Discrete Pole Research Articles

Robust Perturbation Observer-based Finite Control Set Model Predictive Current Control for SPMSM Considering Parameter Mismatch

In order to improve the dynamics of the surface-mounted permanent magnet synchronous motors (SPMSM) used in servo systems, finite control set model predictive current control (FCS-MPCC) methods have been widely adopted. However, because the FCS-MPCC is a model-based strategy, its performance highly depends on the machine parameters, such as the winding resistance, inductance and flux linkage. Unfortunately, the parameter mismatch problem is common due to the measurement precision and environmental impacts (e.g., temperature). To enhance the robustness of the SPMSM FCS-MPCC systems, this paper proposes a Lundberg perturbation observer that is seldom used in the FCS model predictive control situations to remove the adverse effects caused by resistance and inductance mismatch. Firstly, the system model is established, and the FCS-MPCC mechanism is illustrated. Based on the machine model, the sensitivity of the control algorithm to the parameter mismatch is discussed. Then, the Luenberger perturbation observer that can estimate the general disturbance arising from the parameter uncertainties is developed, and the stability of the observer is analyzed by using the discrete pole assignment technique. Finally, the proposed disturbance observer is incorporated into the FCS-MPCC prediction plant model for real-time compensation. Both simulation and experiments are conducted on a three-phase SPMSM, verifying that the proposed strategy has marked control performance and strong robustness.

LMI Pole Regions for a Robust Discrete-Time Pole Placement Controller Design

Herein, robust pole placement controller design for linear uncertain discrete time dynamic systems is addressed. The adopted approach uses the so called “D regions” where the closed loop system poles are determined to lie. The discrete time pole regions corresponding to the prescribed damping of the resulting closed loop system are studied. The key issue is to determine the appropriate convex approximation to the originally non-convex discrete-time system pole region, so that numerically efficient robust controller design algorithms based on Linear Matrix Inequalities (LMI) can be used. Several alternatives for relatively simple inner approximations and their corresponding LMI descriptions are presented. The developed LMI region for the prescribed damping can be arbitrarily combined with other LMI pole limitations (e.g., stability degree). Simple algorithms to calculate the matrices for LMI representation of the proposed convex pole regions are provided in a concise way. The results and their use in a robust controller design are illustrated on a case study of a laboratory magnetic levitation system.

Permanent magnet DC motor (PMDC) model identification and controller design

Abstract System modeling is a set of mathematical equations that describe the dynamical behavior of a system. It is considered as a primary concern in determining a suitable controller to meet specific requirements. An autoregressive with exogenous terms (ARX) model for a PMDC motor is identified experimentally based on the recursive least square (RLS) method. Adaptive discrete pole placement controller (APPC) is proposed and designed aiming to control the motor revolving speed. For the comparison purpose, a discrete Proportional Integral (PI) controller is also considered in this work. The steady step response, transient response, and the mean squared error (MSE) is counted throughout the comparison. The e ect of the uncertainties in the PMDC model is also investigated in this paper. The result shows a superiority in the performance of the proposed controller compared to that obtained using PI controller.

A variant selection mechanism in the deformed and recrystallized β matrix of a metastable β-titanium alloy

ABSTRACTThe variant selection criteria during β to α phase transformations in a metastable β-titanium alloy (Ti-5553) in the presence of deformation are examined. Two distinct metallurgical states in the β matrix, heavily deformed and fully recrystallized, were obtained from a 90% cold-rolled alloy. The deformed and recrystallized samples were subjected to aging heat treatment for a short time to allow the precipitation of an intragranular α phase. Electron backscattered diffraction was used to assess the α crystallographic variant occurrence in the deformed as well as in the recrystallized β grains. A discrete pole figure analysis revealed that a limited number of variants were evolved in the deformed β grains while there was no variant selection in the recrystallized β matrix. The results suggest that activation of {112}<111>β slip systems determines a strong variant selection in the plastically deformed β matrix.

Study of the influence of the parameters of an experiment on the simulation of pole figures of polycrystalline materials using electron microscopy

A two-dimensional mathematical model of a polycrystalline sample and an experiment on electron backscattering diffraction (EBSD) is considered. The measurement parameters are taken to be the scanning step and threshold grain-boundary angle. Discrete pole figures for materials with hexagonal symmetry have been calculated based on the results of the model experiment. Discrete and smoothed (by the kernel method) pole figures of the model sample and the samples in the model experiment are compared using homogeneity criterion χ2, an estimate of the pole figure maximum and its coordinate, a deviation of the pole figures of the model in the experiment from the sample in the space of L1 measurable functions, and the RP-criterion for estimating the pole figure errors. Is is shown that the problem of calculating pole figures is ill-posed and their determination with respect to measurement parameters is not reliable.

Design and implementation of discrete PID control applied to Bitumen tank based on new approach of pole placement technique

This paper develops a novel approach for pole placement method of discrete proportional-integral-derivative (PID) control with industrial application of Bitumen system. The approach utilizes first order discrete-time transfer function (TF) with samples time delay more than unity for tuning the PID compensators, in order to achieve a priori set point of Bitumen mixing temperature. The work also introduces the well established Ziegler Nichols (ZN) and Chien-Hrones-Reswick (CHR) tuning techniques of discrete PID control, when applied to the same TF of Bitumen system, as benchmark. Bitumen system, sited at INSUMAT Company, is considered as a demonstrator for which the discrete PID control with the novel discrete pole placement approach is applied. Here, it is required to achieve a certain temperature for the Bitumen prior to the mixing process with the additives (polymers and fillers) in order to achieve a certain properties for insulation purposes. The key factor for the mixing process is the temperature of Bitumen which should not exceed \(\pm 5\,\%\) of the specified temperature, which ranges from 90 to \(180\,^{\circ }\hbox {C}\), to avoid reaching self-ignition state for the vapor inside the tank (\(\sim \)220\(\,^{\circ }\hbox {C}\)). This explains the avoidance of using conventional online tuning for PID compensators. Simulation results verify the applicability of the new approach and show satisfactory steady state response with very good control action when compared to the noisy control action of the ZN and CHR techniques. Finally, the paper shows successful implementation ‘onsite’ for the discrete PID control using the new approach for pole placement technique, for which all the control design criteria are verified.

Long-Term Prediction of Biological Wastewater Treatment Process Behavior via Wiener-Laguerre Network Model

A Wiener-Laguerre model with artificial neural network (ANN) as its nonlinear static part was employed to describe the dynamic behavior of a sequencing batch reactor (SBR) used for the treatment of dye-containing wastewater. The model was developed based on the experimental data obtained from the treatment of an effluent containing a reactive textile azo dye, Cibacron yellow FN-2R, bySphingomonas paucimobilisbacterium. The influent COD, MLVSS, and reaction time were selected as the process inputs and the effluent COD and BOD as the process outputs. The best possible result for the discrete pole parameter wasα=0.44. In order to adjust the parameters of ANN, the Levenberg-Marquardt (LM) algorithm was employed. The results predicted by the model were compared to the experimental data and showed a high correlation withR2&gt;0.99and a low mean absolute error (MAE). The results from this study reveal that the developed model is accurate and efficacious in predicting COD and BOD parameters of the dye-containing wastewater treated by SBR. The proposed modeling approach can be applied to other industrial wastewater treatment systems to predict effluent characteristics.

Engineering Artificial Signaling Centers to Polarize Embryoid Body Differentiation

Embryonic stem (ES) cells differentiating as aggregates self-organize dependent on Wnt signaling that is initially localized to discrete sites in the aggregate. As differentiation proceeds, Wnt signaling expands to most of the aggregates, thus resulting in widespread differentiation of mesendodermal progenitors. This process resembles primitive streak formation, but the lack of organized positional information makes the differentiating aggregates develop in a disorganized fashion. Here, we report that exogenous, cellular signaling sources can control the site where differentiation initiates in ES cell aggregates. Fibroblasts engineered to express cadherins are assembled with ES cells to form composite aggregates where the fibroblasts are positioned as a discrete pole. When engineered to express secreted Wnt agonists or antagonists, this pole functions to localize signaling in a way that polarizes the differentiating aggregates. The use of cell adhesion molecules to control morphology of developing stem cell aggregates should be widely applicable in tissue engineering.

50%冷間圧延を施したAl-Mg-Si合金の焼鈍に伴う組織変化の同一視野観察 &amp;mdash;その(2)回復により形成される組織&amp;mdash;

Changes in microstructures at recovery stage after cold-rolling at 50% reduction rate were observed in an Al-Mg-Si alloy by means of SEM-EBSD system. The same area in the specimen was observed before and after cold-rolling. Intermittent annealing at 673 K, Ar ion-polishing, and EBSD observation were repeated up to the annealing time of 3.6 ks. Dislocation cells formed by cold-rolling changed into subgrains with annealing. Low and high angle boundaries were formed with surrounding the subgrains depending on misorientations between the neighboring subgrains. The high angle boundaries migrated to form recovered microstructures. Original orientation of the dislocation cell was maintained in the recovered microstructure. Some of the recovered microstructures grew with invading others. Therefore, new discrete poles did not appear in a discrete pole figure during annealing but those in the invaded subgrains disappear, which made the pole figure of the annealed specimen different from that of the cold-rolled specimen. Secondary recovered microstructures were observed to be formed with invading primary formed recovered microstructures. The recovered microstructures were finally invaded by recrystallized grains to disappear. In a region where growth of recrystallized grains was delayed, coarse recovered microstructures composed of large subgrains were formed.

Robust High-Performance Inverter Control Using Discrete Direct-Design Pole Placement

A robust high-performance discrete controller, with a simple implementation and characterizable performance that lend it to high-power industrial applications, is proposed. Discrete direct-design pole placement allows the use of common design parameters such as damping ratio and bandwidth (BW) to define the controller's response. High performance is demonstrated with example systems achieving BWs twice as high as those of traditional cascaded current- and voltage-loop controllers. The controller is shown to be robust against component variations and many different load types, including low-impedance grid connections. Comparisons between the proposed controller and a discretized full-state-feedback continuous-time-derived controller are made and show significant improvements in both BW and stability margins. Practical tests on a parallel 2-MVA test system demonstrate a close correlation with the analysis, with an error of less than 1%.

Evidence for the discrete asymptotically-free BFKL Pomeron from HERA data

We show that the next-to-leading-order renormalization-group-improved asymptotically-free BFKL Pomeron provides a good fit to HERA data on virtual photoproduction at small x and large Q2. The leading discrete Pomeron pole reproduces qualitatively the Q2 dependence of the HERA data for x∼10−3, and a fit using the three leading discrete singularities reproduces quantitatively the Q2 and x dependence of the HERA data for x<10−2. This fit fixes the phase for all the BFKL wavefunctions at a chosen infrared scale.

Peristaltic modes of a single vortex in the Abelian Higgs model

Using the Abelian Higgs model, we study the radial excitations of single vortex and their propagation modes along the vortex line. We call such beyond-stringy modes peristaltic modes of single vortex. With the profile of the static vortex, we derive the vortex-induced potential, i.e., single-particle potential for the Higgs and the photon field fluctuations around the static vortex, and investigate the coherently propagating fluctuations which correspond to the vibration of the vortex. We derive, analyze, and numerically solve the field equations of the Higgs and the photon field fluctuations around the static vortex with various Ginzburg-Landau parameter $\ensuremath{\kappa}$ and topological charge $n$. Around the Bogomol'nyi-Prasad-Sommerfield value or critical coupling ${\ensuremath{\kappa}}^{2}=1/2$, there appears a significant correlation between the Higgs and the photon field fluctuations mediated by the static vortex. As a result, for ${\ensuremath{\kappa}}^{2}=1/2$, we find the characteristic new-type discrete pole of the peristaltic mode corresponding to the quasibound state of coherently fluctuating fields and the static vortex. We investigate its excitation energy, correlation energy of coherent fluctuations, spatial distributions, and the resulting magnetic flux behavior in detail. Our investigation covers not only usual type-II vortices with $n=1$ but also type-I and type-II vortices with $n\ensuremath{\in}Z$ for the application to various general systems where the vortexlike objects behave as the essential degrees of freedom.

A method to obtain uniform magnetic-field energy density gradient distribution using discrete pole pieces for a microelectromechanical-system-based magnetic cell separator

A spatially uniform magnetic energy density gradient (∇B2) distribution offers a controlled environment to separate magnetically tagged cells or biomolecules based on their magnetophoretic mobility [L. R. Moore et al., J. Biochem. Biophys. Methods 37, 11 (1998)]. A design to obtain a uniform ∇B2 distribution for a microelectromechanical-systems-based magnetic cell separator was developed. The design consists of an external magnetic circuit and a microfabricated channel (biochip) with embedded discrete pole pieces on the channel walls. The two-dimensional and three-dimensional magnetostatic simulation softwares utilizing boundary element methods were used to optimize the positions and the dimensions of the discrete pole pieces, as well as the external magnetic circuit—the combination of which would generate a uniform ∇B2 profile over the channel cross section. It was found that the discrete pole pieces required specific magnetic properties (saturation magnetization constant &amp;gt;1.55T) to affect the overall ∇B2 distribution. Investigating different positions of the discrete pole pieces inside the external magnetic field indicated that the proposed design could generate uniform ∇B2 distribution with ±100μm displacements along the height/width and ±1° inclination from the optimum position.

A supervised discrete adaptive control scheme with multiestimation

A discrete pole placement-based adaptive controller with multiestimation is synthesized for linear time-invariant plants. A higher level switching structure between the various estimation schemes is used to supervise the re-parameterization of the adaptive controller in real time. The basic usefulness of the proposed multiestimation scheme relies into the improvement of the adaptation transient behavior while robust closed-loop stability is proved even in the presence of unmodeled dynamics of sufficiently small sizes. The scheme becomes specifically attractive when the various estimators are adaptive identifiers for the plant which is being modeled as possessing different possible amounts of unmodeled dynamics including different nominal orders and parametrical uncertainties. The influence of free design parameters is discussed through exhaustively worked simulations.

Error analysis of the discrete complex image method and pole extraction

Recently, Teo et al (IEEE AP-S Int. Symp., vol. 4, pp. 862-864, 2001) proposed a discrete complex image method that is able to represent both the near and far fields of the Green's function accurately, using only a single approximate Green's function. In this paper, an error analysis of this method is presented. The error analysis shows an additional term, which represents the quasi-static image of the surface-wave poles plays a crucial role in the convergence and accuracy of this new method. As the extraction of poles is required, a recently proposed algorithm by Teo et al (IEEE Trans. Microwave Theory Tech., vol. 50, pp. 440-445, 2002) is also discussed and compared with existing methods in terms of computational speed.

Pole Figure Inversion Using Finite Elements Over Rodrigues Space

Using finite elements over Rodrigues space, methods are developed for the formation and inversion of pole figures. The methods take advantage of the properties of Rodrigues space, particularly the fact that geodesics corresponding to pole figure projection paths are straight lines. Both discrete and continuous pole figure data may be inverted to obtain orientation distribution functions (ODFs) in Rodrigues space, and we include sample applications for both types of data.

Mechatronics of electrostatic microactuators for computer disk drive dual-stage servo systems

A decoupled control design structure and discrete time pole placement design method are proposed for MEMS-based dual-stage servo control design in magnetic disk drives. Dual-stage track following controllers are designed using a decoupled three-step design process: the voice coil motor (VCM) loop design, the microactuator (MA) inner loop design, and the MA outer loop design. Both MIMO (when the MA relative position sensing is available) and SIMO (when the MA relative position sensing is not available) designs are considered. The effect of MA resonance mode variations on the stability and performance of the controllers are analyzed. Self-tuning control and online identification of the MA model are developed to compensate for the variations in the MA's resonance mode.

A new multirate sampled-data technique for adaptive pole positioning in linear systems

The adaptive pole placement problem for linear systems is solved using a new class of multirate controllers, called two-point multirate controllers. In such a type of controller, the control is constrained to a certain piecewise constant signal, while the controlled plant output is detected many times over a fundamental sampling period. On the basis of the proposed strategy, the original problem is reduced to an associate discrete pole placement problem, for which a fictitious static-state feedback controller is needed to be computed. This control strategy allows us to assign the poles of the sampled closedloop system arbitrarily in desired locations, and does not make assumptions on the plant other than controllability and observability of the continuous and the sampled system, and known order. The controller determination relies on a closed-form formula, which can be thought as the extension of the Ackermann formula for multi-input/multi-output (MIMO) systems. Known indirect adaptive pole placement techniques require the solution of matrix polynomial Diophantine equations, which, in many cases, might yield an unstable controller. Moreover, the proposed adaptive scheme is readily applicable to non-minimum phase systems, and to systems which do not possess the parity interlacing property. Finally, persistency of excitation and, therefore, parameter convergence, of the continuous-time plant is provided without making assumptions either on the existence of specific convex sets in which the estimated parameters belong or on the coprimeness of the polynomials describing the ARMA model, or finally on the richeness of the reference signals, as compared to known adaptive pole placement schemes.

Short-range correlations in nuclear matter using Green's functions within a discrete pole approximation

We treat short-range correlations in nuclear matter, induced by the repulsive core of the nucleon-nucleon potential, within the framework of a self-consistent Green's function theory. The effective in-medium interaction sums the ladder diagrams of both the particle-particle and hole-hole type. The demand of self-consistency results in a set of nonlinear equations which must be solved by iteration. We explore the possibility of approximating the single-particle Green's function by a limited number of poles and residues.

Stability of input amplitude constrained adaptive pole placement control systems

This paper presents stability analysis for discrete time pole placement control system with input saturation constraints. It is shown that the adaptive closed-loop system for a class of stable type- m plants is globally stable in the sense that all the signals in the loop remain bounded. It is also shown that certain degree of robustness with respect to modelling uncertainties and disturbances can be achieved for the adaptive control system by implementing a simple fixed dead zone in the parameter estimator. If the plant is free from modelling uncertainties and disturbances and the control input is not saturated for a finite period of time, then the closed-loop adaptive control system will asymptotically be characterized by the desired closed-loop poles within this time period.