Design of an Optimal PID Controller for a Coupled Tanks System employing ADRC

Finding simple and reliable mathematical models for describing a complex process is a difficult task. In deriving a reasonably model, we frequently find necessary to ignore certain properties of the system. Active Disturbance Rejection Control (ADRC) is a method that does not require a detailed mathematical description of the system, it supposes that the unmodeled elements of the dynamics and external disturbances can be estimated trough an Extended State Observer (ESO), and then rejected by adding the estimate in the control law. In this work, the input-output behavior of a coupled tanks system is approximated by a second order uncertain model. This allows employing the Linear Quadratic Regulator (LQR) approach to design a Proportional-Integral-Derivative (PID) controller into the ADRC framework. It is proposed a criterion for selecting the weighting matrices in LQR in order to have a desired percentage overshoot and settling time of the closed loop system response.