Novel environment for the practical implementation of higher order sliding mode controllers

A novel analogue circuit environment to implement higher order sliding mode (HOSM) and continuous finite time (CFT) stabilising controllers is proposed in this paper. The novelty lies in the ability of the circuit to capture the underlying theoretical features by producing non-Lipschtiz controller implementations. The circuit can be built using readily available off-the-shelf components. Since the environment is based on an analogue circuit, the development matches the mathematics of a class of non-Lipschitz differential equations more closely than its digital counterparts thereby narrowing the theory-practice gap. The key contribution is the implementation of a class of non-Lipschitz controllers using analogue components thereby nullifying steady-state tracking errors without the need for integral action, a key concept of both HOSM and CFT philosophies with the former being more robust. The circuit has plug-and-play functionality similar to the ubiquitous PID controllers, where recent results on the tuning of HOSM controller parameters give the potential to replicate the classical PID controller tuning approach. The functionality is demonstrated by the closed-loop speed control of a dc motor, although the results are applicable to other engineering problems which are also discussed.