Operator–Based Double–Coprime Factorization for State Disturbance Rejection

Disturbance elimination is one of the most important problems in the field of control engineering. Disturbances are external factors that affect the state of the system, such as friction and gravity in dynamical systems. They have unexpected effects on the system response, and in the worst case, they cause the system to become unstable. Disturbance observers exist as controllers to eliminate such disturbances. However, disturbance observers treat all disturbances that affect the system as input disturbances, which is not strictly true for nonlinear systems. Therefore, we propose a controller that directly considers disturbances to the internal state of the system and eliminates them more rigorously by using operator–based left–coprime factorization. Furthermore, we propose a control system that simultaneously performs reference value tracking and disturbance suppression with a single controller by combining this theory with an existing control system using operator–based right–coprime factorization using double–coprime factorization. Simulation and actual experiments on a linear motor have confirmed that the designed control system has the two performance features of reference tracking by the existing right–coprime factorization and disturbance elimination by the proposed left– coprime factorization.