University of Texas at Arlington Engineering Center for Distance Education

Homework/Project Cover Sheet

FAX or EMAIL TO: Donya Randolph

drandolph@uta.edu

Fax #: 817-272-5630 Phone #:

817-272-2352

STUDENT INFORMATION

Student Name:

Jesse Terrell

Date:

9/21/11

Total # of pages (including this cover sheet):

23

ASSIGNMENT INFORMATION

Course #:

EE5307

Instructor’s Name:

Dr. Kyriakos Vamvoudakis

Assignment #:

Homework #3

Please put your name, course #, assignment # and page # on the upper right hand side of every sheet you submit. For example page # 1 of (total # of pages).

Inverted Pendulum System Open Loop Response %System in State Variable form % x'=Ax+Bu % y=Cx+Du t = 0:.1:5; A=[0 1 0 0 ; 0 0 -1 0 ; 0 0 0 1 ; 0 0 10 0]; B=[0 ; 0.1 ; 0 ; -0.1]; C=[1 0 0 0]; D=[0]; %Convert to Transfer Function [num,den]=ss2tf(A,B,C,D,1); H1=tf(num,den) %Open loop system response bode(H1) title('Bode Plots Gain & Phase') grid on

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Ball Balancer System Open Loop Response

%System in State Variable form % x'=Ax+Bu % y=Cx+Du t = 0:.1:5; A=[0 1 0 0 ; 0 0 -9 0 ; 0 0 0 1 ; -1 0 0 0]; B=[0 ; 0 ; 0 ; 0.1]; C=[1 0 0 0]; D=0; %Convert to Transfer Function [num,den]=ss2tf(A,B,C,D,1); H1=tf(num,den) %Open loop system response bode(H1) title('Bode Plots Gain & Phase') grid on %Find determinant of the system syms s R=[s -1 0 0 ; 0 s 9 0 ; 0 0 s -1 ; 1 0 0 s]; D=det(R)

Page 11 of 22 Page 5 of 23

Flexible Joint System Open Loop Response %System in State Variable form % x'=Ax+Bu % y=Cx+Du t = 0:.1:5; A=[0 1 0 0 ; -1 -0.2 1 0.2 ; 0 0 0 1 ; 1 0.2 -10 -2.1]; B=[0 ; 1 ; 0 ; 0]; C=[0 0 1 0]; D=0; %Convert to Transfer Function [num,den]=ss2tf(A,B,C,D,1); H1=tf(num,den) %Open loop system response bode(H1) title('Bode Plots Gain & Phase') grid on %Find determinant of the system syms s SIA=[s -1 0 0 ; 1 s+0.2 -1 -0.2 ; 0 0 s -1 ; -1 -.2 10 s+2.1]; DETERMINANT=det(SIA) DETERMINANT=[1 2.3 11.38 3.7 9]; POLES=roots(DETERMINANT)

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Flexible Joint System Step Response %System in State Variable form % x'=Ax+Bu % y=Cx+Du t = 0:.1:100; A=[0 1 0 0 ; -1 -0.2 1 0.2 ; 0 0 0 1 ; 1 0.2 -10 -2.1]; B=[0 ; 1 ; 0 ; 0]; C=[0 0 1 0]; D=0; %Convert to Transfer Function [num,den]=ss2tf(A,B,C,D,1); H1=tf(num,den) %Step Response (using 'Step' function) [y,t]=step(H1,t); plot(t,y) title('Flexible Joint System Step Response') xlabel('Time (sec)') ylabel('Output y(t)') grid on

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Flexible Link System Open Loop Response %System in State Variable form % x'=Ax+Bu % y=Cx+Du t = 0:.1:100; A=[0 1 0 0 ; -1 -0.1 1 0.1 ; 0 0 0 1 ; 1 0.1 -23 -0.3]; B=[0 ; 1 ; 0 ; 0]; C=[1 0 0 0]; D=0; %Convert to Transfer Function [num,den]=ss2tf(A,B,C,D,1); H1=tf(num,den) %Open loop system response bode(H1) title('Bode Plots Gain & Phase') grid on %Find determinant of the system syms s SIA=[s -1 0 0 ; 1 s+0.1 -1 -0.1 ; 0 0 s -1 ; -1 -0.1 23 s+0.3]; DETERMINANT=det(SIA) DETERMINANT=[1 0.4 24.02 2.4 22]; POLES=roots(DETERMINANT)

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Flexible Link System Step Response %System in State Variable form % x'=Ax+Bu % y=Cx+Du t = 0:.1:100; A=[0 1 0 0 ; -1 -0.1 1 0.1 ; 0 0 0 1 ; 1 0.1 -23 -0.3]; B=[0 ; 1 ; 0 ; 0]; C=[1 0 0 0]; D=0; %Convert to Transfer Function [num,den]=ss2tf(A,B,C,D,1); H1=tf(num,den) %Step Response (using 'Step' function) [y,t]=step(H1,t); plot(t,y) title('Flexible Link System Step Response') xlabel('Time (sec)') ylabel('Output y(t)') grid on

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