Please solve neatly and in detailed steps. Thank you.
Please Solve Neatly And In Detailed Steps Thank You 1 (125.77 KiB) Viewed 35 times
T(t) 0(t) k www J Free-clamped Figure 1. Mass Spring Setup of ECP Torsional Plant For this Mass Spring system, torque T(t) is amplified by the real input U(t) with a DC gain which satisfies U 32 and the output Y(t) is a function of the disk angle 8(t). Y₁0₁2546 * 32 (2) If we mathematically build the relationship between T(t), 0₁ (t) without considering the impact of friction, they will satisfy the following equations T = * 0.00675 (1)
T = k₁0₁ = J₁Ö₁ If we consider the friction impact, it becomes The parameters are given below T = J₁Ö₁ + С₁ẻ₁ + k₁0₁ J₁ = 0.0108 C₁ = 0.007 k₁ = 1.37 Gopen (S) (2') Here comes the first task, you need to derive the open loop transfer function model of the system = (3) Y₁(s) U (s) (4) (5) Apply the Laplace transform to obtain the transfer function model of the system with respect to U(s) and Y₁ (s) for both friction and frictionless model.
(2') Here comes the second task, you need to derive the close loop transfer function model of the system Gclose (S) = Y₁(s) U(s) (5) (3') with the close loop transfer function Gclose(s) obtained above, you can directly obtain the natural frequency wn and the damping ratio c.
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