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# hw3sol - Solution If the system were"second order the...

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Solution: If the system were "second order" the equations in the text like 3.64 and 3.65 (6th ed) on page 118 would apply. ( Equations 3.51 and 3.52 (5th ed) page 117 -188.) this leads to ζ : from the 10% overshoot and from the 1% settling time and a settling time of 1.5 sec

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The system needs to be made to look "second order" The closed-loop transfer function is: Either of the following two methods will work. METHOD 1 place the z very close to the plant pole at -3. There will be a pole / zero cancellation and the resulting transfer function is just: It is very likely the the additional pole and zero will degrade the system somewhat, so pick a larger damping ratio. Let ζ = .7 METHOD 2 There are 3 unkowns (z, p, K) and only 2 conditions (equations). The system can again be made to look "second order" if the pole is moved far enough to the left in the complex plan. This will make the complex poles dominate Try p = 10z The overshoot will be too large so increase the damping ratio just to be safe

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