Evaluation of robustness of distributed control system: a case study for temperature control of a packed bed reactor

The control of temperature distribution in a packed bed reactor with no chemical reaction is used to investigate robustness characteristics of distributed parameter systems (DPS). Model partial differential equations are transformed to ordinary differential equations using finite Fourier transforms. A control structure is constructed based on low cut-off eigen mode and a Kalman filter is used for state estimation. Robust stability and performance is evaluated using structured singular value (SSV). Uncertainty in eigen plants are captured using norm bounded uncertainty descriptions obtained from residual analysis of experimental data between the nominal and the perturbed plant. The true unmodelled dynamics which are composed of bias and variance effects are then estimated in the frequency domain via spectral analysis. It is shown that using simple performance weights and proper poles, simple diagonal PI controllers yields both robust stability and performance