A control system project for regulating the angular position of a direct current (DC) motor using different controllers.

Initially, the practical aspects of constructing the physical experiment are presented. In sequence, digital proportional-integral-derivative (PID), proportional-resonant (PR), proportional-multi-resonant (PMR) and proportional-repetitive controllers are implemented. The data is acquired via a serial communication protocol and .csv results can be plotted witth Python or Matlab scripts.

The following programs are available:

• Relay method
• PID controller
• PR controller
• PMR controller
• Repetitive controller

The physical experiment is presented bellow:

Let $r(t)$ be the reference of angular position, $y(t)$ the angular position, $u(t)$ the control signal, and $e(t)$ the tracking error. First, a relay experiment should be performed in order to obtain the critical gain $K_{u}$ and critical period $P_u$ needed to tune (some of) the controllers:

Assuming a problem of sinusoidal reference tracking with a 90 degrees amplitude and frequency of 0.1 Hz, for a tuned PID controller the following response is obtained:

Cosidering a PR controller the following response is obtained:

Cosidering a repetitive controller the following response is obtained:

Assuming a problem of triangular reference tracking with a 90 degrees amplitude and frequency of 0.1 Hz, for a PR controller the following response is obtained:

Cosidering a PMR controller with $h = 6$ resonant modes the following response is obtained: