3 Follow the following steps in Matlab to solve the following question. Consider the system below...

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3 Follow the following steps in Matlab to solve the following question. Consider the system below for G = +1, H = 2s, and F = 1. F(s) s = tf('s'); Gm= 1/(s^2+1) Hm 2 s sisotool. C(s) G(s) (a) Calculate the closed-loop transfer function for C(s) =(. (b) Enter the following commands in the command window of Matlab: H(s) (The commands define the variable s, the transfer functions F(s), G(s), and H(s), and open the sisotool. A description of the sisotool can be found in its help menu or in appendix B.4 at pp. 1270-1279.) i. Select the first control architecture. ii. In the Blocks tab select F=1, G = Gm, and H=Hm. iii. Press the OK button to close the Edit Architecture window. (c) Click on the Edit Architecture button of the Control System tab. This will open the Edit Architecture window. In the Edit Architecture window: y (d) Locate the step response plot. i. Right click on the white area of the plot and select Full View. ii. Right click on the white area of the plot, select Characteristics and then Settling Time. (e) Click on C in the Data Browser/Controllers and Fired Blocks. This will display the value of C in the Preview area of the Data Browser. At the end of this step the sisotool window should be similar to Figure 1. (g) Vary C(s) over the interval 0...100. Let (=C(s). i. Does the rise time of y decrease or increase as ( increases? ii. How does the 2% settling time change when ( is varied? iii. How does the overshoot change as ( is varied? (f) There are several ways to change the value of C. i. Drag up or down the magnitude Bode plot. ii. Drag the purple squares of the Root Locus plot. iii. Open the Edit Architecture window, write the desired value of C, and then close the Edit Architecture window. (j) According to the formula t = However, the formula t, minimizes the settling-time. (h) Measure the settling time for (= 0.2, (0.5, (-0.7, C=1, and (= 5. Note: You may right click the curve and then drag the black square to the point of the curve that you want to measure. (i) The formula t. = can be used to estimate the 2% settling time only when 0 < < <1. Are your results consistent with this statement? Swin the response is faster for ( = 1 than for ( < 1. is an approximation. Use the sisotool to estimate that 3 Follow the following steps in Matlab to solve the following question. Consider the system below for G=21, H = 2s, and F = 1. F(s) C(s) G(s) (a) Calculate the closed-loop transfer function for C(s)=(. (b) Enter the following commands in the command window of Matlab: H(s) s = tf('s'); Gm 1/(s^2+1) Hm= 2*s sisotool (The commands define the variable s, the transfer functions F(s), G(s), and H(s), and open the sisotool. A description of the sisotool can be found in its help menu or in appendix B.4 at pp. 1270-1279.) (e) Click on the Edit Architecture button of the Control System tab. This will open the Edit Architecture window. In the Edit Architecture window: i. Select the first control architecture. ii. In the Blocks tab select F=1, G = Gn, and H=Hm. iii. Press the OK button to close the Edit Architecture window. (d) Locate the step response plot. 1. Right click on the white area of the plot and select Full View. ii. Right click on the white area of the plot, select Characteristics and then Settling Time. (e) Click on C in the Data Browser/Controllers and Fired Blocks. This will display the value of C in the Preview area of the Data Browser. At the end of this step the sisotool. window should be similar to Figure 1. (f) There are several ways to change the value of C. i. Drag up or down the magnitude Bode plot. ii. Drag the purple squares of the Root Locus plot. iii. Open the Edit Architecture window, write the desired value of C, and then close the Edit Architecture window. (g) Vary C(s) over the interval 0...100. Let (=C(s). i. Does the rise time of y decrease or increase as ( increases? ii. How does the 2% settling time change when is varied? iii. How does the overshoot change as ( is varied? (h) Measure the settling time for ( = 0.2, (0.5, 0.7, C = 1, and C= 5. Note: You may right click the curve and then drag the black square to the point of the curve that you want to measure. (i) The formula t, =can be used to estimate the 2% settling time only when 0 < < < 1. Are your results consistent with this statement? (j) According to the formula t = the response is faster for ( = 1 than for ( < 1. (W is an approximation. Use the sisotool to estimate that However, the formula t, minimizes the settling-time. 3 Follow the following steps in Matlab to solve the following question. Consider the system below for G = +1, H = 2s, and F = 1. F(s) s = tf('s'); Gm= 1/(s^2+1) Hm 2 s sisotool. C(s) G(s) (a) Calculate the closed-loop transfer function for C(s) =(. (b) Enter the following commands in the command window of Matlab: H(s) (The commands define the variable s, the transfer functions F(s), G(s), and H(s), and open the sisotool. A description of the sisotool can be found in its help menu or in appendix B.4 at pp. 1270-1279.) i. Select the first control architecture. ii. In the Blocks tab select F=1, G = Gm, and H=Hm. iii. Press the OK button to close the Edit Architecture window. (c) Click on the Edit Architecture button of the Control System tab. This will open the Edit Architecture window. In the Edit Architecture window: y (d) Locate the step response plot. i. Right click on the white area of the plot and select Full View. ii. Right click on the white area of the plot, select Characteristics and then Settling Time. (e) Click on C in the Data Browser/Controllers and Fired Blocks. This will display the value of C in the Preview area of the Data Browser. At the end of this step the sisotool window should be similar to Figure 1. (g) Vary C(s) over the interval 0...100. Let (=C(s). i. Does the rise time of y decrease or increase as ( increases? ii. How does the 2% settling time change when ( is varied? iii. How does the overshoot change as ( is varied? (f) There are several ways to change the value of C. i. Drag up or down the magnitude Bode plot. ii. Drag the purple squares of the Root Locus plot. iii. Open the Edit Architecture window, write the desired value of C, and then close the Edit Architecture window. (j) According to the formula t = However, the formula t, minimizes the settling-time. (h) Measure the settling time for (= 0.2, (0.5, (-0.7, C=1, and (= 5. Note: You may right click the curve and then drag the black square to the point of the curve that you want to measure. (i) The formula t. = can be used to estimate the 2% settling time only when 0 < < <1. Are your results consistent with this statement? Swin the response is faster for ( = 1 than for ( < 1. is an approximation. Use the sisotool to estimate that 3 Follow the following steps in Matlab to solve the following question. Consider the system below for G=21, H = 2s, and F = 1. F(s) C(s) G(s) (a) Calculate the closed-loop transfer function for C(s)=(. (b) Enter the following commands in the command window of Matlab: H(s) s = tf('s'); Gm 1/(s^2+1) Hm= 2*s sisotool (The commands define the variable s, the transfer functions F(s), G(s), and H(s), and open the sisotool. A description of the sisotool can be found in its help menu or in appendix B.4 at pp. 1270-1279.) (e) Click on the Edit Architecture button of the Control System tab. This will open the Edit Architecture window. In the Edit Architecture window: i. Select the first control architecture. ii. In the Blocks tab select F=1, G = Gn, and H=Hm. iii. Press the OK button to close the Edit Architecture window. (d) Locate the step response plot. 1. Right click on the white area of the plot and select Full View. ii. Right click on the white area of the plot, select Characteristics and then Settling Time. (e) Click on C in the Data Browser/Controllers and Fired Blocks. This will display the value of C in the Preview area of the Data Browser. At the end of this step the sisotool. window should be similar to Figure 1. (f) There are several ways to change the value of C. i. Drag up or down the magnitude Bode plot. ii. Drag the purple squares of the Root Locus plot. iii. Open the Edit Architecture window, write the desired value of C, and then close the Edit Architecture window. (g) Vary C(s) over the interval 0...100. Let (=C(s). i. Does the rise time of y decrease or increase as ( increases? ii. How does the 2% settling time change when is varied? iii. How does the overshoot change as ( is varied? (h) Measure the settling time for ( = 0.2, (0.5, 0.7, C = 1, and C= 5. Note: You may right click the curve and then drag the black square to the point of the curve that you want to measure. (i) The formula t, =can be used to estimate the 2% settling time only when 0 < < < 1. Are your results consistent with this statement? (j) According to the formula t = the response is faster for ( = 1 than for ( < 1. (W is an approximation. Use the sisotool to estimate that However, the formula t, minimizes the settling-time.