Increased Robustness to Delay in Incremental Controllers Using Input Scaling Gain

The main advantage of the incremental dynamics formulation is its property of replacing state-dependent aspects of the system dynamics by measurements, solely requiring modeling the input-dependent dynamics. However, incremental controllers assume that state derivative measurements are available. The lack of accurate sensors and communication delay may appear as limitations for the use of incremental techniques. This article applies a second-order differentiator (SOD) for estimating state derivatives and attenuate measurement noise, and an input scaling gain (ISG) for attenuating the effects of high-frequency noise and delay in the feedback loop. A complete analysis of the combined solution is carried out using an incremental nonlinear dynamic inversion (INDI) strategy. First, a simple linear single-input single-output model is used to evaluate the influence of design parameters in the closed-loop response and stability. Then, the combined SOD and ISG approach is illustrated in a more complex case application, where INDI is used to control the lateral motion of an autonomous airship, results of which corroborate the ISG as an asset to increase the maximum delay allowed in the feedback loop.