KG(S) =S(S+20)(S+20)A unity feedback system withis operating at 20% overshoot. Design acompensator to decrease the settling time by a factor of 2 without affecting the percent overshootand do the following:1. Evaluate the uncompensated system's dominant poles, gain and settling time2. Evaluate the compensated systems dominant poles and settling time.3. Evaluate then compensators poles and zero. Find the required gain.

Uncompensated System:Given transfer function: G(s)=s(s+20)(s+20)KThe system is operating at 20%…

Answered: K G(S) = S(S+20)(S+20) A unity feedback…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. The following output from R presents the results from computing a linear model. In our data example we are interested to study the relationship between students' academic performance api00 with variable enroll which is the number of students in the school. Call: Im (formula = api00 enroll, data = d) Residuals: мin 10 Median 30 Маx -285.50 -112.55 -6.70 95.06 389.15 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 744.25141 15.93308 46.711 < 2e-16 *** enroll -0.19987 0.02985 -6.695 7.34e-11 *** --- Signif. codes: O ' *** ' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 135 on 398 degrees of freedom Multiple R-squared: 0.1012, Adjusted R-squared: F-statistic: 44.83 on 1 and 398 DF, p-value: 7.339e-11 0.09898
Chapter 9, Section 1, Exercise 002 Use the computer output to estimate the intercept β0 and the slope β1.The regression equation is Y⁢=810-4.84X. Predictor Coef SE Coef T P Constant 810.004 88.04 9.20 0.000 X -4.841 1.587 -3.05 0.006 Intercept β0: Slope β1: Click if you would like to Show Work for t
#3) A systems specialist has studied the workflow of clerks all doing the same inventory work. Based on this study, she designed a new workflow layout for the inventory system. To compare the average production for the old and new methods, a random sample of 6 clerks was used. The average production rate (number of inventory items processed) for each clerk was measures both before and after the new system was introduced. The results are shown below. Test the claim that the new system speeds up the work rate (use a = 0.05) Clerk B: Old method A: New Method 4 85 3 97 2 110 100 117 101 118 112 115 83 125 109
We are interested in studying cigarette demand by young adults. Lets consider thefollowing model:ncaj = β0 + β1price + β2age + β3income + uwhere ncaj is monthly cigarette consumption in packs, price is the price of a pack ofcigarettes in dollars, age is age in years, and income is annual income in thousandsof dollars. Consider now an extension of the model that allow the effect of theprice to differ by age. Holding all other factors fixed, is the effect of price onncaj constant? (This part is theoretical and you do not have to estimate themodel.)
A computer engineer needs to know how the efficiency of a new computerprogram depends on the size of incoming data. Efficiency will be measuredby the number of processed requests per hour. Applying the program todata sets of different sizes with the following results. The response variableis the number of processed requests (Y) and to predict it from the size of adata set (X). Estimate the quadratic regression model and use it to find theprocessed requests when the data size is 14 GB.Data size (GB) X 6 7 7 8 10 10 15Processed requests Y 50 43 44 37 25 26 15
3
Heteroscedasticity Stigler and Friedland (1983) conducted a study to determine whether the separation of company control from company ownership affects company profits. Using data from 69 companies in the United States, the authors estimate the following model: profiti = α + β1asseti + β2management_controli + ei Where i is company and: profiti = annual profit (in million dollar) asseti = company asset (in million dollar) management_controli = dummy variable that is worth one if the control of the company is held by the manager The regression results are presented in the table in the picture a. Explain whether the statements below are TRUE, FALSE, or CANNOT BE DETERMINED. "If there is a heteroscedasticity problem, the confidence interval of the OLS estimator is not valid." b. Determine the 95% confidence interval for the parameter 2, what can you conclude?
1. Simple Linear Regression Estimation: (а) For the model y; B1 + B2x; + ui, define the fitted value ĝ; and residual û;. (b) x to arrive at estimates for B1 and B2? How does OLS take data on the outcome variable y and the independent variable Suppose you have the OLS estimate of the slope coefficient B2 from regressing ax; is equal to (c) y on x. Show that the slope coefficient if you regressed y on x* for x B2/a, where a is some constant. To be clear, I want you to show that B = B2/a, where B2 is the OLS estimate of B2 from the model Yi = B1 + B2x; + ui, and B is the OLS estimate of B; from the model y; = Bi + B5x + U;.
Provide a coherent answer for items C and D.
7. a) What are residual plots and box plots? b) Do the stability analysis of the following model which is formulated to study the effect of toxicant on one competing species where the environmental toxicant concentration is being taken to change w.r.t. time. dN = rN, - α,Ν,N, - d,C,N , dt dN2 = rN, - α,N,., dt dCo = k,P - g,C, – m¡C, dt dP Q- hp – kPN, + gC,N . dt along with the initial conditions. N, (0) = N10,N2 (0)= N20,C, (0)= 0, P(0)= P, > 0 %3D Here, N1 (t) = Density of prey population

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