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compensator6 - Compensators QUESTION 6 For the closedloop...

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Compensators Q UESTION 6 For the closed–loop system in Figure 6 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. Calculate K such that the steady–state error for a unit ramp input is 0.15. c. For the value of K calculated in part b, simulate the closed–loop system for r ( t ) = 1 and r ( t ) = t . For both simulations plot y ( t ), e ( t ), and u ( t ). d. For the value of K calculated in part b, calculate the closed–loop pole locations. For each complex conjugate pair, determine its natural frequency and damping ratio. For each real pole, determine its time constant. Turn in your Matlab code. G(s) KG C (s) U(s) R(s) + - Y(s) E(s) Figure 6 There are m = 2 finite open–loop zeros at –4 and –6 There are n = 3 finite open–loop poles located at 0 and There are n = 3 branches and n m = 1 branch goes to infinity The Root Locus is on the real axis from 0 to –4 and –6 to –∞ The closed–loop characteristic equation is Substituting s = into the closed–loop characteristic equation and rearranging
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