PID Controller

The PID Controller (Proportional-Integral-Derivative) is a fundamental control algorithm used to regulate systems based on the error signal.Algorithm was developed in MATLAB R2024b enviroment.

The mathematical expression is:

$$ u(t) = K_p e(t) + K_i \int_0^t e(\tau) , d\tau + K_d \frac{d e(t)}{dt} $$

where:

• ( u(t) ) = control signal,
• ( e(t) ) = error,
• ( Kp ) = proportional gain,
• ( Ki ) = integral gain,
• ( Kd ) = derivative gain.

The controller adjusts the output signal based on the error.

Ziegler Nichols 2nd Rule

Ziegler Nichols 2nd rule is a very successful empirical tuning method , especially for linear systems.Tuning operation is based on users observation during the tuning process.In the "Ziegler_Nichols_2nd.m" file it is presented a simple script for supporting the gains computation in a PID controller.