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 non-trivial 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.