Operator Factorization and Other Aspects of the Analysis of Linear Systems

[abstract missing

Linear Control and Estimation Using Operator Factorization

The filtering, prediction and smoothing problems as well as the linear quadratic control problems can very generally be formulated as operator equations using basic linear algebra. The equations are of Fredholm type II and difficult to solve directly. It is shown how the operator can be factorized into two Volterra operators using a matrix Riccati equation. Recursive solution of these triangular operator equations is then obtained by two initialvalue differential equations

Control of Dissolved Oxygen in Stirred Bioreactors

This report discusses control of dissolved oxygen in a bioreactor where the oxygen supply is manipulated using the stirrer speed. In batch and fed-batch cultivations the operating conditions change significantly which may cause tuning problems. Analysis using a linearized process model shows that the process dynamics is mainly affected by changes in the volumetric oxygen transfer coefficient $K_La$. % To account for the process variations, a control strategy based on PID control and gain scheduling from the stirrer speed is suggested. This approach is straightforward to implement in an industrial control system. Experimental results from a laboratory reactor are presented

Analysis of a Probing Control Strategy

In this paper we analyse an extremum controller based on a pulse technique. The idea is to superimpose probing pulses to the control signal and use the size of the pulse response in the output for feedback. The probing control strategy has been used with success for the control of the substrate feeding in E. coli cultivations. The stability analysis is done here for systems of Hammerstein type with a piecewise affine nonlinearity. Stability regions of the closed-loop system are derived by solving suitable linear matrix inequalities. Some robustness results with respect to uncertainty in the plant are also given