Measurement-Noise-Adaptive Sliding-Mode Observer for Sparse State Estimation of a Nonlinear Distillation Column

Abstract

Reliable state estimates are needed when important process variables are not measured directly. This paper develops a measurement-noise-adaptive sliding-mode observer (MN-ASMO) to estimate unmeasured distillate and bottoms compositions in a 32-state binary distillation column. The observer estimates the measurement noise level during operation and uses this estimate to adjust both the boundary-layer thickness and the dead-zone threshold that controls gain adaptation. MN-ASMO is compared to a fixed-gain SMO (FG-SMO), a residual-adaptive SMO (RA-SMO), and an extended Kalman filter with adaptive measurement covariance (R-adaptive EKF), using four internal composition measurements and 30 paired Monte Carlo trials across four scenarios. Between 5 and 80 minutes, MN-ASMO reduces the mean composition root-mean-square error (RMSE) relative to RA-SMO by 15.5%, 23.7%, and 6.4% under increased noise, model mismatch, and combined uncertainty, respectively, but increases the nominal RMSE by 10.0%. The individual and combined effects of the two noise-dependent updates are assessed while all other observer settings remain unchanged. Under increased measurement noise, using both updates reduces composition RMSE by 53.5% compared with keeping both settings fixed and yields lower RMSE than either update alone. Under combined uncertainty, the joint update reduces error variation but does not clearly outperform the individual updates in RMSE. The increased noise scenario produces a noise level similar to that of FG-SMO. These results show that joint adaptation should be considered when measurement noise varies, although the benefits depend on the operating conditions.