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.
The satellite platform BIROS is the second technology demonstrator of DLR's 'FireBIRD' space mission aiming to provide infrared remote sensing for early fire detection. Among several mission goals and scientific experiments, to demonstrate a high-agility attitude control system, the platform is actuated with an extra array of three orthogonal 'High-Torque-Wheels.' However, to enable agile reorientation, a challenge arises from the fact that time-optimal slew maneuvers are, in general, not of the Euler-axis rotation type; especially whenever the actuators are constrained independently. Moreover, BIROS' on-board computer can only accommodate rotational acceleration commands twice per second. The objective is therefore to find a methodology to design fast slew maneuvers while considering a highly dynamic plant commanded by piecewise-constant sampled-time control inputs. This is achieved by considering a comprehensive analytical nonlinear model for spacecraft equipped with reaction wheels and transcribing a time-optimal control problem formulation into a multi-criteria optimization problem. Solutions are found with a direct approach using the trajectory optimization package 'trajOpt' of DLR-SR's optimization tool, Multi-Objective Parameter Synthesis (MOPS). Results based on numerical simulations are presented to illustrate this method.
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