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.
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Publication details:
| Title | Self-tuning control of non-linear ARMAX models |
| Publication Type | Journal Article |
| Year of Publication | 1990 |
| Authors | Sales, K. R., and Billings S. A. |
| Journal | International Journal of Control |
| Volume | 51 |
| Issue | 4 |
| Pagination | 753-769 |
| Date Published | 01/1990 |
| ISSN | 1366-5820 |
| Abstract | A control-weighted self-tuning minimum-variance controller with a non-linear difference equation structure is described. An extended recursive least-squares estimation algorithm is employed to provide the adaptiveness. Performance analysis of the controller is discussed in terms of a cumulative loss function and high-order correlation functions of the system input, output and residuai sequences. Simulation results from an experiment using a model identified from a real system are also provided. |
| DOI | 10.1080/00207179008934096 |