Consider the following block diagram of an internally controlled rotational system. This system has a tunable parameter K that assigns the torque of a motor to the rotating body. Once Ka is chosen, it is a constant. Signal R(s) is a reference state, and T₁(s) is a disturbance. The transfer functions G₁(s) and G₂(s) are: G₁(s) 5000 s + 1000 G₂(s) = 1 s(s +20) Ta(s) R(s) Ка G₁(s) Y(s) G₂(s) 3.1. Using block diagram algebra and the two definitions of G₁(s) and G₂(s), show that the overall transfer functions relating Y(s) to R(s) and Ta(s) are: [4] Y(s) 5000Ka Y(s) s + 1000 = R(s) s³ +1020s² + 20000s + 5000Ka Ta(s) s3 +1020s2+20000s + 5000Ka a Res) Tars) behind 1 KG₁₂(s) A 4 Gr Y(5) Tds' KA H=1 2 1+ 446₁₂(5) -A 5000. 1" (5+1000) (S(5+202)² (5+1000) (S(S+20)) [1 + KA X×5000 × 1^_ Ка 5000 1+KA5000

Consider the following block diagram of an internally controlled rotational system. This system has a tunable parameter K that assigns the torque of a motor to the rotating body. Once Ka is chosen, it is a constant. Signal R(s) is a reference state, and T₁(s) is a disturbance. The transfer functions G₁(s) and G₂(s) are: G₁(s) 5000 s + 1000 G₂(s) = 1 s(s +20) Ta(s) R(s) Ка G₁(s) Y(s) G₂(s) 3.1. Using block diagram algebra and the two definitions of G₁(s) and G₂(s), show that the overall transfer functions relating Y(s) to R(s) and Ta(s) are: [4] Y(s) 5000Ka Y(s) s + 1000 = R(s) s³ +1020s² + 20000s + 5000Ka Ta(s) s3 +1020s2+20000s + 5000Ka a Res) Tars) behind 1 KG₁₂(s) A 4 Gr Y(5) Tds' KA H=1 2 1+ 446₁₂(5) -A 5000. 1" (5+1000) (S(5+202)² (5+1000) (S(S+20)) [1 + KA X×5000 × 1^_ Ка 5000 1+KA5000

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.22P

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