Form Of State Equation Research Articles

NURBS-based three-dimensional analysis of geometrically nonlinear elastic structures

A comprehensive kinematical description with a corotational approach, which is based on exact polar decomposition for solid elements using isogeometric analysis is the main objective of this work. A numerical model using NURBS-based FEM is developed to deal with nonlinear problems in solid mechanics involving large rotations. From the theoretical viewpoint, the rate type form of state equation is formulated within the framework of isotropic infinitesimal elasticity. It is shown in particular that the state equation relates the Jaumann derivative of the Cauchy stress to the Eulerian strain rate. Illustrative examples are analyzed to verify the efficiency in solving a wide variety of strong nonlinear problems. • NURBS-based analysis is employed to deal with nonlinear problems in solid mechanics. • Kinematical description with a corotational-based approach is proposed. • The rate form of state equation is formulated within framework of large rotations. • Several examples of shells structures are analyzed numerically.

Multivariable greenhouse climate control using dynamic decoupling controllers

Multivariable greenhouse climate control is presented. The greenhouse environment is described using a dynamic nonlinear model in state equation form incorporating carbon dioxide concentration, ambient air temperature and humidity concentration. The use of a dynamic linear input/output decoupling controller is described and simulation results are illustrated. The advantages of applying the specific control technique are highlighted as it does not only achieve input/output decoupling but also decreases significantly the settling time of all state variables maintaining control input constraints.

Multiple Input Delays Estimation Using an Artificial Bee Colony Algorithm

This paper focuses on the time delay estimation of the system described in the form of discrete-time state equation with multiple input delays. To estimate the input delays, a new evolutionary computation called the artificial bee colony (ABC) algorithm is utilized. This algorithm is originally motivated from the social behaviors of honeybee organization, and it has been proven to be a powerful means for solving the optimized problem. Based on the proposed algorithm, the unknown system input delays can be further solved by minimizing a quadratic cost function of the system. Two illustrative examples are provided to verify the potential of the presented method in the time delay estimation. Some simulations containing different initial condition examinations and appearance of noises are further given. Numerical results show that the proposed method can do well in the multiple inputs delay estimation of discrete-time state equations.

Modeling and Control of Casterboard Robot

In this paper, we propose a robotic model of a casterboard, which is a commercial variants of skateboards with twistable footplates and passive inclined caster wheels. We then derive its mathematical model in the form of nonlinear state equation; this system is of much interest from both mechanical and control points of view as a new challenging example of nonholonomic mechanics. Based on the observation on preceding works concerning locomotion control for nonholonomic systems, we propose a locomotion control method with sinusoidal periodic control to realize forwarding and turning locomotion. The proposed idea is examined by simulations and physical experiments using the prototype robot developed by the authors. Moreover, we also examine the influences on the driving of the robot of parameter in the sinusoidal reference signals.

Dynamic Responses of Supercavitating Vehicles under Non-Stationary Random Excitation

When the front end of the supercavitating vehicles subjects to very large axial non-stationary random excitation at high speed motion under water, it is necessary to analyze dynamic responses of supercavitating vehicles under non-stationary random excitation. The dynamical equation of supercavitating vehicles is transformed into the form of state equations. The Simpson integration method is going to calculate the integral term of the general solution of state equation to improve the precise integration method. The explicit expression of dynamic responses of supercavitating vehicles is deduced, the means and variances of structural responses are calculated with operation laws of the first moment and second moment. Under different sailing speeds and different cone-cavitator angles dynamic responses of supercavitating vehicles are given by the examples, and the effectiveness of the method was demonstrated.

An Analysis for Stochastic Model of Worm Propagation

Abstract Worm propagation on computer networks is a stochastic process. So it is very important for establishing stochastic models of worm propagation. This paper presents the stochastic model of worm propagation on the basis of epidemic models. At first an analysis is made on the worm propagation linear SEIR model and the form of state equation is written. Then it is changed into a Markov chain. The transition probability of every state, the expected time stayed on each state, and the average time of reaching a recovered state can be solved by the decomposition of the state space of a Markov chain. It is a great help in defending worm attacks.

Multi-domain modeling and simulation of proportional solenoid valve

A multi-domain nonlinear dynamic model of a proportional solenoid valve was presented. The electro-magnetic, mechanical and fluid subsystems of the valve were investigated, including their interactions. Governing equations of the valve were derived in the form of nonlinear state equations. By comparing the simulated and measured data, the simulation model is validated with a deviation less than 15%, which can be used for the structural design and control algorithm optimization of proportional solenoid valves.

Proton Exchange Membrane Fuel Cell(PEMFC) Lumped Modeling and Dynamic Performance Analysis

A model of PEMFC is developed that captures dynamic behavior for control purposes. It analyzes in detail the influence factor of voltage of PEMFC. The model is mathematically simple, and accounts for the essential phenomena that influence the PEMFC performance. The partial pressure of hydrogen and oxygen can be found using the laplace transform and differential form of ideal gas state equation. It is assumed that the mixture ratio of hydrogen and oxygen in the reaction are constant, the dynamic lumped model of PEMFC is proposed. The model is verified by comparing the experiment data with simulation result of model. On the basis of the dynamic model, the partial pressure and voltage are analyzed when when the load current suddenly changes.The research about lumped model has important significance to the research of the distributed generation network in various performances and has guiding meaning to the structure design of fuel cell.

Topological sensitivity analysis for a two-parameter Mooney-Rivlin hyperelastic constitutive model

The Topological Sensitivity Analysis (TSA) is represented by a scalar function, called Topological Derivative (TD), that gives for each point of the domain the sensitivity of a given cost function when an infinitesimal hole is created. Applications to the Laplace, Poisson, Helmoltz, Navier, Stokes and Navier-Stokes equations can be found in the literature. In the present work, an approximated TD expression applied to nonlinear hyperelasticity using the two parameter Mooney-Rivlin constitutive model is obtained by a numerical asymptotic analysis. The cost function is the total potential energy functional. The weak form of state equation is the constraint and the total Lagrangian formulation used. Numerical results of the presented approach are considered for hyperelastic plane problems.

Modeling and stability analysis of cascade buck converters with N power stages

This paper presents a method for stability analysis of N-cell cascade step-down buck converters, which is a kind of complex nonlinear system. A nonlinear model in the form of time-variant state equations is derived, and then the loop gain describing the overall system is introduced. With the help of them, we obtain the equations for phase cross over frequency and gain margin by small-signal perturbation technique, harmonic balance method, and inverse iteration method. Based on the equations, the overall cascade system stability can be analyzed regardless of the number of converters cascaded. Finally, the cascade buck converter with three power stages is used to demonstrate the effectiveness of the proposed stability analysis method.

Inclusion of the frequency effect in the lumped parameters transmission line model: State space formulation

The objective of this paper is to include the frequency dependence of the longitudinal parameters in the lumped parameters line model. The distributed nature of the transmission line was approximated by a cascade of π circuits and the frequency effect was approximated by a rational function which was synthesized by an equivalent circuit. Then, the equivalent circuit was inserted in each π circuit of the cascade. After that, the currents and voltages along the line were described in the form of state equations. This way, it was possible to obtain a formation rule of the state matrices lumped parameters model taking into account the frequency dependence. To confirm the validation of the state matrices obtained, the lumped parameters representation of frequency-dependent lines was used to represent a single-phase line and a three-phase line. The simulations were carried out using state space techniques and an electromagnetic transient program (EMTP) (in this case, the cascade was inserted in the EMTP). It is observed that the simulation results obtained with state space representation are in agreement with those results obtained with EMTP.

Sensorless control of PMSM drive with state and load torque estimation

PurposeThe purpose of this paper is to obtain a fully sensorless permanent magnet synchronous motor (PMSM) drive control algorithm used for robot arm drive with load recognition. The paper shows how to use an extended Kalman filter (EKF) instead of sensors of the mechanical quantities as well as how to adapt the model of the PMSM to the filter procedures and aims at the real time application in the field‐oriented control (FOC) structure of the high‐dynamic drive.Design/methodology/approachThe synthesis of the control system is based on the method of the FOC, theory of the EKF and object description in the form of state equation with suitable choice of state vector. The adequate connection of these three methodologies is a core of the approach to design. First, the control algorithm was tested by means of simulation method then the real laboratory plant was built and investigated.FindingsOwing to task‐oriented formulation of the PMSM model, adequate organization of the EKF procedures and suitable choice of covariance matrices the proper control algorithm was obtained. The algorithm can be applied on DSP and gives a good result for the high dynamic drive in spite of the fact that the Kalman procedures are recognized as a time‐consumed solution of the estimation problem.Research limitations/implicationsThe proposed algorithm can be used also in the case of another type of drive, for instance induction motor drive, although the model of the motor has a different formula. A disadvantage of the method is lack of the general rules for choosing the elements of the covariance matrices.Practical implicationsThe presented algorithm is written in open‐programming language. Obtained results may be important for synthesis of robot arm drive, where the information about load forces is needed.Originality/valueThe paper presents an original sensorless vector control of PMSM with load recognition based on EKF. The originality elements are the choice of the covariance matrix elements and the real‐time realisation of the algorithm on the DSP.

Investigation of Stability in Skydiving by Derivation of State Equation for Body Behavior and Root Analysis

The objective of this study was to investigate the stability during freefall in skydiving, in which the diver has to take various body position in order to control precisely their distance, velocity, and direction relative to the other divers for the group performance. For this objective, the state equation for a simple elliptic cylinder model was firstly derived, considering its equations of motion and the fluid force characteristics. Next, using the form of state equation derived for the elliptic cylinder and the input/output data obtained from the developed simulation method for the body behavior of the skydiver, the state equations of skydiver were identified for various body positions. Finally, roots of the state equations were obtained to investigate the stability. As the results, the causes of instability such as spin and spiral phenomena were clarified as an unstable natural modes, and the stable limit of body position was obtained as a value of parameter which is related to the arch magnitude of the diver's body.

Debye equation of state for fluid helium-3

An equation of state for 3He using the Helmholtz potential function has been developed. The lower limit of the equation of 0.01 K is safely above the superfluid transition at 0.0026 K. The upper limit of 60 K is approximately the upper limit of available 3He property measurements. The new state equation form is based on Debye function which goes smoothly to zero in the limit of zero temperature and reduces to the ideal gas in the limit of zero density and/or very high temperature. The equation combines (a) necessary temperature-independent compressibility terms at the lowest temperatures, (b) terms describing the linear specific heat of a Fermi fluid below 1 K, (c) terms describing the phonon excitations which begin above about 1 K, and (d) terms which attempt to fit the conventional critical point thermodynamics at 3.3157 K and 114 604 Pa. State properties, e.g., p-V-T relations, specific heats, thermal expansion, sound velocity, etc., are determined from the Helmholtz energy by standard thermodynamics. Transport properties, e.g., thermal conductivity and viscosity, are not obtained in this work.

Relations between two bond graph approaches to sensitivity analysis and study of robustness

Recently Borutzky and Granda proposed to construct a so-called incremental bond graph from an initial bond graph with nominal parameters in order to determine unnormalized first order frequency domain sensitivities in symbolic form. At the same time Dauphin-Tanguy and Kam presented a bond graph approach that allowed them to set up a specific form of state equations in symbolic form commonly used for a robustness study of models with uncertain parameters. Both approaches designed for different purposes have been developed independently. Nevertheless, this paper shows that they can be used to obtain each other's results under some reasonable assumptions. For illustration both approaches are applied to an example, which has been kept fairly small for didactic reasons.

A Simple Way of Obtaining the Reduced Jordan Form of a State Equation

This paper presents a succinct and entirely elementary method for determining a minimal Jordan form of a given state equation. It is constructive and is based upon the idea of grouping terms appropriately in the partial fraction expansion. The method is highly suited to presentation in classes in linear systems and control theory, offering a good pedagogical introduction to the topic of Jordan equivalent matrices, although it is not suggested as an efficient computational tool.

Static VAr compensator control for power systems with nonlinear loads

An accurate linearisation technique for multi-input power systems with nonlinear loads is presented. The nonlinear differential algebraic system (NDAS) considered is not in the state equation form. The definitions of M derivative and M bracket are similar to the definitions in classic differential geometric theory and some related revised results are introduced. M derivative and M bracket are used to obtain the feedback control law for the NDAS. The approach is used to design a nonlinear static VAr compensator (SVC) controller for a single-machine infinite system with nonlinear loads. The simulation results show that the nonlinear SVC controller improves damping and the voltage level to a greater extent than conventional controllers. The control law is even effective when the nonlinear loads are varied.

Incremental bond graph approach to the derivation of state equations for robustness study

Aiming at an automated bond graph based determination of unnormalized frequency domain sensitivities in symbolic form Borutzky and Granda proposed the systematic construction of a so-called incremental bond graph from an initial bond graph for the increments (Δ e)( t), (Δ f)( t) of power variables e( t) and f( t) associated with each bond. This paper shows that the incremental bond graph can serve also as a starting point for setting up symbolically the canonical form as well as the standard interconnection form of state equations used for robustness study. The approach applicable to general linear time-invariant systems is illustrated by means of a fairly small example.

Adaptive nonlinear guidance law considering control loop dynamics

A new adaptive nonlinear guidance law is proposed here. The fourth order state equation for integrated guidance and control loop is formulated taking into consideration the target uncertainties and control loop dynamics. The state equation is further changed into the normal form by nonlinear coordinate transformation. Using the normal form of state equation, an adaptive nonlinear guidance law is proposed to compensate for the uncertainties in both target acceleration and control loop dynamics. The proposed law adopts the sliding mode control approach with adaptation for unknown bound of uncertainties. The present approach can effectively solve the existing guidance problem against target maneuver and the limited performance of control loop. We have provided the stability analyses and performed simulations comparing favorably our approach to the state of the art.

Polynomial Solution of Predictive Optimal Control Problems For Systems in State-Equation Form

The solution of linear quadratic predictive optimal control problems for systems represented in state-equation form, but using a polynomial systems approach, is considered. A multistep cost-function is used that includes future set-point information. A novel method is introduced for computing the vector of future controls and for solving a simpler optimization problem for the current control.