{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw_prj_2

# hw_prj_2 - Dr Atilla Dogan MAE 4310 Automatic Control Fall...

This preview shows pages 1–3. Sign up to view the full content.

Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 Homework–2 (Due date: Thursday, Sep 21, 2006) Textbook Readings: Sections 5–1, 5–2, 5–3, 5–4 1. Consider the system ... y ( t ) + 8 ˙ y ( t ) + 25 y ( t ) = 2 ˙ u ( t ) + u ( t ) with y (0) = 1, ˙ y (0) = 0 and ¨ y (0) = 0 (i) Determine the transient and steady-state response to the inputs (a) u ( t ) = 3 × 1(t) (b) u ( t ) = t 2 (c) u ( t ) = cos 3 t by using Laplace transforms and partial fraction expansions. You may use the table of Laplace transforms ( pp. 17-18) of the text and MATLAB for the partial fraction expansions. (iv) Determine whether lim t →∞ y ( t ) exits for inputs a–c, and if so, use the Final Value Theorem to evaluate it. 2. Consider the system shown below Use the Final Value Theorem to find lim t →∞ y ( t ), if it exits, for the following cases: (i) G ( s ) = 1 2 s 2 + s +4 , U ( s ) = 1 s (ii) G ( s ) = 1 s 3 +3 s - 4 , U ( s ) = 1 (iii) G ( s ) = s +2 4 s 2 +2 , U ( s ) = 1 s 2 (iv) G ( s ) = 4 s - 1 , U ( s ) = 1 s 2 (v) G ( s ) = 1 s +2 , U ( s ) = s s 2 +4 3. Find the DC gain and time–constant τ of the following first-order systems: (i) G ( s ) = 9 s +3 (ii) G ( s ) = 1 s +0 . 5 (iii) G ( s ) = 14 s +1 Mechanical and Aerospace Engineering - UTA 1 of 4

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 4. MATLAB (i) Create pole-zero maps for the systems in Problem 3. to do this, type >> num = numerator of G(s),den = denominator of G(s) ; >> sys1=tf(num,den) >> pzmap(sys1) >> axis([xmin xmax ymin ymax]) >> sgrid The second command creates the sys1 with transfer function n um d en . The
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern