{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PracticeProblemsMidterm_solu

K s a in series with gs in a unity s b 1 ignoring

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: r the unit step input. 34. Consider the second-order system G( s ) = 1 s 2 + 2⇣ s + 1 We would like to add a transfer function of the form D(s) = feedback structure. K ( s + a) in series with G(s) in a unity( s + b) (1) Ignoring stability for the moment, what are the constraints on K , a, and b so that the system is Type 1? (2) What are the constraints placed on K , a, and b so that the system is both stable and Type 1? 9 Solution: (1) In a unity feedback structure, E (s) 1 = R (s) 1 + GD To be Type 1, there needs to be a pole at s = 0 in the product GD. Since there is no such pole in G, it must be supplied by D, thus, the answer is b = 0. (2) To assure stability, all poles of the closed loop must be in the left half plane, for which the criterion is by Routh. Thus the characteristic equation is s(s2 + 2⇣ s + 1) + K (s + a) = 0 and the Routh array is 1 2⇣ 2⇣ (1 + K ) 2⇣ aK 1+K aK aK Thus the requirements are ⇣>0 2⇣ (1 + K ) aK > 0 aK > 0 35. Consider the transfer function 1 s2 + s + 2 H (s) = Which of the following is the corresponding unit step response? Explain your choice and why you rejected the other three possibilities. (a) (b) 0.7 (c) 0.8 0.6 (d) 1.4 1 1.2 0.6 0.5 0.8 1 0.4 0.4 0.8 0.6 0.3 0.2 0.6 0.4 0.2 0.4 0 0.1 0 0 5 10 −0.2 0.2 0.2 0 5 10 0 0 5 10 0 0 5 10 Solution: The DC gain of H (s) equals 0.5. so (c) and (d) are immediately rejected because it corresponds to DC gain of 1. The plot (b) shows the correct DC gain, but it has undershoot which indicates the presence of a RHP zero, while H(s) has no zeros. The plot (a) is the correct one. 10...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern