Multi-Parametric Extremum Seeking-based Auto-Tuning for Robust Input-Output Linearization Control

We study in this paper the problem of iterative feedback gains tuning for a class of nonlinear systems. We consider Input-Output linearizable nonlinear systems with additive uncertainties. We first design a nominal Input-Output linearization-based controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model-free multi-parametric extremum seeking (MES) control to iteratively auto-tune the feedback gains. We analyze the stability of the whole controller, i.e. robust nonlinear controller plus model-free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example.Comment: To appear at the IEEE CDC 201

Sampled-data extremum-seeking framework for constrained optimization of nonlinear dynamical systems

Most extremum-seeking control (ESC) approaches focus solely on the problem of finding the extremum of some unknown, steady-state input–output map, providing parameter settings that lead to optimal steady-state system performance. However, many industrial applications also have to deal with constraints on operating conditions due to, e.g., actuator limitations, limitations on tunable system parameters, or constraints on measurable variables. In particular, constraints on measurable variables are typically unknown in terms of their relationship with the tunable system parameters. In addition, the constraints on system inputs as a result of the constraints on measurable variables may conflict with the otherwise optimal operational condition, and hence should be taken into account in the data-based optimization approach. In this work, we propose a sampled-data extremum-seeking framework for the constrained optimization of a class of nonlinear dynamical systems with measurable constrained variables. In this framework, barrier function methods are employed, exploiting both the objective function and constraint functions which are available through output measurement only. We show, under the assumption that the parametric initialization yield operating conditions that do not violate the constraints, that (1) the resulting closed-loop dynamics is stable, (2) constraint satisfaction of the inputs is guaranteed for all iterations of the optimization process, and (3) constrained optimization is achieved. We illustrate the working principle of the proposed framework by means of an industrial case study of the constrained optimization of extreme ultraviolet light generation in a laser-produced plasma source within a state-of-the-art lithography system.</p

Sampled-data extremum-seeking framework for constrained optimization of nonlinear dynamical systems

Most extremum-seeking control (ESC) approaches focus solely on the problem of finding the extremum of some unknown, steady-state input–output map, providing parameter settings that lead to optimal steady-state system performance. However, many industrial applications also have to deal with constraints on operating conditions due to, e.g., actuator limitations, limitations on tunable system parameters, or constraints on measurable variables. In particular, constraints on measurable variables are typically unknown in terms of their relationship with the tunable system parameters. In addition, the constraints on system inputs as a result of the constraints on measurable variables may conflict with the otherwise optimal operational condition, and hence should be taken into account in the data-based optimization approach. In this work, we propose a sampled-data extremum-seeking framework for the constrained optimization of a class of nonlinear dynamical systems with measurable constrained variables. In this framework, barrier function methods are employed, exploiting both the objective function and constraint functions which are available through output measurement only. We show, under the assumption that the parametric initialization yield operating conditions that do not violate the constraints, that (1) the resulting closed-loop dynamics is stable, (2) constraint satisfaction of the inputs is guaranteed for all iterations of the optimization process, and (3) constrained optimization is achieved. We illustrate the working principle of the proposed framework by means of an industrial case study of the constrained optimization of extreme ultraviolet light generation in a laser-produced plasma source within a state-of-the-art lithography system.</p

Lyapunov based optimal control of a class of nonlinear systems

Optimal control of nonlinear systems is in fact difficult since it requires the solution to the Hamilton-Jacobi-Bellman (HJB) equation which has no closed-form solution. In contrast to offline and/or online iterative schemes for optimal control, this dissertation in the form of five papers focuses on the design of iteration free, online optimal adaptive controllers for nonlinear discrete and continuous-time systems whose dynamics are completely or partially unknown even when the states not measurable. Thus, in Paper I, motivated by homogeneous charge compression ignition (HCCI) engine dynamics, a neural network-based infinite horizon robust optimal controller is introduced for uncertain nonaffine nonlinear discrete-time systems. First, the nonaffine system is transformed into an affine-like representation while the resulting higher order terms are mitigated by using a robust term. The optimal adaptive controller for the affinelike system solves HJB equation and identifies the system dynamics provided a target set point is given. Since it is difficult to define the set point a priori in Paper II, an extremum seeking control loop is designed while maximizing an uncertain output function. On the other hand, Paper III focuses on the infinite horizon online optimal tracking control of known nonlinear continuous-time systems in strict feedback form by using state and output feedback by relaxing the initial admissible controller requirement. Paper IV applies the optimal controller from Paper III to an underactuated helicopter attitude and position tracking problem. In Paper V, the optimal control of nonlinear continuous-time systems in strict feedback form from Paper III is revisited by using state and output feedback when the internal dynamics are unknown. Closed-loop stability is demonstrated for all the controller designs developed in this dissertation by using Lyapunov analysis --Abstract, page iv

Extremum seeking control for optimization of an open-loop grinding mill using grind curves

A semi-autogenous grinding mill is simulated with gradient and non-gradient based extremum seeking controllers to maximize the mill performance using grind curves. Grind curves map the essential performance measures of a grinding mill to the mill load and rotational speed. The curves vary with the changes in the feed ore characteristic but show generic parabolic features with extremums. The extremum seeking controllers search along the unknown input–output map to steer the process towards an unknown optimum. In this study, a classical perturbation-based method, a time-varying parameter estimation-based method and the Nelder–Mead simplex method are employed as extremum seeking control (ESC) methods to search along the grind curves to either optimize the mill throughput or grind by means of manipulating the mill feed or rotational speed. The proposed extremum seeking controller could reduce the need for a plant operator to manually select the optimal operating conditions that maximize the performance measures of a grinding mill. Since the controller is agnostic to the process model, the grinding mill can be optimized without the need for a detailed process model. The simulated results show that the extremum seeking controllers steer the mill operating conditions toward the steady-state optimum and can be used to satisfy operational objectives. However, the slow grinding mill dynamics result in a long convergence rate when the initial conditions are far from the optimal operating conditions.The National Research Foundation of South Africa.http://www.elsevier.com/locate/jproconthj2022Electrical, Electronic and Computer Engineerin

Process analytical technology in food biotechnology

Biotechnology is an area where precision and reproducibility are vital. This is due to the fact that products are often in form of food, pharmaceutical or cosmetic products and therefore very close to the human being. To avoid human error during the production or the evaluation of the quality of a product and to increase the optimal utilization of raw materials, a very high amount of automation is desired. Tools in the food and chemical industry that aim to reach this degree of higher automation are summarized in an initiative called Process Analytical Technology (PAT). Within the scope of the PAT, is to provide new measurement technologies for the purpose of closed loop control in biotechnological processes. These processes are the most demanding processes in regards of control issues due to their very often biological rate-determining component. Most important for an automation attempt is deep process knowledge, which can only be achieved via appropriate measurements. These measurements can either be carried out directly, measuring a crucial physical value, or if not accessible either due to the lack of technology or a complicated sample state, via a soft-sensor.Even after several years the ideal aim of the PAT initiative is not fully implemented in the industry and in many production processes. On the one hand a lot effort still needs to be put into the development of more general algorithms which are more easy to implement and especially more reliable. On the other hand, not all the available advances in this field are employed yet. The potential users seem to stick to approved methods and show certain reservations towards new technologies.Die Biotechnologie ist ein Wissenschaftsbereich, in dem hohe Genauigkeit und Wiederholbarkeit eine wichtige Rolle spielen. Dies ist der Tatsache geschuldet, dass die hergestellten Produkte sehr oft den Bereichen Nahrungsmitteln, Pharmazeutika oder Kosmetik angehöhren und daher besonders den Menschen beeinflussen. Um den menschlichen Fehler bei der Produktion zu vermeiden, die Qualität eines Produktes zu sichern und die optimale Verwertung der Rohmaterialen zu gewährleisten, wird ein besonders hohes Maß an Automation angestrebt. Die Werkzeuge, die in der Nahrungsmittel- und chemischen Industrie hierfür zum Einsatz kommen, werden in der Process Analytical Technology (PAT) Initiative zusammengefasst. Ziel der PAT ist die Entwicklung zuverlässiger neuer Methoden, um Prozesse zu beschreiben und eine automatische Regelungsstrategie zu realisieren. Biotechnologische Prozesse gehören hierbei zu den aufwändigsten Regelungsaufgaben, da in den meisten Fällen eine biologische Komponente der entscheidende Faktor ist. Entscheidend für eine erfolgreiche Regelungsstrategie ist ein hohes Maß an Prozessverständnis. Dieses kann entweder durch eine direkte Messung der entscheidenden physikalischen, chemischen oder biologischen Größen gewonnen werden oder durch einen SoftSensor. Zusammengefasst zeigt sich, dass das finale Ziel der PAT Initiative auch nach einigen Jahren des Propagierens weder komplett in der Industrie noch bei vielen Produktionsprozessen angekommen ist. Auf der einen Seite liegt dies mit Sicherheit an der Tatsache, dass noch viel Arbeit in die Generalisierung von Algorithmen gesteckt werden muss. Diese müsse einfacher zu implementieren und vor allem noch zuverlässiger in der Funktionsweise sein. Auf der anderen Seite wurden jedoch auch Algorithmen, Regelungsstrategien und eigne Ansätze für einen neuartigen Sensor sowie einen Soft-Sensors vorgestellt, die großes Potential zeigen. Nicht zuletzt müssen die möglichen Anwender neue Strategien einsetzen und Vorbehalte gegenüber unbekannten Technologien ablegen

Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems With Input Delay via Dynamic Surface Technique

This brief constructs the adaptive backstepping control scheme for a class of pure-feedback systems with input delay and full state constraints. With the help of Mean Value Theorem, the pure-feedback system is transformed into strict-feedback one. Barrier Lyapunov functions are employed to guarantee all of the states remain constrained within predefined sets. By introducing the Pade approximation method and corresponding intermediate, the impact generated by input delay on the output tracking performance of the system can be eliminated. Furthermore, a low-pass filter driven by a newly-defined control input, is employed to generate the actual control input, which facilitates the design of backstepping control. To approximate the unknown functions with a desired level of accuracy, the fuzzy logic systems (FLSs) are utilized by choosing appropriate fuzzy rules, logics and so on. The minimal learning parameter (MLP) technique is employed to decrease the number of nodes and parameters in FLSs, and dynamic surface control (DSC) technique is leveraged to avoid so-called "explosion of complexity". Moreover, smooth robust compensators are introduced to circumvent the influences of external disturbance and approximation errors. By stability analysis, it is proved that all of signals in the closed-loop system are semi-globally ultimately uniform bounded, and the tracking error can be within a arbitrary small neighbor of origin via selecting appropriate parameters of controllers. Finally, the results of numerical illustration are provided to demonstrate the effectiveness of the designed method.Comment: arXiv admin note: text overlap with arXiv:2310.1540

Distributed Extremum Seeking And Cooperative Control For Mobile Cooperative Communication Systems

In this thesis, a distributed extremum seeking and cooperative control algorithm is designed for mobile agents to disperse themselves optimally in maintaining communication quality and maximizing their coverage. The networked mobile agents locally form a virtual multiple-input multipleoutput (MIMO) communication system, and they cooperatively communicate among them by using the decode and forward cooperative communication technique. The outage probability is used as the measure of communication quality, and it can be estimated real-time. A general performance index balancing outage probability and spatial dispersion is chosen for the overall system. The extremum seeking control approach is used to estimate and optimize the value of the performance index, and the cooperative formation control is applied to move the mobile agents to achieve the optimal solution by using only the locally-available information. Through the integration of cooperative communication and cooperative control, network connectivity and coverage of the mobile agents are much improved when compared to either non-cooperative communication approaches or other existing control results. Analytical analysis is carried out to demonstrate the performance and robustness of the proposal methodology, and simulation is done to illustrate its effectivenes

Multi-Objective Control Optimization for Greenhouse Environment Using Evolutionary Algorithms

This paper investigates the issue of tuning the Proportional Integral and Derivative (PID) controller parameters for a greenhouse climate control system using an Evolutionary Algorithm (EA) based on multiple performance measures such as good static-dynamic performance specifications and the smooth process of control. A model of nonlinear thermodynamic laws between numerous system variables affecting the greenhouse climate is formulated. The proposed tuning scheme is tested for greenhouse climate control by minimizing the integrated time square error (ITSE) and the control increment or rate in a simulation experiment. The results show that by tuning the gain parameters the controllers can achieve good control performance through step responses such as small overshoot, fast settling time, and less rise time and steady state error. Besides, it can be applied to tuning the system with different properties, such as strong interactions among variables, nonlinearities and conflicting performance criteria. The results implicate that it is a quite effective and promising tuning method using multi-objective optimization algorithms in the complex greenhouse production