In general, the torque generated by a DC motor is proportional to the armature current and the strength of the magnetic field. In this example we will assume that the magnetic field is constant and, therefore, that the motor torque is proportional to only the armature current by a constant factor as shown in the equation below. This is referred to as an armature-controlled motor.

The back emf, , is proportional to the angular velocity of the shaft by a constant factor.

In SI units, the motor torque and back emf constants are equal, that is, ; therefore, we will use to represent both the motor torque constant and the back emf constant.

From the figure above, we can derive the following governing equations based on Newton’s 2nd law and Kirchhoff’s voltage law.

Rotational speed is considered the output, and the armature voltage is considered the input.

State Variables:

In state-space form, the governing equations above can be expressed by choosing the rotational speed and electric current as the state variables. Again, the armature voltage is treated as the input and the rotational speed is chosen as the output

Please complete the questions below and insert you answers into the relevant sections below.

• Develop the state and output equations for the system (there is only one output – the rotational speed).
• Model the system in.
• Examine the response of rotational speed to a step input.
• Investigate a range of values for k – how does this affect the system?
• Complete the template below to report your.