Performance Improvement of Extremum Seeking Control using Recursive Least Square Estimation with Forgetting Factor (original) (raw)

Analysis and Comparison of Extremum Seeking Control Techniques

2007

Two non-perturvative extremum seeking control approaches are analyzed; the first approach needs the sensing of the function's gradient while the second one does not. Relationships between the algorithms parameters and their dynamic behavior are found. Also expressions for the steady state error of both approaches are derived. Finally, these results are used to verify and to compare, by means of simulation, the performance of both methods.

A time-varying extremum-seeking control approach for discrete-time systems

Journal of Process Control, 2014

This paper considers the solution of a real-time optimization problem using adaptive extremum seeking control for a class of unknown discrete-time nonlinear systems. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The main contribution of the paper is to formulate the extremumseeking problem as a time-varying discrete-time estimation problem. The proposed approach is shown to avoid the need for averaging results which minimizes the impact of the choice of dither signals on the performance of the extremum seeking control system. Several examples are used to illustrate the effectiveness of the proposed technique.

Parameter convergence in adaptive extremum-seeking control

Automatica, 2007

This paper addresses the problem of parameter convergence in adaptive extremum-seeking control design. An alternate version of the popular persistence of excitation condition is proposed for a class of nonlinear systems with parametric uncertainties. The condition is translated to an asymptotic sufficient richness condition on the reference set-point. Since the desired optimal set-point is not known a priori in this type of problem, the proposed method includes a technique for generating perturbation signal that satisfies this condition in closed-loop. This demonstrates its superiority in terms of parameter convergence. The method guarantees parameter convergence with minimal but sufficient level of perturbation. The effectiveness of the proposed method is illustrated with a simulation example.

An extremum-seeking control method driven by input–output correlation

Journal of Process Control, 2017

This paper presents a new extremum-seeking controller (ESC) derived from a statistical interpretation of conventional ESC. The proposed ESC replaces the gradient feedback variable with a normalized correlation coefficient. The algorithm, as presented, can be fully configured with knowledge of only the open-loop response time of the system being optimized and the amplitude of the dither signal. Simulation tests show that the new algorithm has fast convergence times compared with other types of ESC algorithms. The paper also shows that the proposed method is not limited to a periodic dither signal and that it can also utilize a stochastic signal to similar efficacy. The purpose of the paper is to describe the new algorithm and present a practical implementation along with results from simulation tests.

Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties

Automatica, 2003

We pose and solve an extremum seeking control problem for a class of nonlinear systems with unknown parameters. Extremum seeking controllers are developed to drive system states to the desired set-points that optimize the value of an objective function. The proposed adaptive extremum seeking controller is "inverse optimal" in the sense that it minimizes a meaningful cost function that incorporates penalty on both the performance error and control action. Simulation studies are provided to verify the effectiveness of the proposed approach.

Bandwidth Reduction and Convergence Analysis of Extremum Seeking Control with Feedback Encoding

Frontiers in Mechanical Engineering, 2016

Frequently, a physical plant of a control system has an optimum operating point such as the spark (or injection) time of an internal combustion engine that results in maximum torque. Extremum Seeking Control (ESC) is a method of adaptive control capable of locating and maintaining a plant at such an optimum operating point in real time. It is capable of doing so with minimal a priori knowledge of the plant and can also track slowly varying changes. Input perturbed ESC schemes that use periodic dither signals have the disadvantage of requiring a high bandwidth for sampling and correlating the plant output with the dither signal. If the feedback path was to be implemented over a packet switched communication network, the high bandwidth requirement could result in increased congestion and consequently packet delays and dropouts. As a solution encoding using sporadic (aperiodic) sampling techniques can be used in the feedback path of the ESC scheme to reduce the required bandwidth. However, in order to ensure convergence of the ESC scheme with encoding, the effect of the signal reconstruction error due to encoding on the critical correlation stage has to be investigated. The contribution of this paper is an investigation of the convergence requirements and bandwidth performance of two encoding schemes; Memory-Based Event Triggering (MBET) and Event Triggered Adaptive Differential Modulation (ETADM). The results show that MBET can fail for objective functions with plateaus. ETADM fails when the number of ETADM steps used for reconstructing the plant output per perturbation cycle is too low to allow correlation. In terms of bandwidth reduction MBET performs better than ETADM (97% and 70%, respectively). However, the use of MBET results in a longer convergence time.

A framework for extremum seeking control of systems with parameter uncertainties

IEEE Transactions on Automatic Control, 2013

Traditionally, the design of extremum seeking algorithm treats the system as essentially a black-box, which for many applications means disregarding known information about the model structure. In contrast to this approach, there have been recent examples where a known plant structure with uncertain parameters has been used in the online optimization of plant operation. However, the results for these approaches have been restricted to specific classes of plants and optimization algorithms. This paper seeks to provide general results and a framework for the design of extremum seekers applied to systems with parameter uncertainties. General conditions for an optimization method and a parameter estimator are presented so that their combination guarantees convergence of the extremum seeker for both static and dynamic plants. Tuning guidelines for the closed loop scheme are also presented. The generality and flexibility of the proposed framework is demonstrated through a number of parameter estimators and optimization algorithms that can be combined to obtain extremum seeking. Examples of anti-lock braking and model reference adaptive control are used to illustrate the effectiveness of the proposed framework.

Adaptive extremum-seeking receding horizon control of nonlinear systems

Revista Espanola De Cardiologia, 2004

We present a control algorithm that incorporates real time optimization and receding horizon control technique to solve an extremum seeking control problem for a class of nonlinear systems with parametric uncertainties. A Lyapunov-based technique is employed to develop a receding horizon controller that drives the system states to the desired unknown extremum points when it can be shown that a

Adaptive Backstepping Extremum Seeking Control of a Class of Nonlinear Systems

Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2018

Traditional methods for extremum seeking control (ESC) disregard possible prior knowledge of the system model. In practice, however, these models are usually known, but they contain uncertain parameters. Assuming that partial knowledge about the system model is available, ESC problem has been solved recently for two different cases where systems outputs are considered to be measurable in one and immeasurable in the other. Available results in the case with immeasurable outputs are restricted to a certain class of systems in which the cost function only includes the states of the system that are directly affected by the control input. The contribution of this paper is to solve the ECS problem for a wider class of nonlinear system with parametric uncertainty whose outputs are not measurable. To this purpose, we use adaptive backstepping control technique: extremizing the cost function is achieved by driving the states to their desired values using input controls directly or indirectly. To illustrate the efficiency of the proposed framework, we provide simulation results.

Local self-optimizing control based on extremum seeking control

Control Engineering Practice, 2020

Self-optimizing Control (SOC) aims to find controlled variables with which setpoint regulation of the resultant feedback control loops can yield near-optimal operation under a range of disturbances. However, standard local SOC methods, e.g. the null-space SOC, require an offline analysis with large amounts of steady-state data, which can be computationally cumbersome. In this paper, we propose a new SOC procedure enabled by extremum seeking control (ESC) which will largely simplify the offline analysis process of null-space or extended null-space SOC methods. First, ESC is used to determine the optimal manipulated variable values under the nominal condition for the system. Next, by dithering the plant with periodic disturbances, the dither-demodulation technique in ESC is used to estimate the Jacobian and Hessian needed for obtaining the optimal measurement combination; then the null-space and extended null-space methods can be carried out in a computationally efficient fashion, for the scenarios with noise-free and noisy measurements, respectively. The proposed procedure are compared with the standard null-space and extended null-space SOC methods using a Modelica-based dynamic simulation model of an air-source heat pump (ASHP) system. The results show that a similar performance can be achieved with much simpler process of data acquisition and processing.