A DC motor with stator inductance , stator resistance , electromotive force (emf) constant , rotor moment of inertia , and damping ratio is modeled using the following differential equations.
The input variables are the source voltage and the torque load , and the output variables are the rotor angular speed and the stator current .
In state-space form:
For control, the controlled input is the voltage and the controlled output is the DC motor speed . The corresponding subsystem is obtained.
Designing the state feedback controller with gains and () by pole placement with desired poles and .
Obtaining the feedback gain :
The closed-loop equations of the state feedback control system are obtained next.
Using outputtype and augment_output, the transfer function of closed-loop system is obtained. The output vector will contain the controller output .
Assign numerical values for the parameters:
Next, the numeric values for the desired poles are obtained. For 0.1% overshoot, settling time of about 1 sec, the damping ratio and the natural frequency are defined as follows:
Then, the numeric values for the feedback gain and the feed-forward gain are:
Plotting the closed-loop system step response:
Obtain the properties of the step response such as steady-state value and settling-point.