Asymptotic normality analysis of the estimation error of steady-state models for industrial processes: SISO case

The asymptotic normality of the estimation error of steady-state models for industrial processes is investigated under quite mild conditions. The estimate is formed from the estimated parameters of an approximate linear model which is strongly consistent with the steady-state gain of slow time-varying linear SISO systems. In the parameter estimation, the weighted least-squares method is employed. The input signal (the system set point) is the usual step change din the optimization procedure. The rate of convergence is given. The stationarity and the distribution of the stochastic process are not demanded. It is also worth mentioning that, under some acceptable conditions, robustness to the structure of the approximate linear model is achieved. A simulation study shows that, for limited length of the sampled data, the best choice for the structure of approximate models as regards estimation precision is dependent upon the realization of the stochastic noise.