Fall 2001 16.3115-1 Pole placement e So far we have looked at how to pick k to get the dynamics to have some nice properties(i. e stabilize A 入(A)~A1(A-BK) Classic Question: where should we put these closed-loop poles? Of course we can use the time-domain specifications to locate the dominant poles- roots of +2cnS2=0 Then place rest of the poles so they are "much faster"than the dominant behavior. For example Could keep the same damped frequency wd and then move the real part to be 2-3 times faster than real part of dominant pole Just be careful moving the poles too far to the left because it takes a lot of control effortFall 2001 16.31 15—1 Pole Placement • So far we have looked at how to pick K to get the dynamics to have some nice properties (i.e. stabilize A) λi(A) ; λi(A − BK) • Classic Question: where should we put these closed-loop poles? • Of course we can use the time-domain specifications to locate the dominant poles — roots of: s2 + 2ζωns + ω2 n = 0 • Then place rest of the poles so they are “much faster” than the dominant behavior. For example: — Could keep the same damped frequency wd and then move the real part to be 2—3 times faster than real part of dominant poles ζωn • Just be careful moving the poles too far to the left because it takes a lot of control effort