Bridging the gap between the linear and nonlinear predictive control: Adaptations for efficient building climate control

The linear model predictive control which is frequently used for building climate control benefits from the fact that the resulting optimization task is convex (thus easily and quickly solvable). On the other hand, the nonlinear model predictive control enables the use of a more detailed nonlinear model and it takes advantage of the fact that it addresses the optimization task more directly, however, it requires a more computationally complex algorithm for solving the non-convex optimization problem. In this paper, the gap between the linear and the nonlinear one is bridged by introducing a predictive controller with linear time-dependent model. Making use of linear time-dependent model of the building, the newly proposed controller obtains predictions which are closer to reality than those of linear time invariant model, however, the computational complexity is still kept low since the optimization task remains convex. The concept of linear time-dependent predictive controller is verified on a set of numerical experiments performed using a high fidelity model created in a building simulation environment and compared to the previously mentioned alternatives. Furthermore, the model for the nonlinear variant is identified using an adaptation of the existing model predictive control relevant identification method and the optimization algorithm for the nonlinear predictive controller is adapted such that it can handle also restrictions on discrete-valued nature of the manipulated variables. The presented comparisons show that the current adaptations lead to more efficient building climate control.     

Multizone decomposition for simulation of time-dependent problems using the multiquadric scheme

This paper discusses the application of the multizone decomposition technique with multiquadric scheme for the numerical solutions of a time-dependent problem. The construction of the multizone algorithm is based on a domain decomposition technique to subdivide the global region into a number of finite subdomains. The reduction of ill-conditioning and the improvement of the computational efficiency can be achieved with a smaller resulting matrix on each subdomain. The proposed scheme is applied to a hypothetical linear two-dimensional hydrodynamic model as well as a real-life nonlinear two-dimensional hydrodynamic model in the Tolo Harbour of Hong Kong to simulate the water flow circulation patterns. To illustrate the computational efficiency and accuracy of the technique, the numerical results are compared with those solutions obtained from the same problem using a single domain multiquadric scheme. The computational efficiency of the multizone technique is improved substantially with faster convergence without significant degradation in accuracy.     

Computational simulation of transient blast loading on three-dimensional structures

A computing technique is described for the numerical solution of three-dimensional, time-dependent fluid dynamic problems with irregularly shaped and movable boundaries (or internal obstacles) confining the flow. This paper presents in detail the method used in treating the three-dimensional boundary conditions. The numerical solution technique for the full nonlinear Navier-Stokes equations has been presented elsewhere. The general method is illustrated here through comparison of computed surface pressure time histories with the corresponding experimental data for a plane-shock wave (5 psi overpressure) passing over a rectangular parallelepiped.     

Nonlinear transient response of isotropic circular plates

The present work investigates the nonlinear transient response for stresses and deflection of thin linear elastic circular plates subjected to different time-dependent loads. Space-wise discretisation has been done using collocation method with the zeros of a Chebyshev polynomial as collocation points. Newmark-β scheme has been used for time-marching. Time and space-wise convergence studies have been carried out. Both the linear and nonlinear transient response of clamped and simply supported circular plates under six different sets of transient loads have been obtained. Several new useful results are reported in the present study.     

基于非线性卡尔曼平滑的GPS定位估计方法

在GPS单机定位中,通常采用卡尔曼滤波作为位置状态解算的方法.文中提出一种将非线性平滑技术用于GPS定位估计的方法,该方法可用于单机GPS接收机的定位解算,在非线性滤波的基础上进一步提高定位精度.提出一种随接收卫星数量而实时改变测量参数的动态测量模型,根据GPS的伪距、多普勒频移和导航信息等原始数据进行定位模型的解析,运用新型的平淡卡尔曼平滑算法求解该动态模型.GPS定位实验结果表明,与通用的最小二乘迭代法和非线性滤波等方法获得的结果相比,所提出的方法能获得更高的定位精度.     

Looping behavior of arches using corotational finite element

Buckling of arches is studied using a corotational finite element model in conjunction with a modified Riks-Wempner technique. The corotational formulation allows for separation of rigid body displacements from deformation displacements of the element. The program can equally be applied to rigid or prestressed arches, as it takes into account the sequential fabrication of stressed (i.e. prebuckled) arches. Looping paths tracing nonlinear response of arches have been successfully obtained for several cases, including rigid and prestressed elastica arches with both symmetric and asymmetric modes of buckling. Comparisons are made with the results for prestressed arches using shooting method, and with the benchmark results for various rigid arches using discrete element method. When compared to a discrete element technique, the present method appears to be more cost-effective, as a finite element mesh with 60% fewer elements can result in virtually the same degree of accuracy.     

$H_{infty} $ Filter Design for Nonlinear Systems With Time-Delay Through T–S Fuzzy Model Approach

This paper is concerned with the H_infin filter design for nonlinear systems with time-varying delay via Takagi-Sugeno fuzzy model approach. Delay-dependent design method is proposed in terms of linear matrix inequalities (LMIs), which forms the main contribution of this paper. The main technique used is the free-weighting matrix method combined with a matrix decoupling approach. The results for rate-independent case, delay-independent case, and delay-free case are also given as easy corollaries. An illustrative example is given to show the effectiveness of the present method.     

Constructive Tool for Orbital Stabilization of Underactuated Nonlinear Systems: Virtual Constraints Approach

We present a constructive tool for generation and orbital stabilization of periodic solutions for underactuated nonlinear systems. Our method can be applied to any mechanical system with a number of independent actuators smaller than the number of degrees of freedom by one. The synthesized feedback control law is nonlinear and time-dependent. It is derived from a feedback structure that explicitly uses the general or full integral of the systems zero dynamics. The control law generates a periodic solution and makes it exponentially orbitally stable.     

A numerical study of primary instability on viscous high-speed jets

A fully nonlinear model incorporating a weak viscous treatment has been developed to assess the time-dependent evolution of an axisymmetric liquid jet using a boundary element method. Prior research has indicated the importance of the boundary layer structure at the orifice exit plane in generating instabilities just downstream of the injection point. By focusing on the boundary layer instability mechanism, simulations are compared against the experimental results and linear theory. In order to assess viscous effects, the weak viscous method of Lundgren and Mansour is utilized and various parametric studies are performed. Results show that the boundary layer thickness is the dominant factor affecting the nonlinear wave growth near the exit plane of the orifice. Viscosity and surface tension are shown to play minor roles in the initial primary instability. The most unstable wavelength calculated by the model matches linear boundary layer instability theory reasonably well.     

Reduced-order modeling of weakly nonlinear MEMS devices with Taylor-series expansion and Arnoldi approach

In this paper, we present a new technique by combining the Taylor series expansion with the Arnoldi method to automatically develop reduced-order models for coupled energy domain nonlinear microelectromechanical devices. An electrostatically actuated fixed-fixed beam structure with squeeze-film damping effect is examined to illustrate the model-order reduction method. Simulation results show that the reduced-order nonlinear models can accurately capture the device dynamic behavior over a much larger range of device deformation than the conventional linearized model. Compared with the fully meshed finite-difference method, the model reduction method provides accurate models using orders of magnitude less computation. The reduced MEMS device models are represented by a small number of differential and algebraic equations and thus can be conveniently inserted into a circuit simulator for fast and efficient system-level simulation.     

Output tracking control of MIMO fuzzy nonlinear systems using variable structure control approach

The output tracking control problem for nonlinear systems in the presence of both parameter perturbations and external disturbances is studied. Our approach is based on the Takagi-Sugeno (T-S) fuzzy modeling method and a variable structure control (VSC) technique. Therefore, the systems considered are not and need not be in the triangular and parametric strict-feedback form, which are prevalent among adaptive model following control for nonlinear systems, or in the normal form, which pervades almost all existing results in neuro-fuzzy model following control approach. We first study the problem of stabilization of T-S fuzzy systems by using a VSC technique. A method for the design of a switching surface based on linear matrix inequalities is developed and a stabilizing controller based on a reaching law concept in the presence of both parameter perturbations and external disturbances is proposed. Then, the method is extended to design controllers for output tracking of T-S fuzzy nonlinear systems in two cases, i.e. systems which possess the so-called strong passive subsystems and strong stable zero dynamics, respectively. Finally, illustrative examples are presented to demonstrate the whole design procedure from the original nonlinear systems to their fuzzification and finally to the realization of the desired controllers. Simulation results show that the goal of output tracking can be achieved by the proposed controllers.     

Nonlinear circuit analysis using the method of harmonic balance—A review of the art. Part I. Introductory concepts

The harmonic balance method is a technique for the numerical solution of nonlinear analog circuits operating in a periodic, or quasi-periodic, steady-state regime. The method can be used to efficiently derive the continuous-wave response of numerous nonlinear microwave components including amplifiers, mixers, and oscillators. Its efficiency derives from imposing a predetermined steady-state form for the circuit response onto the nonlinear equations representing the network, and solving for the set of unknown coefficients in the response equation. Its attractiveness for nonlinear microwave applications results from its speed and ability to simply represent the dispersive, distributed elements that are common at high frequencies. The last decade has seen the development and application of harmonic balance techniques to model analog circuits, particularly microwave circuits. The first part of this paper reviews the fundamental achievements made during this time. The second part covers the extension of the method to quasi-periodic regimes, optimization analysis, and practical application. A critical assessment of the various types of harmonic balance techniques is given. The different sampling and Fourier transform methods are compared, and numerical speed and precision results are given enabling a quantitative analysis of the merits of the major variants of the harmonic balance technique. Examples of designs which have been modeled using the harmonic balance technique and built both in hybrid and MMIC form are presented.     

Numerical simulation of the active magnetic regenerator

A time-dependent one-dimensional model of the active magnetic regenerator (AMR) that takes into account most of the physical and practical design problems for the AMR is developed as a highly nonlinear system of partial differential equations. The adequateness of the model is tested in the case where there is no magnetization or demagnetization, which is the so-called passive regenerator (PR), through numerical experiments and comparison with experimental results. Highly dependable approximation functions for the physical properties of the heat transfer fluid (water) and the heat capacity of the magnetic material (gadolinium) are obtained by using the least squares curve and surface fitting techniques. The technique of calculation of values of the thermo-magnetic function of the magnetic material through the values of the adiabatic temperature change of the material is worked out and an approximation surface for the adiabatic temperature change of the material is obtained. The numerical scheme for the computer simulations of the active magnetic regenerator is developed and its performance analyzed for stability and convergence.     

Tracking control by the Newton–Raphson method with output prediction and controller speedup

This paper presents a control technique for output tracking of reference signals in continuous-time dynamical systems. The technique is comprised of the following three elements: (i) a fluid-flow version of the Newton–Raphson method for solving algebraic equations, (ii) a system-output prediction which has to track the future reference signal, and (iii) a speedup of the control action for enhancing the tracker's accuracy and, in some cases, stabilizing the closed-loop system. The technique can be suitable for linear and nonlinear systems, implementable by simple algorithms, and can track reference points as well as time-dependent reference signals. Though inherently local, the tracking controller is proven to have a global convergence for a class of linear systems. The derived theoretical results of the paper include convergence of the tracking controller and error analysis, and are supported by illustrative simulation and laboratory experiments.     

An efficient split-step compact finite difference method for the coupled Gross–Pitaevskii equations

ABSTRACT

In this study, we propose an efficient split-step compact finite difference (SSCFD) method for computing the coupled Gross–Pitaevskii (CGP) equations. The coupled equations are divided into two parts, nonlinear subproblems and linear ones. Commonly, the nonlinear subproblems could be integrated directly and accurately, but it fails when the time-dependent potential cannot be integrated exactly. In this case, the midpoint and trapezoidal rules are applied approximately. At the same time, the split order is not reduced. For the linear ones, compact finite difference cannot be designed directly. To circumvent this problem, a linear transformation is introduced to decouple the system, which can make the split-step method be used again. Additionally, the proposed SSCFD method also holds for the coupled nonlinear Schrödinger (CNLS) system with time-dependent potential. Finally, numerical experiments for CGP equations and CNLS equations are well simulated, conservative properties and convergence rates are demonstrated as well. It is shown from the numerical tests that the present method is efficient and reliable.     

基于Volterra模型的预测控制及应用

由于工业实践的需要,非线性预测控制近年来受到广泛地关注.Volterra模型是一类特殊的非线性模型,非常适合描述工业过程中的无记忆非线性对象.传统的基于Volterra模型的控制器合成法及迭代计算预测控制器法计算量大,且不便于处理控制约束.非线性模型预测控制求解是典型的非线性规划问题,序列二次规划(sequential quadratic program,SQP)算法是求解非线性规划问题常用方法之一.针对Volterra非线性模型预测控制求解问题,本文将滤子法与一种信赖域SQP算法相结合,提出一种改进SQP算法用于基于非线性Volterra模型的带控制约束的多步预测控制求解,并分析了所提方法的收敛性.工业实例仿真结果证实了所提方法的可行性与有效性.     

Bias detection and estimation in dynamic data reconciliation

A method for detection and estimation of measurement bias in nonlinear dynamic processes is presented. It employs model-based data reconciliation and requires the examination of the resulting difference between the measured and reconciled values. Since bias is commonly present in process measurements, this technique is an important step toward the ultimate goal of reconciling ‘raw’ process data that may contain bias and gross errors in addition to small random errors. A CSTR example shows that this method does allow for the detection of a single bias in a nonlinear dynamic process whether or not the exact model equations are known.     

The time-dependent rural postman problem: polyhedral results

The Chinese postman problem is a famous and classical problem in graph theory. This paper introduces a new variant of this problem, namely, the time-dependent rural postman problem, which is motivated by applications, involving scheduling with time-dependent processing time. We present an arc-path formulation for the problem with a constraint set that is divided into two parts. The first part is linear and has a strong combinatorial structure, which defines the polytope of the arc-path alternation sequence (APAS), while the second part is nonlinear and is closely related to time-dependent travel time. First, we investigate the facial structure of the APAS polytope and present several facet inequalities. Second, considering the travel and service time functions as piecewise functions, we linearize the nonlinear inequalities and propose several strong, valid inequalities. Finally, we propose a cutting plane algorithm and report numerical results on several randomly generated instances.     

Design of Observer-Based $H_infty$ Control for Fuzzy Time-Delay Systems

This paper addresses the problem of observer-based H_infin control for nonlinear systems with time-varying delay represented by Takagi-Sugeno (T-S) fuzzy model. It presents a single-step linear matrix inequality (LMI) method for the fuzzy control design, which overcomes the drawback of the two-step LMI approach often encountered in the literature. The derivation relies mainly on a proposed matrix decoupling technique using which a resultant matrix inequality can be equivalently converted to strict LMIs. When restricted to delay-free fuzzy systems, the present results improve or reduce to existing ones. Illustrative examples show the effectiveness and merits of the present results.     

Nonlinear analysis of an axisymmetric shell using three noded degenerated isoparametric shell elements

An updated Lagrangian formulation of a quadratic degenerated isoparametric shell element is presented for geometrically nonlinear elasto-plastic shell problems. A finite rotation effect is included in the formulation by adopting a co-rotational scheme. The load stiffness matrix has been derived for the treatment of a pressure load. For elasto-plastic behavior, the layered element model is used. The Newton-Raphson iteration method is employed to solve incremental nonlinear equations. For tracking of post-buckling behavior, the work control method is taken into account. Verification of the present technique is obtained by analyzing the available reference problems. Good correlations between the computed results and referenced data can be drawn.