Homework Answers
Add Answer to:
10. Prove the following theorem Theorem 1 Let H and H denote the input-output transfer functions for the continuous tim...
Standard state-space representations of LTI systems x(t)-Ax(t)+Bu(t); yt)-Cx(t)+Du(f) Two different systems have the following representations: 0...
Standard state-space representations of LTI systems x(t)-Ax(t)+Bu(t); yt)-Cx(t)+Du(f) Two different systems have the following representations: 0 2 -3 a. Determine the input-output transfer functions for the two systems above. Are they the same? b. Explain the result obtained in part a. c. Determine the poles and zeros of the two systems above
B2. (a) Let I denote the interval 0,1 and let C denote the space of continuous functions I-R. Def...
B2. (a) Let I denote the interval 0,1 and let C denote the space of continuous functions I-R. Define dsup(f,g)-sup |f(t)-g(t) and di(f.g)f (t)- g(t)ldt (f,g E C) tEI (i) Prove that dsup is a metric on C (ii) Prove that di is a metric on C. (You may use any standard properties of continuous functions and integrals, provided you make your reasoning clear.) 6 i) Let 1 denote the constant function on I with value 1. Give an explicit...
2. For the transfer functions in problem 1 (a)(d)(e), find the corresponding impulse response functions h(t) using par...
2. For the transfer functions in problem 1 (a)(d)(e), find the corresponding impulse response functions h(t) using partial fraction expansion and determine the value of lim h(t) if the limit exists. Verify that lim- n(t)-0 for stable systems. (optional) After performing the partial fraction expansion by hand (required), yoiu are encouraged to use MATLAB to verify your results. MATLAB has a function called 'residue' that can calculate poles (pi) and residues (ci). For example, the following line will calculate the...
2. Let Bt denote a Brownian motion. Consider the Black-Scholes model for the price of stock St, 2 So-1 and the savings account is given by β,-ea (a) Solve the equation for the price of the stock St a...
2. Let Bt denote a Brownian motion. Consider the Black-Scholes model for the price of stock St, 2 So-1 and the savings account is given by β,-ea (a) Solve the equation for the price of the stock St and show that it is not a (b) Explain what is meant by an Equivalent Martingale Measure (EMM) martingale. State the Girsanov theorem. Give the expression for Bt under the EMM Q, hence derive the expression for St under the EMM, and...
For a control system, its transfer function from the input to the output is H(s) =...
For a control system, its transfer function from the input to the output is H(s) = 4/ (s2 + 2s + 2 ) if the input is r(t) = u(t), the steady-state tracking error is . a. 0 b. 1. c. 2 d. −1 e. None
Problem 1 The following transfer functions are given for a single-loop unity- feedback (H(s)-1) and nonunity-...
Problem 1 The following transfer functions are given for a single-loop unity- feedback (H(s)-1) and nonunity- feedback control system. Find the steady-state errors for both cases due to a unit-step input 1(t),a unit-ramp inputt1(t), and a parabolic input (t2/2)1() (a) Go)+2) (b) Go)5 H(s) = 5 a) G)+12) ( H(s)-5(s + 2) 2)
Assignment: Let us consider the same network of HW3, Figure 1, with the parameter reported in Tab...
Assignment: Let us consider the same network of HW3, Figure 1, with the parameter reported in Table 1. 10 V 1 2 ΙΩ R2 1 H Figure l Table l 1. Which is the order of the system How many input it has? Comment your answer. 2. Obtain (manually) a state space representation of the circuit in the form x(t) - Ax(t) + Bu(t) 3. Assuming that you variable of interest is the current is resistor R1, write an output...
Let a transfer function H be 1000s + 10) 100+1000 Use H to respond to the following questions and...
System dynamics course.
Let a transfer function H be 1000s + 10) 100+1000 Use H to respond to the following questions and imperatives a. Write H as a product of standard-form transfer functions Find the frequency response function H(jaw) without simplifying c. Use the axes below to sketch the Bode plot of H. 20 -20 10-1 10° 101 102 103 10 w (rad/s) 90 45 45 -90 -135 -180 10-T 100 101 102 103 101 w (rad/s)
Let a transfer...
1. Let V be a vector space with bases B and C. Suppose that T:V V is a linear map with matrix representations Ms(T)A and Me(T) B. Prove the following (a) T is one-to-one iff A is one-to-one. (b...
1. Let V be a vector space with bases B and C. Suppose that T:V V is a linear map with matrix representations Ms(T)A and Me(T) B. Prove the following (a) T is one-to-one iff A is one-to-one. (b) λ is an eigenvalue of T iff λ is an eigenvalue of B. Consequently, A and B have the same eigenvalues (c) There exists an invertible matrix V such that A-V-BV
1. Let V be a vector space with bases B...
1. Consider the circuit shown below. Cl e, (0) c, e。(t) Find the transfer function below using t...
Please help with this dynamics circuit
analysis.
Please show work and explain.
Thank you!!
1. Consider the circuit shown below. Cl e, (0) c, e。(t) Find the transfer function below using time-domain and impedance methods. (a) Determine the differential equation for the relationship between eo(1) and e(1) (b) Find the transfer function E, (s)/E,(s) and determine the system time constant in terms of the circuit element values C, C, and R 17 2 (c) Find the transfer function E, (s)/E,...
Standard state-space representations of LTI systems x(t)-Ax(t)+Bu(t); yt)-Cx(t)+Du(f) Two different systems have the following representations: 0 2 -3 a. Determine the input-output transfer functions for the two systems above. Are they the same? b. Explain the result obtained in part a. c. Determine the poles and zeros of the two systems above
B2. (a) Let I denote the interval 0,1 and let C denote the space of continuous functions I-R. Define dsup(f,g)-sup |f(t)-g(t) and di(f.g)f (t)- g(t)ldt (f,g E C) tEI (i) Prove that dsup is a metric on C (ii) Prove that di is a metric on C. (You may use any standard properties of continuous functions and integrals, provided you make your reasoning clear.) 6 i) Let 1 denote the constant function on I with value 1. Give an explicit...
2. For the transfer functions in problem 1 (a)(d)(e), find the corresponding impulse response functions h(t) using partial fraction expansion and determine the value of lim h(t) if the limit exists. Verify that lim- n(t)-0 for stable systems. (optional) After performing the partial fraction expansion by hand (required), yoiu are encouraged to use MATLAB to verify your results. MATLAB has a function called 'residue' that can calculate poles (pi) and residues (ci). For example, the following line will calculate the...
2. Let Bt denote a Brownian motion. Consider the Black-Scholes model for the price of stock St, 2 So-1 and the savings account is given by β,-ea (a) Solve the equation for the price of the stock St and show that it is not a (b) Explain what is meant by an Equivalent Martingale Measure (EMM) martingale. State the Girsanov theorem. Give the expression for Bt under the EMM Q, hence derive the expression for St under the EMM, and...
Problem 1 The following transfer functions are given for a single-loop unity- feedback (H(s)-1) and nonunity- feedback control system. Find the steady-state errors for both cases due to a unit-step input 1(t),a unit-ramp inputt1(t), and a parabolic input (t2/2)1() (a) Go)+2) (b) Go)5 H(s) = 5 a) G)+12) ( H(s)-5(s + 2) 2)
Assignment: Let us consider the same network of HW3, Figure 1, with the parameter reported in Table 1. 10 V 1 2 ΙΩ R2 1 H Figure l Table l 1. Which is the order of the system How many input it has? Comment your answer. 2. Obtain (manually) a state space representation of the circuit in the form x(t) - Ax(t) + Bu(t) 3. Assuming that you variable of interest is the current is resistor R1, write an output...
System dynamics course.
Let a transfer function H be 1000s + 10) 100+1000 Use H to respond to the following questions and imperatives a. Write H as a product of standard-form transfer functions Find the frequency response function H(jaw) without simplifying c. Use the axes below to sketch the Bode plot of H. 20 -20 10-1 10° 101 102 103 10 w (rad/s) 90 45 45 -90 -135 -180 10-T 100 101 102 103 101 w (rad/s)
Let a transfer...
1. Let V be a vector space with bases B and C. Suppose that T:V V is a linear map with matrix representations Ms(T)A and Me(T) B. Prove the following (a) T is one-to-one iff A is one-to-one. (b) λ is an eigenvalue of T iff λ is an eigenvalue of B. Consequently, A and B have the same eigenvalues (c) There exists an invertible matrix V such that A-V-BV
1. Let V be a vector space with bases B...
Please help with this dynamics circuit
analysis.
Please show work and explain.
Thank you!!
1. Consider the circuit shown below. Cl e, (0) c, e。(t) Find the transfer function below using time-domain and impedance methods. (a) Determine the differential equation for the relationship between eo(1) and e(1) (b) Find the transfer function E, (s)/E,(s) and determine the system time constant in terms of the circuit element values C, C, and R 17 2 (c) Find the transfer function E, (s)/E,...
Most questions answered within 3 hours.
-
An MNE is this kind of industry when competition in one country
is essentially independent of...
asked 17 minutes ago -
. For this set of questions, determine what
proportion of a normal distribution is located betweeneach...
asked 52 minutes ago -
A college student is employed as a door-to-door newspaper
salesman. Historical data suggests that the student...
asked 1 hour ago -
MATLAB HW 11 problem using Switch Case and Input commands
Write a script file that calculates...
asked 1 hour ago -
Considering gravitational time dilation, calculate the time that
passes in Earth’s surface while 1 hour passes...
asked 2 hours ago -
Minitab Problem: Take the Lake Hume June rainfall data and find
use the processes outlined in...
asked 3 hours ago -
X Company is trying to decide whether to continue using old
equipment to make Product A...
asked 3 hours ago -
IN PYTHON ONLY !! Program 2: Re-work
program #5 (WeeklyHours) from the previous assignment such that...
asked 3 hours ago -
The average length of time between arrivals at a turnpike
toll-booth is 26 seconds. What is...
asked 5 hours ago -
(a) A piston at 6.1 atm contains a gas that occupies a volume of
3.5 L....
asked 6 hours ago -
Please answer true or false. Words
cannot be changed or added in to make it true...
asked 6 hours ago -
An empty test tube weighs 15.923 grams. Then,
MgCl2•6H2O is added into the test tube. After...
asked 6 hours ago