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Q 6(a) Derive state-variable equations for the circuit in Figure 6, showing all steps clearly and indicating what each state variable represents. +20 Figure 6

Q 6(a) Derive state-variable equations for the circuit in Figure 6, showing all steps clearly and indicating what each state variable represents. +20 Figure 6

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Q 6(a) Derive state-variable equations for the circuit in Figure 6, showing all steps clearly and indicating what each state variable represents. :2C Figure 6 Q 6(b) Consider the Xcos block diagram shown in Figure 7. Find the state-variable equations and the output equation for the output c. Σ 1/s Expression : (ul c0) u2 + (ul 2 0) 2 u2 adot-a 1/8 Σ To worcapace c (10000) bdot->b Expression: 10 sin[100 ul) Figure 7 When documenting simulation results in a report, it's important to include all information about the Xcos model and Scilab code used to generate them. Some can be documented by simply copying the block diagram and Scilab code into the report. Briefly identify any other information, not included in those, that should be documented. Also, briefly explain the importance of recording that information.
Transcribed Image Text:Q 6(a) Derive state-variable equations for the circuit in Figure 6, showing all steps clearly and indicating what each state variable represents. :2C Figure 6 Q 6(b) Consider the Xcos block diagram shown in Figure 7. Find the state-variable equations and the output equation for the output c. Σ 1/s Expression : (ul c0) u2 + (ul 2 0) 2 u2 adot-a 1/8 Σ To worcapace c (10000) bdot->b Expression: 10 sin[100 ul) Figure 7 When documenting simulation results in a report, it's important to include all information about the Xcos model and Scilab code used to generate them. Some can be documented by simply copying the block diagram and Scilab code into the report. Briefly identify any other information, not included in those, that should be documented. Also, briefly explain the importance of recording that information.
Q 6(C) You run the model shown in Figure 7 with the default Xcos Simulation Settings (i.e. with the default variable time-stepping method), with the default sampling clock period of 0.1 s, but with a simulation time of 2 s. You plot the output c values against time. The result is shown on the left in Figure 8. You run that model again with the same Simulation Settings but with the clock period reduced to 0.01 s. You plot the output as before and the result is shown on the right in Figure 8. • Explain the main reason for the big difference between the two results • What should you do to check the accuracy of the second plot? on- Figure 8 Q 6(d) The state-variable equations for a system are 1 * =-[2y – 0.5z2 + I(t)] 1 ý = [ax + by – 2z] i =l-0.5ax + 2by + 4z] 1 You perform this test with the real system: setting 1(t) = 20, you wait until it reaches a steady state and find by measuring that z = -5 and x = -76. • Use that information to find the system parameters a and b. Show the steps clearly. • Could you use further steady-state tests (i.e. tests in which the state of the system is measured when it's in a steady-state) to find the values of J, k and c?
Transcribed Image Text:Q 6(C) You run the model shown in Figure 7 with the default Xcos Simulation Settings (i.e. with the default variable time-stepping method), with the default sampling clock period of 0.1 s, but with a simulation time of 2 s. You plot the output c values against time. The result is shown on the left in Figure 8. You run that model again with the same Simulation Settings but with the clock period reduced to 0.01 s. You plot the output as before and the result is shown on the right in Figure 8. • Explain the main reason for the big difference between the two results • What should you do to check the accuracy of the second plot? on- Figure 8 Q 6(d) The state-variable equations for a system are 1 * =-[2y – 0.5z2 + I(t)] 1 ý = [ax + by – 2z] i =l-0.5ax + 2by + 4z] 1 You perform this test with the real system: setting 1(t) = 20, you wait until it reaches a steady state and find by measuring that z = -5 and x = -76. • Use that information to find the system parameters a and b. Show the steps clearly. • Could you use further steady-state tests (i.e. tests in which the state of the system is measured when it's in a steady-state) to find the values of J, k and c?
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