A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Abstract

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Deposition of UF5 on the surface of steel material having oxide coating in contact with gaseous UF6

When UF6 is handled in leak tight system, the amount of uranium compound formed on the surface of containers, valves, and others in UF6 handling facilities is not so significant for a short term that special attention has not been given to this problem. The present work was done to throw some more light on this problem based on the recent experiment. We discuss the possibility that the intermolecular transfer of a fluorine atom from UF6 to UF5 may participate in the formation of uranium compound. The discussion includes also the unique features contained in the experimental result, the reaction processes assumed in this problem, and the derivation of a rate equation for expressing the deposition of uranium compound. Furthermore, we propose a new method for determining nonlinear parameters included in a governing differential equation having two variables for expressing the deposition of uranium compound from experimental raw data.     

On one boundary problem for nonlinear stationary controlled system

The object of study is nonlinear stationary controlled system of ordinary differential equations with constant disturbance in the right part. The problem of constructing the synthesising control function providing the transfer of this system from the initial state to the origin is considered. The sufficiently simple for numerical implementation algorithm of solution of the above-mentioned problem is obtained. It is shown that for local null controllability of the considered system, it is sufficient that the conditions of the Kalman's type were satisfied. In addition, the estimates restricting the choice of initial conditions and external disturbances under which the transfer is guaranteed are obtained. The main idea of the method of construction of the desired control function consists in reducing the original problem to stabilisation of a special kind linear non-stationary system and solving the Cauchy problem for an auxiliary system of ordinary differential equations closed by stabilising control. The simplicity of the realisation of this algorithm is determined by the construction of the auxiliary system and its stabilisation that could be obtained by analytical methods. The effectiveness of the method is illustrated by solving the problem of crane control and its numerical simulation.     

Delay compensated control of the Stefan problem and robustness to delay mismatch

This paper presents a control design for the one‐phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid‐solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first‐order hyperbolic partial differential equation (PDE), resulting in a cascaded transport‐diffusion PDE system defined on a time‐varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in the norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.     

Filtered adaptive constrained sampled-data control for uncertain multivariable nonlinear systems

A filtered adaptive constrained sampled-data controller for uncertain multivariable nonlinear systems in the presence of various constraints is synthesized in this paper. A piecewise constant adaptive law drives that estimation error dynamics to zero at each sampling time instant yields adaptive parameters. The filtered control scheme consists of two components. Based on an estimation/cancellation strategy, a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters, whereas a constraint violation avoidance control law is designed to solve an online constrained optimization problem. Although a reduced sampling time helps to minimize the estimation error caused by the neglect of unknowns, the resulting aggressive signals put more restrictions on the control law. Greater sacrifice of tracking performance is required to satisfy the constraints. The constraints violation avoidance control law is in favor of a larger sampling time. Sufficient conditions are given to guarantee the stability of the closed-loop system with the sampled-data controller, where the input/output signals are held constant over the sampling period. Numerical examples are provided to validate the theoretical results, comparisons between the constrained sampled-data controller and unconstrained adaptive controller with the implementation of different sampling times are carried out.     

Third order optical nonlinearities characteristics of Disperse Red1 organic dye molecules inside of polymeric nanocapsules

Measuring nonlinear optical response of a specific material in a mixture, not only leads to investigate the behavior of a particular component in various circumstances, but also can be a way to select suitable combination and optimum concentration of additives and therefore obtaining the maximum nonlinear optical signals. In this work, by using dual-arm Z-scan technique, the nonlinear refractive index of Disperse Red1 (DR1) organic dye molecules inside the core of prepared polymeric nanocapsules was measured among various materials which prepared nanocapsules were made of them. Then the measured value was compared with nonlinear refractive index of DR1 solved in dichloromethane.     

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

空间红外大口径折射式低温镜头设计与验证

针对目标探测类空间红外相机大范围成像、高灵敏度探测、高精度定位等应用需求,文中提出采用像方远心光路和低温光学技术结合的解决方案,设计了物方视场角8°×8°、入瞳口径265 mm、工作温度200 K的像方远心折射式光学系统。镜头最大口径280 mm,采用多级分散的弹性支撑设计,解决大口径低温透镜装框、透镜组件支撑和镜头整体安装各环节的热应力卸载问题。在保证高刚度和低漏热的情况下,使低温下透镜的热应力对镜头能量集中度的影响降低到可接受范围内。镜头完成装调及室温下像质确认后,进行了力学振动试验,并将其制冷到200 K水平测试像质,测试结果表明,镜头能量集中度达到轴上75%,边缘视场72%。     

重力坝模型的尺寸效应

利用两个不同比尺预制缝重力坝模型的试验成果，以有限元富集技术进行非线性断裂分析，建立了极限承载力和长度比尺的确定性尺寸效应公式。混凝土重力坝的断裂尺寸效应满足指数衰减关系，用三次指数衰减公式可以准确地预测原型的极限承载力。断裂过程区的相对长度是引起模型试验尺寸效应的主要原因。数值计算结果表明，断裂过程区相对长度不仅是与材料有关的参数，能否充分发展还取决于结构尺寸和几何形状；断裂过程区相对长度的尺寸效应不同于统计尺寸效应和断裂参数尺寸效应，具有尺寸范围效应。断裂过程区相对长度在小试件、大试件和相对无穷大试件的发展程度不同。