Observers for dynamic systems

One of the main limitations to improving monitoring and optimizing the use of microorganisms is undoubtedly the difficulty of measuring chemical or biological variables in a reactor. There are very few sensors available that are reasonably priced, reliable and maintainable enough for on-line monitoring. Measuring certain biological variables (biomass, cell content, etc.) is sometimes very difficult and can be a long and tricky operation, even off-line." This practical situation, taken from the book "Automatique des bioprocédés" , clearly illustrates the problem that the notion of observing a dynamic system seeks to solve.

In fact, the problem is relatively simple, since a dynamic system is an engineering artifact characterized by variables that evolve over time, some of which can be controlled. Of course, since this control involves the instrumentation of the process by actuators and above all sensors, it can sometimes be very useful or relevant to know the evolution of variables which are not directly accessible to physical measurement. The aim of observation is therefore to build an algorithm - sometimes referred to as a software sensor - to be implemented on a process control device, enabling these variables to be estimated without the need for an additional physical sensor. In addition to lower cost, obtaining the information provided by this sensor through computer software implementation of available process measurement processing offers other advantages such as simplified maintenance and lower risk of failure, not to mention the additional dynamics introduced by the physical sensor. Other applications for the use of a software sensor include, but are not limited to, the replacement of a physical sensor that is already instrumenting the process, but is expensive, unreliable or has a low signal-to-noise ratio; the estimation of unknown inputs (faults or disturbances) that could influence process behavior; parameter identification; or, finally, the control of a system by state feedback. In this last application, which is one of the major applications of the use of an observer, several options can be envisaged: either we choose to reconstruct by an observer all the components of the state which are not measured, and in certain practical applications this can go up to a hundred variables; or we choose to directly observe the function of the state variables envisaged for the control. Whichever option is chosen, however, it is not feasible to commission one or more physical sensors to carry out the desired control. Finally, observers can also be used to create redundancy in relation to a physical...