Tuning of Online Feedback Optimization for setpoint tracking in centrifugal compressors

TL;DR

Online Feedback Optimization (OFO) enables autonomous steering of nonlinear dynamic systems toward locally optimal operation by treating iterative optimization as a dynamic subsystem. The paper analyzes how OFO parameters and sampling time affect tracking performance and oscillations, and proposes a framework to jointly tune the sampling interval and optimization gains. The approach is validated on a centrifugal compressor pressure controller, showing substantial improvements over steady-state tuning (up to 87% faster tracking) and providing practical guidelines for balancing speed, accuracy, and oscillations. The work highlights the importance of directly constraining performance metrics via an optimization-based tuning procedure and points to future improvements through surrogate optimization and safe learning for safety-critical applications.

Abstract

Online Feedback Optimization (OFO) controllers steer a system to its optimal operating point by treating optimization algorithms as auxiliary dynamic systems. Implementation of OFO controllers requires setting the parameters of the optimization algorithm that allows reaching convergence, posing a challenge because the convergence of the optimization algorithm is often decoupled from the performance of the controlled system. OFO controllers are also typically designed to ensure steady-state tracking by fixing the sampling time to be longer than the time constants of the system. In this paper, we first quantify the impact of OFO parameters and the sampling time on the tracking error and number of oscillations of the controlled system, showing that adjusting them without waiting for steady state allows good tracking. We then propose a tuning method for the sampling time of the OFO controller together with the parameters to allow tracking fast trajectories while reducing oscillations. We validate the proposed tuning approach in a pressure controller in a centrifugal compressor, tracking trajectories faster than the time needed to reach the steady state by the compressor. The results of the validation confirm that simultaneous tuning of the sampling time and the parameters of OFO yields up to 87% times better tracking performance than manual tuning based on steady state.

Figures (3)

• Figure 1: Impact of parameters $\nu$ and $\Delta T$ (in s) on the performance of OFO with the objective \ref{['eq:CompressorObjective']} and the corresponding control inputs, and a trade-off between the error and the number of oscillations as functions of parameters
• Figure 2: Results of tuning for different setpoints
• Figure 3: Validation of the tuning parameters corresponding to constant tuning trajectory (Set 1), step tuning trajectory (Set 2), and sinusoidal tuning trajectory (Set 3) for two different setpoint trajectories