Nonlinear and adaptive control of a shunt DC motor

Three approaches for nonlinear control are compared; feedback linearization, generalized controller canonical forms, and input/output linearization. To establish a framework for comparison, the example of a shunt DC motor is studied. It was found that the conditions for applying the method of feedback linearization were not satisfied; the full 3D state-space system could not be linearized by state transformation. It was found that, after eliminating a state and therefore reducing the dimension from three to two, the 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.<>