Bioprocess software sensor design based on particle filters G. Goffaux and A. Vande Wouwer Service d’Automatique Facult´ e Polytechnique de Mons Boulevard Dolez 31, B-7000 Mons Guillaume.Goffaux; Alain.VandeWouwer@fpms.ac.be In standard bioprocesses, component concentration mea- surements, i.e. essential substrates, biomass and metabolic products, are usually the results of sampling and off-line lab- oratory analysis. As such, they are available at discrete times only, with a relatively long sampling period (several hours up to 1-2 days), and as any measurements they are corrupted by errors. In recent years, on-line probes for measuring component concentrations, e.g. biomass probes based on capacitance measurements, have been developed, but their use is still very limited due to high costs. In this context, the design of “software sensors” based on state estimation techniques takes on particular importance. Software sensors allow the on-line reconstruction of non-measured variables (i.e. component concentrations) based on a process model and some available (“hardware sensor”) measurements. In the context of bioprocess applications, two major techniques have emerged [1], [2]: • Kalman filtering, and in particular the continuous- discrete Extended Kalman Filter, which allows the use of a continuous-time dynamic model of the biopro- cess together with discrete-time measurements, and which takes the process and measurement noises into account. The process nonlinearity is dealt with in an approximate way, through linearization along the state estimate trajectory. State and measurement noises are assumed to be normally distributed. • Asymptotic observers, which are based on a state transformation eliminating the reaction kinetics from the model equations. This deterministic state estima- tion technique provides an asymptotic convergence whose rate is determined by the process operating conditions (e.g. the dilution rate in fed-batch and con- tinuous processes). In recent years, new state estimation techniques, called par- ticle filtering, have been developed [3] and used mostly in navigation and tracking. The particle filter builds a discrete estimation of the conditional density probability given the measurement information (figure 1). Particle filtering has several interesting features, which makes it potentially at- tractive in the field of bioprocesses: • It is a nonlinear state estimation technique which does not require assumptions on the model equations. • Discrete-time measurements are easily accommo- dated. • It is a general method which handles non-Gaussian noise. • The particle filter is easily implemented and is almost insensitive to state dimension. The objective of this study is to assess the performance of particle filtering in the context of bioprocess applications and to propose an hybrid particle-asymptotic observer which aims at blending the advantages of the particle filter and the asymptotic observer (robustness to uncertainties in the kinetic model and consideration of the measurement statis- tics). Figure 1: Particle filtering with a one-state model. References [1] Bogaerts, P. & Vande Wouwer, A. (2003). Software Sensors for Bioprocesses. ISA Transactions 42, 547-558. [2] Dochain, D. (2003). State and parameter estimation in chemical and biochemical processes: a tutorial. Journal of Process Control, 13, 801-818. [3] Doucet, A., de Freitas, N., & Gordon, N. (2001). Se- quential Monte Carlo Methods in Practice. Springer-Verlag, New-York.