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.     

积分中值屈服准则解析厚板轧制椭圆速度场

为解决非线性Mises比塑性功率积分困难以及由此导致的轧制功率解析式难以获得的问题,本文通过建立并利用线性比塑性功率表达式对提出的椭圆速度场进行能量分析,得到了轧制力能参数的解析解.文中通过对变角度屈服函数求积分中值,构建了一个新的屈服准则,它是主应力分量的线性组合,在π平面上的轨迹是逼近Mises圆的等边非等角的十二边形,其基于Lode参数表达式的理论结果也与实验数据吻合较好.同时,根据厚板轧制时金属流动速度从入口到出口逐渐增大的特点,提出了水平速度分量满足椭圆方程的速度场,该速度场满足运动许可条件.通过相应的轧制能量分析,获得了基于线性屈服准则的内部变形功率以及基于应变矢量内积法上的摩擦功率与剪切功率.在此之上,通过泛函的极值变分导出了轧制力矩、轧制力以及应力状态系数的解析解,并与现场实测数据进行了对比,结果表明利用本文提出的屈服准则与速度场所建立的轧制力矩与轧制力模型与实测值吻合较好,其中轧制力误差小于5.3%,轧制力矩误差在6%左右.     

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.     

Hydrogenation process in multiphase alloys of Ti-Zr-Mn-V system on the example of Ti42.75Zr27Mn20.25V10 alloy

The influence of phase composition and microstructure of Ti_42.75Zr₂₇Mn_20.25V₁₀ alloy on its hydrogenation kinetic and phase composition of hydrogenated product was studied. It is established that the process of dissociation of hydrogen molecules begins on the surface of Laves phase crystallites. The dissolution of atomic hydrogen in the material volume leads to the formation of cracks in the intermetallic crystallites, which further appear as additional centers of dissociation of hydrogen molecules and noticeably accelerate the diffusion of hydrogen into the bulk material. It was shown that the Laves phase acts as a donor of atomic hydrogen for the BCC solid solution during hydrogenation of two-phase structure, initiating intensive hydrogenation of the BCC phase at room temperature.     

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.     

高强WSTi544221合金组织与性能研究

研究了轧制变形量对WSTi544221合金棒材显微组织和力学性能的影响,并对Φ10 mm规格的棒材进行不同制度的固溶+时效处理,对比了不同热处理状态下棒材的组织和力学性能。结果表明,随着轧制变形量的增大,WSTi544221合金棒材的晶粒细化程度增大,强度逐渐提高,但塑性变化不大。经870℃×1 h/WC+520℃×6 h/AC固溶+时效处理后,强度与塑性可以获得良好匹配,当抗拉强度达到1 610 MPa、屈服强度达到1 531 MPa时,延伸率和断面收缩率可分别保持在12%和43%。     

Stability and cytotoxicity study of NiFe2O4 nanocomposites synthesized by co-precipitation and subsequent thermal annealing

In this article, NiFe₂O₄ nanoparticles (NPs) were prepared by co-precipitation method with subsequent thermal annealing leading to obtainment NPs with average sizes of 78 nm. Structure and magnetic analysis were performed by X-ray diffraction, transmission electron microscopy, Mössbauer spectroscopy and vibrating sample magnetometry techniques. Stability of NiFe₂O₄ NPs was evaluated in PBS solution during 20 days. The toxicity of prepared NPs was evaluated in vitro using different cancer cell lines: HeLa (cervical cancer cell), PC-3 (prostate cancer cell). Fibroblasts like cells of L929 obtained from subcutaneous adipose tissue of mouse were used as normal cells. Results indicate successful synthesis of NiFe₂O₄ NPs that exhibit low cytotoxicity in concentration range from 1 to 100 μg/ml. Presented physical and biological results indicate the possibility of application investigated magnetic nanoparticles in hyperthermia, targeted drug delivery, magnetic resonance imaging or cell separation.     

Preparation of biaxially textured Ce1-x(Y0.2Zr0.8)xOδ buffer layers on RABiTS NiW tapes by chemical solution deposition

Highly (100)-oriented Ce_1-x(Y_0.2Zr_0.8)_xO_δ (CYZO) films were prepared on biaxially textured NiW substrates by a chemical solution deposition approach using metal inorganic salts as starting materials. It has been found that both the preferential orientation and surface roughness of CYZO films decrease gradually with increasing of the doping percentage of Y³⁺ and Zr⁴⁺ ions. The epitaxial growth relationship of (220)_CYZO//(200)_NiW and [00?l]_CYZO//[001]_NiW was demonstrated by XRD texture measurement as well as atomic resolution STEM observation. XRD, Raman and XPS spectra results indicate that Y³⁺ and Zr⁴⁺ ions were indeed introduced into CeO₂ lattice to substitute Ce⁴⁺ ions and form cubic fluorite CYZO solid solution. Moreover, CeO₂ buffer layer can be endowed a strong enough capability to prevent element diffusion through co-doping of yttrium and zirconium, provided that an optimal doping ratio of them is adopted. This will provide a new approach to fabricating strong-barrier single buffer layer for coated conductor.