determine the expression of k in terms of a in order to achieve zero steady-state error to a unit step input. (10 points)

Answers

Answer 1

By setting the gain constant to 1, we can achieve zero steady-state error to a unit step input.

To achieve zero steady-state error to a unit step input, the value of the gain constant, "k," can be determined by considering the closed-loop transfer function of the system.

Let's assume the open-loop transfer function of the system is G(s), and the closed-loop transfer function is H(s). The closed-loop transfer function is given by:

H(s) = G(s) / (1 + G(s))

For a unit step input, the Laplace transform of the input is 1/s. The steady-state error, E(s), is given by the difference between the input and the output of the closed-loop system, which can be expressed as:

E(s) = 1/s - H(s) * 1/s

To achieve zero steady-state error, we need to make E(s) equal to zero. So, we set the expression for E(s) to zero and solve for G(s):

0 = 1/s - G(s) / (1 + G(s)) * 1/s

Simplifying the expression, we get:

0 = 1 - G(s) / (1 + G(s))

Solving for G(s), we get:

G(s) = 1

Therefore, the expression for the gain constant, k, in terms of a is:

k = 1

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Related Questions

To put out a class D metal fire, you must _______ the fire.

Answers

To put out a class D metal fire, you must smother the fire and eliminate the oxygen element in the fire.

What is a Class D fire?

A class D fire is a type of fire that cannot be extinguished by water. This is because adding water to it reacts with other elements in the fire intensifying the fire even more.

Smothering in this context involves adding a solution like carbon dioxide (CO2) into the fire, this results in a reduction of oxygen in the atmosphere surrounding the class D fire.

By so doing, smothering the fire eliminates the oxygen element in the fire, thereby extinguishing the fire.

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_____require(s) driving at speeds that are reasonable and prudent for conditions.

Answers

Basic speed law requires individuals driving at speeds that are reasonable and prudent for conditions.

What is Speed?

This is defined as the rate of change of the position of a body with respect to time and the unit is metre per second.

The basic speed law states that speeds which are reasonable and prudent should be adopted by drivers so as to avoid accidents and potential risks to other road users. Appropriate punishment are also meted out to defaulters in this type of scenario.

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what is the basic concept of the finite element method.​

Answers

Answer:

The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements.

The displacement of a particle which moves along the s-axis is given by; = (−2 + 3)−0.5 Where s is in meters and t is in seconds. Determine the time at which the acceleration is zero.

Answers

The time at which the acceleration is zero is given as 4.66 seconds

How to solve for the time

First we have to solve for the velocity. To do this, we would have to take the derivative.

[tex]s = e^-0.5t (3 t - 2)[/tex]

Then velocity =

[tex]ds/dt = e^-0.5t (4 - 1.5 t)[/tex]

The acceleration can be gotten by finding the second derivative

[tex]a = dv/dt = e^-0.5t (.75 t - 3.5)[/tex]

To find t at acceleration = 0

We have

[tex]0 = e^-0.5t (.75t - 3.5)[/tex]

This gives t to be

t = 4.66 sec

Complete question

The displacement of a particle which moves along the s-axis isgiven by

s = (-2+3t)e^(-0.5t), where s is in meters and t is inseconds. Plot the displacement, velocity and acceleration versustime for the first 20 seconds of motion. Determine the time atwhich the acceleration is zero.

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In 2001, a land-development company launched an engineering project on land adjacent to a protected wetlands area

Answers

The statement that summarizes the data is that the population data should be collected over a much lingers period of time in order to draw a valid conclusion.

What is data?

It should be noted that data simply means the facts or statistics that are put together to get more information about a particular issue.

It should be noted that a project simony refers to an individual or collaborative enterprise which is planned in order to achieve a particular aim. In this case, the land-development company launched an engineering project on land adjacent to a protected wetlands area.

It should be noted that the time frame that the data was collected matters a lot in order to get a valid conclusion.

In this case, the statement that summarizes the data is that the population data should be collected over a much lingers period of time in order to draw a valid conclusion.

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The options to the question:

a. The data Gail to represent a broad diversity of species and so do not provide enough information to adequately draw a conclusion.

b. Population data were not sampled frequently enough to draw a valid conclusion.

c. The data show stable population trends in native species providing evidence that the engineering project has no negative impact on the ecosystem.

d. The population data should be collected over a much lingers period of time in order to draw a valid conclusion.

P=3000W
f1=0.9
f2=0.5
A=15mm2
travel speed=?

Answers

The Travel Speed at which the welding operation can be accomplished is given as 7.147mm/s. See the computation below.

What is travel speed?

The travel speed of the welding flame or gun across the workpiece is simply measured in millimeters per minute.

Travel speed, along with voltage and amperage, is one of three factors in arc welding that affect the amount of heat input.

What is the calculation that justifies the above answer is?

We are given the following:


Melting temperature = 1650 K

k = (3.33 * 10⁻⁶) * (1,650)²

k = 9.066 J/mm^3

The formula for velocity here is given as:

V = f1 * f2 * Rh / (k*A)

V = 0.9 * 0.6 * 3000 / (9.066*25)

V = 7.147 mm/s

Hence, the Travel Speed at which the welding operation can be accomplished is given as 7.147mm/s.

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Assignment: Explain any three
ways that research can facilitate
the work of building technicians.

Answers

The three ways that research can facilitate the work of building technicians is that:

They will know the timeframe to start and complete the buildingThey will know the type and right materials to use.It will help them in the area of budgeting of equipment, tools and building materials needed.

What do building technicians do?

Building technicians are known to be people who help with some tasks around construction projects and building works.

Note that building technician overseeing a scope of tasks such as monitoring build progress and as such The three ways that research can facilitate the work of building technicians is that:

They will know the timeframe to start and complete the buildingThey will know the type and right materials to use.It will help them in the area of budgeting of equipment, tools and building materials needed.

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a. Calculate the equivalent resistance of the circuit

Answers

Answer:

no any think photo.

Explanation:

An important difference between expressways and freeways is that expressways feature intersections, whereas freeways use: a) interchanges b) medians c) rumble strips d) green guide signs

Answers

An important difference between expressways and freeways is that expressways feature intersections, whereas freeways use a) interchanges.

Datums and benchmarks are used for ______

Answers

Answer:

Measuring elevations

Explanation:

hope this helps you ♡´・ᴗ・`♡

If extension done in a stork position, during backward bending in a standing position of a special test for lumbar spine, produces pain in the lumbar or sacral regions of the spine, it may indicate _____.

Answers

The answer is 7 because I just took the test!

A company is currently paying its employees $0.38 per mile to drive their own cars on company business. The company is considering supplying employees with cars, which would involve purchasing at $25,000 with an estimated three-year life, a net salvage value of $8,000, taxes and insurance at a cost of $900 per year, and operating and maintenance expenses of $0.22 per mile. If the interest rate is 10% and the company anticipates an employee’s annual travel to be 22,000 miles, what is the equivalent cost per mile (neglecting income taxes)?

Answers

The equivalent cost per mile is mathematically given as

Equivalent kilometer =  0.61

What is Distance?

Distance is a measure of the distance between two places. Depending on context, the term "distance" might refer to a precise measurement or an approximation based on other factors. |AB| can be used to represent the distance between two points.

What is an Equivalent cost per mile?

Generally, the equation for Equivalent annual cost  is  mathematically given as

EAC= $ 25,000 ( A/P, 10% , 3 years ) + $ 900 + $ 0.22 * 22,000 - $ 8000 ( A/F , 10% , 3 years)

Therefore

EAC= $ 25,000 * 0.402115 + $ 5740 - $ 8000 * 0.302115

EAC= $ 13,375.955

In conclusion, the Equivalent cost per kilometer

Equivalent kilometer [tex]=\frac{ 13,375.955}{22,000}[/tex]

Equivalent kilometer =  0.61

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Draw the schematics for the following two battery connections. Can you explain the value of the output voltage in the series connection

Answers

if two 1.5 ya alt batteries are connected to head to the tail the voltage is 3.0 volt it is the because the battery is insidious reduce a voltage equal to number of battery is multiplied by the voltage of individual

based on the graph shown, for any given output level, the veritcal distance between the avc and the atc curves represents

Answers

A a result of the graph shown, for any given output level, the veritcal distance between the avc and the atc curves represents total fixed cost (TFC).

What is Vertical distance?

This is known as vertical separation and it is said to be the distance that exist between two vertical positions.

Note that vertical coordinates are seen for expressing vertical position: depth, and others and as such,

See full question below

The vertical distance between the ATC and AVC curve represents

a) marginal cost (MC)

b) average fixed cost (AFC)

c) total fixed cost (TFC)

d) total cost (TC) - total variable cost (TVC)

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The lights on your vehicle must be turned on at any time, day or night, when persons and vehicles cannot be clearly seen for ___ feet.

Answers

Answer:

500 feet

Explanation:

In order to stop or turn your vehicle around on the highway you must have 500 feet of clear road in both directions. 4. Headlights are required at any time you cannot see persons or vehicles for 500 feet, due to snow, dust, fog, etc. and from ½ after sunset to ½ before sunrise.Hope this helps

The lights on your vehicle must be turned on at any time, day or night, when persons and vehicles cannot be clearly seen for 1000 feet.

What are vehicles?

A vehicle is a piece of equipment, typically with wheels and an engine, used for land-based transportation of people or goods. Cars, buses, and trucks are examples of road vehicles. Farm vehicles include tractors.

Vehicle type refers to a group of power-driven vehicles that share all crucial aspects of their engines, cars, and OBD systems.

When a vehicle is 500 feet away, the driver must dim his headlights.

Avoid looking directly into the light when a car is coming at you; instead, slow down. At least 30 minutes before dusk, headlights must be activated. It is also important to keep in mind that a lower headlight beam improves the driver's ability to see in fog.

Thus, it should be 1000 feet distance.

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Metal wireways are sheet metal troughs with _____________ for housing and protecting electrical conductors and cable.

Answers

Answer:

Metal wireways are sheet metal "U"s with removable housing for protecting electrical equipment, wires, and cables.

Explanation:

These are especially used to run wire in manufacturing environments.

Determine the carburizing time necessary to achieve a carbon concentration of 0.30 wt.% at a position of 4 mm into an iron-carbon alloy that initially contains 0.10 wt.% C. The surface concentration is to be maintained at 0.90 wt.% C, and the treatment is to be conducted at C. Use the diffusion data for -Fe in Table 5.2

Answers

The carburizing time necessary to achieve a carbon concentration is 31.35 hours

How to find the Carburizing Time?

To determine the carburizing time necessary to achieve the given carbon concentration, we will use the equation:

(Cs - Cx)/(Cs - C0) = ERF(x/2√Dt)

where;

Cs is Concentration of carbon at surface = 0.90

Cx is Concentration of carbon at distance x = 0.30

Distance x = 4 mm = 0.004 m

C0 is Initial concentration of carbon = 0.10

ERF() = Error function at the given value

D = Diffusion of Carbon into steel

t = Time necessary to achieve given carbon concentration ,

Thus, plugging in the relevant values gives;

(Cs - Cx)/(Cs - C0) = (0.9 - 0.3)/(0.9 - 0.1)

= 0.6/0.8 = 0.75

now, ERF(z) = 0.75 and as such using ERF table, we can say that;

Z = 0.814. Thus;

(x/2√Dt) = 0.81

Using the table of diffusion data, we have;

At a temperature of  (1100°C) or 1373 K, we have;

D = 5.35 × 10⁻¹¹ m²/sec.

Calculating the carbonizing time by using the equation z = (x/2√Dt);

where;

t is carbonizing time

Thus;

0.814 = (0.004/(2 × √5.35 × 10⁻¹¹ × √t))

0.814 = 0.004 /(1.4628 × 10⁻⁵ × √t)

0.814 × 1.4628 × 10⁻⁵ × √t = 0.004

1.19072 × 10⁻⁵ × √t = 0.004  

√t = 0.004/(1.19072 × 10⁻⁵)

√t = 335.93

t = 112848.96 seconds

Converting to hours gives;

t = 112848.96/3600

t = 31.35 hours

Therefore, the carburizing time necessary to achieve a carbon concentration is 31.35 hours

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An isolation transformer whose main purpose is to reduce voltage spikes will have a turns ratio of?

Answers

Answer:

An isolation transformer whose main purpose is to reduce voltage spikes will have a turns ratio of 1 to 1.

This is due to the windings input and output having the same waveform and amplitude.

Which load balancing method is supported in equal cost multipath (ECMP) load balancing when SD-WAN is enabled

Answers

Volume load balancing method is supported in equal cost multipath (ECMP) load balancing when SD-WAN is enabled.

What is load balancing method?

Load balancing means are regarded as a form of an algorithms or method that is used to rightly share an incoming server request or traffic in the midst or among servers that is from the server pool.

Note that Volume load balancing method is supported in equal cost multipath (ECMP) load balancing when SD-WAN is enabled as that is its role.

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A light weight vehicle traveling 50 mph can stop in approximately
a. 200 meters.
b. 5 blocks.
c. 200 feet.
d. 6 seconds.

Answers

A light weight vehicle traveling 50 mph can stop in approximately 200 feet.

How a car break works?

The break system of a car is composed by several items that are always working together to slow down and bring a vehicle to a complete stop. It also has the function of keeping the car stationary when it is parked. In general, this system has two manual activation modes: the lever and the pedal, with the exception of vehicles adapted for people with disabilities.

Most vehicles today use the disc brake system. Disc brakes work by using pads, which are held inside a hydraulic caliper, receiving pressure to brake. Such pads generate friction on a disc, which makes the vehicle stop permanently.

The drum brake is another type, being older and dependent on the famous linings to cause friction in the wheel and stop the vehicle. A hydraulic cylinder makes the plies move inside the drum, which is a hollow part fastened with screws and attached to the wheels. This type of brake is on the rear wheels, for the most common models.

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When passing another car, make sure you maintain at least a _______ safety cushion

Answers

The answer is 4 because I just took the test!

If a dielectric material, such as teflon®, is placed between the plates of a parallel-plate capacitor without altering the structure of the capacitor, how is the capacitance affected?.

Answers

The capacitance is affected is that the capacitance increases because of the insertion of Teflon.

What is capacitance?

A `is known to be a form of a device that is said to be used to save some amount of charges in any electrical circuit.

Note that the capacitor functions on the principle that the capacitance of a conductor is said to increases if an earthed conductor is  taken close to it.

Hence, The capacitance is affected is that the capacitance increases because of the insertion of Teflon.

See full question below

A dielectric material, such as Teflon®, is placed between the plates of a parallel-plate capacitor without altering the structure of the capacitor. The charge on the capacitor is held fixed. How is the electric field between the plates of the capacitor affected?

The electric field is not altered, because the structure remains unchanged.

The electric field becomes zero after the insertion of the Teflon®.

The electric field decreases because of the insertion of the Teflon®.

The electric field becomes infinite because of the insertion of the Teflon®.

The electric field increases because of the insertion of the Teflon®.

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What is the mode of operation of a ramp digital voltimeter​

Answers

Answer:

The operating principle of a ramp type digital voltmeter is to measure the time that a linear ramp voltage takes to change from level of input voltage to zero voltage (or vice versa).

Through Engineering, human achievement continues to advance. Write about your favorite example of engineering in action and what impresses you about it from an Engineering standpoint.

Answers

Hydroelectric power plants are outstanding engineering devices that allow people to obtain energy from renewable sources.

What is a hydroelectric power plant?

A hydroelectric power plant is a center for the production of electricity based on hydropower energy systems.

Hydroelectric power plants exploit the energy of water masses (e.g., a stream) to produce clean energy for million of people around the world.

These plants have generators capable of converting mechanical energy  into electricity by using simple turbines.

In conclusion, hydroelectric power plants are outstanding engineering devices that allow people to obtain energy from renewable sources.

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The advantage of using a reference line to position a building is that

Answers

Answer:

The reference line helps you achieve the precise connection of Walls for clean intersections.

Explanation:

Reference Lines allow you to place lines on the plot at specific locations to mark important values. You could use these to mark control limits or to indicate a trend line for a set of data.

How are new slip rings attached to the rotor core during alternator rebuilding?

Answers

The new slip rings is been  attached to the rotor core during alternator rebuilding by b. Soldered on.

What is the process of Soldering ?

Soldering  is the use of Solder which is a metal alloy  consisting tin and lead and is the way of joining  different types of metals together by melting solder.

This is been used on new slip rings to get it  attached to the rotor core during alternator rebuilding .

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CHECK THE COMPLETE QUESTION BELOW:

How are new slip rings attached to the rotor core during alternator rebuilding?

a. Machine clamped

b. Soldered on

c. Crimped on

d. epoxy glue

The only difference between all GMA welding machines and some FCA welding machines is that all GMA welding machines must have a ______________.

Answers

Answer: Shielding gas solenoid

Explanation:

If your crew is the first to arrive on the scene of a major mci, what will be a major aspect of your scene size-up?

Answers

If your crew is the first to arrive on the scene of a major MCL, The major aspect of your scene size-up will be to Make a sweep to determine what needs must be met. Option D. This is further explained below.

What is the scene of an MCL?

Generally, If your team is the first to arrive at the scene of a significant MCL, the most important part of your scene size-up will be to do a sweep to identify the requirements that need to be satisfied. Choose option D.

In conclusion, A medial collateral ligament (MCL) injury occurs when the ligament on the inside of the knee is stretched, partially torn, or completely ruptured. Most knee injuries are caused by an excessive amount of valgus stress on the knee, which is one of the most prevalent.

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CQ

If your crew is the first to arrive on the scene of a major​ MCI, what will be a major aspect of your scene​ size-up?

A.

Make an initial scene report to the communications center.

B.

Control​ on-scene communication as help arrives.

C.

Prevent uncoordinated or undirected activity at the scene.

D.

Make a sweep to determine what needs must be met.

Write a class having two private variables and one-member function which will return the area of the rectangle.

Answers

Using the knowledge in computational language in C++ it is possible to write the code being write a class having two private variables

Writting the code in C++:

#include <iostream>

using namespace std;

class Rectangle { /*create a class named Rectangle*/

  private:

  float l,b; /*this class has two private variables l and b*/

  public:

  float getArea(float l, float b) /*this class has one member-function getArea which returns the area of the rectangle*/

  {

   return l*b; /*return the area of the rectangle*/

  }

};

int main () { /*the main function to check the working of our Rectangle class*/

 float l,b;

 Rectangle r1; /*create an object r1 of Rectangle class*/

 cout<<"Enter the length of the rectangle: ";

 cin>>l; /*input the length of the rectangle from the user*/

 cout<<"Enter the breadth of the rectangle: ";

 cin>>b; /*input the breadth of the rectangle from the user*/

 cout <<"Area of the rectangle is: "<< r1.getArea(l,b)<<" square units."; /*find the area of the rectangle using the member function of the class*/

 return 0;

}

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An inverter has a balanced 3-phase, 277/480 V output and is installed a distance, d, ft from the point of utility connection. The DC/AC converter shown below in the inverter. And the distance d is the physical separation between this DC/AC converter and the PCC. (

Answers

An expression for the voltage drop between inverter and PUC

[tex]V D \rightarrow \frac{I(\Omega / k f t) d}{2770}$[/tex]

This is further explained below.

What is an expression for the voltage drop between the inverter and PUC?

Generally, the equation for Voltage drop is  mathematically given as

[tex]V=\frac{I R}{V}[/tex]

Therefore

[tex]\%$ Voltage drop $=\frac{I R}{V} * 100\\\\$\rightarrow \frac{100 I(\Omega / 15 f t) d}{1000 V_{p}}\\\\$V_{P}=277 \mathrm{~V}$[/tex]

[tex]V D=\frac{I(\Omega / \mathrm{kft}) d}{10 * 2770} \rightarrow \frac{I(\Omega / \mathrm{kft}) d}{2770} \mathrm{~V}\\\\$\% V D \rightarrow \frac{I(\Omega / k f t) d}{2770}$[/tex]

In conclusion, the expression for the voltage drop between inverter and PUC

[tex]V D \rightarrow \frac{I(\Omega / k f t) d}{2770}$[/tex]

CQ

An inverter has a balanced 3-phase, 277/480 V output and is installed a distance, d, ft from the point of utility connection. The DC/AC converter is shown below in the inverter. And the distance d is the physical separation between this DC/AC converter and the PCC.

Derive an expression for the voltage drop between inverter and PUC in terms of d using the basic equation %VD =100IR/V.

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Jenna's class brought in 40 pieces of fruit for a celebration and 32 pieces of fruit were eaten. What percentage of the fruit was NOT eaten? in your own words how would you restate the definition of intersubjectivity? Simply the expression by combining the like terms:-6j + 4 + 2j - 1 Please help me fast running out of time............. what was life like for people in medieval japan? A 250 mL glass of orange juice cantains 22 grams of sugar. How much sugar is in a two liter (2,000 mL) bottle of orange juice? Write your own printArray() function found in Processing for the Arduino. For simplicity, you can limit printArray() to integer arrays and you will also pass the size of the array to your function. For example, given the following code: int terps[5] = {7, 9, 12, 1, 46}; void printArray(int arrayToPrint[], int arraySize) { // YOUR CODE HERE } void setup() { // put your setup code here, to run once: Serial.begin(9600); } void loop() { // put your main code here, to run repeatedly: printArray(terps,sizeof(terps)/sizeof(int)); delay(1000); } You should repeatedly see the following in the serial monitor: [0]: 7 [1]: 9 [2]: 12 [3]: 1 [4]: 46 The 75 students in the high school band are going on a trip. The total cost of the trip is $1,410. Each student will pay the same amount. How much will each student have to pay? what creates an electric current in a battery?A. Atoms dissolving B. Metals generating C. Electrons jumping D. Liquids moving why do all the planets in the solar system orbit the sun in the same direction ? need help answering this, Aleks is very picky, and I have been struggling with these questions PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*.. IM GIVING 40 POINTS !! DONT SKIP :((. how do I solve this factoring problem? 2, If you heat water to 100 C, it ..a) boilsb) boilc) will boilplease help The following are Noah's scores on his first ten exams: 89, 90, 79, 92, 80, 94, 86, 91, 82, 89. Calculate the sum of Noah's points(Only enter the numeric answer - NO WORDS!)I What is Macbeth beginning to realize about what the witches told him? What did the emperor Lalibela have architects build in Ethiopia? A Chevy Camaro engine exerts 650 hp to move the car. How many watts of power does the engine exert? In the figure, XYZ MNL.Find mZ. Which line plot displays a data set with an outlier?