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

A nonparametric learning framework for nonlinear robust output regulation

This paper proposes a nonparametric learning solution framework for a generic internal model design of nonlinear robust output regulation. The global robust output regulation problem for a class of nonlinear systems with output feedback subject to a nonlinear exosystem can be tackled by constructing a linear generic internal model, provided that a continuous nonlinear mapping exists. An explicit continuous nonlinear mapping was constructed recently in [1] under the assumption that the steady-state generator is linear in the exogenous signal. We further relax such an assumption to a relaxed assumption that the steady-state generator is polynomial in the exogenous signal. A nonparametric learning framework is proposed to solve a linear time-varying equation to make the nonlinear continuous mapping always exist. With the help of the proposed framework, the nonlinear robust output regulation problem can be converted into a robust non-adaptive stabilization problem for the augmented system with integral Input-to-State Stable (iISS) inverse dynamics. Moreover, a dynamic gain approach can adaptively raise the gain to a sufficiently large constant to achieve stabilization without requiring any a priori knowledge of the uncertainties appearing in the dynamics of the exosystem and the system. We further apply the nonparametric learning framework to globally reconstruct and estimate multiple sinusoidal signals with unknown frequencies without using adaptive techniques. An explicit nonlinear mapping can directly provide the estimated parameters, which will exponentially converge to the unknown frequencies. As a result, a feedforward control design is proposed to solve the output regulation using our nonparametric learning framework.Comment: 15 pages; Nonlinear control; iISS stability; output regulation; parameter estimation; Non-adaptive contro

Analysis and design of robust stabilizing modified repetitive control systems

In control system practice, high precision tracking or attenuation for periodic signals is an important issue. Repetitive control is known as an e.ective approach for such control problems. The internal model principle shows that the repetitive control system which contains a periodic generator in the closed-loop can achieve zero steady-state error for reference input or completely attenuate disturbance. Due to its simple structure and high control precision, repetitive control has been widely applied in many systems. To improve existing results on repetitive control theory, this thesis presents theoretical results in analysis and design repetitive control system. The main work and innovations are listed as follows: We propose a design method of robust stabilizing modi.ed repetitive controllers for multiple-input/multiple-output plants with uncertainties. The parameterization of all robust stabilizing modi.ed repetitive controllers for multiple-input/multiple-output plant with uncertainty is obtained by employing H∞ control theory based on the Riccati equation. The robust stabilizing controller contains free parameters that are designed to achieve desirable control characteristic. In addition, the bandwidth of low-pass .lter has been analyzed. In order to simplify the design process and avoid the wrong results obtained by graphical method, the robust stability conditions are converted to LMIs-constraint conditions by employing the delay-dependent bounded real lemma. When the free parameters of the parameterization of all robust stabiliz-ing controllers is adequately chosen, then the controller works as robust stabilizing modi.ed repetitive controller. For a time-varying periodic disturbances, we give an design method of an opti-mal robust stabilizing modi.ed repetitive controller for a strictly proper plant with time-varying uncertainties. A modi.ed repetitive controller with time-varying delay structure, inserted by a low-pass .lter and an adjustable parameter, is developed for this class of system. Two linear matrix inequalities LMIs-based robust stability con-ditions of the closed-loop system with time-varying state delay are derived for .xed parameters. One is a delay-dependent robust stability condition that is derived based on the free-weight matrix. The other robust stability condition is obtained based on the H∞ control problem by introducing a linear unitary operator. To obtain the desired controller, the design problems are converted to two LMI-constrained opti-mization problems by reformulating the LMIs given in the robust stability conditions. The validity of the proposed method is verified through a numerical example.学位記番号：工博甲46

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

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Identification of Nonlinear Parameter-Dependent Common-Structured models to accommodate varying experimental conditions and design parameter properties

This study considers the identification problem for a class of nonlinear parameter-varying systems associated with the following scenario: the system behaviour depends on some specifically prescribed parameter properties, which are adjustable. To understand the effect of the varying parameters, several different experiments, corresponding to different parameter properties, are carried out and different data sets are collected. The objective is to find, from the available data sets, a common parameter-dependent model structure that best fits the adjustable parameter properties for the underlying system. An efficient common model structure selection (CMSS) algorithm, called the extended forward orthogonal regression (EFOR) algorithm, is proposed to select such a common model structure. Several examples are presented to illustrate the application and the effectiveness of the new identification approach

Constructing an overall dynamical model for a system with changing design parameter properties

This study considers the identification problem for a class of non-linear parameter-varying systems associated with the following scenario: the system behaviour depends on some specifically prescribed parameter properties, which are adjustable. To understand the effect of the varying parameters, several different experiments, corresponding to different parameter properties, are carried out and different data sets are collected. The objective is to find, from the available data sets, a common parameter-dependent model structure that best fits the adjustable parameter properties for the underlying system. An efficient Common Model Structure Selection (CMSS) algorithm, called the Extended Forward Orthogonal Regression (EFOR) algorithm, is proposed to select such a common model structure. Two examples are presented to illustrate the application and the effectiveness of the new identification approach

Mathematical control of complex systems

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