Consider the DC motor control system with rate feedback shown in Figure below. DC Motor Control...
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Consider the DC motor control system with rate feedback shown in Figure below. DC Motor Control System +51 +255 000,0 s(1 5) 8,0 Kp I K ks Σ s(1+5) 1+k's (b) Figure 1: DC motor control system Image by MIT OpenCourseWare. (a) Find values for K' and k' so that the system of Figure 1(b) has the same transfer function as the system of Figure 1(a). Your answers should be in terms of Kp, K, k, Km, and k. (b) Suppose tm = 0.25 sec. For the case with no rate feedback (i.e., k₁=0), use root-locus techniques to select the proportional gain K' to achieve a closed-loop damping ratio of = 0.2. (c) Using the value of K' found in part (b), sketch the locus of closed-loop pole locations for k₂'>0. (d) With respect to tracking 0r, and compute the corresponding error constant in terms of parameters K' and kt. What happens to the steady state error if K' is increased? If k' is increased? Hint: Your tracking error should take the form e(t) = 0,(t)-0(1). Consider the DC motor control system with rate feedback shown in Figure below. DC Motor Control System +51 +255 000,0 s(1 5) 8,0 Kp I K ks Σ s(1+5) 1+k's (b) Figure 1: DC motor control system Image by MIT OpenCourseWare. (a) Find values for K' and k' so that the system of Figure 1(b) has the same transfer function as the system of Figure 1(a). Your answers should be in terms of Kp, K, k, Km, and k. (b) Suppose tm = 0.25 sec. For the case with no rate feedback (i.e., k₁=0), use root-locus techniques to select the proportional gain K' to achieve a closed-loop damping ratio of = 0.2. (c) Using the value of K' found in part (b), sketch the locus of closed-loop pole locations for k₂'>0. (d) With respect to tracking 0r, and compute the corresponding error constant in terms of parameters K' and kt. What happens to the steady state error if K' is increased? If k' is increased? Hint: Your tracking error should take the form e(t) = 0,(t)-0(1).
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