Power based adaptive compensator of output oscillations

TL;DR

The paper addresses oscillation rejection in systems with unknown amplitude $A$ and frequency $\omega$ by introducing a discrete, power-based adaptive compensator. It derives a control law $u(t)=K\,\tilde{\omega}^2\,\tilde{A}(t^*)$ from input-output power balance and analytically determines an optimal $K$, enabling energy-based cancellation over a period. The method is extended to higher-order dynamics via a known transfer function $G(s)$, incorporating amplitude and phase effects through $|G(j\omega)|$, $\arg[G(j2\omega)]$, a time delay $T$, and weighting $L$, with an extrema-detection scheme updating parameters every half-period. Experimental validation on a five-order, two-mass oscillator demonstrates stabilization under disturbances and highlights reduced communication requirements in digitally connected setups. Overall, the work provides a robust, energy-based, discrete control framework for oscillation compensation applicable to complex mechanical systems.

Abstract

Power-based output feedback compensator for oscillatory systems is proposed. The average input-output power of an oscillatory signal serves as an equivalent control effort, while the unknown amplitude and frequency of oscillations are detected at each half-period. This makes the compensator adaptive and discrete, while the measured oscillatory output is the single available signal in use. The resulting discrete control scheme enables a drastic reduction of communication efforts in the control loop. The compensator is designed for 2nd order systems, while an extension to higher-order dynamics, like e.g. in case of two-inertia systems, is also provided. Illustrative experimental case study of the 5th order oscillatory system is provided.

Figures (9)

• Figure 1: Signals flow in 2nd order system with output \ref{['eq:2:1:1']}.
• Figure 2: Simulation results of the second-order oscillatory system with and without use of compensator \ref{['eq:2:1:5']}. The output response and control value, in (a) and (c) for $a=2$, in (b) and (d) for $a=-1$.
• Figure 3: Signals flow in higher-order system with output \ref{['eq:2:1:1']}.
• Figure 4: Simulation results of the fifth-order oscillatory system with and without use of compensator \ref{['eq:2:2:1']}.
• Figure 5: Example of extrema detection from noisy output.