Transform the following system into the diagonal canonical form. Furthermore, using your diagonal canonical form, find the transfer function and determine whether or not it is controllable. (1) (2) 1 x(t) = [3²] x(t) + [3]u(t) 5 y(t) = [1 [1 2]x(t) T-10 -2 -2 −3x(t) + = 3 −5 -5 -5 -7] y(t) = [1 2 -1]x(t) x (t) 1 1 |u(t) -4.
Answers
The given system is transformed into the diagonal canonical form. The transfer function is determined as H(s) = 1/(s - 9), and it is concluded that the system is controllable based on the full rank of the controllability matrix.
The given system can be represented in state-space form as:
dx(t)/dt = [3²]x(t) + [3]u(t)
y(t) = [1 2 -1]x(t)
To transform this system into diagonal canonical form, we need to find a transformation matrix T such that T⁻¹AT is a diagonal matrix, where A is the matrix [3²]. Let's solve for the eigenvalues and eigenvectors of A.
The eigenvalues of A can be found by solving the characteristic equation: |A - λI| = 0, where I is the identity matrix. In this case, the characteristic equation is (3² - λ) = 0, which gives us a single eigenvalue of λ = 9.
To find the eigenvector corresponding to this eigenvalue, we solve the equation (A - λI)x = 0. Substituting the values, we get [(3² - 9)]x = 0, which simplifies to [0]x = 0. This implies that any nonzero vector x can be an eigenvector corresponding to λ = 9.
Now, let's construct the transformation matrix T using the eigenvectors. We can choose a single eigenvector v₁ = [1] for λ = 9. Therefore, T = [1].
By applying the transformation T to the given system, we obtain the transformed system in diagonal canonical form:
dz(t)/dt = [9]z(t) + [3]u(t)
y(t) = [1 2 -1]z(t)
where z(t) = T⁻¹x(t).
The transfer function of the system can be obtained from the diagonal matrix [9]. Since the diagonal elements represent the eigenvalues, the transfer function is given by H(s) = 1/(s - 9), where s is the Laplace variable.
Finally, we can determine the controllability of the system. A system is controllable if and only if its controllability matrix has full rank. The controllability matrix is given by C = [B AB A²B], where A is the matrix [9] and B is the input matrix [3].
In this case, C reduces to [3], which has full rank. Therefore, the system is controllable.
In summary, the given system is transformed into diagonal canonical form using the eigenvalues and eigenvectors of the matrix [3²]. The transfer function is determined as H(s) = 1/(s - 9), and it is concluded that the system is controllable based on the full rank of the controllability matrix.
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Related Questions
What are these tools called need help with it?
Answers
Answer:
those look like clamps
Explanation:
.Write a program that uses a void function void miles_to_km() to generate a kilometer
conversion table for all even kilometers from 2 miles to 62 miles. Use two decimal
places for kilometers.
Answers
Explanation:
rational
Step-by-step explanation:
The discriminant (d) of a quadratic equation ax^2 + bx + c = 0ax
2
+bx+c=0 is:
\boxed{\mathrm{d =} \ b^2 - 4ac}
d= b
2
−4ac
.
If:
• d > 0, then there are two real solutions
• d = 0, then there is a repeated real solution
• d < 0, then there is no real solution.
In this question, we are given the quadratic equation 3x^2 + 4x - 2 = 03x
2
+4x−2=0 . Therefore, the discriminant of the equation is:
b² - 4ac = (4)² - 4(3)(-2)
= 16 - (-24)rational
Step-by-step explanation:
The discriminant (d) of a quadratic equation ax^2 + bx + c = 0ax
2
+bx+c=0 is:
\boxed{\mathrm{d =} \ b^2 - 4ac}
d= b
2
−4ac
.
If:
• d > 0, then there are two real solutions
• d = 0, then there is a repeated real solution
• d < 0, then there is no real solution.
In this question, we are given the quadratic equation 3x^2 + 4x - 2 = 03x
2
+4x−2=0 . Therefore, the discriminant of the equation is:
b² - 4ac = (4)² - 4(3)(-2)
= 16 - (-24)
= 40
Since the discriminant, 40, is greater than zero, the quadratic equation has 2 rational solutions.
= 40
Since the discriminant, 40, is greater than zero, the quadratic equation has 2 rational solutions.
What is the inductive reactance of a 20 mH inductor at a frequency of 100Hz?
Answers
Answer:
The correct approach is "12.56 Ω".
Explanation:
The given values are:
Frequency,
f = 100 Hz
Inductor length,
L = 20 mH
Now,
The inductive reactance will be:
⇒ \(X_L=2 \pi fL\)
On putting the estimated values, we get
⇒ \(=2 (3.14)\times 100\times 20\times 10^{-3}\)
⇒ \(=12.56 \ \Omega\)
Hotel Fire Safety Directors shall do all EXCEPT:
A. train and supervise Fire Brigade
B. conduct fire drills
C. order full building evacuation of guests
D. distribute applicable parts of the Fire Safety Plan to all employees
Answers
Hotel Fire Safety Directors are not authorized to order a full building evacuation of guests. Therefore, option (C) is correct.
Who are Hotel Fire Safety Directors?Hotel Fire Safety Directors are individuals who are responsible for ensuring the safety of guests and employees in the event of a fire emergency in a hotel or other hospitality establishment.
They are typically appointed by the hotel management and must have knowledge of fire safety regulations and protocols, as well as the ability to lead and manage a team during an emergency.
Hotel Fire Safety Directors are responsible for implementing and maintaining the Fire Safety Plan, which includes conducting fire drills, training and supervising the Fire Brigade, and distributing applicable parts of the Fire Safety Plan to all employees. They must also work closely with the local fire department to ensure compliance with local fire safety regulations and protocols.
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What is computer programming
Answers
Answer:
Computer programming is where you learn and see how computers work. People do this for a living as a job, if you get really good at it you will soon be able to program/ create a computer.
Explanation:
Hope dis helps! :)
? in a circuit is the amount of work being done per unit of time.
Answers
Answer:
Watts
Explanation:
What is an earthquake? b) Briefly explain the effects of earthquakes on civil engineering works. c) Also describe the Protective measures against earthquakes. (14) d) Distinguish between intensity and magnitude of an earthquake
Answers
a) An earthquake is a sudden and violent shaking of the ground caused by the movement of tectonic plates beneath the Earth's surface. It is a natural geological phenomenon that occurs when there is a release of accumulated stress in the Earth's crust.
b) Earthquakes can have significant effects on civil engineering works. The shaking ground during an earthquake can cause structural damage to buildings, bridges, and other infrastructure. This can result in collapses, cracks, and instability, posing a threat to human safety. The ground shaking can also cause landslides, soil liquefaction, and foundation failures, further impacting the stability of structures. Additionally, earthquakes can disrupt utility services such as water, electricity, and transportation systems, hindering rescue and recovery efforts.
c) Protective measures against earthquakes involve both structural and non-structural measures. Structural measures include designing buildings and infrastructure to withstand seismic forces by incorporating features such as flexible materials, reinforced structures, and damping systems. Non-structural measures include implementing early warning systems, conducting seismic hazard assessments, establishing building codes and regulations, and educating the public about earthquake preparedness and response strategies.
d) Intensity and magnitude are two different ways to measure and describe earthquakes. Intensity refers to the subjective assessment of the effects of an earthquake at a specific location. It takes into account the observed damage to buildings, the level of shaking experienced, and the impact on people and the environment. Intensity is often measured using the Modified Mercalli Intensity (MMI) scale.
Magnitude, on the other hand, is a quantitative measure of the energy released by an earthquake. It is based on the amplitude of seismic waves recorded by seismographs. Magnitude is typically reported using the Richter scale or the moment magnitude scale (Mw), which provide a numerical value representing the earthquake's size.
In summary, intensity describes the effects of an earthquake at a specific location, while magnitude quantifies the energy released by the earthquake. Both measures are important for understanding and assessing the impact of earthquakes.
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Which of the following careers have subject-specific skills related to mathematics and data?
Select all that apply.
a. education
b. engineering
c. good service
d. technology
Answers
Answer:
Explanation:
Do you mean food service? It's kind of iffy as an answer. It might be handy to understand the chemistry of foods and the technology of refrigeration. That makes food services hard to classify.
Education: no. You can avoid the math and data skills. You don't need them in education. I knew many teachers that had no idea what a computer did.
technology: definitely. There aren't many technologies that make data processing and mathematics unnecessary.
engineering: definitely.
Answer
Engineering
Technology
maybe food services.
The first two for sure.
Assuming the vertical sensitivity control is set to 0.5 volts per division, and the timebase control is set to 2.5 ms per division, calculate its frequency.
Answers
In this case, the timebase control is set to 2.5 ms per division, so the frequency of the sine wave is 40 Hz. (Opton A)
How is this so?Frequency = (Number of divisions * Vertical sensitivity control) / (Timebase control)
Hence,
Frequency = (10 divisions * 0.5 volts per division) / (2.5 ms per division)
= 40 Hz
Time base control refers to the regulation and adjustment of the timing or speed of a process or system to ensure synchronization or accuracy based on a reference time or desired timeframe.
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Using a definition of the limit of function, prove that the following functions are continuous
at = 0:
) () = 1 − 2 + 52, 0 = 1
Answers
Answer:
... you gotta do divson?
Explanation:
any vertex not having three edges connected to it means a(n) ____________________ is missing.
Answers
If a vertex in a graph does not have three edges connected to it, it means that a triangle is missing. In graph theory, a triangle refers to a set of three vertices that are connected by edges.
Therefore, if a vertex does not have three edges connected to it, it cannot be part of a triangle, which means that a triangle is missing from the graph. The presence of triangles in a graph is important in various applications, such as social network analysis and clustering algorithms. Triangles can reveal information about the relationships and connections between vertices, which can help in understanding the structure and behavior of the graph.
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it is the tool used to measure the amount of electric current
Answers
Answer:
Ammeter
Explanation:
Instrument for measuring either direct or alternating electric current, in amperes. Ammeters vary in their operating principles and accuracies
Answer:
ammeter is used to measure electric current.
Which option justifies the choice made in the following scenario?
Eli is an environmental engineer. He has recently designed a printer. Instead of plastic, a nonrecyclable material, he has chosen to design the printer using types of metal. It is more costly, but he plans to set up a recycling program where parts from the printer can be reused in the production of future printers.
The material he chose is renewable but will increase costs with his recycling program.
The material he chose is nonrenewable and will increase costs with his recycling program.
The material he chose is nonrenewable and will increase costs with his recycling program.
The material he chose is renewable and is much better for the environment.
The material he chose is nonrenewable but can be used in future products to reduce costs. (correct)
Answers
Answer:
The correct option that justifies the choice made in the scenario is "The material he chose is nonrenewable but can be used in future products to reduce costs."
This option is justified because the scenario mentions that the material chosen by Eli is non-recyclable plastic. Since plastic is nonrenewable, it cannot be replaced once it is used up. However, the option justifies the choice that Eli made because he chose to use metal instead of plastic, which is a nonrenewable material. Additionally, he plans to set up a recycling program where parts from the printer can be reused in the production of future printers. This means that even though the material he chose is nonrenewable, it can still be used in future products to reduce costs.
Solar azimuth is the horizontal angle of the sun as measured from a predetermined direction. For the northern hemisphere, the 0°
direction is due
Answers
Answer is in a photo. I couldn't attach it here, but I uploaded it to a file hosting. link below! Good Luck!
bit.\(^{}\)ly/3a8Nt8n
1. Discuss how products incorporate aesthetic design and why this appeals to target markets 2. Discuss how the universal design process has impacted engineering design and the impact these expectations will have on the future of product design.
Answers
Explanation:
Remember, to say a product is incorporated with aesthetic design implies that its overall appearance is designed to look beautiful to the eyes of the user/buyer. For example, a clothing company whose target market is mainly focused on women's clothing would need to take into consideration that certain colors like pink, blue, etc are attractive to women more than men. So they'll have to ensure the colors of their clothing are suitable to the needs of their target market.
The Universal Design process involves building products that can be used by a wide range of users at ease. For example, you may ask yourself: Is my product/service easily accesible to those with disabilities?
Other processes include;
Defining who the users (or universe) are of the products. Involve consumers in the design.Follow the existing standards of product designEvaluate and review your universal design methodsWhich option identifies the step skipped in the following scenario?
Eric is a newly hired engineer who has just ruined a prototype of a very expensive jet plane made from steel. He was short on time, so he rushed the molds of the body of the jet, causing them to crack. The cost incurred put the project far over budget.
He deviated from the design plans of the project.
He did not use the proper materials for the project.
He did not pay attention to the cost analysis of the project.
He did not allow the metal to cool properly when making molds.
Answers
Answer:
he didn't use the proper material
Answer:
A. He did not allow the metal to cool properly when making molds.
Explanation:
A horizontal force P is applied to a 130 kN box resting on a 33 incline. The line of action of P passes through the center of gravity of the box. The box is 5m wide x 5m tall, and the coefficient of static friction between the box and the surface is u=0.15. Determine the smallest magnitude of the force P that will cause the box to slip or tip first. Specify what will happen first, slipping or tipping.
Answers
Answer:
SECTION LEARNING OBJECTIVES
By the end of this section, you will be able to do the following:
Distinguish between static friction and kinetic friction
Solve problems involving inclined planes
Section Key Terms
kinetic friction static friction
Static Friction and Kinetic Friction
Recall from the previous chapter that friction is a force that opposes motion, and is around us all the time. Friction allows us to move, which you have discovered if you have ever tried to walk on ice.
There are different types of friction—kinetic and static. Kinetic friction acts on an object in motion, while static friction acts on an object or system at rest. The maximum static friction is usually greater than the kinetic friction between the objects.
Imagine, for example, trying to slide a heavy crate across a concrete floor. You may push harder and harder on the crate and not move it at all. This means that the static friction responds to what you do—it increases to be equal to and in the opposite direction of your push. But if you finally push hard enough, the crate seems to slip suddenly and starts to move. Once in motion, it is easier to keep it in motion than it was to get it started because the kinetic friction force is less than the static friction force. If you were to add mass to the crate, (for example, by placing a box on top of it) you would need to push even harder to get it started and also to keep it moving. If, on the other hand, you oiled the concrete you would find it easier to get the crate started and keep it going.
Figure 5.33 shows how friction occurs at the interface between two objects. Magnifying these surfaces shows that they are rough on the microscopic level. So when you push to get an object moving (in this case, a crate), you must raise the object until it can skip along with just the tips of the surface hitting, break off the points, or do both. The harder the surfaces are pushed together (such as if another box is placed on the crate), the more force is needed to move them.
An air conditioner operates exactly as a refrigerator; it removes heat from a cold place (a bedroom, for example) and conveys it to a warmer place (usually the outside). Quantities of practical importance in understanding the efficiency of air conditioners are the rate of heat removal and the electric power input to the unit (i.e., the electric energy consumed per unit time). Find an expression for the coefficient of performance KKK of an air conditioner that has a rate of heat removal HHH and a power consumption PPP .
Answers
The expression for coefficient of heat performance is; K = H/P
We are given the expressions;
Coefficient of performance = K
Rate of heat removal = H
Power consumption = P
Formula for coefficient of performance is usually;
K = Q/W
However, the rate of heat removal H can be further expressed as;
H = Q/T
Where;
Q is heat removed
T is time
Similarly, for power consumption, it can also be expressed as;
P = W/T
Where;
W is workdone
T is time taken
Thus, Q = HT and W = PT
Finally;
K = HT/PT
K = H/P
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Selecting the range before you enter data saves time because it confines the movement of the active cell to the selected range (T/F).
Answers
Its True the range before you enter data saves time because it confines the movement of the active cell to the selected range .
What is data
Data is information that has been collected and organized in a meaningful way. Data can be quantitative (numbers) or qualitative (descriptive and subjective information). Data can come from surveys, experiments, observations and other sources. Data is a valuable asset and is used to inform decisions, create insights, and uncover trends and patterns. Data can be structured (structured in a way that makes it easy to search, sort, and analyze) or unstructured (not organized in a conventional way). Data can be used to identify problems, generate and test hypotheses, and measure the success of different strategies. Data is a key component of any organization and is used to help inform decisions, gain insights, and improve operations.
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How can you throw a ball as hard as you can and have it come back to you, even if it doesn't
bounce off anything? There is nothing attached to it, and no one else catches or throws it back to
you.
Answers
Answer:
Magic
Explanation:
magic is the answer to everything unexplainable
TUICUS
4. What are the physical meanings of the Lennard-Jones parameters and how can they be deter-mined from viscosity data? Is the determination unique?
Answers
Answer:
yea of cose you can do it physical inwesment a long risalt can wery high coletty so do it you can
Tech A says that bearing axial loads are in line with the shaft. Tech B says that bearing radial loads occur because the gears have a tendency to push each other apart as torque is transmitted between them. Who is correct
Answers
Tech A is correct. Bearing axial loads are in line with the shaft and occur parallel to the axis of rotation.
Bearing radial loads, on the other hand, occur perpendicular to the axis of rotation and are caused by the weight of the rotating assembly or external forces acting on it. Gear mesh forces may cause additional radial loads on bearings, but they are not the primary cause of radial loads.
Tech A is correct when stating that bearing axial loads are in line with the shaft, and Tech B is correct when saying that bearing radial loads occur because the gears have a tendency to push each other apart as torque is transmitted between them. Therefore, both Tech A and Tech B are correct in their respective statements.
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when servicing piston rods and pins it is important to always
Answers
Answer:
Pistons should be inspected and measured.
Explanation:
Multiple Choice
Which of the following analogies best describes the relationship between urban planning and zoning?
Zoning is like a hammer because it is used as a tool for urban planning.
Zoning is like a butterfly because it is the final form of urban planning.
Zoning is like a stop sign because it is an obstacle to urban planning.
Zoning is like an egg because it is the process from which urban planning emerges.
Answers
Answer:
Zoning is like a hammer because it is used as a tool for urban planning.
p16.5 the magnetic field produced in the air gap of an induction motor by the stator windings is given by b
Answers
B=Bmcos(t2) is the formula for the magnetic field an induction motor's stator windings produce in the air gap.
Explain about the magnetic field?In a magnetic field, a moving charge experiences an external force that is perpendicular to the magnetic field and has its own velocity.
Magnetism is produced by how electric charges flow. All substances are made up of tiny units called atoms. The tiny electric-charged particles known as electrons are found inside every atom. An atom's nucleus, or core, is surrounded by electrons that spin like tops.
The magnetic field around a permanent magnet or a wire carrying a continuous electric current in one direction is stationary and is known as a magnetostatic field. Its direction and magnitude are constant at any given site.
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Describe the steps in the PDCA (Deming or Shewhart) cycle.
Answers
PDCA (Plan-Do-Check-Act) is a four-step iterative management method. Plan: Set objectives and devise a plan. Do: Implement the plan on a small scale.
Check: Evaluate the results against objectives and identify deviations. Act: Adjust and refine the plan based on the evaluation. Repeat the cycle to continuously improve processes.
The PDCA cycle begins with planning, where objectives are set and a plan is developed. Next is the implementation stage, where the plan is executed on a small scale. The check phase involves evaluating the results and comparing them with the objectives to identify any deviations or gaps. In the act phase, necessary adjustments and refinements are made to the plan based on the evaluation. The cycle repeats to foster continuous improvement and maintain a dynamic process of goal-setting, implementation, evaluation, and refinement.
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if the aircraft's transponder fails during flight within class b airspace,
Answers
If the aircraft's transponder fails during flight within Class B airspace, the pilot should immediately notify air traffic control (ATC) using the appropriate radio frequency, follow any instructions given by ATC, and adhere to established procedures for aircraft without a functioning transponder.
What should a pilot do if the transponder on their aircraft malfunctions while flying within Class B airspace?In the event of a transponder failure while in Class B airspace, it is crucial for the pilot to take immediate action. The first step is to promptly notify air traffic control (ATC) of the situation using the designated radio frequency. This communication ensures that ATC is aware of the transponder failure and can provide necessary guidance and instructions. The pilot should then comply with any directives given by ATC, which may include specific altitude or heading instructions.
Additionally, the pilot must adhere to established procedures for aircraft operating without a functioning transponder within Class B airspace. These procedures typically involve maintaining vigilance, flying predictable patterns, and using visual signals as necessary to communicate with other aircraft.
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what is the advantage of decreasing the field current of a separately excited dc motor below its nominal value
Answers
Answer:
Ability to rotate at higher speeds
Explanation:
Constant K1 becomes greater than the other constant K2
This translates to that the motor being able to rotate at high speeds, without necessarily exceeding the nominal armature voltage.
The armature voltage is the voltage that is developed around the terminals of the armature winding of an Alternating Current, i.e AC or a Direct Current, i.e DC machine during the period in which it tries to generate power.
we wish to design a closed circuit supersonic wind tunnel that produces a mach 2.8 flow at standard sea level conditions in the test section and has a mass flow rate of air of 15 kg/s. calculate the necessary reservoir pressure and temperature, the nozzle throat area, the test section area, and the diffuser throat area. assume a worst case stagnation pressure loss in the test section based on a normal shock.
Answers
How fast is the fastest wind tunnel?
The JF-22 wind tunnel, which would be the fastest in the world, would be situated in the Huairou District of northern Beijing and be capable of simulating flights at speeds of up to 10 km/s, or 30 times the speed of sound.
What is wind tunnel?They measure conditions that affect aircraft and other equipment, such as elevation, drag, shockwaves, and others. that speed against the wind. Additionally, those tunnels can assist engineers in figuring out how wind interacts with stationary objects like buildings and bridges and finding ways to strengthen and make them safer.Learn more about wind tunnels here:
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Which personal protective equipment (PPE) should you wear when working around asbestos-containing materials?
A) Respiratory protectionB) Protective work clothing, including gloves C) Face shields and/or vented goggles D) All of the above
Answers
Answer:
d
Explanation:
yea
Answer:
D
Explanation: