Tham khảo tài liệu 'wiley wastewater quality monitoring and treatment_15', khoa học tự nhiên, công nghệ môi trường phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 256 State Estimation for Wastewater Treatment Processes structure to design observers that are independent of the uncertain reaction rates via a linear change of variables. As we shall see the main condition to design a so-called asymptotic observer is that enough variables are measured. Note also that asymptotic observers fall into the broad class of observers with unknown inputs Kudva et al. 1980 Hou and Muller 1991 Darouach et al. 1994 whose principle relies on cancellation of the unknown part via a change of variables. Preliminaries Throughout this section we consider mass-balance models for WWTPs of the following form Bastin and Dochain 1990 d Kr x D t x D t xin t Q x 5 dt where x xin e K represent the concentrations in the reactor and the influent respectively D e K x the dilution rate matrix Q x e K the gaseous exchange between the reaction medium and the environment r x e Kp the reaction rates and K e K xp a constant pseudo-stoichiometric coefficient matrix. In this representation Kr x stands for the biological and biochemical conversions in the reactor per unit of time according to the underlying macroscopic reaction network. Suppose that the set of available measurements y corresponds to is partitioned into y1 and y2 such that y1 is a set of q n measured state variables without loss of generality we assume that y1 corresponds to the first q components of x y1 x1 . xq T. y2 consists of the measured gaseous flow rates y2 q1 x . qn x T. The measurements y1 induce a partition of the state variables x x1 x2 with x1 y1. Accordingly Equation 5 can be rephrased as x1 K1r x Dx1 Dx1i Q1 x dt dx2 K2r x Dx2 Dx2in Q2 x 6 dt where matrices K1 and K2 vectors x1i x2in q1 and q2 are such that Observers for Mass-balance-based System 257 Asymptotic Observers Constructing an asymptotic observers for system 5 requires the following two technical assumptions to hold 1 There are more measured quantities than reactions . q p. 2 Matrix K1 has full rank. These .
