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. Two nonlinear feedback laws are considered based on feedback linearization and input-output linearization, respectively. Both of these control laws require knowledge of the speed and load-torque. The speed/torque estimation scheme and the control schemes are valid in the presence of magnetic saturation in the field circuit and when high-speed field-weakening is employed. By neglecting the armature inductance, the estimation is accomplished 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 nontrivial state-space transformation allowing control of the full state trajectory. An input-output linearization controller with stable internal dynamics is also explicitly constructed. Finally, simulations are given to demonstrate the algorithms.>