Question

In: Physics

] Consider the following dynamic equations: ?1̇ = −2?1 + 6?2 ?2̇ = −4?1 + ?(?)...

] Consider the following dynamic equations: ?1̇ = −2?1 + 6?2 ?2̇ = −4?1 + ?(?) ?(?) = ?1 The control is obtained through state feedback with ?(?) = −?1?1 − ?2?2 + ?(?), where ?(?) is reference input. Find the ?1 and ?2 if the closed-loop system has a natural undamped frequency of 10 rad/sec and a damping ratio of 0.707.

Solutions

Expert Solution


Related Solutions

2. Consider the following data: x= 1, 2, 3, 4, 5 y =3, 2, 4, 6,...
2. Consider the following data: x= 1, 2, 3, 4, 5 y =3, 2, 4, 6, 5 By hand, not using Matlab, and showing your work: (a) Compute the correlation coefficient. (b) Find the least-squares line. (c) Find the standard deviation around the least-squares line.
2. Consider functions f : {1, 2, 3, 4, 5, 6} → {1, 2, 3, 4,...
2. Consider functions f : {1, 2, 3, 4, 5, 6} → {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (a) How many of these functions are strictly increasing (i.e. f(1) < f(2) < f(3) < f(4) < f(5) < f(6))? Hint: How many different possibilities are there for the range of f? For each range of f, how many strictly increasing functions are there? (b) How many of these functions are non-decreasing (i.e. f(1) ≤ f(2) ≤...
Find equations of the following. 2(x − 9)2 + (y − 6)2 + (z − 1)2...
Find equations of the following. 2(x − 9)2 + (y − 6)2 + (z − 1)2 = 10,    (10, 8, 3) (a) the tangent plane (b) the normal line (x(t), y(t), z(t))=
Consider the following pairs of observations.X 1 4 3 5 7 2 6 20
Consider the following pairs of observations. X 1 4 3 5 7 2 6 20 Y 3 12 10 12 19    7 17   60 A) Calculate the least squares line. B) Determine a 95% confidence interval for the mean value of Y using X = 6 C) Determine a 95% prediction interval for the Y value using X = 6
Consider a set A = { 1, 2, 3, 4, 5, 6, 8} Consider these relations,...
Consider a set A = { 1, 2, 3, 4, 5, 6, 8} Consider these relations, 1. R1 = { ( a, b) | a = 3b } Can you write down the pairs ? one such pair is ( 3, 1) 2. R2 = { (a, b) | 2a = b } Can you write down the pairs ? one such pair is (2, 4) 3. R3 = { ( a, b) | a >= 2b } Can you...
Solve the following first order differential equations: (a) 2/?^ ???/?? = 4?^2? ; ?(0) = −1/...
Solve the following first order differential equations: (a) 2/?^ ???/?? = 4?^2? ; ?(0) = −1/ 3 (b) ??/?? + ? = ? ; ?(0) = 5 (c) ??/?? + ? /? = ? 3 ; ? ( 1/2 ) = 1
Problem 6-01 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6...
Problem 6-01 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6 Value 18 12 16 10 19 13 Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy. Mean absolute error. If required, round your answer to one decimal place. Mean squared error. If required, round your answer to one decimal place. Mean absolute percentage error. If required, round your intermediate calculations and final...
Consider the following set of ordered pairs. x 4 2 4 3 6 4 y 5...
Consider the following set of ordered pairs. x 4 2 4 3 6 4 y 5 7 7 4 2 7 ​a) Calculate the correlation coefficient. ​b) Using alpha equals 0.05​, perform a hypothesis test to determine if the population correlation coefficient is less than zero. LOADING... Click the icon to view a portion of the​ Student's t-distribution table. ​a) requals nothing ​(Round to three decimal places as​ needed.) ​b) Determine the null and alternative hypotheses. Upper H 0​: rho...
Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 4 6...
Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 4 6 7 2 0 1 4 3 3 5 6 4 5 7 8 (b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round your...
Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 4 6...
Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 4 6 7 2 2 3 6 3 3 5 6 4 5 7 8 Compute seasonal indexes and adjusted seasonal indexes for the four quarters (to 3 decimals). Quarter Seasonal Index Adjusted Seasonal Index 1 (___) (___) 2 (___) (___) 3 (___) (___) 4 (___) (___) Total (___) Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 5 5 6...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT