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compensator12

# compensator12 - Compensators QUESTION 12 For the closedloop...

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Compensators Q UESTION 12 For the closed–loop system in Figure 12 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 = 12 and r ( t ) = 0.4 t 2 , calculate the steady–state error. c. For K = 12 and r ( t ) = 0.4 t 2 , simulate the closed–loop system and plot y ( t ), e ( t ), and u ( t ). d. For K = 12 and r ( t ) = 0.8 t , simulate the closed–loop system and plot y ( t ), e ( t ), and u ( t ). Turn in your Matlab code. G(s) KG C (s) U(s) R(s) + - Y(s) E(s) Figure 12 There are m = 3 finite open–loop zeros at and –10 There are n = 4 finite open–loop poles at 0, 0, –3, and –5 There are n = 4 branches and n m = 1 branch goes to infinity The Root Locus is on the real axis between 0 and –3, between –5 and –7, and between –10 and –∞ The closed–loop characteristic equation is Substituting s = into the closed–loop characteristic equation and rearranging

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