An optimization tuning method of nonlinear non-minimum phase systems and its application to chemical process

Abstract

For State-feedback linearization control method for nonlinear systems based on differential geometry, using differential homeomorphism transformation, the original nonlinear systems can be divided into two parts: the external dynamics described by linear subsystem and the internal dynamics (namely zero dynamics) described by nonlinear subsystem. For non-minimum phase systems whose zero dynamics are instable, the traditional controller is difficult to guarantee the stability of zero dynamics although it can make the external dynamics meet some performance requirements. Therefore, non-minimum phase character becomes a bottleneck of the practical engineering application of the feedback linearization method. For this reason, an optimization controller design method for nonlinear non-minimum phase systems based on quadratic optimal control theory and Lyapunov stability theory is proposed. The controller design method can make sure external dynamics meet the performance requirements, and it can also guarantee the stability of the zero dynamics at the same time. Finally, the method is applied to chemical process which uses continuous stirred tank reactor (CSTR) to produce cyclopentenol, and this chemical process have typical non-minimum phase characteristics. The simulation results show that this method has good control ability and verify the effectiveness of the proposed method.