Nonlinear joint state and parameter estimation: Application to a wastewater treatment plant

Abstract

A systematic approach to joint state and time-varying parameter estimation for nonlinear systems is proposed in this paper. Applying the sector nonlinearity transformation to both the system nonlinearities and the time-varying parameters, the original system is equivalently rewritten as a Takagi-Sugeno system with unmeasurable premise variables. A joint state and parameter observer whose parameters are designed by solving an LMI optimization problem is then proposed. The target application is a realistic model of an activated sludge wastewater treatment plant, being an uncertain nonlinear system affected by a time-varying parameter.Keywords: Time-varying nonlinear system, Takagi-Sugeno model, joint state and parameter observer, waste water treatment plant.

Distributed simultaneous state and parameter estimation of nonlinear systems

“…Hence, it is more favorable if the states and parameters are both estimated based on the measured data. There have been some results on simultaneous state and parameter estimation for linear systems [17], nonlinear systems [18,19], and other industrial applications, including sludge wastewater treatment plants [20] and flooding forecasting [21]. In addition, simultaneous state-parameter estimation is of importance for fault diagnosis and control.…”

Adaptive Monitoring of Biotechnological Processes Kinetics

“…Such an operational model was proposed by Bastin and Dochain [4] as the general dynamical model (GDM) of bioprocesses in stirred tank reactors (STR). Approaches based on GDM software sensors are widely applied simultaneously with other approaches for nonlinear systems, such as extended Kalman and Luenberger filters [5][6][7][8], moving horizon [9,10] neural-network based observers [11], high-gain approach [12], multirate observers [13], sliding mode-observers [14,15], interval SS [16], cascade SS [17][18][19], and joint estimation of state variables and parameters [1,20,21], among others.…”

“…Usually, the software sensors are designed using operational models with constant yield coefficients [4,12,15,20,21]. For many industrial biotechnological processes, like wastewater treatment and processes in inhomogeneous mediums, the reproducibility is poor [18,22].…”

Generalized dynamic observers for quasi‐LPV systems with unmeasurable scheduling functions

“…From the previous works, it can be noted that the study of a quasi‐LPV observer with unmeasured parameters is addressed for the proportional observer (PO), proportional‐integral observer (PIO), and adaptive observer frameworks, respectively. More recently, the study of a new dynamic observer, called the generalized dynamic observer (GDO), has been introduced for LTI systems, descriptor systems, and LPV systems .…”