Nonlinear and adaptive control of a shunt DC motor

Three approaches for nonlinear control: feedback linearization, generalized controller canonical forms, and input/output linearization, are compared. To establish a framework for comparison, the example of a shunt DC motor is studied. It was found that the conditions to apply the method of feedback linearization were not satisfied. In other words, the full three-dimensional state-space system could not be linearized by state transformation. It was found that, after eliminating a state and therefore reducing the dimension from 3 to 2, the new system became feedback linearizable. In other words, the dynamics associated with the remaining two states could be linearized by change of coordinates and state feedback. A similar situation occurred with the input/output linearization, except that the dynamics that were linearized were those associated with the rotor position and velocity, while the remaining dynamics (associated with the field current) were made unobservable.