Selected State Variables Research Articles

Parameter Sensitivity Analysis of a Spouted Bed

AbstractA three‐layer neural network, based on 192 sets of experimental data obtained by the authors, was built in order to simulate the influence of four main process parameters on the minimum and stationary spouting velocity and on the pressure drop in a spouted bed. The simulations with the neural net are in good agreement with experimental learning data, and the overall average absolute error is 5.43 %. The neural net was used in the framework of a Monte Carlo simulation using CRYSTAL BALL®. The result of 100,000 trials revealed the percentage contributions of the process parameters to the variance of the selected state variables. Since there is significant uncertainty concerning the design equations of spouted beds, the results of this work should be useful for the design of such devices.

TIME DOMAIN DIAKOPTIC ANALYSIS BASED ON REDUCED-ORDER STATE EQUATIONS

In this paper we present some new tearing techniques to systematically formulate the state equations in symbolic normal-form for linear and/or nonlinear time-invariant large-scale analog circuits. The excess elements of the first and of the second kind are unitarily treated in order to allow a symbolic representation of the circuit with a minimum number of state variables. A procedure to reduce the state equation number of each subcircuit is also presented. The reduced-order is based on an implicit integration algorithm and on the successive elimination of the selected state variables. Examples are given to illustrate the decomposition procedure, the assignment of the connection sources and the reduced-order technique.

Automatic generation of explanations: AGE

Explaining how engineering devices work is important to students, engineers, and operators. In general, machine generated explanations have been produced from a particular perspective. This paper introduces a system called automatic generation of explanations (AGE) capable of generating causal, behavioral, and functional explanations of physical devices in natural language. AGE explanations can involve different user selected state variables at different abstraction levels. AGE uses a library of engineering components as building blocks. Each component is associated with a qualitative model, information about the meaning of state variables and their possible values, information about substances, and information about the different functions each component can perform. AGE uses: (i) a compositional modeling approach to construct large qualitative models, (ii) causal analysis to build a causal dependency graph, (iii) a novel qualitative simulation approach to efficiently obtain the system's behavior on large systems, and (iv) decomposition analysis to automatically divide large devices into smaller subsystems. AGE effectiveness is demonstrated with different devices that range from a simple water tank to an industrial chemical plant.

Modelling Pseudocalanus elongatus stage-structured population dynamics embedded in a water column ecosystem model for the northern North Sea

This paper outlines an approach to couple a structured zooplankton population model with state variables for eggs, nauplii, two copepodites stages and adults adapted to Pseudocalanus elongatus into the complex marine ecosystem model ECOHAM2 with 13 state variables resolving the carbon and nitrogen cycle. Different temperature and food scenarios derived from laboratory culture studies were examined to improve the process parameterisation for copepod stage dependent development processes. To study annual cycles under realistic weather and hydrographic conditions, the coupled ecosystem–zooplankton model is applied to a water column in the northern North Sea. The main ecosystem state variables were validated against observed monthly mean values. Then vertical profiles of selected state variables were compared to the physical forcing to study differences between zooplankton as one biomass state variable or partitioned into five population state variables. Simulated generation times are more affected by temperature than food conditions except during the spring phytoplankton bloom. Up to six generations within the annual cycle can be discerned in the simulation.

Recursive prediction error identification and scaling of non-linear state space models using a restricted black box parameterization

A recursive prediction error algorithm for identification of systems described by non-linear ordinary differential equation (ODE) models is presented. The model is an ODE model, parameterized with coefficients of a multi-variable polynomial that describes one component of the right-hand side function of the ODE. This avoids over-parameterization problems. The selected model can also handle systems with more complicated right-hand side structure, by identification of a local input–output equivalent system in the coordinate system of the selected state variables. A novel technique based on scaling of the sampling period is proposed. The technique can improve the conditioning of the identification problem, thereby enhancing the chances of convergence to the correct minimum of the criterion. The algorithm is applied to live data from a system consisting of two cascaded tanks, with promising results. A MATLAB software package, which implements the proposed algorithm and a set of support scripts, can be freely downloaded from http://www.it.uu.se/research/reports/.

The SHIFT programming language for dynamic networks of hybrid automata

SHIFT is a programming language for describing and simulating dynamic networks of hybrid automata. Such systems consist of components which can be created, interconnected, and destroyed as the system evolves. Components exhibit hybrid behavior, e.g. continuous-time phases separated by instantaneous discrete-event transitions. Components may evolve independently, or they may interact through selected state variables and events. The interaction network itself may evolve. The SHIFT model and language were motivated by our need for tools that support dynamically reconfigurable hybrid systems. Our primary application is the specification and analysis of different designs for automatic control of vehicles and highway systems. From our previous experience in modeling, analysis, and implementation, we adopted the hybrid systems approach for modeling the system components. Since spatial relationships between vehicles change as they move, our application is characterized by a dynamically changing network of interactions between system components. SHIFT has also since been used in coordinated autonomous submarines, air traffic control systems, and material handling systems. We examine other work related to the SHIFT approach. In we describe the main features of the SHIFT language-states, inputs, outputs, differential equations, and algebraic definitions, discrete states, and state transitions. We give a simplified version of the SHIFT model. We discuss the models of a type, a component, and the world and give the formal semantics of the model.

Application of repro-modeling for the reduction of combustion mechanisms

The basic problem of mechanism reduction methods is to find functional relationships between selectedstate variables (e.g., some concentrations and temperature) and their rates. However, this information is present during the simulations with the full chemical model. As a new application of the repro-modeling approach, information for rates is extracted from detailedchemical calculations and stored in the form of high-order multivariate, polynomials. For an efficient utilization of the polynomials, a computer program was written that rearranges them to the form of multivariate Horner equations. The repro-modeling method is an alternative to the application of the quasi-steady-state approximation (QSSA) and of the low-dimensional manifold method. Pros and cons of these three methods are discussed in detail considering the preparations required, the accuracy attainable, the yield in computer time, and the limitations of the techniques. Simulations of the combustion of wet CO using two-variable and three-variable repro-models were24,000 and 11,700 times faster, respectively, than the SENKIN calculation using the full model. These calculations represent the first use of repro-modeling for combustion mechanism reduction.

A new implementation for analytical derivatives of thermodynamic properties and its beneficial application on dynamic simulation

A formulation to obtain analytical partial thermodynamic derivatives (PTHDS) of thermodynamic functions with respect to selected state variables for liquid, vapour or liquid—vapour systems, is presented. The objective of this paper is first to illustrate the advantages using analytical PTHD information and secondly to present a systematic procedure, based on an implicit system of nonlinear equations, which allows the user to choose his own state variables and to obtain analytical derivaties of any property (also chosen by the user) with respect to these state variables. The procedure is based on few PTHDs with respect to a basic set of state variables, coded explicitly and an algorithm that allows to compute all the other PTHDs needed, with respect to any set of state variables. The algorithm presented is completely independent of the mathematical solution procedure and independent of the thermodynamic model used. It therefore does not modify the structure of the system describing the plant units. It is now implemented in BELSIM-EPIC thermodynamic package. Its flexibility and contribution to solution accuracy are illustrated. Computer time savings using the algorithm, are presented and analyzed in the case of liquid—vapour equilibria calculations using different thermodynamic models and also in dynamic simulation of multicomponent distillation units in refinery plants.

Robust Stability and Performance Analysis for State-Space Systems via Quadratic Lyapunov Bounds

For a given asymptotically stable linear dynamic system it is often of interest to determine whether stability is preserved as the system varies within a specified class of uncertainties. If, in addition, there also exist associated performance measures (such as the steady-state variances of selected state variables), it is desirable to assess the worst-case performance over a class of plant variations. These are problems of robust stability and performance analysis. In the present paper, quadratic Lyapunov bounds used to obtain a simultaneous treatment of both robust stability and performance are considered. The approach is based on the construction of modified Lyapunov equations, which provide sufficient conditions for robust stability along with robust performance bounds. In this paper, a wide variety of quadratic Lyapunov bounds are systematically developed and a unified treatment of several bounds developed previously for feedback control design is provided.

Suboptimal Direct Digital Control of a Trickle-Bed Absorption Column

For the selection of the best process variables to be used in a suboptimal feedback controller the design scheme proposed by Crosby and Durbin is further investigated and the selection procedure is improved. Furthermore, the suboptimal controllers formed by the selected variables are tested on-line on a trickle bed absorption column. The controllers used include the integral mode for the controlled variable plus the proportional mode for some selected state variables including the controlled variable. Substantial reductions in the performance index and peak overshoot are obtained by using the suboptimal controllers instead of conventional feedback controllers.

A least squares approach to model reduction and the design of low‐order controllers

AbstractState space process models and feedback control laws are simplified by eliminating selected state variables using a modified least squares technique. The revised technique uses random perturbations to excite the high order system and the resulting reduced‐order models tend to be more robust than those derived using conventional least squares and deterministic inputs. Low‐order controllers were designed for a pilot scale, double effect evaporator using the modified least squares approach. These controllers performed well in both experimental and simulated response tests.

On the Equations of Nonlinear Networks

A systematic method of selecting state variables and formulating the normal form differential equations of general classes of nonlinear networks is presented. It is shown that the key problem in the formulation of the differential equations is the calculation of certain functions which appear in these equations. Iterative procedures for the calculation of these functions are given for certain classes of networks, and it is shown that the conditions for convergence of these procedures are closely related to certain physical properties of the network. These procedures are readily adaptable to machime computation and can be made an integral part of any numerical method used for the solution of the differential equations of the network.