陈述式基于方程仿真模型的约简

为解决复杂多领域连续系统的高效仿真问题,研究了陈述式基于方程仿真模型的约简策略.基于符号处理技术,提出了一种模型约简方法.该方法从方程的规范转换入手,通过消除特定形式方程缩减系统规模,将整个方程系统规划分解为一个可顺序求解的子系统序列.给出的实例表明文中约简方法效果显著.文中策略与算法已在多领域物理系统混合建模与仿真平台EMWorks中实现.     

An output feedback precompensator for nonlinear DAE systems with control-dependent state-space

This note considers singular systems of nonlinear differential and algebraic equations (DAEs) whose constrained state space depends on the control inputs. A state-space realization of such systems cannot be derived independently of the controller design. An output feedback precompensator is derived, which results in a modified DAE system whose state-space is invariant under any feedback control law and can be used for output feedback controller synthesis. Its application is illustrated by a nonlinear electrical circuit example.     

Robust nonlinear control of spacecraft formation flying using constraint forces

A robust nonlinear control method is presented for spacecraft precise formation flying.With the constraint forces and consid-ering nonlinearity and perturbations,the problem of the formation keeping is changed to the Lagrange systems with the holonomic constraints and the differential algebraic equations (DAE).The nonlinear control laws are developed by solving the DAE.Because the traditional numerical solving methods of DAE are very sensitive to the various errors and the resulting con-trol laws are not ro...     

Symbolic manipulation techniques for model simplification in object-oriented modelling of large scale continuous systems

In the present work, techniques for the symbolic manipulation of general nonlinear differential algebraic equation (DAE) systems are presented, and used for model simplification purposes, to support efficient simulation of large scale continuous systems in an object-oriented modelling environment. The specific problems addressed are efficient elimination of trivial equations by means of substitution, system block lower triangular (BLT) partitioning, and tearing, i.e. hiding of algebraic variables. Moreover, the weakening heuristic criterion for decoupling of large systems, via dynamic approximation, is studied. All these techniques have been successfully implemented and tested in MOSES (modular object-oriented software environment for simulation), in order to define a complete model simplification process. The results achieved by applying the discussed algorithms and criteria on serial multibody systems are illustrated. A brief overview on further known symbolic manipulation techniques is also given, comparing them with the proposed ones, throughout the paper.     

Symbolic preprocessing for simulation of PDE models of chemical processes

First principle modeling of chemical processes very often leads to a mixed system of partial differential equations (PDEs) and differential algebraic equations (DAEs) which must be preprocessed for use in standard DAE numerical simulation or optimization tools. This contribution presents the symbolic preprocessing tool SyPProT developed for the simulation environment Diva in order to apply DAE numerics also to PDEs. The method-of-lines (MOL) approach for the required PDE discretization is implemented in SyPProT by configurable finite-difference and finite-volume schemes. The model as well as the MOL parameters are represented in a tailor-made Mathematica data structure (MDS). The preprocessing of a PDE model is illustrated by the example of a circulation-loop-reactor (CLR).     

基于接触碰撞理论的锭子动力学仿真研究及实践

为减小锭杆顶端振幅对纺纱质量的影响，分析了基于接触碰撞理论的锭子动力学仿真中的分离－接触－碰撞三状态，建立了非变形经典碰撞模型和接触变形模型。建立切换点判定方程计算状态切换点，求解动力学微分方程以获得接触力和碰撞冲量作为失空输入求得模态振型和不平衡响应。比较两类多体动力学仿真结果，提出用碰撞耗能来研究锭子振动控制问题的方法。     

MBS Approach to Generate Equations of Motions for HiL-Simulations in Vehicle Dynamics

Numerical simulation of system dynamics is today a standard in the design of cars and trucks. The multibody system (MBS) analysis is applied to suspension kinematics and compliant kinematics, handling performance and ride comfort as well as to the generation of load data for lifetime prediction. These simulation tasks are carried out as an off-line simulation. Over the last couple of years the MBS method has been established in the real-time simulation domain, typically for the design of vehicle control systems and the test of electronic control units, using Hardware-in-the-Loop (HiL) simulation. This paper shows how the transition from offline multi-body-system (MBS) models to real-time simulation can be achieved automatically by using a component oriented reduction procedure for vehicle suspensions, which keeps the full component parameterization. This necessitates a transformation of the equations of motion from differential algebraic equations (DAE) into ordinary differential equations (ODE). For use in HiL-simulators the equations of motion with open interfaces of the applied forces and torques are provided to be integrated in a modular dynamic ride model. The work has been carried out during the employment of the author at INTEC GmbH, Argelsrieder Feld 13; 82234 Wessling, Germany; e-mail: intec@simpack.de     

基于简化ASM1模型的污水处理厂曝气系统优化控制

本文建立了基于ASM1模型的曝气系统简化数学模型,在此基础上提出了以曝气能量消耗最小为目标函数的曝气系统优化控制问题。采用联立配置法进行优化问题的求解,把非线性微分代数方程组的DAE系统转化为非线性代数方程组,将动态优化问题转化为非线性规划问题,最后调用IPOPT解法器求解。在动态入水的条件下进行曝气池的优化控制仿真,其结果显示比传统定值PID控制可节约近40%的能耗。     

面向性能仿真的非连续微分代数模型的指标分析

针对物理系统性能仿真形成的非连续高指标微分代数模型,提出一种基于加权二部图的指标转换方法．该方法将微分代数系统表示为加权二部图,基于二部图匹配算法可以判定微分代数系统是否为高指标系统．对于高指标系统,采用文中方法可以找出需要求导的最小结构奇异方程子集,以便将高指标系统转换为低指标形式．最后,针对定结构与变结构的非连续微分代数模型给出了相应的指标分析策略．文中策略与相关算法已在基于Modelica语言的建模仿真平台MWorks上实现．     

Semi‐Global Robust Output Regulation for A Class of Singular Nonlinear Systems with Unknown Algebraic Equations

This paper considers semi‐global robust output regulation problem for a class of singular nonlinear systems whose algebraic equations are not precisely known. Since the algebraic equations are not known, the output regulation problem of singular nonlinear systems cannot be solved by directly reducing the singular nonlinear system into a normal nonlinear system. Based on internal model principle, we convert the robust output regulation problem of singular nonlinear systems into a robust stabilization problem of an augmented singular nonlinear system. The augmented singular nonlinear system is also with unknown algebraic equations. However, without transforming the singular nonlinear system into a normal nonlinear system, it is shown that the augmented singular nonlinear system can be semi‐globally stabilized by a high gain output feedback control law under some reasonable assumptions. Moreover, the semi‐global stabilization control law of the augmented singular nonlinear systems also solves the semi‐global robust output regulation problem of the original singular nonlinear system.     

Frequency limited Gramians-based structure preserving model order reduction for discrete time second-order systems

A new technique for frequency limited model order reduction of discrete time second-order systems is presented. Discrete time frequency limited Gramians (DFLGs) and corresponding discrete algebraic Lyapunov equations are developed. An efficient technique for the computation of DFLGs and their Cholesky factors is presented. Computed DFLGs are partitioned to obtain position and velocity Gramians. These Gramians are balanced with different combinations to obtain various balanced transformations that yield Hankel singular values (HSVs) for order reduction. Frequency limited discrete time balanced truncation framework is proposed and truncation based on magnitudes of HSVs is applied to obtain the reduced order model. Moreover, stability conditions for reduced order models are stated. Results of the proposed technique are compared with infinite Gramians balancing scheme in order to certify the usefulness of the presented technique for frequency limited applications.     

Sign analysis technique for predicting system behavior

Sign analysis is a technique for deriving the behavior of a system when it is subjected to a disturbance. the technique is for systems whose mathematical models are of the form of algebraic equations. the technique is based on generating sign combinations of total differentials of system parameters in table form from closed form algebraic functions which model the system. Sign combinations are then analyzed to predict system behavior with respect to a disturbance from the equilibrium state. the technique may be applied to total differentials of gains as well. © 1992 John Wiley & Sons, Inc.     

On output feedback stabilization of Euler-Lagrange systems with nondissipative forces

This paper provides a solution to the problem of output feedback stabilization of systems described by Euler-Lagrange equations perturbed by nondissipative forces. This class of forces appears in some applications where we must take into account the interaction of the system with its environment. The nonlinear dependence on the unmeasurable part of the state and the loss of the fundamental passivity property render most of the existing results on stabilization of nonlinear systems unapplicable to this problem. The technique we use consists of finding a dynamic output feedback controller and a nonlinear change of coordinates such that the closed loop can be decomposed as a cascade of an asymptotically stable system and an input-to-state stable system. This should be contrasted with the well-known passivity-based technique that aims at a feedback interconnection of passive systems. We believe this design methodology to be of potential applicability to other stabilization problems where passivity arguments are unapplicable.     

Asymptotic rejection of unknown sinusoidal disturbances in nonlinear systems

This paper deals with global disturbance rejection of nonlinear systems. The disturbance is assumed to be sinusoidal with completely unknown phases, amplitude, and frequencies, but the number of distinct frequencies or the order of the corresponding unknown linear exosystem is known. Different from the common structural assumptions of nonlinear systems needed in literature for disturbance rejection of nonlinear systems, the proposed method only requires the information of control design with a known Lyapunov function when the system is disturbance-free, and a mild assumption needed for internal model design. The proposed disturbance rejection algorithm extends complete global rejection of unknown sinusoidal disturbances for nonlinear dynamic systems beyond the common nonlinear models such as the strict feedback forms and the output feedback forms.     

A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation

This paper presents a numerical solution for solving a nonlinear 2-D optimal control problem (2DOP). The performance index of a nonlinear 2DOP is described with a state and a control function. Furthermore, dynamic constraint of the system is given by a classical diffusion equation. It is preferred to use the Ritz method for finding the numerical solution of the problem. The method is based upon the Legendre polynomial basis. By using this method, the given optimisation nonlinear 2DOP reduces to the problem of solving a system of algebraic equations. The benefit of the method is that it provides greater flexibility in which the given initial and boundary conditions of the problem are imposed. Moreover, compared with the eigenfunction method, the satisfactory results are obtained only in a small number of polynomials order. This numerical approach is applicable and effective for such a kind of nonlinear 2DOP. The convergence of the method is extensively discussed and finally two illustrative examples are included to observe the validity and applicability of the new technique developed in the current work.     

Numerical solution of nonlinear differential equations using computer algebra

This paper describes a numerical method for finding periodic solutions to nonlinear ordinary differential equations. The solution is approximated by a trigonometric series. The series is substituted into the differential equation using the FORMAC computer algebra system for the resulting lengthy algebraic manipulations. This lead to a set of nonlinear algebraic equations for the series coefficients. Modern search methods are used to solve for the coefficients. The method is illustrated by application to Duffing’ equation.