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compensator17 - Compensators QUESTION 17 For the closedloop...

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Compensators Q UESTION 17 For the closed–loop system in Figure 17 with and , complete the following: a. Sketch the Root Locus Diagram. Qualitatively describe the closed–loop system stability and transient characteristics for 0 < K < ∞. b. For K = 5 and r ( t ) = 5, calculate the steady–state error. c. For K = 5 and r ( t ) = 5, simulate the closed–loop system and plot y ( t ), e ( t ), and u ( t ). d. Graphically determine the percent overshoot and 2% settling time. Turn in your Matlab code. G(s) KG C (s) U(s) R(s) + - Y(s) E(s) Figure 17 There are m = 2 finite open–loop zeros located at –5 and –8 There are n = 3 finite open–loop poles located at –12, –2 and –6 There are n = 3 branches and n m = 1 branch goes to infinity The Root Locus is on the real axis from –2 to –5, –6 to –8, and –12 to –∞ The closed–loop characteristic equation is Substituting s = into the closed–loop characteristic equation and rearranging
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