A simple armature-controlled DC electric motor (the kind you see in toys) can be

Question

A simple armature-controlled DC electric motor (the kind you see in toys) can be modeled as follows. (Refer to class notes for more details u(t is the input voltage and w, the rotational velocity of the shaft, is the output. Write the model of the system in state-space form. (Variables are l and omega) Write the differential model in terms of i only. Draw the block diagram for the equation in part b. Write the transfer functions l/u and omega/u of the system Simplify the block diagram to write the differential equation of this system. For k = k_e = 0.05 N, m/A, c = 10^4 N, m, s/rad R = o.5 omega, L = 2 times 10^-3 H, I = 9 times 10^-5 kg, m^2, and u(t) = 10 v (a step function input of magnitude o v applied at t = o) solve the different al equation analytically and find the response for current in the armature and the shaft angular velocity, i(t) and omega(t). What is the steady state value of armature current i? What is the maximum value of armature current i? Model the system using either of the simulation tools that you have learned. Paste the response curves for i(t) and omega(t) versus time. Solve problem 6.57 of the textbook and provide the needed plots.

Explanation / Answer

Simple Armature Dc motor:

MODEL:

Pole-Placement design technique is used for the state feedback controller

ISSN 2348-5426 International Journal of Advances in Science and Technology (IJAST)

Differential model in terms of i only

V=L(di/dt)+Ri+e

T=kt.i

T=J +b

E=ke

THE TRANSFER FUNCTION :

(s)/v(s)= k(s)[(LS+R) (JS+b)+k^2]

where, R= Armature resistance in ohm,

L=Armature inductance in henry,

i= Armature current in ampere,

V=Armature voltage in volts,

e=back emf voltage in volts,

K=Ke=electromotive force constant in volt/(rad/sec),

Kt=torque constant in N-m/Ampere,

T=torque developed in N-m,

=angular displacements of shaft in radians,

J= moment of inertia of motor and load in Kg-m2/rad,

b=damping ratio of mechanical system in

N-m/(rad/sec).

Block Diagram:

Steady State Value and Maximum value of Armature Current:

In field controlled dc motor, the armature current is kept constant while the field current is varied which will vary the field flux and interacts with the armature of motor and produce rotation. Armature current will not change when flux interaction is there with the armature and voltages are flowing around the motor. The armature current remain constant. The speed of rotor changes to bring the armature current back to the constant value.

The armature current decreases, the motor continues to accelerate until it reaches a definite, maximum speed.

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