Question

AP1.

Wm(?)/Va(s)= ?/(? + ?)
where the output, ?"(?), is the rotor speed in rad/s and the input, ?'(?), is the applied armature
voltage in volts.
A DC motor is being benchmark tested to determine its transfer function. The input voltage is
held constant at 7 V. At time t = 2.5 seconds, the rotor speed is 40 rad/s. The steady-state
speed of the of motor (? → ∞) is 120 rad/s. \

The answer for this part was (k=2.781, ?=0.162)

Using the result from AP1, create a single script file and perform the following within it:
a. Using the values determined for k and ?, create the motor transfer function Wm(?)/Va(s).
b. Using the step function, plot the transfer function output response, ?+(?), for a constant
input voltage, ?.(?) = 7 ? from t = 0 to t = 60 seconds.
Label the x-axis and y-axis appropriately.

Answer 1

Script:

t = 0:0.001:60; % define time variable

syms s; %define symbolic variable s

K = 2.781; a = 0.162;

V = 7;

num = K; % numerator of transfer function

den = sym2poly(s + a); %denominator defined with symbolic variable s

G = tf(num, den); % define G(s)

figure;step(V*G,t); % step response for constant input V=7 volt, t=0 to 60 seconds

Step response plot: