Interaction Analysis in Multivariable Control Systems Applications to Bioreactors for Nitrogen Removal

Abstract: Many control systems of practical importance are multivariable. In such systems, each manipulated variable (input signal) may affect several controlled variables (output signals) causing interaction between the input/output loops. For this reason, control of multivariable systems is typically much more difficult compared to the single-input single-output case. It is therefore of great importance to quantify the degree of interaction so that proper input/output pairings that minimize the impact of the interaction can be formed. For this, dedicated interaction measures can be used.The first part of this thesis treats interaction measures. The commonly used Relative Gain Array (RGA) is compared with the Gramian-based interaction measures the Hankel Interaction Index Array (HIIA) and the Participation Matrix (PM) which consider controllability and observability to quantify the impact each input signal has on each output signal. A similar measure based on the norm is also investigated. Further, bounds on the uncertainty of the HIIA and the PM in case of uncertain models are derived. It is also shown how the link between the PM and the Nyquist diagram can be utilized to numerically calculate such bounds. Input/output pairing strategies based on linear quadratic Gaussian (LQG) control are also suggested. The key idea is to design single-input single-output LQG controllers for each input/output pair and thereafter form closed-loop multivariable systems for each control configuration of interest. The performances of these are compared in terms of output variance.In the second part of the thesis, the activated sludge process, commonly found in the biological wastewater treatment step for nitrogen removal, is considered. Multivariable interactions present in this type of bioreactor are analysed with the tools discussed in the first part of the thesis. Furthermore, cost-efficient operation of the activated sludge process is investigated.