It is neither stable nor marginally stable 3 4

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Unformatted text preview: st column of Routh array. it is neither stable nor marginally stable. 3 4 Example 1 Example 1: K(s)=K Characteristic equation Characteristic Routh array Routh Design K(s) that stabilizes the closed-loop Design system for the following cases. K(s) = K (constant) K(s) K(s) = KP+KI/s (PI (Proportional-Integral) controller) K(s) (Proportional5 Example 1: K(s)=KP+KI/s 6 Example 1: Range of (KP,KI) Characteristic equation Characteristic From Routh array, From 3.5 Routh array Routh 3 2.5 2 1.5 1 0.5 0 -1 7 0 1 2 3 4 5 6 7 8 9 8 Example 1: K(s)=KP+KI/s (cont’d) Select KP=3 (<9) Select Routh array (cont’d) Routh Example 1: What happens if KP=KI=3 Auxiliary equation Auxiliary 2 1.8 1.6 1.4 1.2 Oscillation frequency Oscillation 1 0.8 0.6 Period Period If we select different KP, the range of KI changes. If...
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