# Laboratory Scale Liquid Level System

## Model description:

The system consists of a DC water pump feeding a conical flask which in turn feeds a square tank, giving the system second-order dynamics. The controllable input is the voltage to the pump motor and the system output is the height of the water in the conical flask. The aim, under simulation conditions, is for the water height to follow some demand signal. The plant model was identified as

\begin{align*}z(t) &=0.9722z(t-1)+0.3578u(t-1)-0.1295u(t-2)-\\ &-0.3103z(t-1)u(t-1)-0.04228z^6(t-2)+0.1663z(t-2)u(t-2)+\\ &+0.2573z(t-2)e(t-1)-0.03259z^2(t-1)z(t-2) - 0.3513z^2(t-1)u(t-2)+\\ &+0.3084z(t-1)z(t-2)u(t-2)+0.2939z^2(t-2)e(t-1)+\\ &+0.1087z(t-2)u(t-1)u(t-2)+0.4770z(t-2)u(t-1)e(t-1)+\\ &+0.6389u^2(t-2)e(t-1)+e(t), \end{align*}

where $e(t)$ is a noise.

2

## Publication details:

 Title Self-tuning control of non-linear ARMAX models Publication Type Journal Article Authors Sales, K. R., and Billings S. A.