This paper develops a persistently exciting input generating Online Feedback Optimization (OFO) controller that estimates the sensitivity of a process ensuring minimal deviations from the descent direction while converging. This eliminates the need for random perturbations in feedback loop. The proposed controller is formulated as a bilevel optimization program, where a nonconvex full rank constraint is relaxed using linear constraints and penalization. The validation of the method is performed in a simulated scenario where multiple systems share a limited, costly resource for production optimization, simulating an oil and gas resource allocation problem. The method allows for less input perturbations while accurately estimating gradients, allowing faster convergence when the gradients are unknown. In the case study, the proposed method achieved the same profit compared to an OFO controller with random input perturbations, and 1.4% higher profit compared to an OFO controller without input perturbations.

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.

Performance-based maintenance of machinery relies on detection and prediction of performance degradation. Degradation indicators calculated from process measurements need to be approximated with degradation models that smooth the variations in the measurements and give predictions of future values of the indicator. Existing models for performance degradation assume that the performance monotonically decreases with time. In consequence, the models yield suboptimal performance in performance-based maintenance as they do not take into account that performance degradation can reverse itself. For instance, deposits on the blades of a turbomachine can be self-cleaning in some conditions. In this study, a data-driven algorithm is proposed that detects if the performance degradation indicator is increasing or decreasing and adapts the model accordingly. A moving window approach is combined with adaptive regression analysis of operating data to predict the expected value of the performance degradation indicator and to quantify the uncertainty of predictions. The algorithm is tested on industrial performance degradation data from two independent offshore applications, and compared with four other approaches. The parameters of the algorithm are discussed and recommendations on the optimal choices are made. The algorithm proved to be portable and the results are promising for improving performance-based maintenance.

This article investigates the optimization of yaw control inputs of a nine-turbine wind farm. The wind farm is simulated using the high-fidelity simulator SOWFA. The optimization is performed with a modifier adaptation scheme based on Gaussian processes. Modifier adaptation corrects for the mismatch between plant and model and helps to converge to the actual plan optimum. In the case study the modifier adaptation approach is compared with the Bayesian optimization approach. Moreover, the use of two different covariance functions in the Gaussian process regression is discussed. Practical recommendations concerning the data preparation and application of the approach are given. It is shown that both the modifier adaptation and the Bayesian optimization approach can improve the power production with overall smaller yaw misalignments in comparison to the Gaussian wake model.