DC Motor Modelling & Control The following diagram illustrates the

DC Motor Modelling & Control
The following diagram illustrates the model structure for a separately excited DC motor drive system :
where the system variables are :
Va and Ia are the DC Armature voltage (V) and current (A)
Ea is the back emf (V) produced at the Armature
Vf and If are the DC Field voltage (V) and current (A)
Te and TL are the electrical drive and load torques (Nm)
ω is the drive speed (rads/sec)
And The Parameter Constants :
Ra
Armature resistance
see section A1
La
Armature inductance
see section A3
Rf
Field resistance
Lf
Field inductance
50 H
Ke
Back emf constant
0.5
J
Drive systems moment of inertia
0.2 kgm2
B
Drive systems friction coefficient
0.067 kgm2/s
Section A : DC Motor Modelling
Prove, using elemental analysis, that the differential equation describing the motor’s armature is
The value of Ra is based upon the last 3 digits of your University of Sunderland Student ID number, where
The back emf of a DC motor is defined via the relationship (Keis a constant) :
Using this relationship construct a Simulink model of the motor’s armature current given that the armature voltage is held at 100V and the field current and drive speed are constants of zero.
The test described in A2 above was performed on an actual system and it was found that it took 5ms for the armature’s current to reach 63.2% of its maximum value.
Use your simulation to determine the value of the armature’s inductance, La.
Explain how the maximum armature current and the value of Lacould be found theoretically from the equation provided in A1
Section B : Drive System Modelling
The differential equation describing the motor’s drive system is
where Te is the electrical torque supplied by the dc motor and is defined via :
Expand your previous simulation to incorporate the drive system.
Maintaining the armature voltage at 100V, develop a plot of how the speed of theDrive, , varies with time when it is subjected to a 0 to 2A step in field current forconstant load torques in the range of 0 to 100Nm (in 10Nm steps).
Comment upon the variation in response seen and the maximum load torque permitted before stalling occurs.
Section C : Speed Control
Speed control is to be achieved using an Integral control system to ‘drive’ the field’s voltage via a voltage/voltage converter. The system is described via :
Where e is the error e sp , and sp is the set point value (the constant speed desired from the system).
Construct the system.
Using this simulation determine a value for the controller gain KIwhich provides 10% overshoot when the system (Va = 100V, TL = 0 ) experiences a step change in set point from 0 to 10 rads/sec starting after 1 second.
Using the controller designed in C2 perform a set point change from 20 to 30 rads/sec (Va= 100V, TL = 0 ) and ensure that the system is in steady state both before and after the test.
Compare the resulting performance with that of C2 and comment on your findings.

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