Robust model predictive control of Wiener systems

Block-oriented models (BOMs) have shown to be appealing and efficient as nonlinear representations for many applications. They are at the same time valid and simple models in a more extensive region than time-invariant linear models. In this work, Wiener models are considered. They are one of the most diffused BOMs, and their structure consists in a linear dynamics in cascade with a nonlinear static block. Particularly, the problem of control of these systems in the presence of uncertainty is treated. The proposed methodology makes use of a robust identification procedure in order to obtain a robust model to represent the uncertain system. This model is then employed to design a model predictive controller. The mathematical problem involved in the controller design is formulated in the context of the existing linear matrix inequalities (LMI) theory. The main feature of this approach is that it takes advantage of the static nature of the nonlinearity, which allows to solve the control problem by focusing only in the linear dynamics. This formulation results in a simplified design procedure, because the original nonlinear model predictive control (MPC) problem turns into a linear one.     

LTI approximation of nonlinear systems via signal distribution theory

L₂ and L₁ optimal linear time-invariant (LTI) approximation of discrete-time nonlinear systems, such as nonlinear finite impulse response (NFIR) systems, is studied via a signal distribution theory motivated approach. The use of a signal distribution theoretic framework facilitates the formulation and analysis of many system modelling problems, including system identification problems. Specifically, a very explicit solution to the L₂ (least squares) LTI approximation problem for NFIR systems is obtained in this manner. Furthermore, the L₁ (least absolute deviations) LTI approximation problem for NFIR systems is essentially reduced to a linear programming problem. Active LTI modelling emphasizes model quality based on the intended use of the models in linear controller design. Robust stability and LTI approximation concepts are studied here in a nonlinear systems context. Numerical examples are given illustrating the performance of the least squares (LS) method and the least absolute deviations (LAD) method with LTI models against nonlinear unmodelled dynamics.     

直线伺服系统非线性自适应鲁棒控制器的优化设计

对永磁直线电动机伺服系统提出了非线性自适应鲁棒控制器的优化设计方法.在系统非线性数学模型的基础上,建立了误差系统的动态模型.将跟踪和干扰抑制归结为非线性自适应鲁棒控制器的设计问题,通过构造存储函数得到自适应鲁棒控制器的定理,以及电阻和电感的辨识算法.证明了定理给出的控制器能满足干扰抑制和系统渐近稳定,并用遗传算法对控制器的参数进行优化.仿真结果验证了该方法是有效的.     

一类新型神经网络模型及其控制器设计

提出一种新型神经网络模型(HNM)。此模型是一种本质非线性模型，但可以应用线性控制理论的成果来设计稳定的控制器，并且模型中的连接权系数有各自的物理意义，可以通过经验来确定其初始值。同时通过分析对角矩阵的稳定性，给出了基于HN模型的控制器的设计方法及稳定性证明。仿真结果表明HN模型的有效性及控制器的优良性能。     

An Indirect Adaptive Fuzzy Control Scheme for a Class of Nonlinear Systems

This paper presents an indirect adaptive control scheme, for a class of nonlinear systems in controller canonical form. Owing to the universal approximation property of a Takagi–Sugeno (T–S) fuzzy model, controller design is simplified by utilizing the T–S fuzzy model representation of a nonlinear system. An adaptation mechanism ensures that the estimator model asymptotically follow the actual T–S fuzzy model and thus removes the need of any a priori identification of the T–S fuzzy model of the system. The overall controller gain is a convex combination of the local linear gains which vary adaptively to ensure the convergence of the tracking error. Preliminary simulation results indicate the potential of the proposed method.     

Application of gap metric to model bank determination in multilinear model approach

This paper presents a gap metric based method which aims to perform the operating range decomposition and the minimum linear model bank determination of a nonlinear system when multilinear model approach is employed to design a controller for this nonlinear system. For a prescribed distance level, the minimum linear model bank determined by the proposed method can provide sufficient information for multilinear model controller design of the nonlinear system. To illustrate the usefulness of the proposed method, two examples of nonlinear systems are presented. Moreover, a mixed logical dynamical model-based MPC (MLD–MPC) controller is designed based on the minimum model bank. Simulations confirm the method for selecting linear model bank in multilinear model approach.     

Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method

In this study, we present a Takagi–Sugeno (T–S) fuzzy model for the modeling and stability analysis of oceanic structures. We design a nonlinear fuzzy controller based on a parallel distributed compensation (PDC) scheme and reformulate the controller design problem as a linear matrix inequalities (LMI) problem as derived from the fuzzy Lyapunov theory. The robustness design technique is adopted so as to overcome the modeling errors for nonlinear time-delay systems subject to external oceanic waves. The vibration of the oceanic structure, i.e., the mechanical motion caused by the force of the waves, is discussed analytically based on fuzzy logic theory and a mathematical framework. The end result is decay in the amplitude of the surge motion affecting the time-delay tension leg platform (TLP) system. The feedback gain of the fuzzy controller needed to stabilize the TLP system can be found using the Matlab LMI toolbox. This proposed method of fuzzy control is applicable to practical TLP systems. The simulation results show that not only can the proposed method stabilize the systems but that the controller design is also simplified. The effects of the amplitude damping of the surge motion on the structural response are obvious and work as expected due to the control force.     

Linear control of nonlinear systems based on nonlinearity measures

In reality, virtually every process is a nonlinear system. Nevertheless, linear controller design methods have proved to be adequate in many applications. In practice, the linear controller design is usually done disregarding a possible nonlinear plant/linear model mismatch. In this work we introduce a general framework for the development of linear controllers for nonlinear systems based on nonlinearity measures. Nonlinearity measures are tools to assess the extent of a system’s inherent nonlinearity instead of just recognizing a system as being linear or nonlinear. Recent work shows that nonlinearity measures characterize the magnitude of the modeling error when an optimal linear model is used for the nonlinear system. The best linear model can then be used to design a linear controller that robustly stabilizes the linear system in presence of the nonlinear modeling error. A crucial point is that both, the best linear model and the modeling error, are determined for a specified region of operation, thus significantly increasing the class of applicable nonlinear systems. Examples demonstrate the (necessity and) effectiveness of the proposed approach.     

A novel on-line OCID method and its application to input-constrained active fault-tolerant tracker design for unknown nonlinear systems

ABSTRACT

The existing off-line observer/controller identification (OCID) method for linear systems is newly extended in this paper for off-line/on-line identification of known/unknown highly nonlinear systems, and a new input-constrained active fault-tolerant tracker is developed, based on the identified linear models. The advantages of the proposed extended on-line OCID method for linear/nonlinear systems are briefly described as follows: (i) Implement novel servo-control-oriented off-line OCID methods in observer and controller canonical forms for highly nonlinear systems; (ii) Is able to overcome the discontinuity induced by the singular value decomposition (SVD) that should be carried out at each sampling instant; (iii) It directly realises the identified parameters in the observer/controller canonical forms; this simplifies the identification process; (iv) Can be practically implemented for the on-line control of an unknown nonlinear system which was constituted by an unknown open-loop plant, an existing but unknown controller and/or an unknown observer; and (v) Can be utilised to develop a new active fault-tolerant controller to compensate the immovable existing controller of the practical operating system. Finally, the servo-control-oriented off-line OCID method for the highly nonlinear PUMA 560 manipulator is shown in the illustrative examples to demonstrate the superiority of the proposed method.     

Real-time design of an adaptive nonlinear predictive controller

Based on real-time identification and using the concept of NARX (Nonlinear AutoRegressive with exogenous inputs) models, a new adaptive nonlinear predictive controller (ANPC) design is proposed. NARX models represent a natural way to describe the input-output relationship of severely nonlinear systems. From an initial batch of input-output data, a parsimonious NARX model is obtained using the Modified Gram-Schmidt (MGS) orthogonalization algorithm. Following this initial off-line identification and model reduction procedure, the control loop is closed. The ANPC directly uses the obtained structure and initial parameter estimates, which are updated each time step using recursive identification. The controller is designed similar to a typical linear predictive controller based on solving a nonlinear programming (NLP) problem. This paper shows how to solve this NLP problem on-line without the knowledge of the NARX model structure. The design is given for the multi-input multi-output (MIMO) case.     

On linear models for nonlinear systems

Best linear time-invariant (LTI) approximations are analysed for several interesting classes of discrete nonlinear time-invariant systems. These include nonlinear finite impulse response systems and a class of nonsmooth systems called bi-gain systems. The Fréchet derivative of a smooth nonlinear system is studied as a potential good LTI model candidate. The Fréchet derivative is determined for nonlinear finite memory systems and for a class of Wiener systems. Most of the concrete results are derived in an ?_∞ signal setting. Applications to linear controller design, to identification of linear models and to estimation of the size of the unmodelled dynamics are discussed.     

Fuzzy network model-based fuzzy state controller design

The performance of model-based controller design relies heavily on the quality and suitability of the utilized process model. This contribution proposes a fuzzy network based nonlinear controller design methodology. Fuzzy networks are a model approach combining high approximation quality with high interpretability. The input/output (I/O) models commonly used for identification are transformed to fuzzy state-space models. Transferring and adjusting methods from linear state-space theory a control concept consisting of a fuzzy state controller and an adaptive set-point filter for nonlinear dynamic processes is deduced. The capability of the method is demonstrated for a hydraulic drive     

Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems

This paper presents a switching fuzzy controller design for a class of nonlinear systems. A switching fuzzy model is employed to represent the dynamics of a nonlinear system. In our previous papers, we proposed the switching fuzzy model and a switching Lyapunov function and derived stability conditions for open-loop systems. In this paper, we design a switching fuzzy controller. We firstly show that switching fuzzy controller design conditions based on the switching Lyapunov function are given in terms of bilinear matrix inequalities, which is difficult to design the controller numerically. Then, we propose a new controller design approach utilizing an augmented system. By introducing the augmented system which consists of the switching fuzzy model and a stable linear system, the controller design conditions based on the switching Lyapunov function are given in terms of linear matrix inequalities (LMIs). Therefore, we can effectively design the switching fuzzy controller via LMI-based approach. A design example illustrates the utility of this approach. Moreover, we show that the approach proposed in this paper is available in the research area of piecewise linear control.     

Observer-based dynamic surface control for a class of nonlinear systems: an LMI approach

This note presents a new analysis method to design an observer-based dynamic surface controller (ODSC) for a class of nonlinear systems. While the separation principle from linear system theory does not generally hold for nonlinear systems, a separation principle for the ODSC systems will be shown for a class of nonlinear systems, thus enabling the independent design of the observer and DSC. Furthermore, a convex optimization problem to test quadratic stability of ODSC will be formulated later.     

基于神经网络补偿的非线性时滞系统时滞正反馈控制

A new adaptive time-delay positive feedback controller (ATPFC) is presented for a class of nonlinear time-delay systems. The proposed control scheme consists of a neural networks-based identification and a time-delay positive feedback controller. Two high-order neural networks (HONN) incorporated with a special dynamic identification model are employed to identify the nonlinear system. Based on the identified model, local linearization compensation is used to deal with the unknown nonlinearity of the system. A time-delay-free inverse model of the linearized system and a desired reference model are utilized to constitute the feedback controller, which can lead the system output to track the trajectory of a reference model. Rigorous stability analysis for both the identification and the tracking error of the closed-loop control system is provided by means of Lyapunov stability criterion. Simulation results are included to demonstrate the effectiveness of the proposed scheme.     

基于虚拟模型的自适应解耦抗扰控制

针对一类多变量非线性耦合系统,提出了一种基于虚拟模型的非线性自适应控制器.首先将非线性系统线性化处理并将其作为虚拟模型,对该模型设计线性自适应控制律.然后将线性控制律分别应用在虚拟系统和受控的实际非线性系统上,根据两者的输出误差设计补偿控制律,以达到对实际被控对象进行自适应解耦抗扰的目的.利用李雅普诺夫稳定理论给出了控制系统稳定性条件.实验仿真验证了控制算法的有效性.     

An Internal-Model Controller for a Class of Single-Input Single-Output Nonlinear Systems: Stability and Robustness

A controller design procedure for a class of nonlinear systems is presented. The structure of the control system corresponds to the so-called internal-model controller that, for linear systems, has exhibited good performance and stability robustness with respect to disturbances and to uncertainty in the plant parameters. The systems involved are single-input single-output and fully linearizable by coordinates transformation and state feedback. It is shown that the plant output converges to a constant reference, even under the presence of constant disturbances and parameter uncertainties, provided the closed-loop system has an asymptotically stable equilibrium point placed anywhere. This scheme does not need an explicit design of a nonlinear observer; instead, it uses the state of a plant model. A conservative stability robustness margin is estimated by applying standard results of Lyapunov theory.