Internal Code: 1HJAG
Engineering Assignment Help:
Task:
There are 7 problems, each worth the same point value.
•Show all work, including any frequency response information needed to solve the problem. (NOTE: You may use MATLAB to check your answers, and to generate frequency responses, but you must show the hand analysis that is the basis of your answer for each problem.)
• Put your work in order (including all pages of the exam and your worksheets).
• Clearly indicate your answer or answers for each problem.
• If a problem is not solvable, be sure to explain why.
demonstrate that each of the compensators you have derived result in a successful system design. (This can be in the form of an appropriately annotated frequency response listing or frequency response plot.)
1.
(a) Let D(z) = 1. Is the closed-loop system stable? (Fully support your answer.)
(b) Let D(z) = K. Is there any value of K such that the system becomes
stable/unstable (changes from the existing condition to the opposite one)? If “Yes”, what is it? If “No”, why?
2. If possible, design a compensator (D(z)) for the system shown to achieve a 30E phase margin at 0.5813446 rad/sec.
3. On an attached page, a solar collector control system is shown. Is the system stable with D(z) = 1? If so, specify any gain and phase margins that exist. Next, if possible, design a lag compensator for this system at ? = .1045309 rad/sec such that the compensated system has a phase margin of 30E.
4. For the system of Problem 3, generate a set of closed-loop state equations, using the physical states x1 = angular position and x2 = angular velocity for the state equations of the plant. Use your D(z) from Problem 3 for generating the controller state equations.
5. For the system of Problem 3, it is desired to obtain a phase margin of at least 20E with a steady-state error of zero due to a ramp input. Design a D(z) that will satisfy these criteria, if possible. (This is independent of Problem 3.)
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