point drains capacitively coupled interference without creating a path for circulating ground current. Connecting both ends forms a ground loop that can inject noise into the signal pair.

Question 14Measurement and Instrumentation

A magnetic flowmeter is unsuitable for which service?

  1. A hydrocarbon stream of very low conductivity Correct answer.
  2. Clean cooling water in a 12-inch carbon steel line
  3. Municipal wastewater carrying rags and suspended solids
  4. A conductive slurry with moderate solids in a 4-inch line

Explanation

A magnetic flowmeter works from the voltage induced in a conductor moving through a magnetic field, so the liquid must have adequate conductivity. Hydrocarbons are essentially non-conductive and produce no usable signal.

Question 15Measurement and Instrumentation

In a vortex-shedding flowmeter, the frequency of vortices shed from the bluff body is proportional to what?

  1. The fluid density only
  2. The square of the pipe diameter
  3. The fluid velocity through the meter Correct answer.
  4. The viscosity of the fluid raised to the 0.5 power

Explanation

Strouhal's relationship makes shedding frequency proportional to velocity divided by the bluff-body width, which is why the meter can infer flow from frequency. Density and viscosity enter only through the Reynolds-number limits of the meter.

Question 16Measurement and Instrumentation

What does a current-to-pressure (I/P) transducer do in a pneumatic valve actuator loop?

  1. It converts a digital HART command into a valve position
  2. It converts a 3–15 psi pneumatic signal into a 4–20 mA electrical signal
  3. It converts valve stem position into a feedback current
  4. It converts a 4–20 mA output into a proportional 3–15 psi air pressure Correct answer.

Explanation

The I/P transducer receives the controller's 4–20 mA signal and outputs a proportional pneumatic pressure, normally 3–15 psi, that positions the actuator. It is the interface between the electronic controller and the pneumatic final element.

Question 17Measurement and Instrumentation

A transmitter's readings are repeatable but consistently about 2 psi above the true value. How is this best described?

  1. Neither accurate nor precise
  2. Both accurate and precise
  3. Accurate but not precise
  4. Precise but not accurate Correct answer.

Explanation

Precision describes how closely repeated readings agree with one another, while accuracy describes how close they are to the true value. Consistent readings with a fixed offset are precise but biased, hence inaccurate.

Question 18Measurement and Instrumentation

A pressure transmitter is calibrated 0 to 400 inH2O with a 4–20 mA output. What pressure corresponds to an output of 8 mA?

  1. 100 inH2O Correct answer.
  2. 200 inH2O
  3. 320 inH2O
  4. 50 inH2O

Explanation

The 4–20 mA span is 16 mA, so an 8 mA output is 4 mA above the zero, or 25 percent of span. Twenty-five percent of 400 inH2O is 100 inH2O.

Question 19Measurement and Instrumentation

What is the effect of increasing the damping setting on a transmitter output?

  1. It smooths process noise but slows the response Correct answer.
  2. It shifts the zero point of the measurement upward
  3. It increases the minimum loop supply voltage required
  4. It increases the calibrated span of the measurement

Explanation

Damping applies a time filter to the output, which suppresses short-term fluctuations such as turbulence or electrical noise. The trade-off is a lag in responding to genuine process changes, which can matter for fast control loops.

Question 20Measurement and Instrumentation

Which flowmeter determines mass flow directly, without needing separate density compensation?

  1. Turbine flowmeter
  2. Coriolis flowmeter Correct answer.
  3. Positive displacement flowmeter
  4. Ultrasonic flowmeter

Explanation

A Coriolis meter measures the mass flow rate from the phase shift between the oscillations of two tubes carrying the fluid. Because the measurement is inherently mass-based, changes in density, temperature, and pressure do not require correction.

Question 21Measurement and Instrumentation

A two-wire transmitter needs at least 12 V dc across its terminals and the loop is powered by a 24 V dc supply. What total loop resistance (receiving resistor plus wiring) will just keep it working at 20 mA?

  1. 240 ohms
  2. 1200 ohms
  3. 300 ohms
  4. 600 ohms Correct answer.

Explanation

At full-scale current the supply may drop no more than 24 minus 12, or 12 V, across the entire loop. Dividing 12 V by 0.020 A gives 600 ohms of maximum permissible loop resistance.

Question 22Measurement and Instrumentation

A Pt100 RTD with a sensitivity of about 0.385 ohm/°C is wired two-wire, and each lead has 1.0 ohm of resistance. What temperature error results?

  1. About 5.2 °C high Correct answer.
  2. No error, since lead resistance cancels
  3. About 26 °C high
  4. About 0.5 °C high

Explanation

In a two-wire hookup the excitation current passes through both leads, so 2 ohms is added to the element resistance. Dividing 2 ohms by 0.385 ohm/°C gives roughly 5.2 °C of positive measurement error.

Question 23Measurement and Instrumentation

With flange taps on an orifice plate installation, where are the pressure taps located?

  1. Two and one-half pipe diameters upstream and eight diameters downstream
  2. At the corner where the plate meets the pipe wall
  3. One inch (25 mm) upstream and one inch downstream of the plate faces Correct answer.
  4. One pipe diameter upstream and one-half pipe diameter downstream of the plate

Explanation

Flange taps are drilled in the pipe flanges holding the plate, one inch from the upstream face and one inch from the downstream face. Corner taps sit directly at the plate, and pipe taps use 2.5 diameters upstream and 8 diameters downstream.

Question 24Measurement and Instrumentation

In a HART multidrop configuration with several transmitters on one pair, what is the loop current?

  1. It is fixed at 4 mA for each device Correct answer.
  2. It is proportional to the number of devices on the bus
  3. It varies between 4 and 20 mA for each transmitter
  4. It is 20 mA regardless of the measurement

Explanation

Multidropping disables analog signaling, so every device draws a constant 4 mA and all process values are read digitally. The total cable current therefore equals about 4 mA times the number of connected devices.

Question 25Measurement and Instrumentation

During a calibration check, a transmitter ranged 0–100 psig with a 4–20 mA output produces exactly 4.00 mA at 0 psig and 19.20 mA at 100 psig. How is this best described?

  1. A zero shift of −5 percent with correct span
  2. A zero shift of +5 percent with a span error of −5 percent
  3. Correct zero but a span error of about −5 percent Correct answer.
  4. Correct zero and correct span

Explanation

The measured output span is 15.2 mA against the expected 16 mA, which is a span shortfall of about 5 percent. Because the output at 0 psig is exactly 4.00 mA, the zero is correct and only the span needs adjustment.

Question 26Measurement and Instrumentation

In instrument terminology, what is hysteresis?

  1. Difference in output for the same input approached from opposite directions Correct answer.
  2. Change in output per unit change in input across the calibrated span
  3. Closeness of agreement among repeated measurements of the same variable
  4. Smallest input change that produces a detectable change in output

Explanation

Hysteresis is the maximum difference between readings taken at the same input when that input is reached by increasing it and then by decreasing it. It is caused by mechanical friction, magnetic effects, or elastic memory in the sensing element.

Question 27Measurement and Instrumentation

A type K thermocouple is made from which pair of materials?

  1. Copper and constantan
  2. Platinum and a platinum-rhodium alloy
  3. Chromel and alumel Correct answer.
  4. Iron and constantan

Explanation

Type K uses the nickel-chromium alloy chromel as the positive leg and the nickel-aluminium alloy alumel as the negative leg. It is a general-purpose type with good oxidation resistance at elevated temperature.

Question 28Measurement and Instrumentation

Why does the 4–20 mA standard use 4 mA rather than 0 mA to represent the zero value?

  1. It reduces the voltage drop across the measuring resistor at zero flow
  2. It increases the resolution of the signal compared with a 0–16 mA span
  3. It lets the receiver distinguish a valid zero reading from a broken or dead loop Correct answer.
  4. It allows the transmitter to be loop-powered from the same two wires

Explanation

A live zero gives the receiver a reference current that a working transmitter must always draw, so a current near 0 mA can be flagged as an open circuit or power failure. Values below about 3.6 mA are conventionally treated as a fault.

Question 29Measurement and Instrumentation

In a variable-area (rotameter) flowmeter, the float settles at a height where:

  1. The fluid velocity falls below the settling velocity of the float material
  2. The annular flow area has opened enough that the differential pressure force balances the float weight Correct answer.
  3. The pressure drop across the float matches the pressure drop across an orifice plate downstream of it
  4. The float reaches the top of the tapered tube and the reading is taken at that point

Explanation

A rotameter keeps differential pressure essentially constant and varies the annular area with flow. The float rises until the upward drag from the pressure differential equals its submerged weight. The height of the float is then read against a calibrated scale.

Question 30Measurement and Instrumentation

A differential-pressure transmitter on an orifice is ranged so that 0–100 inH2O corresponds to 0–500 gpm. What flow is indicated when the measured differential is 25 inH2O?

  1. 250 gpm Correct answer.
  2. 354 gpm
  3. 125 gpm
  4. 500 gpm

Explanation

Flow through an orifice varies with the square root of differential pressure, so the flow fraction is the square root of the differential fraction. Here 25/100 = 0.25 and its square root is 0.5, giving half of 500 gpm.

Question 31Measurement and Instrumentation

For the same line size and the same flow rate, increasing the bore of an orifice plate (a higher beta ratio) will:

  1. Leave the differential pressure unchanged while raising permanent pressure loss
  2. Lower the differential pressure and reduce permanent pressure loss Correct answer.
  3. Lower the differential pressure but increase permanent pressure loss
  4. Raise the differential pressure and increase permanent pressure loss

Explanation

A larger bore gives a larger flow area, so the fluid accelerates less through the restriction and the developed differential falls for the same flow. Because the permanent loss is a fraction of that differential, the unrecovered pressure loss also drops.

Question 32Measurement and Instrumentation

At 25 °C, an ideal glass pH electrode changes its output by approximately how much for each unit change in pH?

  1. 59 mV Correct answer.
  2. 29.6 mV
  3. 120 mV
  4. 5.9 mV

Explanation

The Nernst equation gives about 59.16 mV per pH unit at 25 °C (2.303RT/F). The slope is proportional to absolute temperature, which is why pH analyzers include temperature compensation.

Question 33Measurement and Instrumentation

A Doppler ultrasonic flowmeter requires which condition in the process fluid?

  1. A fluid temperature below 100 °C at the measuring point
  2. An electrical conductivity of at least 5 µS/cm across the pipe
  3. A fully developed turbulent profile with no entrained gas or solids
  4. Suspended particles or bubbles that can reflect the ultrasonic beam Correct answer.

Explanation

A Doppler meter measures the frequency shift of sound scattered from moving reflectors such as particles or bubbles. Clean liquids are normally measured with the transit-time technique instead, because there is nothing to scatter the beam.

Question 34Measurement and Instrumentation

A strain-gauge load cell is rated 2.0 mV/V at its 1000 lb capacity and is excited with 10 V dc. What output does it produce at a 400 lb load?

  1. 20 mV
  2. 8.0 mV Correct answer.
  3. 5.0 mV
  4. 4.0 mV

Explanation

Rated output times excitation gives 2.0 mV/V × 10 V = 20 mV at full capacity of 1000 lb. The applied load is 400/1000 = 0.4 of capacity, so the output is 0.4 × 20 mV = 8.0 mV.

Question 35Measurement and Instrumentation

A turbine flowmeter has a K factor of 200 pulses per gallon. If it produces 400 pulses in 30 seconds, what is the volumetric flow rate?

  1. 13.3 gpm
  2. 2 gpm
  3. 4 gpm Correct answer.
  4. 8 gpm

Explanation

Dividing pulses by the K factor gives 400/200 = 2 gallons collected during the 30 second interval. Two gallons in half a minute is 4 gallons per minute.

Question 36Measurement and Instrumentation

Under NAMUR NE43, a 4–20 mA transmitter output that falls below 3.6 mA is normally interpreted as:

  1. A calibration offset that can be corrected by zeroing
  2. A fault or failure in the transmitter or its wiring Correct answer.
  3. A high-temperature alarm generated by the transmitter
  4. A valid reading slightly below the lower range value

Explanation

NE43 defines the usable signal range as roughly 3.8 to 20.5 mA, with currents at or below 3.6 mA and at or above 21.0 mA reserved for failure signalling. This lets the control system detect a dead transmitter rather than treat the current as a real measurement.

Question 37Measurement and Instrumentation

Which statement correctly describes an NTC thermistor used for temperature measurement?

  1. It generates a small voltage that is proportional to the temperature difference between its two junctions
  2. It needs cold-junction compensation in order to give an accurate reading
  3. Its resistance increases in a nearly linear manner over a very wide temperature range
  4. Its resistance falls sharply with rising temperature, giving high sensitivity over a limited range Correct answer.

Explanation

A negative-temperature-coefficient thermistor loses resistance rapidly as it warms, which produces a large, easily measured change over a narrow span. The response is strongly non-linear, so it is normally linearized or used over a limited range.

Question 38Measurement and Instrumentation

A type K thermocouple produces 12.00 mV while its reference junction is held at 25 °C, where a standard type K table lists 1.00 mV. The table lists 13.00 mV at about 319 °C. What process temperature is indicated?

  1. About 319 °C Correct answer.
  2. About 295 °C
  3. About 340 °C
  4. About 271 °C

Explanation

The emf generated at the reference junction must be added to the measured emf, giving 12.00 + 1.00 = 13.00 mV. Entering the table with the corrected emf gives the true process temperature of about 319 °C.

Question 39Measurement and Instrumentation

A DP transmitter measures level in a closed tank using a wet reference leg filled with the tank liquid. The high-side tap is at the tank bottom, level with the transmitter, and the low-side tap is 100 in above it. The liquid has a specific gravity of 1.0. With the tank empty, what differential does the transmitter see and how should it be ranged?

  1. −100 inH2O at empty, with the range set −100 to 0 inH2O Correct answer.
  2. +100 inH2O at empty, with the range set +100 to +200 inH2O
  3. −100 inH2O at empty, with the range set −100 to +100 inH2O
  4. 0 inH2O at empty, with the range set 0 to 100 inH2O

Explanation

The wet leg permanently applies 100 in of liquid head (100 inH2O at specific gravity 1.0) to the low side, while the empty tank applies nothing to the high side. The differential is therefore −100 inH2O at empty, and it rises to 0 inH2O at full level, so the transmitter must be ranged from −100 to 0 inH2O.

Question 40Measurement and Instrumentation

A differential-pressure gas flow measurement is corrected to standard conditions using static pressure. If the absolute static pressure doubles while temperature and differential pressure stay the same, the corrected flow becomes:

  1. Half of the original value
  2. 1.41 times the original value Correct answer.
  3. The same as the original value
  4. 4 times the original value

Explanation

For a gas, corrected mass or standard-volume flow varies as the square root of absolute pressure divided by absolute temperature, with the differential held constant. Doubling the absolute pressure therefore multiplies the corrected flow by the square root of two.

Question 41Control Systems Analysis and Design

A self-regulating process has the transfer function G(s) = K/(τs + 1) and is subjected to a unit step change in input. At what time does the output reach 63.2 percent of its final value?

  1. Three time constants, t = 3τ
  2. One time constant, t = τ Correct answer.
  3. Half a time constant, t = 0.5τ
  4. Two time constants, t = 2τ

Explanation

For a first-order lag the step response is y(t) = K(1 − e^(−t/τ)). Substituting t = τ gives 1 − e^(−1) = 0.632, so the output is at 63.2 percent of its final value after one time constant.

Question 42Control Systems Analysis and Design

A unity-feedback loop has the forward transfer function G(s) = K/[s(s + 2)], which is a type 1 system. What is the steady-state error for a unit step setpoint change?

  1. Zero Correct answer.
  2. Infinite
  3. Equal to 1/K
  4. A finite nonzero value that shrinks as K increases

Explanation

A type 1 loop contains one integrator, so the position error constant Kp is infinite and the step error 1/(1 + Kp) is zero. This can also be shown by applying the final value theorem to the error transform.

Question 43Control Systems Analysis and Design

For a standard second-order system with damping ratio ζ, which value of ζ produces no overshoot at all in the response to a unit step?

  1. ζ = 0.3
  2. ζ ≥ 1 Correct answer.
  3. 0 < ζ < 0.707
  4. ζ = 0.707

Explanation

Overshoot occurs only when the poles are complex, that is, when ζ < 1. At ζ = 1 the response is critically damped and for ζ > 1 it is overdamped, and in both cases the response approaches the setpoint without crossing it.

Question 44Control Systems Analysis and Design

In frequency-response analysis of a feedback loop, what does the gain margin represent?

  1. The phase shift present at the gain crossover frequency
  2. The frequency at which the loop phase equals minus 180 degrees
  3. The additional phase lag that can be tolerated at the gain crossover frequency
  4. The gain increase that would make the loop unstable Correct answer.

Explanation

Gain margin is evaluated at the phase crossover frequency, where the loop phase is minus 180 degrees, and equals the reciprocal of the loop magnitude there. It states how much additional proportional gain could be added before the closed loop reaches the stability boundary.

Question 45Control Systems Analysis and Design

Which controller mode removes steady-state offset for a step setpoint change in a self-regulating process?

  1. Proportional action
  2. Derivative action
  3. Feedforward action
  4. Integral action Correct answer.

Explanation

Integral action continues to move the controller output as long as any error remains, so the loop is driven to zero offset at steady state. Proportional action alone leaves an offset, and derivative action has no influence on the final steady-state value.

Question 46Control Systems Analysis and Design

When a Routh array is constructed for a closed-loop characteristic polynomial, what does the number of sign changes in the first column indicate?

  1. The number of closed-loop poles in the right half-plane Correct answer.
  2. The number of open-loop poles at the origin
  3. The relative degree of the characteristic polynomial, which sets the high-frequency roll-off
  4. The number of closed-loop poles on the imaginary axis

Explanation

The Routh criterion counts right-half-plane roots as the number of sign changes down the first column of the array. It is a counting test for stability and does not give the numerical values of the roots.

Question 47Control Systems Analysis and Design

Under which condition does the final value theorem give a valid limit for the time response of a Laplace transform Y(s)?

  1. The input must be a sinusoid of constant amplitude and frequency
  2. The plant transfer function must have no zeros in the right half-plane
  3. The system order must be at least three so the response can settle
  4. sY(s) must have all poles strictly in the left half-plane Correct answer.

Explanation

The final value theorem states that the limit as t goes to infinity of y(t) equals the limit as s goes to zero of sY(s), but only if sY(s) has no poles on or to the right of the imaginary axis. Otherwise the time function does not settle to a constant.

Question 48Control Systems Analysis and Design

As the gain K of a unity-feedback loop is varied from zero to infinity, the branches of the root locus do which of the following?

  1. Start at the open-loop zeros and terminate at the open-loop poles as gain grows
  2. Start at the open-loop poles and end at the zeros or infinity Correct answer.
  3. Start at the breakaway points and terminate on the imaginary axis
  4. Start at the closed-loop poles and terminate at the closed-loop zeros

Explanation

At K = 0 the closed-loop poles coincide with the open-loop poles of G(s)H(s), so the branches begin there. As K increases the branches terminate on the open-loop zeros, and any excess branches go to infinity along asymptotes.

Question 49Control Systems Analysis and Design

A unity-feedback second-order system has a damping ratio of 0.5. What is the percent overshoot of its response to a unit step?

  1. 16.3% Correct answer.
  2. 44.4%
  3. 4.3%
  4. 25.4%

Explanation

Percent overshoot is given by 100 times exp(−πζ divided by the square root of 1 minus ζ squared). For ζ = 0.5 the exponent is −1.814, giving an overshoot of about 16.3 percent.

Question 50Control Systems Analysis and Design

A second-order loop has natural frequency 5 rad/s and damping ratio 0.4. Using the two-percent criterion, what is the approximate settling time?

  1. 2.0 s Correct answer.
  2. 0.8 s
  3. 2.5 s
  4. 5.0 s

Explanation

The two-percent settling time is approximately 4 divided by the product of damping ratio and natural frequency. Here that product is 2, so the settling time is about 2 s.