Observer Based Temperature Control of a Tank: From Constant to Nonlinear State-Dependent Delay

Abstract

The problem of temperature control of a fluid in a tank is expounded in this paper. In our problem, the delay is a an explicit nonlinear function of the state (temperature) of the system and the resulting dynamics are governed by a nonlinear State-Dependent Delay differential Equation (SD-DDE). We perform the stability analysis using Lyapunov-Razumikhin based approach. Using the new concept of delay injection with inversion, an infinite dimensional observer is designed to estimate the state of the system. We also shed some light on the state space required for characterizing the Cauchy problem and the evolution of the SD-DDE based system. A juxtaposition of fixed delay and state-dependent delay is given for a better illustration, comparison and contrast of results. Simulation results are depicted at the end which portray the effectiveness, validity and usefulness of the proposed observer scheme.