Showing papers on "State variable published in 1995"

A survey of the maximum principles for optimal control problems with state constraints

Abstract: This paper gives a survey of the various forms of Pontryagin’s maximum principle for optimal control problems with state variable inequality constraints. The relations between the different sets of optimality conditions arising in these forms are shown. Furthermore, the application of these maximum principle conditions is demonstrated by solving some illustrative examples.

An elasto-plastic critical state framework for unsaturated soil

Abstract: Data from a series of controlled suction triaxial tests on samples of compacted speswhite kaolin were used in the development of an elasto–plastic critical state framework for unsaturated soil. The framework is defined in terms of four state variables: mean net stress, deviator stress, suction and specific volume. Included within the proposed framework are an isotropic normal compression hyperline, a critical state hyperline and a state boundary hypersurface. For states that lie inside the state boundary hypersurface the soil behaviour is assumed to be elastic, with movement over the state boundary hypersurface corresponding to expansion of a yield surface in stress space. The pattern of swelling and collapse observed during wetting, the elastic–plastic compression behaviour during isotropic loading and the increase of shear strength with suction were all related to the shape of the yield surface and the hardening law defined by the form of the state boundary. By assuming that constant–suction cross–secti...

Volatility structures of forward rates and the dynamics of the term structure1

Abstract: For general volatility structures for forward rates, the evolution of interest rates may not be Markovian and the entire path may be necessary to capture the dynamics of the term structure. This article identifies conditions on the volatility structure of forward rates that permit the dynamics of the term structure to be represented by a two-dimensional state variable Markov process. the permissible set of volatility structures that accomplishes this goal is shown to be quite large and includes many stochastic structures. In general, analytical characterization of the terminal distributions of the two state variables is unlikely, and numerical procedures are required to value claims. Efficient simulation algorithms using control variates are developed to price claims against the term structure.

The representation of AC machine dynamics by complex signal flow graphs

Abstract: Induction motors are modeled by nonlinear higher-order dynamic systems of considerable complexity. The dynamic analysis based on the complex notation exhibits a formal correspondence to the description using matrices of axes-oriented components; yet differences exist. The complex notation appears superior in that it allows the distinguishing between the system eigenfrequencies and the angular velocity of a reference frame which serves as the observation platform. The approach leads to the definition of single complex eigenvalues that do not have conjugate values associated with them. The use of complex state variables further permits the visualization of AC machine dynamics by complex signal flow graphs. These simple structures assist to form an understanding of the internal dynamic processes of a machine and their interactions with external controls. >

The use of multi-state capture-recapture models to address questions in evolutionary ecology

Abstract: Multi-state capture-recapture models can be used to estimate survival rates in populations that are stratified by location or by state variables associated with individual animals. In populations stratified by location, movement probabilities can be estimated and used to test hypotheses relevant to population genetics and evolutionary ecology. When the interest is in state variables, these models permit estimation and testing of hypotheses about state-specific survival probabilities. If the state variable of interest is reproductive activity or success, then the multi-state modeling approach can be used to test hypotheses about life history trade-offs and a possible cost of reproduction.

State assignment for low power dissipation

Abstract: We address the problem of reducing the power dissipated by synchronous sequential circuits. We target the reduction of the average switching activity of the input and output state variables by minimizing the number of bit changes during state transitions. Using a probabilistic description of the finite state machines, we propose a state assignment algorithm that minimizes the Boolean distance between the codes of the states with high transition probability. We formulate a general theoretic framework for the solution of the state assignment problem, and propose different algorithms trading off computational effort for quality. We then generalize our model to take into account the estimated area of a multilevel implementation during state assignment, in order to obtain final circuits where the total power dissipation is minimized. A heuristic algorithm has been implemented and applied to standard benchmarks, resulting in a 16% average reduction in switching activity. >

Stable adaptive control of robot manipulators using “neural” networks

Abstract: The rapid development and formalization of adaptive signal processing algorithms loosely inspired by biological models can be potentially harnessed for use in flexible new learning control algorithms for nonlinear dynamic systems. However, if such controller designs are to be viable in practice, their stability must be guaranteed and their performance quantified. In this paper, the stable adaptive tracking control designs employing "neural" networks, initially presented in Sanner and Slotine (1992), are extended to classes of multivariable mechanical systems, including robot manipulators, and bounds are developed for the magnitude of the asymptotic tracking errors and the rate of convergence to these bounds. This new algorithm permits simultaneous learning and control, without recourse to an initial identification stage, and is distinguished from previous stable adaptive robotic controllers, e.g. (Slotine and Li 1987), by the relative lack of structure assumed in the design of the control law. The required control is simply considered to contain unknown functions of the measured state variables, and adaptive "neural" networks are used to stably determine, in real time, the entire required functional dependence. While computationally more complex than explicitly model-based techniques, the methods developed in this paper may be effectively applied to the control of many physical systems for which the state dependence of the dynamics is reasonably well understood, but the exact functional form of this dependence, or part thereof, is not, such as underwater robotic vehicles and high performance aircraft.

Stochastic maximum principle for optimal control problem of forward and backward system

Abstract: The maximum principle for optimal control problems of stochastic systems consisting of forward and backward state variables is proved, under the assumption that the diffusion coefficient does not contain the control variable, but the control domain need not be convex.

An on-line adaptation method in a neural network based control system for AUVs

Abstract: A neural network based control system "Self-Organizing Neural-Net-Controller System: SONCS" has been developed as an adaptive control system for Autonomous Underwater Vehicles (AUVs) In this paper, an on-line adaptation method "Imaginary Training" is proposed to improve the time-consuming adaptation process of the original SONCS The Imaginary Training can be realized by a parallel structure which enables the SONCS to adjust the controller network independently of actual operation of the controlled object The SONCS is divided into two separate parts: the Real-World Part where the controlled object is operated according to the objective, and the Imaginary-World Part where the Imaginary Training is carried out In order to adjust the controller network by the Imaginary Training, it is necessary to introduce a forward model network which can generate simulated state variables without involving actual data A neural network "Identification Network" which has a specific structure to simulate the behavior of dynamical systems is proposed as the forward model network The effectiveness of the Imaginary Training is demonstrated by applying to the heading keeping control of an AUV "Twin-Burger" It is shown that the SONCS adjusts the controller network-through on-line processes in parallel with the actual operation >

State of the art of controlled AC drives without speed sensor

Abstract: The operation of speed controlled AC motor drives without mechanical speed or position sensors requires the estimation of internal state variables of the machine. The assessment is based exclusively on measured terminal voltages and currents. Low cost, medium performance sensorless drives can be designed using simple algebraic speed estimators. High-performance systems rely on dynamic models for the estimation of the magnitude and spatial orientation of magnetic flux waves in the stator or in the rotor. Open loop estimators and closed loop observers differ with respect to accuracy, robustness, and limits of applicability. The overview in this paper uses signal flow graphs of complex space vector quantities to give an insightful description of the physical and mathematical systems used in sensorless control. >

A variable structure controller for a tentacle manipulator

Abstract: The paper presents a class of tentacle arms based on the use of flexible composite materials in conjunction with active-controllable electrorheological (ER) fluids. The model consists of a finite number of segments, each segment having a specific structure and control. The dynamic behaviour of the arm is obtained using Lagrange's principle developed for infinite-dimensional systems. This model is represented by a set of integral-differential equations. An approximate model is then derived as a set of differential equations with variable coefficients. Two cases are discussed: the sliding mode with the bang-bang control; and the direct mode in which the controller is based on the use of the direct evolution of the system on the switching line by switching the fluid viscosity. The numerical simulations are presented. A nonlinear observer is introduced to estimate the inaccessible state variable distributed on the length of the arm. The conditions which assure the convergence to zero of the errors are proved.

Small-signal analysis of DC-DC converters with sliding mode control

Abstract: The paper deals with small-signal analysis of DC-DC power converters with sliding mode control. A suitable small-signal model is developed, which allows selection of control coefficients, analysis of parameter variation effects and characterization of the closed-loop behavior in terms of audiosusceptibility, output and input impedances and reference-to-output transfer function. Unlike previous analyses, the model includes effects of the filters used to evaluate state variable errors. Simulated and experimental results demonstrate model potentialities. >

Transient behavior of biological loop models with application to the droop model

Abstract: In this paper we study the transient behavior of a class of nonlinear differential systems verifying sign conditions through the succession of extrema of the state variables. This analysis does not depend, for the main part, on the analytical formulation of the model. The possible scenarios of sequences for the extrema, are represented on a graph and can be compared with the experimental data to validate the model. An application to the Droop model illustrates this method; we obtain as a result the global stability of the equilibrium and the possible successions of the extrema.

State variable decoupling and power flow control in PWM current source rectifiers

Abstract: Current source PWM rectifiers among others are gradually replacing thyristor line commutated rectifiers as a source of variable DC power. Advantages include reduced line current harmonic distortion and complete power factor control, including unity power factor operation. However, due to intrinsic nonlinearities and stability problems, the control of the rectifier has usually been achieved using off-line patterns or direct line current control in the abc frame. This paper proposes a state variable control technique that introduces more flexibility in the control of the rectifier and a more straightforward approach to controller design. The proposed technique consists in linearizing the state variable model of the system in the dq frame, decoupling and independently controlling the two components of the line current (active and reactive), eliminating the input damping resistors, and rejecting the effect of supply voltage variations. Also, a space vector modulation technique is used to maximize the current gain and switch utilization of the rectifier. The paper includes a complete formulation of the equations of the decoupled system and a controller design procedure. Experimental results on a 2 kVA DSP based prototype confirm the theoretical considerations.

Output feedback stabilization using variable structure control

Abstract: We consider the stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using variable structure output feedback control In particular, the system can be transformed into a normal form with no zero dynamics A robust high-grain observer is used to estimate the state variables while rejecting the effect of disturbance A globally bounded discontinuous variable structure controller is designed to compensate for modelling error We show that the controller can stabilize the closed-loop system and does not suffer from the peaking phenomenon that exists in previous designs

Complexity of state-variable planning under structural restrictions

Abstract: Computationally tractable planning problems reported in the literature have almost exclusively been defined by syntactical restrictions. To better exploit the inherent structure in problems, it is ...

A state variable model for high strength polymers

Abstract: Displacement controlled experiments on nylon 66, poly(etherether ketone), and poly(ether imide) at room temperature suggest that nonlinear elastcity is not a good model for these polymers. Rather, qualitative evidence is presented that a state variable model shows promise. In this model, the rate of deformation is the sum of the elastic and the inelastic rates of deformation. The elastic rate of deformation is given by an objective formulation of Hooke's law, and the inelastic deformation is an increasing function of the overstress, the difference between the Cauchy stress and the equilibrium stress. The equilibrium stress is a state variable, and represents the stress that can be sustained at rest following deformation. Load controlled tests, intended to verify or falsify the model, show that the creep rate at the same stress level can be different on loading and unloading, and that the creep rate need not increase with an increase in creep stress level. These anomalous results can easily be explained by the introduction of the overstress concept, and by proper evolution of the equilibrium stress. They confirm the usefulness of the overstress concept for the modeling of these polymers.

Optimal finite-time endoreversible processes.

Abstract: We treat the general problem of transferring a system from a given initial state to a given final state in a given finite time such that the produced entropy or the loss of availability is minimized. We give exact equations for the optimal process for the general case of a system with several state variables. For linear processes, e.g., in the limit of slow processes or if the Onsager coefficients do not depend on the fluxes, we find a constant entropy production rate or constant loss rate of availability. An alternative kinetic process length is introduced. The entropy production rate is the square of the speed based on this length and clock time. This length adequately treats variations of the system time scale matrix along the path. For the nonlinear case, the entropy production rate or loss rate of availability is generally not constant for an optimal process.

Identification of hysteretic oscillators under earthquake loading by nonparametric models

Abstract: Nonparametric identification techniques are used to process recorded data of nonlinear structural responses and to represent the constitutive relationship of the structure. When hysteretic systems are dealt with, attention must be given to the appropriate subspace of the state variables in which the restoring force can be approximated by a single-valued surface. Nonparametric models are investigated, defined by two different descriptions: the first, in which the restoring force is a function of displacement and velocity, is commonly used; and the second, in which the incremental force is a function of force and velocity is less adopted. The ability of the second variable space to better reproduce the behavior of hysteretic oscillators is shown by analyzing different cases. Meanwhile, approximation of the real restoring function in terms of orthogonal (Chebyshev) polynomials and nonorthogonal polynomials is investigated. Finally, a mixed parametric and nonparametric model that exhibits a very satisfactory behavior in the case of important hardening and viscous damping is presented.

Arbitrary Lagrangian–Eulerian finite element analysis of strain localization in transient problems

Abstract: Non-local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents strain localization with zero global dissipation of energy, and consequently finite element calculations converge upon mesh refinements to non-zero width localization zones. One of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the internal length. Hence, the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity. This paper deals with the application of the arbitrary Lagrangian–Eulerian (ALE) formulation, well known in hydrodynamics and fluid–structure interaction problems, to transient strain localization in a non-local damageable material. It is shown that the ALE formulation which is employed in large boundary motion problems can also be well suited for non-linear transient analysis of softening materials where localization bands appear. The remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable. Two well known one-dimensional examples illustrate the capabilities of this technique: the first one deals with localization due to a propagating wave in a bar, and the second one studies the wave propagation in a hollow sphere.

L-h confinement mode dynamics in three-dimensional state space

Abstract: A dynamical model for the low-high (L-H) confinement mode transitions consisting of three ordinary differential equations (3-ODE model) for the essential state variables is proposed The model is derived from the energy balance equations for the resistive pressure-gradient-driven turbulence and describes temporal evolutions of three characteristic variables (u, k, f), the potential energy contained in the pressure gradient, the turbulent kinetic energy and the shear flow energy The energy input to the peripheral plasma region is included as an external control parameter in the model The model equations have stationary solutions corresponding to the L- and H-modes The L to H and H to L transitions are obtained by varying the energy input parameter The type of L-H transition, whether like a first- or second-order transition, is shown to be determined by the sheer flow damping At a higher level of the energy input parameter the H-mode stationary solution becomes unstable and bifurcates to a limit cycle which shows periodic oscillations characteristic of the H-localized mode (ELM) confinement state

Time‐delay control of structures

Abstract: Time-delay causes unsynchronized application of the control forces which may not only degrade the performance of the control system but also even induce instability to the dynamic system. Time-delay control algorithm is developed in this paper to solve this practical problem. The control system is first formulated in discrete-time form. In the presence of time-delay, the motion equation of the discrete-time control system remains a difference equation which can be transformed into first-order difference equation by augmenting the state variables. Optimal time-delay control algorithm is derived based on the augmented system. The time-delay control forces are simply generated from the time-delay states multiplied by the constant feedback gain. Numerical simulation is illustrated to verify the feasibility of the proposed control algorithm. Since time-delay effect is incorporated in the mathematical model for the structural control system throughout the derivation of the proposed algorithm, system performance and dynamic stability are guaranteed.

Solution of aircraft inverse problems by local optimization

Abstract: A feedforward control technique is presented for the determination of the input/output map associated to the inverse problem of the simulated motion of an aircraft. The procedure is particularly suitable in the redundant cases, which are reduced to nominal ones by imposing physically reasonable constraints on the state variables through a local optimization algorithm. Comparisons with already available solutions are shown together with some significant applications.

Clamped state solution of artificial neural network for real-time economic dispatch

Abstract: This paper presents a novel method for the real-time economic dispatch using clamped state variable formulation of the Kennedy, Chua and Lin (1988) artificial neural network (ANN). An efficient economic power dispatch algorithm must use real-time load conditions and the loss penalty-factor for representation of transmission losses in power system. The approach described in this paper assumes that an interface program will calculate the penalty factors for the current power flow state, as calculated by a state estimation program. The proposed method employs an ANN to enhance the speed and capability of algorithms which may use heuristics for online use. The ability of processing feedbacks in a collective parallel analog mode enables a neural network to simulate the dynamics that represent the optimization of an objective function subjected to its constraints for a given optimization model. Different techniques may be used to simulate the neural dynamic system. In this study, the authors propose a new method of simulation called the clamped state variable (CSV) technique. The new approach is very simple and it takes smaller computer time for the algorithm to converge than the complete circuit simulation. The results obtained by the CSV method are very close to that of numerical methods and are reported in this paper. >

Direct phase-domain calculation of transmission line transients using two-sided recursions

Abstract: This paper presents a new method for the simulation of electromagnetic transients on transmission lines. Instead of using convolutions of the input variables only, we perform short convolutions with both input and output variables. The result is a method of two-sided recursions (TSR), which is comparable in efficiency with the existing recursive convolutions or with their equivalent state variable formulations. It is, however, conceptually simpler and can be applied, in addition to fast modal-domain solutions, to the direct phase-domain calculation of transmission line transients with very accurate results. >