Mapping filtered forwarding control for non-linear systems with input saturation

Mapping filtered forwarding control as a novel method has been provided for controlling high-order non-linear systems in strict-feedback form, whereas control input saturation in the practical applications has not been taken into account yet by this technique. In the proposed work, an n-dimensional strict-feedback non-linear system in the presence of input saturation is mainly considered as the research object, and an effective control algorithm is developed. By employing a well-defined hyperbolic tangent function to approximate the saturation, the initial plant can be transformed into a standard system with a smooth input non-linearity, and a bounded unknown disturbance arising from the approximation error. Unlike fuzzy or neural network control schemes for the systems with input saturation, the developed controllers do not require fuzzy logic systems or RBF networks to approximate the given function on a compact space. The benefit of the proposed algorithm lies in its direct design and controller modularisation for real-time applications. A magnetic levitation system is used to demonstrate the designing procedures and controller performance, and a comparison with the system without considering input saturation is made through numerical simulations.