Experimental and Numerical Validation of a Reliable Sliding Mode Control Strategy Considering Uncertainty with Interval Arithmetic

Real applications are often affected by uncertainty caused by, for example, unknown parameters, sensor inaccuracies, and noise processes. These effects influence control procedures in a significant way and have to be taken into consideration in simulations and experiments to ensure stability of a real system. Often, the dynamics of a considered system can be described by nonlinear equations. To control such systems, sliding mode techniques are advantageous in compensating not explicitly modeled disturbances that influence a system. In this contribution, common sliding mode controllers are extended and combined with interval arithmetic to enhance their performance. This can be achieved by an adaptive calculation of the state-dependent gain stabilizing the variable-structure part of the system—the so-called switching amplitude. Therefore, an exact knowledge of the system parameters is not necessary because their true values are assumed to be located in specified range bounds. Moreover, stochastic uncertainty is taken into consideration representing process and measurement noise that affect practically every real system.