ColorUntitled Jeffrey Schiano 2014. All rights reserved. Rec 14. EE 350Continuous-Time Linear SystemsRecitation 151 Jeffrey Schiano 2014. All rights reserved. Rec 14. Recitation 15 Topics2• Solved Problems – Analysis of Feedback Control Systems– Bode Plots• MATLAB Exercises– SIMULINK graphical programming language Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 1• Derive the Final Value Theorem30lim ( ) lim ( )Provided that ( ) has no poles on theimaginary axis or in th right-half lanetsft sFssF s Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 1 Solution4 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 2• Determine the final value of f(t) by– Solving for f(t) and taking the limit as t approaches infinity– Applying the final value theorem512F(s)= 2( 3)sss s Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 2 Solution6 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 2 Solution7 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 3• A certain plant has the transfer function representation• Is the zero-state unit-step response of the plant overdamped, critically damped, or underdamped?• Choose the proportional gain KPso that the zero-state unit-step response of the closed-loop system is critically damped, and determine the resulting steady-state error8210G(s) = 710pssRYPKpGsE Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 3 Solution9 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 3 Solution10 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 3 Solution11 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 4• Determine the closed-loop transfer function Y(s)/R(s) for the following feedback system• Is the closed-loop system BIBO stable? If so, is the zero-state unit-step response underdamped, overdamped, or critically damped?12RY611sE14s Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 4 Solution13 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 4 Solution14 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 4 Solution15 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 5• Sketch the Bode magnitude and phase plot of the following frequency response functionsVerify your answers using the MATLAB command bode1621000H( ) = 10100H( ) = 10jjjjj Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 5 Solution17 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 5 Solution18 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 6• Simulate the closed-loop system in Problem 3 using SIMULINK• Write a MATLAB M-file that– Represents the system using a transfer function– Plots the zero-state unit-step response19 Jeffrey Schiano 2014. All rights reserved. Rec 14. EE 350Continuous-Time Linear SystemsRecitation 151 Jeffrey Schiano 2014. All rights reserved. Rec 14. Recitation 15 Topics2• Solved Problems – Analysis of Feedback Control Systems– Bode Plots• MATLAB Exercises– SIMULINK graphical programming language Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 1• Derive the Final Value Theorem3 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 1 Solution4 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 2• Determine the final value of f(t) by– Solving for f(t) and taking the limit as t approaches infinity– Applying the final value theorem5 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 2 Solution6 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 2 Solution7 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 3• A certain plant has the transfer function representation• Is the zero-state unit-step response of the plant overdamped, critically damped, or underdamped?• Choose the proportional gain KPso that the zero-state unit-step response of the closed-loop system is critically damped, and determine the resulting steady-state error8 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 3 Solution9 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 3 Solution10 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 3 Solution11 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 4• Determine the closed-loop transfer function Y(s)/R(s) for the following feedback system• Is the closed-loop system BIBO stable? If so, is the zero-state unit-step response underdamped, overdamped, or critically damped?12 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 4 Solution13 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 4 Solution14 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 4 Solution15 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 5• Sketch the Bode magnitude and phase plot of the following frequency response functionsVerify your answers using the MATLAB command bode16 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 5 Solution17 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 5 Solution18 Jeffrey Schiano 2014. All rights reserved. Rec 14. Problem 6• Simulate the closed-loop system in Problem 3 using SIMULINK• Write a MATLAB M-file that– Represents the system using a transfer function– Plots the zero-state unit-step
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