Nonlinear analysis of combined rate and acceleration limits effect on actuator performance

This paper explores the nonlinear effects of rate and acceleration limits in actuation systems, focusing on the actuator steady-state response to sinusoidal input and the effectiveness of closed-loop control systems. The saturation regimes determined by rate and acceleration limits are investigated, and analytical formulations are derived for the nonlinear actuator response and the boundaries of these regimes within the two-dimensional parameter space defined by non-dimensional rate and acceleration limits. Describing functions for each regime are determined in a closed form, establishing the relationship between actuator input and output in the frequency domain. Combined rate and acceleration limits are found to induce a low-pass filter behaviour in the actuator, with a -40 dB/decade roll-off, and can lead to nonsmooth phase dependence on frequency. The describing functions of combined rate and acceleration limits are applied to the analysis of an aeroservoelastic wing model developed for gust load alleviation (GLA) purposes. The effect of the actuator limits is investigated by evaluating the onset point of the nonlinear behaviour and an equivalent describing function for the entire actuatorplant-control feedback loop. The resulting findings illustrate that rate and acceleration limits can substantially affect the performance of closed-loop systems, leading to phenomena such as jump resonances when partial-to-full saturation regime transitions occur, and thereby constraining the effective frequency range of the GLA control systems.