Estimation and control of a one-tank process with time-varying delays

Abstract

This thesis presents the estimation and control of a one-tank system with varying time-delay. A part of the nonlinear system at UiS known as the two-tank is linearized around an equilibrium point and given as a state-space representation. The input of the 1T system is given an artificial variable delay that is assumed to be unknown. The original state delay observer given in [1] is used to estimate the state and delay of a noise-free model of the system. The original state delay observer is modified to improve the estimations by adding a known lower bound of the delay. An attempt is made to minimize the effect of the singularities in the input. The robustness of the observer is tested for sensitivity to inaccuracies in both the model and in the added lower limit. The modified state delay observer is then tested against a nonlinear model of the system around the equilibrium point it was designed and around other equilibrium points. Noise is added to see how this will affect the modified state delay observer before it is tested on the actual 1T system. While the observer is successful at estimating the delay in the noise-free scenario, the addition of noise causes the estimation to deteriorate; the attempts at adjusting the observer to compensate for these cause inaccuracies in the state estimates. As the experiments on the noisy 1T system are unsuccessful, an experimental test is performed to see if an accurate estimation of the variable delay could be used with a regular Smith predictor to improve control of the system compared to a standard PID-controller and a Smith predictor using a constant model-delay.