Consider the basic servo loop shown in Figure 1. Find the closed- loop transfer function Ger(s)...

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Consider the basic servo loop shown in Figure 1. Find the closed- loop transfer function Ger(s) = ê(s)/(s). For the remainder of the problem, consider the plant 2 G(s) (1) s³ +88² +88-14' and the controller Ge(s)=k, where k is a real number. Find the values of k such that Ger is asymptotically stable. Assume that the command r(t) is the unit-step function, and find the steady-state error e(o)= lim, e(t) as a function of k. What is the achievable range for le(oc)]? Find the values of k such that le(0)| <0.5. e(s) f(s) Ge(8) û(s) G(s) Figure 1: Basic Servo Loop. ŷ(s) Consider the basic servo loop shown in Figure 1. Find the closed- loop transfer function Ger(s) = ê(s)/(s). For the remainder of the problem, consider the plant 2 G(s) (1) s³ +88² +88-14' and the controller Ge(s)=k, where k is a real number. Find the values of k such that Ger is asymptotically stable. Assume that the command r(t) is the unit-step function, and find the steady-state error e(o)= lim, e(t) as a function of k. What is the achievable range for le(oc)]? Find the values of k such that le(0)| <0.5. e(s) f(s) Ge(8) û(s) G(s) Figure 1: Basic Servo Loop. ŷ(s)