State Variable Technique Research Articles

Event-triggered Control of Discrete-time Switched Linear Systems with an Arbitrary Sampling Period

In this paper, the event-triggered control problem for discrete-time switched linear systems with an arbitrary sampling period is considered. At each sampling instant, only the sampled information of system state and switching signal is available to the controller. Particularly, the sampling period is arbitrary in this paper and frequent switching is allowed to happen in an inter-event period. Based on that, by constructing a time- and mode-dependent quadratic piecewise Lyapunov function, a new globally exponentially stability (GES) result under modal dwell time (MDT) criteria is obtained. By the novel Lyapunov function and the state variable transformation technique, a statefeedback controller is designed for the switched linear system. At last, a numerical example is proposed to illustrate our approach.

Integrated lean concepts and continuous/discrete-event simulation to examine productivity improvement in door assembly-line for residential buildings

Efforts within the construction-manufacturing domain to improve assembly-line operations have benefited from paradigms emerging in the late-1990s such as lean manufacturing. This study investigates lean concept solutions to enhance productivity prior to capital investments. The investigation is carried on a case study of a single-door assembly line for residential buildings. Lean improvements are examined through an integrated continuous/discrete-event simulation approach, aiming to increase the productivity of the assembly line. The proposed simulation model incorporates factors representing the system reliability. Continuous simulation modelling, using state variable technique, is implemented to facilitate the observation of door unites in targeted sections to track the accumulation levels in these particular sections of the assembly line. In addition, proposed solutions for productivity improvements are implemented within the simulation model, such as introducing advanced alternatives for the automated stations and adding parallel stations. The effect on the productivity of the assembly line was successfully evaluated after the implantation of the proposed improvements in the simulation model. Relevant approaches can be implemented to evaluate and improve modular construction assembly lines prior to incurring capital investment.

Maximizing the Data Rate of an Inductively Coupled Chip-to-Chip Link by Resetting the Channel State Variables

A technique is proposed for increasing the data rate transmitted through an inductively coupled chip-to-chip link by resetting the channel state variables. This allows the data rate to be increased well beyond what is implied by the channel bandwidth. In the proposed scheme, the two sides of the link are resonated at the highest possible quality factor, maximizing link gain, and minimizing interference. The transmit signal is a binary matched pulse which maximizes the received signal for a given transmitter voltage limit. High-efficiency switching transmitters can be used for this type of signal. The proposed technique can be applied to communication links in which channel state variables are accessible for reset. For increasing the data rate, it is shown that the proposed state-variable reset technique results in a higher signal-to-noise ratio of the received signal and a higher energy efficiency compared to reducing the quality factor to widen the bandwidth, using equalization, or using multi-level signaling. The technique is demonstrated on a chip-to-chip link with coupled 1.5 mm $\times1.5$ mm planar inductors separated by 0.5 mm in a 0.18 $\mathrm {\mu m}$ CMOS process. 500 Mb/s data rate is achieved over a link which has a band-pass bandwidth of 185 MHz.

State variable technique islanding detection using time-frequency energy analysis for DFIG wind turbine in microgrid system

This paper introduces a new combined technique for wind turbine islanding detection using the trajectory of state variables and wavelet transform in microgrid system. The proposed relay is utilized of energy variation state of time-frequency transform coefficients of local signals in two-dimensional space. In order to improve of the proposed relay performance, a signal selection method based on the correlation concept between islanding and non-islanding signals. From of all patterns, the best of them with high correlation in islanding status is selected for the proposed relay learning. A neuro-fuzzy machine is used as learning of selected patterns to avoid threshold selection. The proposed technique is utilized to wind turbine islanding detection in a microgrid system contains various types of distributed generation including wind turbine, Combined Heat and Power (CHP) and photovoltaic system. Many islanding and non-islanding situation including motor starting, various load and capacitor switching in various operation conditions in the studied microgrid are simulated. Millstone characteristics of the proposed technique are included passive-based technique, negligible None Detection Zone (NDZ), suitable for microgrid application, performance increment in detection and fast detection time. Operation results of the proposed relay in various conditions confirm the performance of the proposed detection relay.

Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework

This paper investigates an asset allocation problem for defined contribution pension funds with stochastic income and mortality risk under a multi-period mean–variance framework. Different from most studies in the literature where the expected utility is maximized or the risk measured by the quadratic mean deviation is minimized, we consider synthetically both to enhance the return and to control the risk by the mean–variance criterion. First, we obtain the analytical expressions for the efficient investment strategy and the efficient frontier by adopting the Lagrange dual theory, the state variable transformation technique and the stochastic optimal control method. Then, we discuss some special cases under our model. Finally, a numerical example is presented to illustrate the results obtained in this paper.

Influence of Actuator Reluctance Force on Linear Oscillating Systems

The operation of linear oscillating system is complicated, involving system nonlinearities of both actuator and load, and variations of driving frequency in order to track the mechanical resonance. In this paper, the state-variable modeling technique is used to analytically investigate the influence of actuator reluctance force on the performance of linear oscillating systems. The analytical derivations will be validated by simulations, and good agreements are achieved.

Transient analysis and fault compensation during module failure in paralleled power modules

This paper investigates the transient behavior of a power supply comprising paralleled power modules when one of its modules fails. A detailed transient analysis is presented using the principle of superposition and the state variable technique to investigate the effects of the faulty module on system performance. A fault compensation strategy is proposed to allow smooth ride-through during fault. This enhances the supply's reliability and robustness. The analysis results and compensation methods are verified via simulation and experiments for the case of three paralleled buck converters with a shorted switch, and smooth ride-through of output voltage is achieved.

Eigenanalysis and continuum modelling of a curved repetitive beam-like structure

A curved repetitive pin-jointed structure is analysed using a state variable transfer matrix technique. Within a global Cartesian coordinate system, the transfer matrix G of each cell is different, but within a polar coordinate system they are identical, implying circumferential symmetry. Eigenanalysis provides the rates of decay of self-equilibrated end loading, as anticipated by Saint-Venant's principle, two real unity eigenvalues associated with rigid body rotation and pure bending, and repeated conjugate complex unity eigenvalues, associated with the rigid body displacements, and tension and shear. Interpretation of the eigen- and principal vectors, and also combined vectors from different eigenspaces, allows one to determine the equivalent continuum beam properties, e.g. second moment of area, location of the neutral axis, cross-sectional area, and shear coefficient. The transfer matrix approach is validated by comparison with what may be regarded as exact finite element predictions, and also compared with a (believed novel) thick curved beam strain energy analysis employing the derived equivalent continuum properties and the use of Castigliano's theorems. Agreement is found to be excellent.

Eigenanalysis and continuum modelling of pre-twisted repetitive beam-like structures

A repetitive pin-jointed, pre-twisted structure is analysed using a state variable transfer matrix technique. Within a global coordinate system the transfer matrix is periodic, but introduction of a local coordinate system rotating with nodal cross-sections results in an autonomous transfer matrix for this Floquet system. Eigenanalysis reveals four real unity eigenvalues, indicating tension–torsion coupling, and equivalent continuum properties such as Poisson’s ratio, cross-sectional area, torsion constant and the tension–torsion coupling coefficient are determined. A variety of real and complex near diagonal Jordan decompositions are possible for the multiple (eight) complex unity eigenvalues and these are discussed in some detail. Analysis of the associated principal vectors shows that a bending moment produces curvature in the plane of the moment, together with shear deformation in the perpendicular plane, but no bending–bending coupling; the choice of a structure having an equilateral triangular cross-section is thought responsible for this unexpected behaviour, as the equivalent continuum second moments of area are equal about all cross-sectional axes. In addition, an asymmetric stiffness matrix is obtained for bending moment and shearing force coupling, and possible causes are discussed.

Sensorless Monitoring of Induction Motor Drive Systems

The paper deals with sensorless monitoring of induction motor drive systems. It is well known that induction motor drives are very important parts of any industrial application involving electrical equipment. They must be carefully surveyed to ensure reliable and profitable operations. However induction motor drive systems are also known as complex nonlinear time-varying systems. Thus entails great difficulties for monitoring purposes. Based on the fact that the system model can be significantly simplified if one applies the d-q Park transformation and an appropriate field orientation technique, an adequate model structure is obtained. An observer-based state variable estimation technique is used for sensorless monitoring of a general induction motor drive system. The sensorless monitoring procedure uses a simple curves plotting of the estimated state variables. The approach permits to detect up to five percent changes in the estimated state variables information. Copyright © 2004 IFAC

Eigenanalysis and continuum modelling of an asymmetric beam-like repetitive structure

An asymmetric repetitive pin-jointed structure, based upon a 3-D NASA framework, is analysed using a state variable transfer matrix technique. A conventional transfer matrix cannot be constructed due to the singularity of one partition of the stiffness matrix; instead, a cell (rather than cross-sectional) state vector consisting of displacements only is employed, leading to a generalised eigenvalue problem. The asymmetry of the structure leads to tension–torsion and bending–shear couplings, which may be explained in terms of the tension–shear coupling of a single face of the structure. Equivalent continuum beam properties and coupling coefficients are determined, and the effect of (a)symmetry discussed as a trade between, for example, tension-Poisson's ratio contraction for a symmetric structure, against tension–torsion coupling for the asymmetric.

On the realization of oscillators using state equations

In this work, an extension to the oscillator synthesis method using the state variable technique is presented. It is shown that using suitable block diagrams, which represent the state equations, systematic circuit realizations can be performed. The most critical steps of the presented method are the selection of the suitable characteristic equation and thederivation of the corresponding sub-circuits. The selection criteria of thecharacteristic equations for the realization of single resistance controlled oscillators (SRCOs) are also given. By using the extended state variable synthesis method, SRCOs employing a single current feedback amplifier (CFA)are obtained. Furthermore, a new active element, namely the differentialvoltage current feedback amplifier (DVCFA) is proposed for the realization of oscillators employing only grounded capacitors and new SRCOs employing thisactive element are presented. SPICE simulations and experimental results confirm the operation of the presented oscillators.

Thermal Deformation of Antisymmetric Angle-ply Laminated Plate Strips in Cylindrical Bending

Exact analytical solutions for the thermal deformations of antisymmetric angle-ply laminated plate strips in cylindrical bending are developed. The state variable technique in conjunction with Jordan canonical form is used to obtain these solutions for plate strips with arbitrary boundary conditions. Deflections are computed for laminates subjected to linearly varying transverse temperature distribution. Numerical results are presented emphasizing the effects of shear deformation, number of layers, ply-angles, transverse shear correction factor and boundary conditions on the thermal response.

A method for dynamic response analysis of time-variant discrete systems

A method is proposed for analysing the transient response of structures when variation with respect to time of the stiffness and damping coefficients are taken into account. The state-variable technique is employed to formulate the dynamic equilibrium equation for the time-variant system. Excitation is represented as a series of impulses. It allows introduction of virtual initial conditions which are equivalent to the impulse excitations in the state space equations. The effective method for evaluation of a state transition matrix is used. Numerical tests of an illustrative example demonstrate the validity and effectiveness of the approach suggested in this paper. The method has great advantages when the behaviour of the semi-active system is calculated and the optimal control of the systems is simulated.

Finite-difference model for computing the response of multiconductor transmission lines interconnected by load circuits

In this paper, we describe a time-domain technique to calculate the induced currents and voltages on multi-conductor transmission line (mtl) networks, which contain resistive circuits in the junctions. The network can be excited by an external plane wave or by voltage sources which are located at any circuit of the system. The method is based on a time-space centered finite-difference technique to solve the time-domain mtl coupled equations. This approach makes it possible to solve a linear matrix system which can be expressed under the AX = B form. We apply the method to mtl networks solved by a frequency analysis based on a state variable technique and to previously published examples solved by other numerical methods. The results correspond closely enough for the approach to be validated.

On fast FIR filters implemented as tail-canceling IIR filters

We have developed an algorithm based on synthetic division for deriving the transfer function that cancels the tail of a given arbitrary rational (IIR) transfer function after a desired number of time steps. Our method applies to transfer functions with repeated poles, whereas previous methods of tail-subtraction cannot. We use a parallel state-variable technique with periodic refreshing to induce finite memory in order to prevent accumulation of quantization error in cases where the given transfer function has unstable modes. We present two methods for designing linear-phase truncated IIR (TIIR) filters based on antiphase filters. We explore finite-register effects for unstable modes and provide bounds on the maximum TIIR filter length. In particular, we show that for unstable systems, the available dynamic range of the registers must be three times that of the data. Considerable computational savings over conventional FIR filters are attainable for a given specification of linear-phase filter. We provide examples of filter design. We show how to generate finite-length polynomial impulse responses using TIIR filters. We list some applications of TIIR filters, including uses in digital audio and an algorithm for efficiently implementing Kay's optimal high-resolution frequency estimator.

ADAPTIVE CONTROL FOR A MECHANICAL SYSTEM WITH OSCILLATION DISTURBANCE

A two-stage spring-lumped mass system was designed and built to investigate the suppression of vibration amplitude and the coupling tracking control problems. Disregarding the non-linear factors and unknown parameters, the system mathematical model could be formulated by using the state variable technique. A corresponding observable discrete time model was identified from a modified recursive least squares method based on the input and output data of this system. Then a robust multi-variable adaptive control strategy with pole assignment structure was proposed to control this mechanical system. Experiments were performed to evaluate the feasibility of this active vibration control strategy and the influence of the parameters estimator on the control performance. The experimental results showed that this approach can effectively diminish the amplitude of vibration and overcome the system coupling effect to obtain accurate position tracking.

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

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. >

State-plane approach for the analysis of half-bridge parallel resonant converters

Generalised state-plane analysis for a half-bridge parallel resonant converter (PRC) operating in continuous conduction mode is presented. It is shown that a PRC circuit of any order can be analysed in terms of simple two-dimensional state-plane diagrams, without having to use any sinusoidal approximation. The approach presented makes use of the state-variable transformation technique previously used for the analysis of second- and third-order resonant converters. This method is applied to a specific example of a sixth-order parallel resonant converter operated in the continuous conduction mode.

A Dynamic Absorber With Active Vibration Control

The design and construction of a dynamic absorber incorporating active vibration control is described. The absorber is a two-degrees-of-freedom spring — lumped mass system sliding on a guide pillar, with two internal vibration disturbance sources. Both the main mass and the secondary absorber mass are acted on by DC servo motors, respectively, to suppress the vibration amplitude. The state variable technique is used to model this dynamic system and a decoupling PID control method is used. First, the discrete time state space model is identified by using the commercial software MATLAB. Then the decoupling controller of this multi-input/multi-output system is derived from the identified model. Finally the results of some experiments are presented. The experimental results show that the system is effective in suppressing vibration. Also, the performance of this control strategy for position tracking control is evaluated based on experimental data.