Stability analysis of a dynamic inversion based pitch rate controller for an unmanned aircraft

Nonlinear dynamic inversion (NDI) is a very popular method employed in aircraft automatic flight control systems. However, it is known that this technique may have stability and robustness issues as soon as the model parameters used in the inversion process are uncertain or when the measurement data are noisy and biased. Many advanced analysis techniques have been presented to quantify the stability of a control system using NDI but very few papers have actually shown the physical effects of uncertainties on the behavior of the system. This paper considers the dynamic inversion process employed in the inner loop of a pitch rate control system for an aircraft and shows the effects of parameter and measurement uncertainties on the inversion process. In this paper, an explicit transfer function from the plant input to the plant output is derived, which includes the dynamic inversion process and all the relevant model parameter and measurement uncertainties. In this way the stability of the controlled system can be assessed and a systematic procedure for the selection of the uncertain model parameters involved in the dynamic inversion paths can be derived to guarantee that the plant together with the NDI process is a stable system.