plz solve these questions What is a transfer function? What is a first order tra
ID: 3864086 • Letter: P
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plz solve these questions
What is a transfer function? What is a first order transfer function? For a motor actuating a spinning disk with moment of inertia J and viscous friction D, Newton's laws give the following ordinary differential equation (ODE): Jx(t) + Dx(t) = k_m u(t) where x is the angular velocity of the disk, u is the motor torque, and k_m is the motor constant. (a) Assuming that the output y is the angular velocity of the disk, derive the transfer function Y (s)/U(s). (b) A general form of a first order transfer function is given below: Y(s)/U(s) = K/Ts + 1 where K is the steady-state gain, and tau is the time constant, which is the time it takes to reach 1-1/e of the final value (about 63%). Using your answer from part (a.), find K and tau in terms of J, D, km.Explanation / Answer
1. A transfer function is given by the ratio of the output from system to the input provided to that system. The system response is determined from the transfer function and the system input. A Laplace transform converts the input from the time domain to the spatial/frequency domain by using Laplace transform relations. The transformed spatial input is multiplied by the transfer function to get the output in the spatial domain. It is then converted back to the time domain using an inverse Laplace transform.
The order of a system is the order of the highest derivative of its differential equation. Equivalently, it is the highest power of s in the denominator of system transfer function.
A first order system will have differential equation as given below.
tdx/dt + x(t) = Gu(t)
With this differential equation, the terms are:
x(t) = Response of the System,
u(t) = Input to the System,
t = The System Time Constant,
G = The Gain of the System.
If the differential equation is Laplace transformed we get:
tX(s) + X(s) = GU(s)
Other wise the transfer function is:
Transfer Function = X(s)/U(s) = G/(st + 1)
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