On-line calibration of spectroscopic sensors based on nonlinear observers

Abstract

Spectroscopic sensors provide on-line information about process variables and they have been widely used for monitoring and control. These sensors measure the spectral responses at a large number of wavelengths correlated with the process variables of interest. However the spectral measurement can also be affected by external factors such as changes in temperature. In order to estimate the process variables from the acquired spectrum it is necessary the use multivariate calibration methods. Additive effects of external factors can be easily compensated by standard calibration methods, but multiplicative effects require complex off-line calibration procedures. This work, shows that this problem can be modeled by a non-linear state space equation. In addition, it also proposes an on-line calibration method based on a state observer for compensating multiplicative effects and at the same time estimating the desired process variable from the spectrum. The convergence of the observer requires a uniform observability condition to be satisfied. Simulation results obtained by using a spectral sensor for monitoring a mixing process under time-varying temperature show the main features and potential of the proposed approach. More complex spectral models for modeling the effect of temperature and other variables can be considered and included in the proposed framework.