Control of a continuously stirred tank reactor using an asymmetric solution of the state-dependent Riccati equation

The state-dependent Riccati equation (SDRE) method is used to control the nonlinear nonminimum-phase dynamics of a continuously stirred tank reactor (CSTR). The benefits of using the SDRE method are that it can be directly applied to the nonminimum-phase system and hard bounds can be imposed on the control activity. From simulation analysis, it is determined that a complicated state-dependent state weighting matrix Q(x) would be required in order to produce satisfactory responses to changes in the set point of the reactor. To avoid the problem of finding such a state weighting matrix, an asymmetric solution of the SDRE is used instead of the symmetric positive-definite solution. Since there are an infinite number of asymmetric solutions, the paper discusses the process that was used in obtaining the selected asymmetric solution. Simulations are performed which produce a level of confidence that the closed loop system is asymptotically stable and is robust to parameter variations in the chemical concentration level in the educt flow.