1. (40 pts.) Consider a closed-loop block diagram with the following transfer functions: Ko Gm =...

 

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1. (40 pts.) Consider a closed-loop block diagram with the following transfer functions: Ko Gm = Gd = o, Gc = Kc, G = 1, Gs = 1. S Suppose that Ko > 0 and Kc>0. The closed-loop transfer functions, Gsp and GL, were determined in problem set 6. GL was found to be G = K TS +1 1 1 with KL = and T = Kc Ko Kc Consider the regulator problem (Ysp = 0) and suppose that d(t) = A 8(t) where 8(t) is the delta function and A > 0. (a) (10 pts.) Find the initial value of the closed-loop response, y(0), using the initial value theorem. (b) (10 pts.) Find the steady-state value of the closed-loop response, y(), using the final value theorem. (c) (10 pts.) (d) (6 pts.) (e) (4 pts.) Using table 3.1, find the closed-loop response, y(t). Sketch y(t) vs t. Include t <0 values in the graph. Note that y(t) = 0 for t < 0. Find the offset. 1. (40 pts.) Consider a closed-loop block diagram with the following transfer functions: Ko Gm = Gd = o, Gc = Kc, G = 1, Gs = 1. S Suppose that Ko > 0 and Kc>0. The closed-loop transfer functions, Gsp and GL, were determined in problem set 6. GL was found to be G = K TS +1 1 1 with KL = and T = Kc Ko Kc Consider the regulator problem (Ysp = 0) and suppose that d(t) = A 8(t) where 8(t) is the delta function and A > 0. (a) (10 pts.) Find the initial value of the closed-loop response, y(0), using the initial value theorem. (b) (10 pts.) Find the steady-state value of the closed-loop response, y(), using the final value theorem. (c) (10 pts.) (d) (6 pts.) (e) (4 pts.) Using table 3.1, find the closed-loop response, y(t). Sketch y(t) vs t. Include t <0 values in the graph. Note that y(t) = 0 for t < 0. Find the offset.