Khalid Tourkey Atta

Extremum seeking control based on phasor estimation

Abstract We present an extremum seeking control algorithm based on the estimation of the phasor of the perturbation frequency in the output of the plant. The phasor estimator is based on a continuous time Kalman filter, which is reduced into a variable gain observer by explicitly solving the special case of the Riccati equation. Local stability of the proposed algorithm for general non-linear dynamic systems using averaging and singular perturbations is presented for the single input case. The advantage of the presented algorithm is that it can be used on plants with large and even variable phase lag.

Phasor extremum seeking and its application in Kaplan turbine control

The Combinator is an important part in Kaplan turbine control. It ensures that the turbine will operate in an optimum way, in terms of maximum efficiency of the plant. This work suggests a new sinusoidal perturbation based extremum seeking algorithm based on the phasor of the output. We propose to use this algorithm for generating the required data to build and correct the combinator. Simulations are presented showing the applicability of the proposed methods.

Accuracy Improvement of Extremum Seeking Control

In this work, we present a modification for the classic and phasor extremum seeking control algorithms in order to improve the accuracy by removing or reducing the convergence error. The modulation signals were replaced by a sum of sinusoids in order to remove the equilibrium shift in the controlled variable of the averaged system. The convergence error is calculated as a function of the number of sinusoids used in the modulation signal. A simulation example is presented to illustrate the improvement.

On the stability analysis of phasor and classic extremum seeking control

Abstract In this work we present a semi-global practical asymptotic stability analysis for phasor extremum seeking control with a general non-linear dynamic system. With the same technique applied to the classic band pass filter algorithm, we present a more relaxed (less constrained) semi-global practical asymptotic stability condition compared to earlier work. The results are based on a non approximated averaging for both control techniques.

Maximum power point tracking for micro hydro power plants using extremum seeking control

In this work, we propose using extremum seeking control (ESC) as a tool for maximum power point tracking in micro hydro power plants. The phasor ESC, which is based on estimating the phasor of the plant output at the perturbation frequency, was modified by estimating the phasors of multiple harmonics of this frequency. This modification will improve the performance of ESC by reducing the fluctuations in control variables that may appear in noisy environments as a result of high-amplitude perturbation signals. A test rig was used to experimentally verify the proposed approach and to demonstrate the usability of ESC in hydro power plants.

On-line optimization of cone crushers using Extremum-Seeking Control

This article demonstrates the ability of on-line optimization of cone crushers, specifically maximization of the total throughput of the crusher by adjusting the eccentric speed (ω). The on-line optimization was based on the Extremum-Seeking Control (ESC) approach, which is advantageous when optimizing systems with unknown time varying characteristics. Two types of gradient based approaches are tested in simulation, the traditional Band-pass filters method and a method utilizing the Extended Kalman Filter (EKF). Both methods perform satisfactory, demonstrating the good potential of ESC for online-optimization of cone crushers. To deal with unwanted behavior of the EKF based approach for situations when the gradient is not correctly estimated, a modification is suggested based on detecting this condition and accommodating for it.

Phasor extremum seeking control with adaptive perturbation amplitude

In this paper, we propose a perturbation amplitude adaption scheme for phasor extremum seeking control based on the plants estimated gradient. By using phasor extremum seeking instead of classical extremum seeking, the problem of algebraic loops in the controller formulation is avoided. Furthermore, a stability analysis for the proposed method is provided, which is the first stability analysis for extremum seeking controllers using adaptive amplitudes. The proposed method is illustrated using numerical examples and it is found that changes in optimum can be tracked accurately while the steady-state perturbations can be reduced significantly.

On the Generalization and Stability Analysis of Pareto Seeking Control

In this letter, we address a multi-objective on-line optimization problem for unknown dynamical systems by providing a generalization of the Pareto seeking controller (PSC). The idea of the PSC is to drive the system to the Pareto front in the absence of knowledge of the values of the objectives or the input values to achieve Pareto optimality. Two special cases are presented, for two objectives and three objectives. A stability analysis is presented for the case of two objectives and two inputs, which shows that the controller practically drives the system into the neighborhood of the Pareto front, for any initial condition. Two simulation examples for the special cases are also presented.

Towards autonomous synthesis of building substation control loops

The main contribution of this paper is to study the feasibility of an automated approach to the assessment and synthesis of control loops in substations of a district heating and cooling system. The low-level controllers in substation are usually PID-type controllers and can not easily be changed. Moreover, the tuning of these controllers is often done in an ad-hoc manner and remains in the initial tuning despite changes in the substation over their operational life. Consequently, insufficient control performance due to false tuning can be misinterpreted as a hardware issue and lead to unnecessary replacement of parts. In order to solve this problem, the paper proposes an approach to assess the control loop performance based on logged data from substations, and to subsequently tune the current substation controllers, when no hardware issues are detected. The approach is applied to a well-known building substation model in simulation, which indicates that the approach is feasible. Analysis of acquired data from a number of substations in the DHC system of Luleå Energi AB, provides evidence for the problem and how the approach can be applied in its future implementation. Moreover, a number of challenges and future work are indicated.