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E(t)=u(t) 5 S+5 Zero-Order Hold Transfer Fon Y(t) Fig. 2 A closed-loop sampled-data system 2. Write a MATLAB program that accepts the characteristic equation of the discrete transfer function, sampling time T and calculates the z-plane poles result in the s-plane poles. Also, it determines the time constant (t), damping ratio (c), and natural frequency (w). Finally, the program calculates the percentage of overshot (P.O) and settling time t,of the system by using the t, C, and W. Assume that the input of the system is always unit-step function and the mathematical expressions for the P.O and ts are given in Ogata**. a) Before the experiment, calculate the transfer function of the system that is given in Fig. 2. Find the roots of the characteristic equation and map them into the s-plane. Then, calculate t, C, W, P.O, and ts. b) Run the MATLAB program for the transfer function of the system that is given in Fig. 2. Observe the results. Check the validity of your program. c) Plot the step response of the system by using "dstep" command. Observe the P.O and ts from the figure. Use "damp" command to find the 5 and w₁. Compare the results with a and b. Is there any difference or similarities between them? If any, explain the reason. Also, discuss the relation between the transient response and the z-plane pole locations. d) Repeat the b and c for the transfer function that are given below: z - 0.8 1.85z+0.854 z + 0.3625 ii) G₂(z) = = z² - z+1 i) G₁(z) = z² - z + 0.4562 z + 2.13 iii) G3(z) = z² - z + 0.5 iv) G₁(z) = = z + 0.814

E(t)=u(t) 5 S+5 Zero-Order Hold Transfer Fon Y(t) Fig. 2 A closed-loop sampled-data system 2. Write a MATLAB program that accepts the characteristic equation of the discrete transfer function, sampling time T and calculates the z-plane poles result in the s-plane poles. Also, it determines the time constant (t), damping ratio (c), and natural frequency (w). Finally, the program calculates the percentage of overshot (P.O) and settling time t,of the system by using the t, C, and W. Assume that the input of the system is always unit-step function and the mathematical expressions for the P.O and ts are given in Ogata**. a) Before the experiment, calculate the transfer function of the system that is given in Fig. 2. Find the roots of the characteristic equation and map them into the s-plane. Then, calculate t, C, W, P.O, and ts. b) Run the MATLAB program for the transfer function of the system that is given in Fig. 2. Observe the results. Check the validity of your program. c) Plot the step response of the system by using "dstep" command. Observe the P.O and ts from the figure. Use "damp" command to find the 5 and w₁. Compare the results with a and b. Is there any difference or similarities between them? If any, explain the reason. Also, discuss the relation between the transient response and the z-plane pole locations. d) Repeat the b and c for the transfer function that are given below: z - 0.8 1.85z+0.854 z + 0.3625 ii) G₂(z) = = z² - z+1 i) G₁(z) = z² - z + 0.4562 z + 2.13 iii) G3(z) = z² - z + 0.5 iv) G₁(z) = = z + 0.814

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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E(t)=u(t) 5 S+5 Zero-Order Hold Transfer Fon Y(t) Fig. 2 A closed-loop sampled-data system 2. Write a MATLAB program that accepts the characteristic equation of the discrete transfer function, sampling time T and calculates the z-plane poles result in the s-plane poles. Also, it determines the time constant (t), damping ratio (c), and natural frequency (w). Finally, the program calculates the percentage of overshot (P.O) and settling time t,of the system by using the t, C, and W. Assume that the input of the system is always unit-step function and the mathematical expressions for the P.O and ts are given in Ogata**. a) Before the experiment, calculate the transfer function of the system that is given in Fig. 2. Find the roots of the characteristic equation and map them into the s-plane. Then, calculate t, C, W, P.O, and ts. b) Run the MATLAB program for the transfer function of the system that is given in Fig. 2. Observe the results. Check the validity of your program. c) Plot the step response of the system by using "dstep" command. Observe the P.O and ts from the figure. Use "damp" command to find the 5 and w₁. Compare the results with a and b. Is there any difference or similarities between them? If any, explain the reason. Also, discuss the relation between the transient response and the z-plane pole locations. d) Repeat the b and c for the transfer function that are given below: z - 0.8 1.85z+0.854 z + 0.3625 ii) G₂(z) = = z² - z+1 i) G₁(z) = z² - z + 0.4562 z + 2.13 iii) G3(z) = z² - z + 0.5 iv) G₁(z) = = z + 0.814
Transcribed Image Text:E(t)=u(t) 5 S+5 Zero-Order Hold Transfer Fon Y(t) Fig. 2 A closed-loop sampled-data system 2. Write a MATLAB program that accepts the characteristic equation of the discrete transfer function, sampling time T and calculates the z-plane poles result in the s-plane poles. Also, it determines the time constant (t), damping ratio (c), and natural frequency (w). Finally, the program calculates the percentage of overshot (P.O) and settling time t,of the system by using the t, C, and W. Assume that the input of the system is always unit-step function and the mathematical expressions for the P.O and ts are given in Ogata**. a) Before the experiment, calculate the transfer function of the system that is given in Fig. 2. Find the roots of the characteristic equation and map them into the s-plane. Then, calculate t, C, W, P.O, and ts. b) Run the MATLAB program for the transfer function of the system that is given in Fig. 2. Observe the results. Check the validity of your program. c) Plot the step response of the system by using "dstep" command. Observe the P.O and ts from the figure. Use "damp" command to find the 5 and w₁. Compare the results with a and b. Is there any difference or similarities between them? If any, explain the reason. Also, discuss the relation between the transient response and the z-plane pole locations. d) Repeat the b and c for the transfer function that are given below: z - 0.8 1.85z+0.854 z + 0.3625 ii) G₂(z) = = z² - z+1 i) G₁(z) = z² - z + 0.4562 z + 2.13 iii) G3(z) = z² - z + 0.5 iv) G₁(z) = = z + 0.814
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