Set up the following characteristic equations in the form suited to Evanss root-locus method. Give L(s), a(s), and b(s) and the parameter, K, in terms of the original parameters in each case. Be sure to select K so that a(s) and b(s) are monic in each case and the degree of b(s) is not greater than that of a(s).
a) s + (1/τ) = 0 versus parameter τ
b) s2 + cs + c + 1 = 0 versus parameter c
c) (s + c)3 + A(Ts + 1) = 0
i. versus parameter A
ii. versus parameter T
iii. versus the parameter c, if possible. Say why you can or can not. Can a plot of the roots be drawn versus c for given constant values of A and T by any means at all.
d) 1 + (kp + k1/s + kDs/Ts + 1)G(s) = 0. Assume that G(s) = A c(s)/d(s), where c(s) and d(s) are monic polynomials with the degree of d(s) greater than that of c(s).
i. versus kp
ii. versus kI
iii. versus kD
iv. versus τ
Answers
Answer:
attached below is the detailed solution and answers
Explanation:
Attached below is the detailed solution
C(iii) : versus the parameter C
The parameter C is centered in a nonlinear equation, therefore the standard locus will not apply hence when you use a polynomial solver the roots gotten would be plotted against C
Answer: a(s) is of degree n and b(s) is of degree n-1.
a)Characteristic equation in form suitable for Evans's root-locus method is given by a(s) + b(s)K = 0, where a(s) and b(s) are polynomials of s with real coefficients. Now, given equation can be represented as: s + (1/τ) = 0 => s + (1/τ) = 0s + (1/τ)K = 0=> K = -τs/τ + 0Thus, L(s) = s, a(s) = 1, b(s) = 1 and K = -τ.
b)The characteristic equation is given by:s^2 + cs + c + 1 = 0For the root-locus method, we have to write the characteristic equation in the form a(s) + b(s)K = 0. Since the degree of a(s) is 2, we select K such that the degree of b(s) is also 2, and so b(s) will be monic.s^2 + cs + c + 1 = 0=> (s + c/2)^2 + 1/4 - c^2/4 + c = 0=> s^2 + (2c)s + (1 + c - c^2/4) = 0Now, taking a(s) = s^2 + (2c)s + (1 + c - c^2/4) and b(s) = 1 with K = -1/c^2, we have:a(s) + b(s)K = s^2 + (2c)s + (1 + c - c^2/4) - 1/c^2 = 0
c) The characteristic equation is given by:(s + c)3 + A(Ts + 1) = 0
i. versus parameter A:s = -c is a repeated root of multiplicity 3 when A = 0For s = -c, the characteristic equation becomes:-A(Tc + 1) = 0If A = 0, the characteristic equation will be (s + c)^3 = 0 and will have a repeated root at s = -c with a multiplicity of 3.
ii. versus parameter T:s = -c is a repeated root of multiplicity 3 when T = 0.For s = -c, the characteristic equation becomes:3c^2s + A = 0If A = 0, the characteristic equation will be (s + c)^3 = 0 and will have a repeated root at s = -c with a multiplicity of 3.
iii. versus the parameter c:We cannot draw the root locus of (s + c)3 + A(Ts + 1) = 0 with respect to the parameter c because there is no c term in the characteristic equation; it only contains c cubed.
d) The characteristic equation is given by:1 + (kp + k1/s + kDs/Ts + 1)G(s) = 0Assuming G(s) = Ac(s)/d(s), where c(s) and d(s) are monic polynomials with the degree of d(s) greater than that of c(s), the characteristic equation becomes:
d(s) + kp d(s) + k1 d(s)/s + kDs c(s)/T = 0.
Thus, a(s) = d(s) + k1 d(s)/s and b(s) = kDc(s)/T + kp d(s) with K = -1.
Therefore, a(s) is of degree n and b(s) is of degree n-1.
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Related Questions
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. Ex = 6 − 5x, (0, 1) The equation ex = 6 − 5x is equivalent to the equation f(x) = ex − 6 + 5x = 0. F(x) is continuous on the interval [0
Answers
Answer:
some part of your question is incomplete
attached below is the complete question
Answer :
F(0) = -5 < 0
F(1) = e - 1 > 0
since the functions : f(0) and f(1) have opposite signs then there is a 'c' whereby F(c) = 0 ( intermediate value theorem fulfilled )
Hence there is a root in the given equation : [tex]e^x = 6 - 5x[/tex]
Explanation:
using Intermediate value Theorem
If F(x) is continuous and f(a) and f(b) have opposite signs then there will be a'c'E (a,b) whereby F(c) = 0
given equation : [tex]e^x = 6 - 5x[/tex] on (0,1)
and F(x) = [tex]e^x - 6 + 5x = 0[/tex]
This shows that the F(x) is continuous on (0,1)
F(0) = [tex]e^0 - 6 + 5(0)[/tex] = -5 which is < 0
F(1) = [tex]e^1 -6 + 5(1)[/tex] = e -1 > 0 and e = 2.7182
since the functions : f(0) and f(1) have opposite signs then there is a 'c' whereby F(c) = 0 ( intermediate value theorem fulfilled )
Hence there is a root in the given equation : [tex]e^x = 6 - 5x[/tex]
Stack memory is implemented as a stack data structure. Provide the sequence of push and pop operations on stack memory when the collatz method (provided below) is called with n = 5. Note that an enqueue and dequeue is associated with a method call. For example, the first and last operations in the sequence should be push(collatz(4)) and pop(collatz(4)) respectively. public void collatz(int n) { if (n == 1) return; else if (n % 2 == 0) collatz(n / 2); else collatz(3*n + 1); }
Answers
Answer:
attached below is the solution
Explanation:
hello attached below is the sequence of push and pop operations on stack memory
For The collatz method below
public void collatz(int n) {
if (n == 1) return;
else if (n % 2 == 0)
collatz(n / 2);
else collatz(3*n + 1); }
Experimental Design Application Production engineers wish to find the optimal process for etching circuit boards quickly. They create a single replicate 24experiment to test the effect of the following factors on time to etch a circuit board: (A) Concentration of nitric acid in the etchant, (B) temperature of the etchant, (C) stirring rate in the etching tank, (D) surface area of the board. Running this experiment, they obtain the data in HW_EDA_137.csv.Preview the document Which factors effects and interaction effects are significant?
Answers
Answer:
Hello your question is incomplete attached below is the missing part and answer
options :
Effect A
Effect B
Effect C
Effect D
Effect AB
Effect AC
Effect AD
Effect BC
Effect BD
Effect CD
Answer :
A = significant
B = significant
C = Non-significant
D = Non-significant
AB = Non-significant
AC = significant
AD = Non-significant
BC = Non-significant
BD = Non-significant
CD = Non-significant
Explanation:
The dependent variable here is Time
Effect of A = significant
Effect of B = significant
Effect of C = Non-significant
Effect of D = Non-significant
Effect of AB = Non-significant
Effect of AC = significant
Effect of AD = Non-significant
Effect of BC = Non-significant
Effect of BD = Non-significant
Effect of CD = Non-significant
in a vehicle you're servicing the fuel pressure drops rapidly when the engine is says that one or more turned off. Technician a says that one or more could be leaking technician b says that a defective check valve in the fuel pump could be the cause who is correct
Answers
Answer:
Both Technicians A and B are correct
Explanation:
If the fluid pressure will decrease quickly in a car when the ignition says that one or more has been switched off. One or two could be leaking or the source could be a faulty check mechanism in the catalytic converter.
5-81 The shaft is made of A-36 steel and is fixed at end D, while end A is allowed to rotate 0.005 rad when the torque is applied. Determine the torsional reactions at these supports.
Answers
Answer:
The answer is "7.73 kip-ft".
Explanation:
Using this equation, calculate the polar moment of shaft inertia:
[tex]J= \frac{\pi }{32} d^4\\\\[/tex]
[tex]= \frac{\pi}{ 32} \times 6^4\\\\= 127.234 \ \ in^4[/tex]
Equate the number of moments in x:
[tex]\sum M_x =0[/tex]
[tex]\to T_A-T_B +T_C+T_D =0\\\\\to T_A-40 +20+T_D =0[/tex]
Calculate the torsional response at A using the superposition method:
[tex]\to \phi_A =(\phi_A)_{T} - (\phi_A)_{T_A}\\\\[/tex]
[tex]= \frac{T_B L_{BC}}{JG}+ \frac{T_C L_{CD}}{JG} - \frac{T_A L_{AD}}{JG}\\\\[/tex]
[tex]0.05= \frac{40 \times 12 \times 2 \times 12}{127.234 \times 11 \times 10^3}+ \frac{20 \times 12 \times 1.5 \times 12 }{127.234 \times 11 \times 10^3} - \frac{T_A \times 12 \times 5 \times 12}{127.234 \times 11 \times 10^3}[/tex]
[tex]0.05= (8.22 \times 10^{-3})+ (3.086 \times 10^{-3})- (5.14 \times 10^{-4} \ T_A)\\\\[/tex]
[tex]\to T_A =12.27 kip \ ft \\\\[/tex]
The torsional answer in help A is 12.27 kip- ft. It replace the necessary equation values:
[tex]\to T_A-40 +20+T_D =0 \\\\\to 12.27-40+20+T_D=0\\\\T_D=7.73 kip \ ft[/tex]
The torsional reactions at the given supports are;
T_a = 12.3 Kip.ft and T_d = 7.7 Kip.ft
What are Torsional Reactions from Torque?From the image of the shaft attached, if we take a free body diagram and torsion about x, we will have;
∑Mₓ = 0;
T_a + T_d + 20 - 40 = 0 -----(1)
Using the method of superposition, we have;
Φ_a = (Φ_a)_T - (Φ_a)_T_a
Formula for rotation Φ is;
Φ = TL/(JG)
Thus;
0.005 = [tex][\frac{40 * 12 * 2 * 12}{(\pi/2) *3^{4} * 11 * 10^{3}} + \frac{20 * 12 * 1.5 * 12}{(\pi/2) *3^{4} * 11 * 10^{3}}] - \frac{T_{A} * 12 * 5 * 12}{(\pi/2) *3^{4} * 11 * 10^{3}}[/tex]
Solving for T_a in this gives;
T_a = 12.3 Kip.ft
Thus, from eq 1;
12.3 + T_d + 20 - 40 = 0
T_d = 20 - 12.3
T_d = 7.7 Kip.ft
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Why do the changes to the mass of the planet NOT AFFECT the orbital path of the Planet?
Answers
Answer:
changes of Mass affect the planet because... I'm sorry If this didn't help.
g At this party, is the fact that a person is from South America independent of that person being majoring in biomedical engineering?
Answers
Answer:
Yes, this is completely independent.
Explanation:
Yes, this is completely independent. Even though there are no South American individuals that are majoring in biomedical engineering in this party it is still a completely independent factor. The origin of birth of an individual does not tie them to a specific degree or field of expertise, therefore a South American individual can study anything they want including mechanical engineering, electrical engineering, or biomedical engineering.
(a) At a simple interest rate of 12% per year, determine how long it will take $5000 to increase to twice as much. (b) Compare the time it will take to double if the rate is 20% per year simple interest.
Answers
Explanation:
10000=5000(1.12^x)
2=1.12^x
(log_1.12)(2)=x
x= about 6.1163
10000=5000(1.2^x)
2=1.2^x
(log_1.2)(2)=x
x= about 3.8019
compare them by saying like 20% will be 6.12/3.8 times faster
A closed system of mass 20 kg undergoes a process in which there is a heat transfer of 1000 Q6: ki from the system to the surroundings. The work done on the system is 200 kl. If the initial 5 specific internal energy of the system is (250+R:) kl/kg, what is the final specific internal energy, in kj/kg? Neglect changes in kinetic and potential energy:
Answers
The final specific internal energy : 190 kJ/kg
Further explanationThe laws of thermodynamics 1 state that: energy can be changed but cannot be destroyed or created
The equation is:
[tex]\tt E_{in}-E_{out}=\Delta E~system\\\\\Delta E=\Delta U+\Delta KE+\Delta PE\\\\\Delta U=m(U_2-U_1)\\\\Q-W=\Delta U+\Delta KE+\Delta PE[/tex]
Energy owned by the system is expressed as internal energy (U)
This internal energy can change if it absorbs heat Q (U> 0), or releases heat (U <0). Or the internal energy can change if the system does work or accepts work (W)
The sign rules for heat and work are set as follows:
• The system receives heat, Q +
• The system releases heat, Q -
• The system does work, W -
• the system accepts work, W +
A closed system of mass 20 kg⇒m=20 kg
Heat transfer of 1000 kJ from the system to the surroundings⇒Q=-1000 kJ
The work done on the system is 200 kJ⇒W=+200 kJ
The initial specific internal energy of the system is 250 kJ /kg⇒U₁ = 250 kj/kg
Neglect changes in kinetic and potential energy⇒ΔKE+ΔPE=0, so
Q-W = ΔU
Input in equation
[tex]\tt -1000-200=20(U_2-250)\\\\-1200=20U_2-5000\\\\3800=20U_2\\\\U_2=190~kJ/kg[/tex]
Help please all of the numbers b4 the equal sign are wrong
Answers
Answer:
3/5" = 12'1 3/4" = 35'1 1/4" = 25'9/10" = 18'2 13/20" = 53'Explanation:
One number is wrong; they all lack units.
The basic ratio is 1" = 20', so you can divide feet by 20 to find inches.
3/5" = 12'1 3/4" = 35'1 1/4" = 25'9/10" = 18'2 13/20" = 53'Perhaps you want decimal inches:
0.60" = 12'1.75" = 35'1.25" = 25'0.90" = 18'2.65" = 53'What motivated software engineers to move from the waterfall model to the incremental or spiral model
Answers
Answer:
1. They needed to develop multiple components in software programs.
2. The ability to overlap the development to be more evolutionary in nature.
3. The need to be more risk-averse or the unwillingness to take risks led to the use of a spiral model.
Explanation:
Software development life cycle (SDLC) can be defined as a strategic process or methodology that defines the key steps or stages for creating and implementing high quality software applications.
In SDLC, a waterfall model can be defined as a process which involves sequentially breaking the software development into linear phases. Thus, the development phase takes a downward flow like a waterfall and as such each phase must be completed before starting another without any overlap in the process.
An incremental model refers to the process in which the requirements or criteria of the software development is divided into many standalone modules until the program is completed.
Also, a spiral model can be defined as an evolutionary SDLC that is risk-driven in nature and typically comprises of both an iterative and a waterfall model. Spiral model of SDLC consist of these phases; planning, risk analysis, engineering and evaluation.
What motivated software engineers to move from the waterfall model to the incremental or spiral model is actually due to the following fact;
They needed to develop multiple components in software programs. The ability to overlap the development to be more evolutionary in nature. The need to be more risk-averse or the unwillingness to take risks led to the use of a spiral model.Under a subsection for geological hazards the buyer is encouraged to obtain an read the booklet
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Answer:
Buyer is encouraged to obtain and read the booklet entitled "The Homeowners Guide to Earthquake Safety." In most cases a questionnaire within the booklet must be completed by Seller and the entire booklet given to the Buyer if the Property was built prior to 1960.
Don't break or crush mercury-containing lamps because mercury powder may be released.
A) TrueB) False
Answers
It would be released without a doubt so be careful!
Hope this helps :)
An engineer is trying to build a new measurement tool. Which step should the engineer complete first? A. Design a model of the tool to be tested. B. Precisely define the problem that is to be solved. Selected:c. Write a list of the criteria and constraints for the tool.This answer is incorrect. D. Conduct research on how similar problems were solved in the past.
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Answer:
B. Precisely define the problem that is to be solved.
Explanation:
Engineering can be defined as the scientific and technological principles that is used for the design, development, operation and control of tools, machines or equipments, structures and systems. These machines, tools, systems and structures are typically designed and developed for the purpose of solving peculiar problems relating to human life. Simply stated, engineering is focused on proffering solutions to real life problems through a design process.
Generally, the design process comprises of series of steps used for the development of various tools, machines, structures and systems. In a chronological order, the basic steps of a design process are;
1. Define the problem: to proffer a solution to any problem, you have to precisely define the problem that is to be solved. Therefore, this is the first step of the design process.
2. Conduct a research: the engineer should collect or gather data (informations) relating to the project.
3. Brainstorming and analysis of data: this is the stage where the engineer conceptualize his or her ideas.
4. Create a prototype or simulated model of the product.
5. Product analytics and test: this is where the product is being used and tested for any flaw, error or defects. Thus, troubleshooting is also required at this stage.
Hence, if an engineer is trying to build a new measurement tool; the first step the engineer should complete is to precisely define the problem that is to be solved so as to have a good clear-cut understanding of the problem.