Scalar Control Research Articles

Procedure for regularization of bilinear optimal control problems based on a finite-dimensional model

An optimization problem of a linear system of ordinary differential equations on a set of piecewise continuous scalar controls with two-sided restrictions is considered. The cost functional contains the bilinear part (control, state) and a control square with a parameter, which plays the role of a regularization term. An approximate solution of the optimal control problem is carried out on a subset of piecewise constant controls with a non-uniform grid of possible switching points. As a result of the proposed parametrization, reduction to the finite-dimensional problem of quadratic programming was carried out with the parameter in the objective function and the simplest restrictions. In the case of a strictly convex objective function, the finite-dimensional problem can be solved in a finite number of iterations by the method of special points. For strictly concave objective functions, the corresponding problem is solved by simple or specialized brute force methods. In an arbitrary case, parameter conditions and switching points are found at which the objective function becomes convex or concave. At the same time, the corresponding problems of mathematical programming allow a global solution in a finite number of iterations. Thus, the proposed approach allows to approximate the original non-convex variation problem with a finite-dimensional model that allows to find a global solution in a finite number of iterations.

Three-phase inverter with a variable control algorithm

The paper presents the construction of a three-phase frequency converter with the possibility of choosing the type of PWM modulation and a smooth change of the frequency of the modulated signal. In a practical way, various inverter control algorithms were implemented in the same hardware system using the STM ARM Cortex M3 processor. The use of THIPWM modulation allowed to reduce the harmonic content in the output signal and effectively use the possibilities of the power source. The system can choose one of two scalar control algorithms, with the option of compensation for the influence of the stator resistance on the motor shaft torque in the initial range of the linear control characteristic at a constant voltage to frequency ratio. The research confirmed that the most advantageous type of PWM in this system is unipolar double-edge modulation. The use of the THIPWM method resulted in a gain in the amplitude of the fundamental harmonic of the output voltage for the three-phase inverter operation mode compared to the SPWM method. The appropriate precision of the frequency control step was also obtained, and the test results confirmed the functionality of the converter.

Smart actuator for IM speed control with F28335 DSP application

In the industrial application, the induction motors (IMs) and the digital signal processing (ZQ28335) combination are very important in the scientific field. Two thirds of consumption of electricity is due to motor driven equipment. The direct torque control (DTC) is the standard of the industry and it has fast response control system applications. The drawback of DTC is the flux and torque ripples in the measurements. The scalar control can be considered as a solution to this drawback but with poor response. Torque and speed of IM are controlling individually, the variable speed drive (VSDs) is used. This occurs with variation of the voltage and frequency of IM supply. To decrease the levels of flux and torque ripples, 3-level inverters represent an attractive technique. The compromise of a huge flux and torque at the beginning level and low values at steady state of operation is crucial to ensure better stability with feedback linearization of the nonlinear behavior. In this paper, VSD with DTC IM with multilevel inverter with the newest version of ZQ28335 digital signal processor (DSP) is proposed. Emulation and the results of experiment through DSP ZQ28335 make certain correct dynamic response to the operations of torque and flux.

MINIMIZATION OF ELECTRICAL CONSUMPTION OF A FREQUENCY-REGULATION INDUCTION MOTOR WITH A FAN LOAD IN START-BRAKING REGIMES

Purpuse. To minimize the total power consumption in start-braking regimes by a three-phase squirrel-cage frequency-regulated induction motor, loaded a centrifugal fan (or smoke exhauster), and also to obtain analytical dependencies for calculating the optimal durations of acceleration and deceleration times, corresponding to minimizing the total energy consumption of this motor in start-braking regimes with the indicated type of load. Metodology. Based on the methods of calculus of variations and numerical solution of non-linear differential equations, the quasi-optimal type of trajectories of speed change (tachograms) of the motor with the considered load in start-braking regimes is determined. Using the methods of mathematical analysis and similarity, the acceleration and deceleration times of an induction motor with a fan load were optimized for different (linear, parabolic and quasi-optimal) types of tachograms. Using the method of computer simulation, the energy consumption in the start-braking regimes of an induction motor with the indicated load for these types of tachograms was quantified. Results. Refined analytical dependencies are obtained for calculating the consumed active power and energy in start-braking regimes by a frequency-regulated induction motor with a fan load for the mentioned various types of tachograms. Analytical optimization of the consumption of active energy of this motor in start-braking regimes has been carried out. The change at the optimal durations for the starting-braking regimes and the corresponding it’s total energy consumption of the motor with varying the maximum value of the motor speed in these regimes has been researched. A quantitative assessment of transient electromechanical and energy processes in the considered motor with a fan load has been carried out. For this motor, as applied to the non-regenerative version of the static frequency converter, a scalar automatic control system is proposed, by means of which the motor accelerates with a constant rotor flux linkage with a given (linear, parabolic or quasi-optimal) speed trajectory and brakes on freewheel. The expected annual saving of active energy by an induction motor, loaded with a smoke exhauster, in starting and braking regimes, achieved by optimizing the form of the tachograms and the duration of the acceleration and deceleration times, is determined. Originality. Analytical dependencies are obtained for calculating the optimal durations of the acceleration and deceleration times of an induction motor with a fan load, corresponding to minimizing the energy consumption of this motor in start-braking regimes. The "U"-shaped form of dependences of the total energy, consumed during acceleration (or the total generated energy during braking) of the induction motor in function the duration of the deceleration (or braking) times is established. An analytical dependence is obtained for changing the speed of a motor loaded by a fan or a smoke exhauster during the freewheel braking regime, and an analytical expression is proposed for determining the duration of the indicated braking time. Practical value. On the example of an induction motor loaded by a smoke exhauster, the possibility of saving the total energy consumption in start-braking regimes was identified: from 77 to 90 % – due to the use of the proposed quasi-optimal tachogram and the use of practically realizable optimal acceleration and deceleration times, and also in the amount of 10 % – through the transition from freewheel braking to regenerative braking. Figures 6, tables 6, references 22.

Improving the energy efficiency of electric drives for auxiliary units of traction rolling stock

The review of technical solutions and schematic characteristics of auxiliary drives for traction vehicles has shown that the most rational variant is an electric drive with an induction machine. Given the operating modes of the auxiliary drives and the share of their power consumption in the total locomotive power, the task of using scalar control systems for induction machines becomes relevant. Based on a mathematical model describing the dynamic energy conversion processes in the T-shape substitution circuit of an induction motor, taking into account stator steel losses and current displacement effects in the rotor winding and saturation along the main magnetic path, possibilities for reducing stator current have been investigated. In order to improve the energy efficiency of electric drives two variants of control system have been proposed. One based on search method of self-tuning to the stator current minimum and the other - on maintaining the power factor of induction motor at the level that ensures equality of active and reactive components of stator current. The hardware and software requirements for implementing control systems have been analysed. Modelling using Matlab has shown that both control systems work - power loss reduction can be as low as 50% and as high as 60% in certain modes.

Implementation and Control of Six-Phase Induction Motor Driven by a Three-Phase Supply

This paper is interested in implementing and controlling a modified six-phase induction motor (MSPIM) when fed from a three-phase supply either via an inverter or with a direct grid connection loaded by a centrifugal pump. The main aims of using the MSPIM are to enhance motor reliability and reduce torque pulsation. A three-to-six phase transformer has been designed, implemented, and employed to enable the SPIM to be driven from a three-phase supply. It is preferable to use the three-to-six phase transformers integrated with three-phase inverter on using the six-phase inverter to generate lower values of harmonics and lower steady-state error of speed and reduce the starting current and because also it isolates the primary circuit from the secondary, and the cost will be lower compared to the design of a special six-phase inverter. Dynamic models of SPIM, three-to-six phase transformer, and three-phase variable speed drive are derived. Then, a scalar (V/F) closed-loop control of SPIM is employed, and the results are discussed. Fine-tuning of PID controllers is used to keep the motor speed tracking the reference value. A low pass filter is connected to reduce the ripple of voltage and current waveforms. An experimental setup has been built and implemented to check the possibility of controlling SPIM by a variable speed drive system fed from a three-to-six phase transformer. It is found that the proposed method can be effectively used to drive the SPIM from a three-phase supply.

Design of Efficient Off-Grid Solar Photovoltaic Water Pumping System Based on Improved Fractional Open Circuit Voltage MPPT Technique

The main application of off-grid solar photovoltaic (SPV) systems is water extraction in rural areas where access to the grid is restricted. In this application, photovoltaic (PV) and pump system regulation are crucial to increase its overall efficiency. In this context, this work presents a simple and efficient off-grid SPV water pumping system (SPVWPS). The designed system is based on a DC-DC boost converter, a three-phase DC-AC inverter, and a three-phase induction motor (IM) coupled to the centrifugal pump. The proposed solution is operated using a control strategy that associates an improved fractional open-circuit voltage (FOCV) method for maximum power point tracking (MPPT) and closed-loop scalar control. This association avoids the use of a speed sensor/encoder and a current sensor for the IM. Finally, the effectiveness of the proposed off-grid SPVWPS and its control system for both steady-state and dynamic conditions of insolation change is verified using a 1KVA rated prototype. The relevance of the drive is also checked in various operating conditions and is found to be adequate for pumping water. Moreover, the proposed method guarantees a fast response, less oscillations around the MPP, a system efficiency of 99%, and a high flow rate due to the extraction of maximum power.

A Holographic Metasurface Based on Orthogonally Discrete Unit-Cell for Flexible Beam Formation and Polarization Control

In this letter, we present a holographic metasurface (HMS) based on an orthogonally discrete unit-cell. The proposed unit-cell possesses discrete surface impedance tuning abilities in two orthogonal directions, providing flexible beam formation as a scalar unit-cell and polarization control as a tensor unit-cell. Operation principle and design formulas for generating independently linearly polarized beams and circularly polarized beams using the orthogonal components are concluded. Two example antennas utilizing this HMS are measured to demonstrate the beam formation and polarization control abilities at 11.0 GHz. The first example antenna generates dual beams with independently linear polarizations whereas the second example antenna generates dual beams with independently circular polarizations. Our letter indicates that there exists a middle type of HMS between scalar and tensor HMSs.

Energy-efficient variable frequency asynchronous electric drive

Currently, there are quite a large number of various scientific papers on the creation of a controlled asynchronous engine and the optimization of its modes, and the availability of acceptable results for practical implementation, but there is still no single generally accepted approach to solving the problem. In this regard, the issue of synthesis of scalar control systems that provide the minimum value of one or another criterion of energy efficiency is relevant. In this paper, we consider the obtained mathematical model of an asynchronous engine (AE), which differs from the known ones in that the parameters of the substitution scheme are expressed in terms of the stator and rotor conductivities. The energy characteristics of the AE in the sliding function are obtained, which make it possible to determine the dependences of the active and reactive components of the AE current and the possibility of their redistribution within the nominal value of the AE phase current. The principle of optimal frequency-current control of AE is formulated, which differs from the known ones in that, as an energy efficiency indicator, the value of the maximum energy efficiency of AE is used, expressed as the ratio of the active resistance of the rotor circuit to the total conductivity of the AE phase.

Speed Control Using an Integral Sliding Mode Controller for a Three-Phase Induction Motor

Induction motors are widely used in commercial and industrial applications due to their robustness, high efficiency, low maintenance requirements and durability among other reasons. Consequently, their speed should be controlled for better performance. This paper describes utilization of a scalar speed control of a three-phase squirrel cage induction motor (SCIM) to control a motor’s speed using an integral sliding mode controller (ISMC). The controller was tested under various operating conditions. The results are compared with a case employing a conventional PI controller. It was found that speed control by ISMC has a 0.16 RPM steady-state error, 0.03 s to reach steady-state from a standstill, and a 5% overshoot. All of these are lower values as compared to the results of a conventional PI controller. In this paper, the robustness of each controller to uncertainties is checked. Simulation results show the advantages of ISMC control methods. The system is simulated using MATLAB SIMULINK R2017a.

Robust saddle‐point criterion in second‐order partial differential equation and partial differential inequation constrained control problems

AbstractIn this article, for a given class of multi‐dimensional scalar variational control problems (named ) with mixed constraints implying second‐order partial differential equations and inequations, we introduce an auxiliary (modified) class of variational control problems (named ), which is much easier to study, and provide some characterization results of and by using the notions of normal weak robust optimal solution and robust saddle‐point associated with a Lagrange functional corresponding to . For this aim, we consider scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi‐time controlled second‐order Lagrangian.

Correction of the static characteristic of a frequency converter to reduce the amplitudes of resonance vibrations of the vibrating table

It is known that vibration systems of directional vibrations based on asynchronous vibration motors are currently widely used in practice, but at the same time they have a significant drawback - a sharp increase in vibration amplitudes when passing through the resonance zone at the time of acceleration and deceleration of vibration motors, which negatively affects their operation. The article discusses a vibration table with two unbalanced asynchronous vibration motors. The calculation scheme and equations of motion of such a vibration system are presented. It is shown that the vibration table as a control object is an oscillatory link with a pronounced resonant frequency. The equations of motion of asynchronous vibration motors with scalar frequency control are given. A structural diagram of a vibration table with unbalanced exciters has been developed, the modeling of which made it possible to determine the amplitudes of resonant oscillations. It is proposed to apply correction of the static characteristics of the frequency converter, which connects the effective value of the output voltage with the frequency, to reduce the resonance amplitudes. Equations of the desired static characteristics of the inverter and analytical dependences for calculating the necessary coefficients for its implementation are given. A computational model has been developed that makes it possible to take into account the effect of the corrected static characteristic of the frequency converter on the operation of the vibrating table at the stages of acceleration and deceleration. The results of computer simulation are given, convincingly showing that the correction of the static characteristics of the inverter is an effective means of reducing the amplitudes of resonant oscillations. It is shown that modern frequency converters have functionality that makes it easy to correct the dependence of the effective value of the output voltage on the frequency. The need to adjust the static characteristics of the inverter for a specific type of product tested on the vibration table is noted.

RECIRCULATION PUMP SCALAR CONTROL SYSTEM ELECTRICAL DRIVE MODEL S DEVELOPMENT AND RESEARCH

On the basis of the analysis of the used models of the electric motor at synthesis of the asynchronous electric drive with frequency control mathematical and simulation models are received. The structural scheme of the three-circuit scalar control system of the electric drive of the recirculation pump in the form of the simulation model for which the parameters of the scalar control system were calculated is offered and realized. The calculation of parameters and coefficients of the mathematical model of the solar control system of the electric drive is given. The calculations of the pressure of the recirculation pump are presented. The scheme of the simulation model of the subsystem of the unit for calculating the performance and pressure of the recirculation pump is given. Calculations and simulation model of PI current regulator are presented. Calculations and simulation model of PID-speed controller subsystem are given. Calculations andsimulation model of PI-pressure regulator subsystem are presented. Calculations of scalar control system parameters in the form of MathCad scripts are presented. On the received model processes of work of the electric drive of the pump in normal and emergency operating modes were considered. Calculations and simulation model of voltage and frequency converter subsystem are given. Calculations of parameters and coefficients of the scalar control system are given. The simulation model of the sensor unit subsystem is given. The calculations of the frequency converter and the voltage converter are given. The transfer functions of the voltage and frequency converter of the scalar control system of the asynchronous electric drive of the recirculation pump are presented. The simulation model of the fan load subsystem of the scalar control system of the boiler's recirculation pump is presented. The table presents an analysis of the transient characteristics of a two-phase mathematical model of an induction motor. The analysis of transient characteristics of the scalar control system of the recirculation pump is presented.

An Optimal Fuzzy Logic-based PI Controller for the Speed Control of an Induction Motor using the V/F Method

The Induction Motor (IM) is popular because of its low price, higher efficiency, and low maintenance cost. A comparative analysis of IM speed controllers using Voltage/Frequency (V/F) control or Scalar Control (SC) is presented in this paper. SC is commonly used due to its ease of implementation, simplicity, and low cost. To decrease the difficulty and cost of hardware implementation, this paper proposes an optimal Fuzzy Proportional Integral (Fuzzy-PI) controller. Firstly, the speed of IM using the V/F control technique is discussed. Then, speed control of IM using a conventional PI controller is performed. Finally, a simplified-rules Fuzzy-PI controller is developed in MATLAB/SIMULINK and its performance is compared with that of open-loop SC and the traditional PI controller. The performance of the simplified-rules Fuzzy-PI controller is superior to that of an open-loop constant V/F control and a conventional PI controller.

On the Physical Nature of Frequency Control Problems of Induction Motor Drives

This article considers the possibility of connecting the problems of the engineering synthesis of frequency control systems for induction motor drives (IMD) with the theory of the identification of IMD based on the equations of a generalized AC electric machine. The article presents experimental studies of load parrying in IMD with vector (VC) and scalar (SC) controls. These results indicate the absence of fundamental advantages in a drive with VC. This advantage should manifest in a more efficient formation of the moment and fast transients. A method was proposed for describing IMD by nonlinear transfer functions, making it possible to formulate the principle of the correction of IMD and a method for assessing their efficiency. The article shows that the correction based on the proposed nonlinear transfer functions of the induction motor is much more efficient than the traditional VC, which was confirmed by detailed experiments and modeling. The most important results are given in the article. An assumption was made that the efficiency advantage was due to more accurate identification of the dynamics of an IMD with a gear function instead of vector equations.

Scalar Control of Induction motor using Fuzzy logic

The main objective of the paper is to control the speed of an induction machine with scalar control technique using Fuzzy logic controller. Here the PI controller is replaced with Fuzzy Logic controller. By using Fuzzy Logic controller there are wider range of operating conditions can be covered and easier to adapt. For Fuzzy Logic controller some rules are written which play major role to control the speed of induction motor in an effective manner. The errors are evaluated according to rules defined.

On a Class of Second-Order PDE&PDI Constrained Robust Modified Optimization Problems

In this paper, by using scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian, we develop a new mathematical framework on multi-dimensional scalar variational control problems with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Concretely, we introduce and investigate an auxiliary (modified) variational control problem, which is much easier to study, and provide some equivalence results by using the notion of a normal weak robust optimal solution.

A Current Sensor Fault Tolerant Control Strategy for PMSM Drive Systems Based on Cri Markers

The paper describes a vector-controlled fault tolerant control (FTC) structure for permanent magnet synchronous motor (PMSM) drives. As a control algorithm, the classical field oriented control was applied. For the proper operation of this drive, minimum two current sensors are necessary, however, in the FTC drives additional redundant transducers are applied. Each measuring sensor, including current sensors, are susceptible to damage and can lead to unstable operation of the drive. The presented control structure, with a diagnostic and compensation system, is robust to the typical current sensor faults—lack of signal, intermittent signal, variable gain, signal noise and signal saturation. The fault detection algorithm is based on the signal method. The fault diagnostic system is tested in two control algorithms—the scalar control and vector control ones—to demonstrate the transient of the faulted signals, detection signals and detection time. After current sensor fault appearance, its influence on the control structure, especially speed transient, is compensated using non-sensitive components. The analysis is presented for all the abovementioned faults for different speed conditions.

Rescaled Einstein-Hilbert gravity from f(R) gravity: Inflation, dark energy, and the swampland criteria

We consider a class of exponential models of $f(R)$ gravity, in the presence of a canonical scalar field, for which at early times the effective Lagrangian of the theory becomes that of a rescaled canonical scalar field with the Einstein-Hilbert term becoming $\sim \alpha R$, with $\alpha$ a dimensionless constant. This rescaled Einstein-Hilbert scalar field theory at early times alters the inflationary phenomenology of well-known scalar field models of inflation, but more importantly, in the context of this rescaled theory, the Swampland criteria are easily satisfied, assuming that the scalar field is slowly rolling. We consider two models of inflation to exemplify our study, a fibre inflation model and a model that belongs to the general class of supergravity $\alpha$-attractor models. The inflationary phenomenology of the models is demonstrated to be viable, and for the same set of values of the free parameters of each model which ensure their inflationary viability, all the known Swampland criteria are satisfied too, and we need to note that we assumed that the first Swampland criterion is marginally satisfied by the scalar field, so $\phi\sim M_p$ during the inflationary era. Finally, we examine the late-time phenomenology of the fibre inflation potential in the presence of the full $f(R)$ gravity, and we demonstrate that the resulting model produces a viable dark energy era, which resembles the $\Lambda$-Cold-Dark-Mater model. Thus in the modified gravity model we present, the Universe is described by a rescaled Einstein-Hilbert gravity at early times, hence in some sense the modified gravity effect is minimal primordially, and the scalar field controls mainly the dynamics with a rescaled Ricci scalar gravity. However $f(R)$ gravity dominates at late-times, where it controls the dynamics, synergistically with the scalar field.

Simple position sensorless V/f scalar control method for permanent-magnet synchronous motor drives

When permanent magnet synchronous motors (PMSM) are used in pump and fan applications where no excessive performance is required, the V/f scalar control method can be applied to enhance the ease of use for end users. For the voltage reference generation in V/f control, existing methods requires motor parameters such as the stator resistance, inductance, and back EMF constant of the permanent magnet, which is identified before or during operation. However, this paper proposes a simple and convenient V/f control method that utilizes the motor parameters given on the name plate. In the proposed method, stable operations are ensured for the rated speed and load ranges without position sensors. For successful starting operation, a DC current control loop is included to calculate the initial offset voltage reference for the V/f pattern. The stability and effectiveness of the proposed method are analyzed and verified by MATLAB/Simulink and 3.7 kW IPM motor drive experiments.