Differential Algebraic Equation Model Research Articles

Structural solvability analysis of dynamic process models

The variable structure of dynamic process models is represented by a directed graph termed as the representation graph for the purpose of solvability analysis in this paper. Structural solvability analysis, the determination of the structural differential index and the structural decomposition of the differential–algebraic equations (DAE) model set can be performed using the representation graph. The characteristic features of the representation graph for both index 1 and high index semi-explicit DAE models are presented. Based on the above a novel index reduction procedure for high index models is proposed. The notions and methods are illustrated on simple process examples.

Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

Random and uncertainty analysis of cylindrical alkaline cells

A method is presented to analyze the performance of a cylindrical Zn–MnO 2 alkaline cell with parameter randomness and uncertainties. Two kinds of parameters are recognized with different random and uncertain characteristics. These are parameters with randomness such as the particle size, and parameters with uncertainties such as kinetic and transport coefficients. A sampling procedure based on a differential-algebraic equation model of the alkaline cell is developed to simulate a cell's statistical performance. A numerical example is illustrated with an AA-size cell under a 1 A constant current discharge.

Dynamic data reconciliation for a class of nonlinear differential-algebraic equation models using the extended kalman filter

In this paper a method is presented for dynamic data reconciliation of nonlinear systems described by a class of differential-algebraic models, using the extended Kalman filter. A time-varying linearization is derived for a semi-explicit index one DAE. A simplified extended Kalman filter algorithm is then presented, and its integration with the DAE model is described. Finally, a simulation study is presented using a DAE model of a batch chemical reactor.

Design of force/position control laws for constrained robots, including effects of joint flexibility and actuator dynamics

In this paper, a mathematical representation of constrained robot systems in the form of a differential-algebraic equation model is first considered. This model in modified further to include the joint flexibility between the linkages of the robot, and the actuator dynamics. The objective is to design a feedback control law for the system so that the position output variables (typically the end-effector position) and the force output variables (typically the contact force between the robot's end-effector and the contact surface) of the robot follows the desired position and the desired force trajectories, respectively, despite the presence of joint flexibility and actuator dynamics. A systematic procedure is developed for designing a feedback control law which ensures that the position variables track the desired position trajectories exponentially, and the force variables track the desired force trajectories exponentially. Since the development of the control law is based on the model of a constrained robot system which includes the effects of actuator dynamics and joint flexibility, it is possible to achieve better tracking performance using the force/position control law developed in this paper in cases where such effects are significant.

Variable Fidelity Differential-Algebraic Equation Model Correlation

ABSTRACT A formulation for selecting operator and control inputs to a high fidelity dynamics model, governed by differential-algebraic equations, is presented to minimize deviation in its response relative to that of a lower fidelity model that is also governed by differential-algebraic equations of motion. An adjoint variable method for computing sensitivity of the error measure defined is derived and implemented in a nonlinear programming formulation that is suitable for iterative minimization of the error functional. A numerical example using a multibody mechanism is presented to demonstrate effectiveness of the method and provide insights into means for effectively formulating problems of model correlation and strategies for their solution

The treatment of non-integer exponents in reaction rate expressions

The modelling of chemical reactions relies upon expressions being supplied which give the rate of reaction as a function of local temperature and local concentrations. When power law rate expressions are used with concentrations to integer powers, the analysis and numerical solution of these equations is made easier. In this note the numerical difficulties that arise when the order is non-integer are described and one method is proposed which overcomes them in a differential-algebraic equation model of a catalytic monolith reactor.

Structural analysis of differential-algebraic equation systems—theory and applications

The choice of a feasible numerical method for the solution of a Differential-Algebraic Equation (DAE) model of general type F(z,z,u) = 0 requires knowledge about its solvability, index, number and type of dynamic degrees of freedom as well as the set of equations to be satisfied by consistent initial conditions. Furthermore, a set of design quantities has to be specified. Important properties of DAEs are concisely defined and related among each other. A new structural algorithm which determines structural properties of DAEs is developed and compared to another conceptually different structural algorithm proposed earlier by Pantelides [(1988) SIAM J. Sci. Stat. Comput.9, 213 231]. Both algorithms were implemented as structural analysis tools to provide a fast a prion characterization of general DAEs F(z,ż,u)=0 prior to any numerical solution. Some examples illustrate how the information obtained can be used to address various significant issues in process modelling, simulation, and in the evaluation of control configurations for nonlinear systems.

An energy function method for determining voltage collapse during a power system transient

The occurrence of a voltage collapse is often described as a small-signal stability problem resulting from a bifurcation of the equilibrium load flow equations as the bus loads and generator power injections incur small changes. However, during a transient period, a voltage collapse may occur as a bifurcation of the transient load flow equations as the generator rotor angles vary. The purpose of this paper is to address voltage collapse in the general context of a transient stability problem for a differential algebraic equation (DAE) power system model. In particular, we define a stability region that guarantees both rotor angular stability and voltage stability. The stability region does not intersect the surface, the surface on which the bus voltage variables are not defined as functions of the generator rotor angles. Bifurcation theory is used along with some recent results that characterize the stability boundary for DAE models, to show that an important component of the stability boundary is formed by the trajectories that are tangent to the impasse surface at a fold bifurcation point. An energy function transient stability method is developed that uses a sustained fault trajectory to find the first point of intersection with the impasse surface and then involves solving for the (stability) limiting trajectory that is tangent to the impasse surface at this point. This new transient stability method is somewhat similar in theory to the potential energy boundary surface method. Also, this method can be extended to develop stability estimates for power system models in which the stability region is more complex, possibly constrained by line power flow limits, voltage magnitude limits, etc. >