Second-Order Sliding Mode Control of an Induction Motor

The induction motor is probably the most used electrical motor today. Its main advantage over other motors is that it can be built without brushes for electrical power transfer to the rotor. It is thus very reliable. Although it was invented almost 130 years ago, it is only recently that the problem of speed control was solved efficiently. Still, the performance of existing controllers suffers from sensitivity to motor parameter variations. The rotor resistance is of particular importance because it can increase drastically when the temperature rises. One class of controllers adapt to parameter changes by estimating them online. This strategy, called adaptive control, might not work in all operation regimes and increases overall controller complexity. Another strategy is to design a controller which is less sensitive to parameter variations (robust control). That is the focus of this work. In the 1950s and 1960s, Russian scientists investigated switching control laws, e.g., control laws with an on/off element. Their goal was to realize robust control systems, i.e., control systems which are less sensitive to parameter variations and disturbances. Their research evolved into the theory of sliding mode control. The fundamental result of the theory is that an infinitely fast switching control can constrain the controlled system to only evolve (slide) along a certain surface, which has a lower dimension than the original system dynamics. On this so-called sliding surface, the system is perfectly immune to a broad class of disturbances. Of course, any practical realization will be limited to a finite switching frequency. This will introduce an error. This work is focused on second-order sliding mode controllers. They feature smaller errors than standard sliding mode controllers when the switching frequency is not infinite. Such a controller is designed for an induction motor with the goal of achieving highly robust speed control. The design also includes a sliding mode observer to estimate the rotor flux. The flux is used as part of the feedback control. Certain derivatives of motor state variables are required by the controller as well. A recently developed robust finite-time differentiator is applied to estimate those derivatives. To test the proposed design, a 1.5 kW induction motor is chosen, a load benchmark is specified and the control system performance is carefully examined by simulation.