Comparison of Linear Controllers for Nonlinear, Open-loop Unstable Reactor

Abstract

Many industrially important reactors are operated over a regime where they exhibit nonlinear behavior. Exothermal reactors are often open-loop unstable. For such reactors, safe operation with good performance requires good control. We have considered linear controllers and tested these on a simple chemical engineering non-linear, open loop unstable model and an extension of the model in order to do a basic test of model uncertainty. Specifically, a PI controller has been tuned and tested, the operation of an Extended Kalman Filter (EKF, KF) has been tuned and tested. Based on feedback from estimated states in the EKF, a linear quadratic controller with integral action (LQG+I) has been tuned and tested; the study has been carried out using MATLAB for KF and LQG+I tuning; the remaining study has been carried out in a Jupyter Notebook using Python in tandem with Modelica. The PI controller lead to negative cooling water temperature upon a step change in temperature reference. When constraining the input to liquid water with anti-windup, PI control gives considerable undesirable overshoot in the reactor temperature. The LQG+I controller performs much better wrt. temperature overshoot. Overall, the reported work has demonstrated how a modern simulation set-up (OpenModelica + Python) can be used for model based control analysis and design.