Fully-discrete, decoupled, second-order time-accurate and energy stable finite element numerical scheme of the Cahn-Hilliard binary surfactant model confined in the Hele-Shaw cell

We consider the numerical approximation of the binary fluid surfactant phase-field model confined in a Hele-Shaw cell, where the system includes two coupled Cahn-Hilliard equations and Darcy equations. We develop a fully-discrete finite element scheme with some desired characteristics, including linearity, second-order time accuracy, decoupling structure, and unconditional energy stability. The scheme is constructed by combining the projection method for the Darcy equation, the quadratization approach for the nonlinear energy potential, and a decoupling method of using a trivial ODE built upon the ``{zero-energy-contribution}" feature. The advantage of this scheme is that not only can all variables be calculated in a decoupled manner, but each equation has only constant coefficients at each time step. We strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation process. Various numerical examples are further carried out to prove the effectiveness of the scheme, in which the benchmark Saffman-Taylor fingering instability problems in various flow regimes are simulated to verify the weakening effects of surfactant on surface tension.

Visual Measurement and Calibration of Geometric Errors of Rotating Axes for Five-axis Platform

In this paper, a method for identifying and decoupling geometric errors of rotation axes using vision measurement is proposed. Based on screw theory and exponential product formula, identification equations of position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) of the rotation axes are established. The mapping relationships between the error twist and geometric errors are established. The error model provides the coupling mechanism of PDGEs and PIGEs. Furthermore, a progressive decoupling method is proposed to separate PDGEs and PIGEs without additional assumptions. The pose parameters, required for solving the identification equations, are obtained by visual measurement. Then, the error terms of PIGEs and PDGEs are determined. Lastly, the error calibration of the rotation axes is investigated, thus providing an average rotary table orientation error reduction of 28.1% compared to the situation before calibration.

Research and Implementation of SCD Precision Decoupling in Intelligent Substation for Single Equipment Replacement

In the process of reconstruction and expansion of intelligent substation, it is difficult to accurately define the influence scope of SCD file upgrade. In the wake of each modification of SCD file, all configuration information contained in SCD needs to be re-verified, which greatly increases the workload of debugging, operation and maintenance of intelligent substation. Via decoupling SCD files, the problems of modification and re-verification of SCD files in the reconstruction and expansion stage can be tackled. In this paper, SCD precision decoupling method for smart substation with single equipment replacement is proposed, which makes SCD decoupling work more detailed, adaptable to various expansion and technical transformation of substation. The decoupling of SCD is refined from logical structure to physical link level, and the decoupling range of SCD is precisely determined, so as to minimize the modification and reverification range of SCD files and reduce the change risk caused by SCD modification.

Decentralised PI controller design based on dynamic interaction decoupling in the closed-loop behaviour of a flotation process

An enhanced method for design of decenralised proportional integral (PI) controllers to control various variables of flotation columns is proposed. These columns are multivariable processes characterised by multiple interacting manipulated and controlled variables. The control of more than one variable is not an easy problem to solve as a change in a specific manipulated variable affects more than one controlled variable. Paper proposes an improved method for design of decentralized PI controllers through the introduction of decoupling of the interconnected model of the process. Decoupling the system model has proven to be an effective strategy to reduce the influence of the interactions in the closed-loop control and consistently to keep the system stable. The mathematical derivations and the algorithm of the design procedure are described in detail. The behaviour and performance of the closed-loop systems without and with the application of the decoupling method was investigated and compared through simulations in MATLAB/Simulink. The results show that the decouplers - based closed-loop system has better performance than the closed-loop system without decouplers. The highest improvement (2 to 50 times) is in the steady-state error and 1.2 to 7 times in the settling and rising time. Controllers can easily be implemented.

Composite Decoupling Control of PMSM Based on Extended State Observer

In order to solve the problem that the dynamic decoupling performance of the traditional decoupling method is reduced due to the parameter disturbance of permanent magnet synchronous motor (PMSM), a composite decoupling control method based on extended state observer (ESO) is proposed in this paper. In this method, voltage drop across stator resistance, cross coupling terms, internal uncertains and external load torque are taken as disturbances. The disturbance is observed in real time by using the extended state observer and compensated to the output end of the current controller, so as to realize the current decoupling control of the system and achieve the purpose of precise control of the current loop. The results of theoretical analysis show and simulation show that the composite decoupling control strategy based on extended state observer has better dynamic decoupling effect.

Dynamic Decoupling and Intelligent Optimal PID Controller Tuning of Multivariable Qua-drones

This paper deals with dynamic decoupling and its intelligent PID control method of multivariable qua-drone. Up to this time, many sophisticated intelligent algorithms and control methods for drone systems have been mentioned. However, almost many cases have been focusing on single loop control methods and general multivariable systems. Therefore, we cannot guarantee its stability and optimal response by PID control used in multivariable qua-drone. Herein, this paper suggests a novel control method for PID control for multivariable qua-drone. As first step, this paper decouples dynamic of multivariable qua-drone using diagonal method of system matrix and then applies intelligent method PSO and GA to single loop obtained by decoupling method to obtain optimal response.

Design of Decoupled Pi Controllers for Two-Input Two-Output Networked Control Systems with Intrinsic and Network-Induced Time Delays

Proportional integral controller design for two-input two-output (TITO) networked control systems (NCSs) with intrinsic and network-induced time delays is studied in this paper. The TITO NCS consists of two delayed sub-systems coupled in a 1-1/2-2 pairing mode. In order to simplify the controller design, a decoupling method is first applied to obtain a decoupled system. Then, the controllers are designed based on the transfer function matrix of the obtained decoupled system and using the boundary locus method for determining the stability region and the well-known Mikhailov criterion for the stability test. A comparative analysis of the designed controllers and other controllers proposed in previous literature works is thereafter carried out. To demonstrate the validity and efficacy of the proposed method and to show that it achieves better results than other methods proposed in earlier literature works, the implementation in simulation of Wood–Berry distillation column model (methanol–water separation), a well-known benchmark for TITO systems, is carried out.

Extended PKM Fixturing System for Micro-Positioning and Vibration Rejection in Machining Application

The paper aims to present a mechatronic device able to micro-position the workpiece and to reject disturbances due to machining operation. A decoupling method is proposed for a parallel kinematic machine (PKM) fixturing platform composed by a 3-DoF flexure-based piezo-actuated mechanism. The parallel platform, with a vertical motion and two rotations, is described and its kinematics and dynamics are studied. The coupling undesirable effect is investigated based on a set of poses. To improve the quasi-static regulator model for a set-point following system, a bump less switching controller and a fine-tuning procedure, to estimate the parameter uncertainty and enable the external disturbance containment in an extended broadband frequency range, are presented. The platform and the piezo-actuator controllers are modelled based on a gain scheduling, standard ISA form method, to guarantee the stability. The accuracy is demonstrated through a set of simulations and experimental comparisons. A sensitivity analysis that evaluates the tracking performance and the disturbance rejection based on the number of signal amplitudes, frequencies, and phases is discussed. A validation phase has shown that the developed architecture presents a steady state error lower than 1.2 µm, a vibration reduction of 96% at 1130 Hz with a maximum resolving time of 6.60 ms.

Interval Type-2 Fuzzy Dynamic High Type Control of Permanent Magnet Synchronous Motor with Vector Decoupling Method

This paper presents an interval type-2 fuzzy dynamic high type (IT2FDHT) control based on vector decoupling method for permanent magnet synchronous motor (PMSM) to improve the dynamic characteristics of the system. Firstly, to address the shortcomings of the traditional PI regulator used in the current loop of PMSM, an improved PI regulator based on voltage feed-forward decoupling is used. Then, considering the characteristics that the higher the system type, the smaller the steady-state error and the shorter the regulation time, the high type control structure is added. However, a purely high type structure amplifies the oscillations of the system and is extremely sensitive to perturbations, which can easily lead to system divergence. Therefore, in order to solve the problems caused by high type structure, finally we designed dynamic high type control with the help of fuzzy logic systems (FLSs), which successfully achieved automatic switching of system type while improving response speed and steady-state accuracy. Meanwhile, quantum-behaved particle swarm optimization (QPSO) algorithm is employed to determine the parameters of FLSs. In summary, five methods including conventional PI, feed-forward decoupling PI (FDPI), FDPI high type (FDPI-HT), FDPI type-1 fuzzy dynamic high type (FDPI-T1FDHT), and FDPI-IT2FDHT, are compared to show the superiority of the proposed method. By means of simulations, the excellence of proposed FDPI-IT2FDHT is verified.