UFMFV7-15-2 - Control - DC Motor with Mechanical Load - Engineering Assignment Help

Assignment Task

Assignment Task
System Modelling

A common actuator in control systems is the DC motor. It directly provides rotary motion and, coupled with mechanical loads such as wheels or drums and cables, can provide translational motion. The electric circuit of the armature and the free-body diagram of the rotor are shown in the following figure:

Figure 1: DC motor with mechanical load

In the figure above, v is the armature voltage, i is the armature current, e is the back electromotive force (emf), R is the armature resistance, L is the armature inductance and ω is the shaft speed of the motor; J is the equivalent inertia on the motor shaft, T is the driving torque generated by the motor, and TL is the resistive torque from the load. It is known that e
= Keω, T = Kt i and TL = Kt iL, where Ke and Kt are respectively the back emf and torque
 
constants of the motor, and iL is the equivalent load current reflected by the load torque TL to the motor armature.
The physical parameters are:

Moment of inertia of the rotor        J=0.01 kg.m2 Motor viscous friction constant        b=0.1 N.m.s Electromotive force constant    Ke=0.01 V/rad/sec Motor torque constant    Kt=0.01 N.m/Amp
Electric resistance    R=1 Ohm

In general, the torque generated by a DC motor is proportional to the armature current (i) and the strength of the magnetic field. Here, we assume that the magnetic field is constant and, therefore, the motor torque is proportional to only the armature current i by a constant factor Kt as shown in the equation below. This is referred to as an armature-controlled motor. For a small motor, the armature inductance is small, ie L ≈ 0, and hence can be neglected. Also, at the start of the motor, e = Keω ≈0. Ignoring the resistive torque, your task is to develop the controller algorithms to control the rotation of the load. That is, to control the angular position of the DC motor with certain performance parameters.

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