Multiple Poles Research Articles

Numerical solution of Cauchy problems with multiple poles of integer order

We consider Cauchy problem for ordinary differential equation with solution possessing a sequence of multiple poles. We propose the generalized reciprocal function method. It reduces calculation of a multiple pole to retrieval of a simple zero of accordingly chosen function. Advantages of this approach are illustrated by numerical examples. We propose two representative test problems which constitute interest for verification of other numerical methods for problems with poles.

Tuning of PID Control for the Double Integrator Plus Dead Time Model by Modified Real Dominant Pole and Performance Portrait Methods

The paper discusses the proportional-integral-derivative (PID) controller from the viewpoint of (a) the analytical tuning of the PID controller for the double integrator plus dead time (DIPDT) model and (b) the numerical tuning using the performance portrait method (PPM). In the first case, the already published tuning with multiple real dominant pole, extended by integrated tuning procedures, which incorporate the inevitable low-pass filters by delay equivalences, is elaborated for modified sets of real poles. By considering several such modified sets of real poles, resulting in several new sets of controller parameters, the design can be better adapted to the requirements of the control tasks solved and to the limitations of the existing control loop hardware. In a noisy and uncertain environment, the balance between speed of setpoint and disturbance responses and acceptable excessive controller effort can thus be improved. The effectiveness of the analytical design can be evaluated using the numerical performance portrait method (PPM). For an already generated performance portrait (PP), it can offer a broad spectrum of controller settings that satisfy various design constraints. However, the results of the analytical design are still important as they facilitate the initial steps in the elaboration of the PPM and in explaining the nature of PID control. The developed controller tuning are compared using a new interpretation of PID controller as an extension of the stabilising PD controller by disturbance observer (DOB). The input disturbances reconstructed by DOB by evaluating the controller output of an integral process model in steady-state, can be estimated by a low-pass filter with a sufficiently long (integral) time constant. All analysed results are in full agreement with the proposed DOB interpretation, which furthermore contributes significantly to the explanation of the problems related to the optimal design of PID controllers.

Detection of Structural Magnet Defects for Permanent Magnet Synchronous Motors

This paper presents a novel method for the detection of magnet cracks or defects through back electromotive force (EMF) voltage, line current and vibration signals for radial flux permanent magnet (PM) synchronous motors. An integer slot PM motor with 12 poles is used in the study. Different types of faults including both radial and axial magnet crack defects with multiple magnet fault scenarios and multiple pole fault cases are studied in detail. In addition, the severity of magnet fault is also investigated. Random forest based magnet defect detection is utilized and a classification scheme is proposed in order to analyze the changes in the harmonics arising from single or multiple, radial or axial magnet defects. The results clearly show that the harmonics is altered in such a manner that it is possible to determine not only the magnet fault but the type of the magnet defect using motor voltage, current or vibration data.

PTEN: Sumoylation Function is the Key to the Maintenance of Genomic Stability of Cell

Phosphatase and tensin homolog deleted on chromosome 10 (PTEN), a tumor suppressor protein with dual phosphatase activity, is found to be frequently mutated in various cancers. PTEN is post-translationally modulated at various amino acid residues which are crucial for sub-cellular localization as well as its catalytic functions rendering genomic stability. Recent reports suggest that PTEN also acts as a DNA repair protein. But how post-translational modulation of PTEN affects cytological damage and aneuploidy is not studied in detail. Here, we focus on the role of sumoylation of PTEN in context with DNA damage induced cytological damage like micronucleus (MNi), nuclear bud (NB), and nuclear bridge formation. Our data suggest that wild type PTEN but not sumo-dead PTEN significantly reduces cytological damage in PTEN mutant PC3 cells. In case of sumo-dead PTEN, the cytological parameters are increased during 24[Formula: see text]h recovery time point after DNA damage. Next, we measured the effectiveness of the sumo-dead (PTEN-K254R) mutant on aneuploidy, where we found that sumoylation is essential for maintaining chromosome number. As chromosome number variation in daughter cell is due to multiple spindle pole formation, we qualitatively and quantitatively evaluate the [Formula: see text] tubulin pole formation in PTEN-K254R clone transfected cells. We found aberrant pole formation is significantly increased in PTEN-K254R transfected cells compared to wild-type PTEN. Further depletion of sumoylation activity of PTEN increases the expression of phosphorylated form of Aurora kinase A (AURKA) (T288) and PLK1 (T210) proteins with or without nocodazole, a microtubule depolymerizing agent compared to cells expressing wild-type PTEN. Thus, sumoylation of PTEN is essential for maintaining genomic stability.

Riemann–Hilbert problem for the focusing nonlinear Schrödinger equation with multiple high-order poles under nonzero boundary conditions

The Riemann–Hilbert (RH) problem is developed to study the focusing nonlinear Schrödinger (NLS) equation with multiple high-order poles under nonzero boundary conditions. Laurent expansion and Taylor series are employed to replace the residues at the simple- and the second-poles. Furthermore, the solution of RH problem is transformed into a closed system of algebraic equations, and the soliton solutions corresponding to the transmission coefficient 1/s11(z) with an N-order pole are obtained by solving the algebraic system. Then, in a more general case, the transmission coefficient with multiple high-order poles is studied, and the corresponding solutions are obtained. In addition, for high-order pole, the propagation behavior of the soliton solution corresponding to a third-order pole and the mixed case of a second-order pole and a simple pole are given as example.

Multi-Agent Position Estimation in Modular Motor Drives Using Low-Resolution Sensors

Because a modular motor drive is composed of multiple identical pole drive units and controllers, it can be considered as a multi-agent system. This makes modular motor drives particularly interesting during faults, when the remaining healthy agents assure the continuity of operation. Nevertheless, for some crucial information such as the rotor position, these drives still rely on a single sensor which introduces a single point of failure. In this work, this single high-resolution position sensor is replaced by multiple binary, low-resolution position sensors. A vector tracking observer algorithm, implemented in the different controllers, processes this low-resolution sensor data into a position estimate. Subsequently, these position estimates of the different agents are exchanged with other agents using a distributed averaging algorithm. For this latter approach, it is shown in this work that it improves the position estimation under healthy conditions as well as during agent malfunctions. The concept is demonstrated on a modular axial-flux permanent magnet synchronous machine with fifteen pole drive units, each equipped with a low-resolution position sensor, that are assigned to five agents.

Disturbance Observer in PID Controllers for First-Order Time-Delayed Systems

The article shows that the stabilizing P, PD, or PDA controllers for time-delayed first-order systems extended by automatic reset (disturbance reconstruction and compensation) established by evaluating the steady state output values of the controller, yield series PI, PID or PIDA controllers. By comparing the parameters of the given controllers tuned by the method of multiple real dominant pole, it can be shown that the obtained values of the integration time constant are many times larger than the time constants of the transients of the equivalent circuits with the stabilizing controller. The proposed interpretation of the functionality of disturbance observer included in controllers with disturbance compensation significantly helps in understanding principles of their optimal tuning, can also be used for further modifications of their operation taking into account various other limitations and establishes a unique educational framework covering most of the existing traditional, modern and postmodern controllers.

Tuning PID and PI-PI servo controllers by multiple pole placement

Tuning PID and PI-PI servo controllers by multiple pole placement

Characterization of a recently synthesized microtubule-targeting compound that disrupts mitotic spindle poles in human cells

We reveal the effects of a new microtubule-destabilizing compound in human cells. C75 has a core thienoisoquinoline scaffold with several functional groups amenable to modification. Previously we found that sub micromolar concentrations of C75 caused cytotoxicity. We also found that C75 inhibited microtubule polymerization and competed with colchicine for tubulin-binding in vitro. However, here we found that the two compounds synergized suggesting differences in their mechanism of action. Indeed, live imaging revealed that C75 causes different spindle phenotypes compared to colchicine. Spindles remained bipolar and collapsed after colchicine treatment, while C75 caused bipolar spindles to become multipolar. Importantly, microtubules rapidly disappeared after C75-treatment, but then grew back unevenly and from multiple poles. The C75 spindle phenotype is reminiscent of phenotypes caused by depletion of ch-TOG, a microtubule polymerase, suggesting that C75 blocks microtubule polymerization in metaphase cells. C75 also caused an increase in the number of spindle poles in paclitaxel-treated cells, and combining low amounts of C75 and paclitaxel caused greater regression of multicellular tumour spheroids compared to each compound on their own. These findings warrant further exploration of C75’s anti-cancer potential.

Revisiting quantum Zeno effect and anti-Zeno effect: Universality vs non-universality

Universality vs non-universality on the quantum Zeno effect and the anti-Zeno effect is discussed. It is well-known that the Zeno effect is a result of the branch point effect based on the constraint that the energy spectrum is bounded from below. On the other hand, we show that the anti-Zeno effect arises from the interference of multiple complex poles in the lower half energy plane on a larger time scale compared with the Zeno time. Since the production of extra complex poles depends on the characteristics of the interaction Hamiltonian, we emphasize that the anti-Zeno effect is model-dependent and non-universal, while the Zeno effect is a universal phenomenon independent of the form of the interaction.

Design and experimental evaluation a novel magneto-rheological brake with tooth shaped rotor

In this study, a novel magnetorheological brake (MRB) with tooth-shape rotor is developed. In this new MRB, traditional cylindrical rotor is replaced by a new one with tooth-shaped rotor. The teeth on the rotor act as multiple magnetic poles of the brake. Two magnetic coils are placed on side-housings of the brake to generate a mutual magnetic field of the MRB. The inner face of each side-housing has tooth shaped features as well. These tooth shaped features interact with the rotor teeth via magnetorheological fluid (MRF) medium. By using the tooth shaped rotor, more interface area between the rotor and the working MRF can be archived, which can improve performance characteristics of the proposed MRB such as compact size, low power consumption and high braking torque. After an introduction of state of the art of MRB development, the schematics and working principle of the MRB with tooth-shaped rotor is proposed. The modeling of the MRB is then derived based on magnetic finite element analysis and Bingham rheological model of MRF. Optimal design of the MRB considering mass and braking torque of the MRB is then conducted. From the optimal design result, it is shown that the mass and power consumption of the proposed MRB are significantly smaller than those of previously developed ones. In details, at high value of the maximum braking torque (100 Nm), the proposed MRB mass is only around 31.3% of the mass of the thin-wall single-coil and 42.6% of the mass of the thin-wall double coil MRB. In addition, at small values of the maximum braking torque (5 Nm), power consumption of the proposed MRB is only around 33% of that of the thin-wall single-coil and 45.5% of that of the thin-wall double coil MRB. Experimental works on prototypes of the proposed MRB are then performed for validation.

Close Reading on a Global Scale

Close Reading on a Global Scale

On singular elliptic boundary value problems via a harmonic analysis approach

We consider a class of elliptic problems in the half-space R + n with nonhomogeneous boundary conditions containing nonlinearities and critical singular potentials. We obtain existence and regularity results by means of a harmonic analysis approach based on a framework of weighted spaces in Fourier variables. This framework seems to be new in the context of elliptic boundary value problems and allows us to consider Hardy's potential λ 1 / | x | 2 in R + n and Kato's potential λ 2 / | x ′ | on the boundary ∂ R + n , as well as their versions with multiple poles, without using the so-called Kato and Hardy inequalities. Singular boundary forcing terms can also be addressed. Moreover, our results cover supercritical nonlinearities, such as ± u p in R + n and ± u q on ∂ R + n with integers p > 2 ⁎ − 1 and q > 2 ⁎ − 1 .

Desired Characteristic Equation Based PID Controller Tuning for Lag-Dominating Processes With Real-Time Realization on Level Control System

Objective of this study is to design proportional-integral-derivative (PID) controller with cascaded lag filter based on desired characteristic equation for lag-dominating processes. Here, attempt is made to formulate the closed-loop characteristic equation which comprises of multiple poles placed at the desired locations. Moreover, a guideline is also provided to choose the parameters of the closed-loop characteristic equation based on optimal values for performance and robustness indices. Efficacy of the proposed scheme is verified through simulation study with first-order plus dead time (FOPDT), second-order plus dead time (SOPDT), and pure integrating plus dead time (IPDT) processes in comparison with recently reported PID tuning relations. Robustness of the proposed controller is also tested in presence of perturbation for process model parameters. In addition, Kharitonov's interval polynomial is used for robust stability analysis. Real-time experimentation is also performed on a level control loop.

Development of a novel MR clutch featuring tooth-shaped disc

In this research, we focus on development of a new configuration of magneto-rheological fluid (MRF) based clutch (MRC) featuring a tooth-shaped disc with multiple teeth acting as multiple magnetic poles of the clutch. The tooth-shaped disc is placed in a clutch housing composed of the left housing and the right housing. The inner face the housing also has tooth shaped features mating with the teeth of the disc through the working MRF. Excitation coils are placed directly on stationary winding cores placed on both side of the clutch housing. An air gap of 0.3 mm is left between the housing and the winding cores to ensure the housing can freely rotate against the winding cores. After the introductory part, configuration of the MRC is introduced and the transmitted torque of the MRC is derived. An optimization process to minimize the overall volume of the proposed clutch, which can generate a required maximum braking torque, is then conducted. The optimal results show that the overall volume of the proposed MRC is significantly reduced compared to a referenced conventional MRC (0.159 m3 vs. 0.295 m3). A prototype of the proposed MRC is fabricated for experimental works and good agreement between the experimental results and simulated ones is archived.

Networked partisanship and framing: A socio-semantic network analysis of the Italian debate on migration.

The huge amount of data made available by the massive usage of social media has opened up the unprecedented possibility to carry out a data-driven study of political processes. While particular attention has been paid to phenomena like elite and mass polarization during online debates and echo-chambers formation, the interplay between online partisanship and framing practices, jointly sustaining adversarial dynamics, still remains overlooked. With the present paper, we carry out a socio-semantic analysis of the debate about migration policies observed on the Italian Twittersphere, across the period May-November 2019. As regards the social analysis, our methodology allows us to extract relevant information about the political orientation of the communities of users—hereby called partisan communities—without resorting upon any external information. Remarkably, our community detection technique is sensitive enough to clearly highlight the dynamics characterizing the relationship among different political forces. As regards the semantic analysis, our networks of hashtags display a mesoscale structure organized in a core-periphery fashion, across the entire observation period. Taken altogether, our results point at different, yet overlapping, trajectories of conflict played out using migration issues as a backdrop. A first line opposes communities discussing substantively of migration to communities approaching this issue just to fuel hostility against political opponents; within the second line, a mechanism of distancing between partisan communities reflects shifting political alliances within the governmental coalition. Ultimately, our results contribute to shed light on the complexity of the Italian political context characterized by multiple poles of partisan alignment.

Miniaturized Wideband Bandpass Filter based on Capacitor-loaded One-eighth Wavelength Coupled Line

A novel miniaturized wideband bandpass filter (BPF) using capacitor-loaded microstrip coupled line is proposed. The capacitors are loaded in parallel and series to the coupled line, which makes the filter just require one one-eighth wavelength coupled line and achieve filtering response with multiple transmission poles (TPs) and transmission zeros (TZs). Compared with the state-of-the-art microstrip wideband BPFs, the proposed filter has the advantages of compact size and simple structure. A prototype centered at 1.47 GHz with the 3-dB fractional bandwidth of 86.5% is demonstrated, which exhibits the compact size of 0.003λ2 g (λg is the guided wavelength at the center frequency) and the minimum insertion loss of 0.37 dB.

Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov–Ivanov equation under the zero/nonzero background

In this article, the inverse scattering transform is considered for the Gerdjikov–Ivanov equation with zero and non-zero boundary conditions by a matrix Riemann–Hilbert (RH) method. The formula of the soliton solutions is established by Laurent expansion to the RH problem. The method we used is different from computing solution with simple poles since the residue conditions here are hard to be obtained. The formula of multiple soliton solutions with one high-order pole and N multiple high-order poles are obtained, respectively. The dynamical properties and characteristic for the high-order pole solutions are further analyzed.

The bound-state soliton solutions of a higher-order nonlinear Schrödinger equation for inhomogeneous Heisenberg ferromagnetic system

The inverse scattering of a higher-order nonlinear Schrödinger equation for inhomogeneous Heisenberg ferromagnetic system with zero boundary condition is calculated by an appropriate Riemann–Hilbert (RH) problem. The RH problem of reflection coefficient with multiple high-order poles is obtained. Meanwhile, the calculation formulas of bound-state (BS) solitons and multiple BS solitons corresponding to one high-order pole and multiple high-order poles are also calculated, respectively. Finally, the corresponding soliton solution model is calculated according to the corresponding formula. Simultaneously, we also obtain the BS soliton, the multiple BS soliton and the interaction between multiple BS solitons and multiple BS solitons.

The multiple solitons of the short pulse equation

By applying the inverse scattering method, we solve the soliton and bound‐state soliton solutions of the short pulse equation (SPE), corresponding to the multiple simple poles and one higher order pole of the scattering data, respectively. The formulae of these solutions are expressed in an unified determinant form.