Robust PI and PID Stabilization of a Chemical Reactor

Possibility to stabilize open-loop unstable processes using robust static output feedback controllers was studied. The non-iterative algorithm based on solving of linear matrix inequalities was used for design of robust PID like controllers. The design procedure guarantees with sufficient conditions the closed-loop robust quadratic stability and the guaranteed cost of control. Possibility to use robust PI and PID controllers for stabilization of a continuous stirred tank reactor was verified by simulations. Considered reactor with one first order exothermic reaction had two uncertain parameters: reaction rate constant and the reaction enthalpy. Furthermore, the reactor had multiple steady states and it was stabilized in the surroundings of its open-loop unstable steady state. The results confirmed that the presented simple non-iterative algorithm based on solving of two sets of LMIs is an effective tool for the design of robust stabilizing controllers. Its advantage is that it can be used for P, PI and PID controller design. Robust static output feedback PI or PID controllers can be successfully used for control of CSTRs with multiple steady states, uncertainties and disturbances, even though CSTRs are very complicated systems from the control viewpoint. Both, PI and PID controllers are able to stabilize the open-loop unstable processes and their advantage in comparison with the robust P controller is that they do not retain offsets. The disadvantage of PID controllers is their more complicated implementation and they are not suitable for using in the presence of noise.