Power-based control of output oscillations with online estimation of biased harmonics

TL;DR

The paper addresses suppressing marginally damped output oscillations in non-collocated systems by integrating a discrete power-based control with online finite-time estimation of biased harmonics. The method uses $u'(t)= k \hat{\omega}^2 \hat{A}(t^*)$ with phase synchronization via $T=(2\pi+\arg[\tilde{G}(j 2\hat{\omega})])\hat{\omega}^{-1}$ and a gain constraint $1<K<|\tilde{G}(j\omega)|^{-1}$, while estimating $[\hat{Y}_0,\hat{A},\hat{\omega}]$ through two linear-regression stages: frequency from $\tilde{y}(t)=\tilde{\varphi}(t)\theta_0+\tilde{v}(t)$ and amplitude/bias from $y(t)=\varphi^T(t)\theta+v(t)$. Finite-time convergence is achieved under suitable excitation, with ISS guarantees under noise, and the approach is validated experimentally on a fifth-order actuator with a gravity-affected free-hanging load, showing effective oscillation suppression with reduced communication. The results demonstrate practical viability for fast online adaptation in non-ideal, noisy environments, supporting broader adoption in non-collocated control applications.

Abstract

The recently introduced discrete power-based control (Ruderman (2024b)) reduces largely the communication efforts in the control loop when compensating for the marginally damped or even slowly diverging output oscillations. The control commutates twice per oscillations period (at the amplitude peaks) and uses the measured harmonic output only. The power-based control scheme requires the knowledge of the instantaneous frequency, amplitude, and bias parameters of the harmonic signal. This paper extends the power-based control by the finite-time estimation of the biased harmonics (Ahmed et al. (2022)). Also an improved analytic calculation of the impulse weighting factor is provided. The power-based oscillations control with online estimation of the harmonic parameters is evaluated experimentally on the fifth-order actuator system with a free hanging load under gravity and measurement noise.

Figures (7)

• Figure 1: Discrete power-based control $u^{\prime}$ subject to the gain shaping and time-delay synchronization.
• Figure 2: Simulated response of the stabilized oscillating output for two boundary gain values $K$.
• Figure 3: Experimental oscillatory setup: laboratory view (left) and equivalent mechanical scheme (right).
• Figure 4: Unstable load position response of PI-control.
• Figure 5: Online estimation of harmonic parameters at unstable response: frequency (a), bias (b), amplitude (c).