Integral Nonlinear Dynamic Inversion based Control of Input-Derivative Affine Systems

In recent times, development of economical yet powerful microprocessors, and increasing demands on performance characteristics have spurred great advancements in the field of nonlinear control. However, most of the nonlinear control theory and its techniques are developed for input affine systems, whereas the dynamics of many physical systems depends not only on the inputs but also on their derivatives. While this phenomenon can be easily catered for in linear systems through either state-space or transfer function representations, it is not as straightforward for nonlinear systems. In this paper, it is shown that Input-Derivative Affine (IDA) systems can be transformed to remove explicit dependency on input-derivative, but the resulting system is generally non-affine with respect to input. It is a difficult proposition to accrue nonlinear control for a non-affine system. In this paper, a novel Integral Nonlinear Dynamic Inversion (i-NDI) based control scheme is presented to deal directly with IDA systems. An example of Twin Rotor MIMO system, having strong coupling between pitch and yaw dynamics, is illustrated to demonstrate the efficacy of the presented scheme.