Development of U-model enhansed nonlinear systems

Nonlinear control system design has been widely recognised as a challenging issue where the key objective is to develop a general model prototype with conciseness, flexibility and manipulability, so that the designed control system can best match the required performance or specifications. As a generic systematic approach, U-model concept appeared in Prof. Quanmin Zhu’s Doctoral thesis, and U-model approach was firstly published in the journal paper titled with ‘U-model based pole placement for nonlinear plants’ in 2002.The U-model polynomial prototype precisely describes a wide range of smooth nonlinear polynomial models, defined as a controller output u(t-1) based time-varying polynomial models converted from the original nonlinear model. Within this equivalent U-model expression, the first study of U-model based pole placement controller design for nonlinear plants is a simple mapping exercise from ordinary linear and nonlinear difference equations to time-varying polynomials in terms of the plant input u(t-1). The U-model framework realised the concise and applicable design for nonlinear control system by using such linear polynomial control system design approaches.Since the first publication, the U-model methodology has progressed and evolved over the course of a decade. By using the U-model technique, researchers have proposed many different linear algorithms for the design of control systems for the nonlinear polynomial model including; adaptive control, internal control, sliding mode control, predictive control and neural network control. However, limited research has been concerned with the design and analysis of robust stability and performance of U-model based control systems.This project firstly proposes a suitable method to analyse the robust stability of the developed U-model based pole placement control systems against uncertainty. The parameter variation is bounded, thus the robust stability margin of the closed loop system can be determined by using LMI (Linear Matrix Inequality) based robust stability analysis procedure. U-block model is defined as an input output linear closed loop model with pole assignor converted from the U-model based control system. With the bridge of U-model approach, it connects the linear state space design approach with the nonlinear polynomial model. Therefore, LMI based linear robust controller design approaches are able to design enhanced robust control system within the U-block model structure.With such development, the first stage U-model methodology provides concise and flexible solutions for complex problems, where linear controller design methodologies are directly applied to nonlinear polynomial plant-based control system design. The next milestone work expands the U-model technique into state space control systems to establish the new framework, defined as the U-state space model, providing a generic prototype for the simplification of nonlinear state space design approaches.The U-state space model is first described as a controller output u(t-1) based time-varying state equations, which is equivalent to the original linear/nonlinear state space models after conversion. Then, a basic idea of corresponding U-state feedback control system design method is proposed based on the U-model principle. The linear state space feedback control design approach is employed to nonlinear plants described in state space realisation under U-state space structure. The desired state vectors defined as xd(t), are determined by closed loop performance (such as pole placement) or designer specifications (such as LQR). Then the desired state vectors substitute the desired state vectors into original state space equations (regarded as next time state variable xd(t) = x(t) ). Therefore, the controller output u(t-1) can be obtained from one of the roots of a root-solving iterative algorithm.A quad-rotor rotorcraft dynamic model and inverted pendulum system are introduced to verify the U-state space control system design approach for MIMO/SIMO system. The linear design approach is used to determine the closed loop state equation, then the controller output can be obtained from root solver. Numerical examples and case studies are employed in this study to demonstrate the effectiveness of the proposed methods

Advanced control designs for output tracking of hydrostatic transmissions

The work addresses simple but efficient model descriptions in a combination with advanced control and estimation approaches to achieve an accurate tracking of the desired trajectories. The proposed control designs are capable of fully exploiting the wide operation range of HSTs within the system configuration limits. A new trajectory planning scheme for the output tracking that uses both the primary and secondary control inputs was developed. Simple models or even purely data-driven models are envisaged and deployed to develop several advanced control approaches for HST systems

Data-driven Adaptive Stabilizer for Unknown Nonlinear Dynamic MIMO Systems Using a Cognition-based Framework

This thesis focuses on a cognitive stabilizer concept which is an adaptive discrete control method based on a cognition-based framework. The aim of the cognitive stabilizer is to autonomously stabilize a specific class of unknown nonlinear multi-input-multi-output (MIMO) systems. The cognitive stabilizer is able to gain useful local knowledge of the unknown system and can autonomously define suitable control inputs to stabilize the system. The development of different kinds of adaptive, data-driven, and model-free controllers shows a clear tendency towards research on control methods with high autonomy. Here the term autonomy is used to describe the fact that the control approach/the related programming is organized such that the algorithm is able to handle the feedback design autonomously without instructions from outside the algorithm. Typical methods affected by this definition are adaptive control method, data-driven control method, and model-free control method. In this thesis, the state-of-the-art of them is reviewed. The main focus is given to the autonomy of the realized approaches. It can be concluded that the existing methods still show some open points achieving highly autonomous control. In order to address these open points, a framework similar to modeling approaches concerning the human cognition processes [Cac98] can be introduced in the engineering context, which is denoted as cognition-based framework. As stabilization control task is the most basic control task, the cognition-based framework for stabilization is established in this thesis. It is assumed, that the mathematical model of the system to be controlled is unknown and fully controllable, as well as the state vector can be measured. The cognitive stabilizer is realized based on the cognitive framework by its four main modules: (1) “perception and interpretation” using system identifier for the system local dynamic online identification and multi-step-ahead prediction; (2) “expert knowledge” relating to the stability criterion to guarantee the stability of the considered motion of the controlled system; (3) “planning” to generate a suitable control input sequence according to certain cost functions; (4) “execution” to generate the optimal control input in a corresponding feedback form. Each module can be realized using different methods. In this thesis, “perception and interpretation” is realized using neural networks, Gaussian process regression, or combined identifier. “Expert knowledge” consists of the data-driven quadratic stability criterion, the quadratic Lyapunov stability criterion with a certain Lyapunov function, and the uniform stability criterion. The modules “planning” and “execution” are realized together with exhaustive grid search method or direct input optimization using inverse model. The whole cognitive stabilizer is realized using the autonomous communication among each module. The cognitive stabilizer are tested using numerical examples or experimental results in this thesis. Pendulum system and Lorenz-system are considered as simulation examples. Both are benchmark examples for the nonlinear dynamic control design. The cognitive stabilizer is experimentally implemented and evaluated to a threetank-system. All the numerical examples and experimental results demonstrate the successful application of the proposed methods.Das Thema dieser Arbeit ist ein kognitives Stabilisierungsverfahren, das basierend auf einem kognitionsbasierten Framework ein adaptives diskretes Regelungsverfahren darstellt. Ziel des kognitiven Stabilisierungsverfahrens ist es, eine spezifische Klasse von unbekannten, nichtlinearen, Mehrgrößensystemen autonom zu stabilisieren. Das kognitive Stabilisierungsverfahren ist in der Lage, relevante lokale Informationen über das unbekannte System zu erlangen. Es kann autonom geeignete Steuergrößen definieren, um das System zu stabilisieren. Die Entwicklung von verschiedenen adaptiven, datenbasierten und modellfreien Reglern zeigte bereits die Tendenz der Erforschung von Regelungsmethoden mit hoher Autonomie. Der Begriff Autonomie wird hier verwendet, um die Tatsache zu beschreiben, dass das Regelungsverfahren bzw. die dazugehörige Programmierung so durchgeführt wird, dass der zugehörige Algorithmus den Rückführungsentwurf autonom ohne Einwirkungen von außerhalb des Algorithmus festlegen kann. Typische Methoden, die von dieser Definition beeinflusst werden sind die adaptive Regelungsmethode, die datenbasierte Regelungsmethode oder die modellfreie Regelungsmethode, deren Stand der Forschung in dieser Arbeit zusammengefasst wird. Der Hauptfokus liegt dabei auf der Autonomie der realisierten Verfahren. Es kann gezeigt werden, dass die existierenden Methoden immer noch einige offene Probleme aufweisen, um eine hohe autonome Regelung zu erreichen. Um diese offenen Probleme weiterzuentwickeln, kann ein Framework in den Ingenieurskontext eingeführt werden, das den Modellierungsverfahren bezüglich der menschlichen Kognitionsprozesse [Cac98] ähnelt und als kognitives Framework bezeichnet werden kann. Da Stabilisierungsaufgaben die elementarsten Regelungsaufgaben sind, wird in dieser Arbeit ein kognitionsbasiertes Framework zur Stabilisierung entwickelt. Zunächst wird angenommen, dass das mathematische Modell des zu regelnden Systems unbekannt, vollständig steuerbar und der Zustandsvektor messbar ist. Der kognitive Stabilisierungsregler wird basierend auf dem kognitiven System durch seine vier Hauptmodule realisiert: (1) ”Wahrnehmung und Interpretation“ durch einen Systemidentifikator zur Echtzeit-Identifikation der lokalen Systemdynamik und Mehr-Schritt-Vorhersage; (2) ”Expertenwissen“ bezogen auf das Stabilitätskriterium um die Stabilität der betrachteten Bewegung des geregelten Systems zu garantieren; (3) ”Planung“ um eine geeignete Eingangsgrößensequenz nach bestimmten Gütefunktionen zu erzeugen; (4) ”Ausführung“ um die optimalen Steuergrößen in eine entsprechende Rückführungsform zu generieren. Jedes Modul kann durch verschiedene Methoden realisiert werden. In dieser Arbeit wird das Modul ”Wahrnehmung und Interpretation“ durch neuronale Netzwerke, Gauß-Prozess-Regression oder einen kombinierten Identifikator umgesetzt. Das Modul ”Expertenwissen“ besteht aus dem datenbasierten quadratischen Stabilitätskriterium, dem quadratischen Lyapunov Stabilitätskriterium mit einer bestimmten Lyapunov-Funktion und dem gleichmäßigen Stabilitätskriterium. Die Module ”Planung“ und ”Ausführung“ werden zusammen durch das inverse Modell mit dem vollständigen ”Grid-Search“-Verfahren oder direkter Steuergrößenoptimierung realisiert. Die gesamte kognitive Stabilisierungsmethode wird durch die autonome Kommunikation zwischen jedem Modul realisiert. Die kognitive Stabilisierungsmethode wird in dieser Arbeit durch numerische Beispiele oder experimentelle Ergebnisse getestet. Zwei Simulationsbeispiele (Pendel-System sowie Lorenz-System) werden betrachtet. Beide sind Benchmarkbeispiele für den nichtlinearen dynamischen Regelungsentwurf. Die kognitive Stabilisierungsmethode wird experimentell auf das Drei-Tank-System angewendet und die entsprechenden Ergebnisse werden bewertet. Die numerischen Beispiele sowie die experimentelle Umsetzung zeigen die erfolgreiche Anwendung des dargestellten Verfahrens

Adaptive Control

Adaptive control has been a remarkable field for industrial and academic research since 1950s. Since more and more adaptive algorithms are applied in various control applications, it is becoming very important for practical implementation. As it can be confirmed from the increasing number of conferences and journals on adaptive control topics, it is certain that the adaptive control is a significant guidance for technology development.The authors the chapters in this book are professionals in their areas and their recent research results are presented in this book which will also provide new ideas for improved performance of various control application problems

Development of adaptive control methodologies and algorithms for nonlinear dynamic systems based on u-control framework

Inspired by the U-model based control system design (or called U-control system design), this study is mainly divided into three parts. The first one is a U-model based control system for unstable non-minimum phase system. Pulling theorems are proposed to apply zeros pulling filters and poles pulling filters to pass the unstable non-minimum phase characteristics of the plant model/system. The zeros pulling filters and poles pulling filters derive from a customised desired minimum phase plant model. The remaining controller design can be any classic control systems or U-model based control system. The difference between classic control systems and U-model based control system for unstable non-minimum phase will be shown in the case studies.Secondly, the U-model framework is proposed to integrate the direct model reference adaptive control with MIT normalised rules for nonlinear dynamic systems. The U-model based direct model reference adaptive control is defined as an enhanced direct model reference adaptive control expanding the application range from linear system to nonlinear system. The estimated parameter of the nonlinear dynamic system will be placement as the estimated gain of a customised linear virtual plant model with MIT normalised rules. The customised linear virtual plant model is the same form as the reference model. Moreover, the U-model framework is design for the nonlinear dynamic system within the root inversion.Thirdly, similar to the structure of the U-model based direct model reference adaptive control with MIT normalised rules, the U-model based direct model reference adaptive control with Lyapunov algorithms proposes a linear virtual plant model as well, estimated and adapted the particular parameters as the estimated gain which of the nonlinear plant model by Lyapunov algorithms. The root inversion such as Newton-Ralphson algorithm provides the simply and concise method to obtain the inversion of the nonlinear system without the estimated gain. The proposed U-model based direct control system design approach is applied to develop the controller for a nonlinear system to implement the linear adaptive control. The computational experiments are presented to validate the effectiveness and efficiency of the proposed U-model based direct model reference adaptive control approach and stabilise with satisfied performance as applying for the linear plant model

Deep learning for robust adaptive inverse control of nonlinear dynamic systems: Improved settling time with an autoencoder

An adaptive deep neural network is used in an inverse system identification setting to approximate the inverse of a nonlinear plant with the aim of constituting the plant controller by copying to the latter the weights and architecture of the converging deep neural network. This deep learning (DL) approach to the adaptive inverse control (AIC) problem is shown to outperform the adaptive filtering techniques and algorithms normally used in adaptive control, especially when in nonlinear plants. The deeper the controller, the better the inverse function approximation, provided that the nonlinear plant has an inverse and that this inverse can be approximated. Simulation results prove the feasibility of this DL-based adaptive inverse control scheme. The DL-based AIC system is robust to nonlinear plant parameter changes in that the plant output reassumes the value of the reference signal considerably faster than with the adaptive filter counterpart of the deep neural network. The settling and rise times of the step response are shown to improve in the DL-based AIC system