Nonlinear Differential-Geometric Techniques for Control of a Series DC Motor

The problem of controlling a Series DC motor using only current measurements is considered. It is shown that both speed and load-torque may be estimated from the current measurements for use in two proposed nonlinear controllers. The two proposed feedback laws are based on feedback linearization and input-output linearization. Further, both the speed/torque estimation scheme and the control schemes are valid in the prescence of magnetic saturation in the field circuit and when high-speed field-weakening is employed. The estimation is accomplished by using nonlinear state-space and output-space transformations to construct an observer with linear error-dynamics whose rate of convergence may be arbitrarily specified. (Such an observer could provide reliability to existing systems in the event of a speed sensor failure.) The feedback-linearization controller involves a non-trivial state-space transformation allowing control of the full state trajectory. It is then shown that a simpler input-output linearization controller with stable internal dynamics exists and is explicitly constructed.