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.



Model order: 


Time domain: 


Publication details: 

TitleSelf-tuning control of non-linear ARMAX models
Publication TypeJournal Article
AuthorsSales, K. R., and Billings S. A.