# PI(D) tuning for Flight Control Systems via Incremental Nonlinear Dynamic Inversion

## TL;DR

This paper demonstrates that incremental nonlinear dynamic inversion (INDI) is equivalent to time-delay control (TDC), enabling systematic PI(D) control tuning for robust nonlinear flight control systems without relying on effector blending models.

## Contribution

It establishes the equivalence between INDI and TDC and introduces a systematic method for PI(D) control tuning in nonlinear flight systems.

## Key findings

- INDI is equivalent to TDC in control theory.
- A reformulation of plant dynamics inversion simplifies control law design.
- The method enhances robustness and model-free control in flight systems.

## Abstract

Previous results reported in the robotics literature show the relationship between time-delay control (TDC) and proportional-integral-derivative control (PID). In this paper, we show that incremental nonlinear dynamic inversion (INDI) - more familiar in the aerospace community - are in fact equivalent to TDC. This leads to a meaningful and systematic method for PI(D)-control tuning of robust nonlinear flight control systems via INDI. We considered a reformulation of the plant dynamics inversion which removes effector blending models from the resulting control law, resulting in robust model-free control laws like PI(D)-control.