Coefficient Diagram Method Research Articles

The Influence of Switching Frequency on Control in Voltage Source Inverters

This paper aims to show how the switching frequency influences the properties of the digitally controlled voltage source inverter (VSI). The measurements of the Bode plots of the inverter are shown and discussed to present the existing signal delays and power conversion efficiency, depending on the switching/sampling frequency. Two types of controllers are presented, Single-Input–Single-Output (SISO) and Multi-Input–Single-Output (MISO), and adequate prediction units (the Smith Predictor for SISO—Coefficient Diagram Method and the full-state Luenberger Observer for MISO—Passivity Based Control) were used to compensate for the delays. It will be shown by comparing the THD of the VSI output voltage that prediction is useful with low VSI switching frequency (about 10 kHz) but is not important for the middle switching frequencies (about 25 kHz) or the high switching frequency (>50 kHz). This paper shows that increasing the switching frequency simplifies digital control without reasonably decreasing efficiency. The theoretical considerations, the Matlab/Simulink 2021b simulations, the final experimental laboratory verification are presented.

An observer for magnetic levitation system control based on a coefficient diagram method and backstepping

An observer for magnetic levitation system control based on a coefficient diagram method and backstepping

A coefficient diagram method based AGC mechanism for an interconnected power system in coordination with UPFC and AC/DC link

A coefficient diagram method based AGC mechanism for an interconnected power system in coordination with UPFC and AC/DC link

Design and experimental implementation of voltage control scheme using the coefficient diagram method based PID controller for two-level boost converter with photovoltaic system

Introduction. Currently, in the solar energy systems and a variety of electrical applications, the power converters are essential part. The main challenge for similar systems is controller design. In the literature, the PID controller has proved its effectiveness in many industrial applications, but determining its parameters remains one of the challenges in control theory field. The novelty of the work resides in the design and experimental implementation of a two-level boost DC-DC converter controlled by a PID controller for photovoltaic (PV) maximum power extraction. Purpose. Analysis and control of the two-level boost topology with renewable energy source and design of the PID controller parameters using simple and accurate method. Methods. PID coefficients are optimized using Coefficient Diagram Method (CDM) in the MATLAB environment. Results. A mathematical model of a two-level boost converter with PID controller and PV energy source was developed and analyzed. The model allows to design the controller parameters of the proposed system. Practical value. A prototype steered by the proposed CDM-PID controller was tested using an Arduino embedded board. A comparison between the simulation results and the experimental one is presented. The obtained results illustrate that the experimental results match the simulation closely, and the proposed CDM-PID controller provides a fast and precise results.

Neuromechanical Model-Based Corrective Torque Estimation During Weight Shifting in Lower Limb Amputees

As a consequence of limb loss, unilateral lower limb amputees (LLAs) exert additional flexion torque in the intact limb during postural balance, leading to other secondary complications. A prosthetic device with torque delivery is required to avoid such complications. However, estimating desired torque is an acknowledged challenge in this domain. Motivated by the above, this paper focuses on estimating the corrective torque required from an assistive device to balance the individual while performing weight-shifting exercises. Further, a healthy individual’s inverted pendulum (IP) model is explored to model LLA’s dynamics during weight-shifting. The model and the control strategy are validated using forward and backward body lean angles recorded from healthy and LLA individuals. Finally, a robust Proportional Integral Derivative controller is designed to estimate the corrective torque for maintaining the postural balance during weight-shifting. Along with the IP dynamics, a suitable control law based on Coefficient Diagram Method achieves the experimentally recorded body lean angle. The proposed control scheme is validated through simulation studies to evaluate the tracking performance in two different biomechanically relevant IP postural models. The findings assist in determining the external torque required to maintain the postural balance during gait initiation and compensatory measures for pathologically reduced torque. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Gait initiation is a transition between vertical posture and gait. Since vertical stance is inherently unstable, a postural adjustment occurs before gait initiates, propelling the center of mass forward and towards the first stance leg. The absence of flexor torque in the amputated limb causes a loss of postural stability during weight shifting activities. In the case of powered exoskeletons and prosthetic devices, a prior estimation of corrective torque through a computational approach helps to select a suitable actuator that provides an appropriate joint torque while maintaining the postural balance. As a result, an efficient computational model of gait initiation that accounts for neuromuscular system components before designing assistive devices is necessary. The controllers further provide corrective action to the assistive device to obtain robust and optimal coordination between the prosthetic element and gait. Therefore, this study demonstrates the significance of neuromuscular controller and assists in determining how much corrective torque from an external device is required to maintain postural stability and adaptability during weight shifting exercises. The effectiveness of the neural controller is also tested for real-time data to compensate for the effect of external disturbance and noise, thereby achieving a proper and controlled degree of movement in amputee users. These findings could provide one of the fundamental aspects of gait initiation model paradigms of compensatory measures for pathologically diminished torque and contribute to developing low-cost prosthetic solutions for the benefit of the rehabilitation society in developing countries.

The implementation of a coefficient diagram method based polynomial controller for a non-linear process with a distributed control system in a chlorine scrubber system

The implementation of a coefficient diagram method based polynomial controller for a non-linear process with a distributed control system in a chlorine scrubber system

Adaptive frequency control in smart microgrid using controlled loads supported by real-time implementation.

The operation of the system's frequency can be strongly impacted by load change, solar irradiation, wind disturbance, and system parametric uncertainty. In this paper, the application of an adaptive controller based on a hybrid Jaya-Balloon optimizer (JBO) for frequency oscillation mitigation in a single area smart μG system is studied. The proposed adaptive control approach is applied to control the flexible loads such as HPs and EVs by using the JBO which efficiently controls the system frequency. The suggested technique uses the power balance equation to provide a dynamic output feedback controller. The main target is to regulate the frequency and power of an islanded single area μG powered by a PV and a diesel generator with integrations of smart bidirectional loads (HPs and EVs) that are controlled by the proposed adaptive controller in presence of electrical random loads. Moreover, the JBO is designed to minimize the effect of the system load disturbance and parameter variations. For a better assessment, the proposed controller using JBO technique is compared with two other methods which are the coefficient diagram method (CDM) and adaptive one using classical the Jaya technique. In the obtained results, the frequency deviation is found as 0.0015 Hz, which is fully acceptable and in the range of the IEEE standards. The MATLAB simulation results reveal that the suggested technique has a substantial advantage over other techniques in terms of frequency stability in the face of concurrent disturbances and parameter uncertainties. The real-time simulation tests are presented using a dSPACE DS1103 connected to another PC via QUARC pid_e data acquisition card and confirmed the MATLAB simulation results.

Frequency control scheme based on the CDM-PID controller for the hybrid microgrid system with stochastic renewable generators

In this paper, we introduce a Coefficient Diagram Method (CDM) to design a conventional PID controller. This controller is used to decrease the frequency fluctuations of a microgrid system composed of two renewable energy sources (WTG and STPG) and four controlled elements (UC, FESS, BESS and DEG). The method compares two characteristic polynomials of the same order:, the coefficients of the first polynomial are a function of microgrid parameters and the unknown gains of the PID controller. The second is called the target polynomial; its coefficients are calculated by choosing the stability indices and the equivalent time constant to satisfy the desired performances of the closed-loop system. Mathematically, the order of the polynomial controller determines the type of linear system of equations to solve: undetermined or overdetermined. In our application, the least squares method is used to find an approximate solution to the overdetermined system resulting from this comparison. Digital simulation is performed to test the performance of the microgrid controlled by the CDM-PID controller. The obtained results are compared with two recently published works where the parameters of the PID controllers are tuned by DE and chaotic PSO algorithms. The results show that the CDM-PID controller gives better performance.

A novel computational technique using coefficient diagram method for load frequency control in an interconnected power system

This paper proposes a novel load frequency control (LFC) approach formulated on an optimal structure of the coefficient diagram method (CDM) in a two-area thermal power system. As part of a realistic analysis, nonlinearities related to governor dead band (GDB) and generation rate constraint (GRC) have been considered. In this article, a hybrid CDM method is combined with the optimization of its mathematical equations to achieve an innovative controller. Furthermore, a new metaheuristic optimization technique called the water cycle algorithm (WCA) is used to determine the optimal coefficients of the CDM controller. For the purpose of demonstrating the validity of the proposed scheme, a wide range of uncertainties in the dynamic parameters of a nonlinear power system were tested. In addition, a comparative study is presented between the results obtained from a classical integral, CDM alone, optimized fuzzy, optimized PID, and the suggested controller. In this new approach to improved control, algebraic support provides a robust and responsive controller that can provide fast and stable dynamic responses and effectively overcome the detrimental effects of nonlinearities and uncertainties in the parameters of the power system.

The Effect of Replacing Si-MOSFETs with WBG Transistors on the Control Loop of Voltage Source Inverters

The operation of a voltage source inverter (VSI) depends on its output LC filter and the PWM modulator delay. The VSI model includes serial equivalent resistance based on the resistances of the active inverter bridge transistors, the filter coil winding, and additional PCB elements, such as traces and connectors, in addition to the large equivalent resistances that result from power losses in the coil core and switches. These dynamic power losses depend on the switching frequency and the inverter load. This paper investigates the change in equivalent serial resistance that occurs if the standard Si-MOSFET switches are replaced with wide bandgap (WBG) transistors with correspondingly lower equivalent serial resistance. The paper further investigates how such a change influences the design of the controller, given that replacement of the switches shifts the roots of the closed-loop characteristic equation. Theoretical analyses of the influence of equivalent serial resistance for a multi-input single-output passivity-based controller and a single-input single-output coefficient diagram method are also presented. These analyses are applied to both types of switches. Two methods are used to measure the serial equivalent resistance for a given VSI using Si and WBG switches. The possibility of replacing switches with WBG technology in existing inverters was assessed, and the corresponding controller adjustment that would be required. The theoretical analysis is verified via the use of an experimental VSI.

Coefficient Diagram Method Based Decentralized Controller for Fractional Order TITO Systems

Fractional calculus has gained increasing attention from researchers because of providing accurate modelling and flexible controller design in control applications. More research to design controllers for Fractional Order Two-Input Two-Output (FOTITO) systems, which inherently have certain difficulties, is needed when the studies about these control applications are considered. In this study, Coefficient Diagram Method (CDM) based decentralized controllers are designed for FOTITO systems. For this, integer order approximate models of FOTITO systems are obtained and decoupled into two subsystems by using simplified and inverted decoupling configurations. Obtained high-order approximate subsystem transfer functions are reduced by a model reduction method to facilitate CDM-based decentralized controller design. Then, CDM-based decentralized controllers are designed for each subsystem, which enables to obtain the controllers of the FOTITO system. Simulation results for two different FOTITO systems, one of which is a time delay fractional order system, are demonstrated that the proposed approach exhibits successful performance.

Optimized Load Frequency Control for Single Area Power System Using Linear Quadratic Gaussian Technique and Coefficient Diagram Method

Optimized Load Frequency Control for Single Area Power System Using Linear Quadratic Gaussian Technique and Coefficient Diagram Method

Adaptive LFC Incorporating Modified Virtual Rotor to Regulate Frequency and Tie-Line Power Flow in Multi-Area Microgrids

This research investigates a new coordination strategy for both isolated single-area and interconnected multi-area microgrids (MGs) using a modified virtual rotor-based derivative technique supported with Jaya optimizer based on balloon effect modulation (BE). Accordingly, the main concept of BE is to assist the classic Jaya to be more sensitive and trackable in the event of disturbances, as well as to provide optimum integral gain value on the secondary frequency controller adaptively for both suggested MGs. The proposed modified virtual rotor mechanism is consisting of virtual inertia and virtual damping that are added as a tertiary controller within proposed MGs considering full participation of the inverter-based energy storage systems. The proposed virtual rotor mechanism is consisting of virtual inertia and virtual damping that are added as a tertiary controller within proposed MGs to emulate the reduction in system inertia and the enhanced damping properties. Several nonlinearities were proposed in this work such as a dead band of governor, generation rate constraints, and communication time-delay are considered within the dynamic model of the suggested MGs. In addition, the proposed design of multi-area MGs takes the interval time-varying communication delays into account for stability conditions. In this study, A comparative study using unimodal (i.e., Sphere) and multimodal (i.e., Rastrigin) benchmark test functions are conducted to validate the proposed direct adaptive Jaya-based BE. Furthermore, Wilcoxon’s rank-signed non-parametric statistical test using a pairwise comparison was performed at a 5 % risk level to judge whether the proposed algorithm output varies from those of the other algorithms in a statistically significant manner. Thence, the superiority and effectiveness of the proposed method have also been verified against a variety of other metaheuristics optimization techniques, including classic electro-search, particle swarm, multi-objective seagull, and Jaya optimizers. In addition, an operative performance is assessed against the conventional integral controller, coefficient diagram method, and classic Jaya with/without virtual inertia. The final findings emphasize the superiority of the proposed direct adaptive Jaya-based BE supported by a modified virtual rotor and state better performance and stability compared to existing controllers.

A phase-locked loop with an improved dynamic response under abnormal grid conditions

The cascaded delayed signal cancelation (CDSC) method has attracted much attention recently as an efficient filtering technique to improve synchronous reference frame phase-locked loop (PLL) performance in grid synchronization under adverse grid conditions. The CDSC-based PLL suffers from slow transient response. Therefore, this study proposes a solution for grid synchronization under abnormal conditions utilizing an arbitrary time-delay operator to mitigate the DC offset and frequency adaptive CDSC operators for harmonic filtering. An accurate small-signal model was derived, opening the door to design the loop filter. The coefficient diagram method was adopted to systematically design the gains of the proportional–integral controller and a lead–lag compensator, yielding a faster dynamic response than the symmetrical optimum method-based design. The proposed PLL effectiveness was verified numerically under abnormal conditions, showing better dynamic and steady-state performance than other related PLLs. The proposed PLL requires less than two grid cycles to synchronize without ripples, meeting the grid code's requirement.

Control system design of a low‐frequency‐switchingsingle‐phase four‐quadrant PWMconverter

This work is focused on the control of low-frequency-switching single-phase four-quadrant pulse width modulation (PWM) converters used in grid-connected modern power electronics applications. The switching frequency is chosen to be lower than that used in industrial applications in order to use the designed control system in high-power applications such as railway electrical traction systems. The control system is designed under three main headings: grid synchronization, input current control, and voltage control, where grid synchronization is achieved by a single-phase phase-locked loop (PLL). The current loop is designed by using a proportional-resonant (PR) controller, and the classical proportional-integral (PI) controller is employed in the voltage control loop. The parameters of the PI controller are determined by using the coefficient diagram method (CDM). The control system is modelled as a discrete-time system to get the response closest to the actual system and to be easily implemented on the TMS320F28335 DSP platform. The performance of designed control system is tested on a 30-kW single-phase PWM converter test set-up, and experimental results show that bidirectional power flow, sinusoidal input current, power factor correction, and constant output voltage are achieved. This study is aimed to be a guide for the designers, from the selection of converter passive elements to controller design and experimental verification.

Robust Controller Design for Multi-Input Multi-Output Systems Using Coefficient Diagram Method.

The coupling between variables in the multi-input multi-output (MIMO) systems brings difficulties to the design of the controller. Aiming at this problem, this paper combines the particle swarm optimization (PSO) with the coefficient diagram method (CDM) and proposes a robust controller design strategy for the MIMO systems. The decoupling problem is transformed into a compensator parameter optimization problem, and PSO optimizes the compensator parameters to reduce the coupling effect in the MIMO systems. For the MIMO system with measurement noise, the effectiveness of CDM in processing measurement noise is analyzed. This paper gives the control design steps of the MIMO systems. Finally, simulation experiments of four typical MIMO systems demonstrate the effectiveness of the proposed method.

Sampling Rate and Performance of DC/AC Inverters with Digital PID Control—A Case Study

The huge influence of the sampling rate on the performance of the digital PID control of a voltage source inverter (VSI) is revealed. It is shown that an appropriately chosen continuous-time model of a digital controller with the PWM power converter behaves like the actual discrete-time system, which allows for a simple controller analysis and design. The variable structure nature of the inverter with both the RC rectifier and an abruptly changing resistive load with two modes of operation within the sampling period is directly taken into account. Two simulation models, a discrete-time PWM and a continuous-time, of an inverter are presented, which are used to tune the PID controller and to evaluate the control performance. The behavior of the system in both modes is explained on the basis of the root loci and frequency characteristics. The results obtained for three sampling rates: 12.8, 25.6, and 51.2 kHz, are presented and compared with an actual VSI experiment. A comparison with other results obtained for this VSI shows that properly tuned PID control outperforms the more sophisticated solutions based on the coefficient diagram method (CDM) and the passivity based control (PBC).

Design of Double Loop CDM Controllers for Proton Exchange Membrane Fuel Cell Fed DC-DC Boost Converter Under Wide Source and Load Variations

Proton Exchange Membrane Fuel Cell (PEMFC) are emerging as the new renewable energy source. The output voltage of PEMFC is not sufficient to fulfill the load demands which varies with variations in temperature and load. So, it is integrated with a properly designed power conditioning unit to enhance and stabilize the voltage. In this paper Nexa 1.2 KW PEMFC is initially modeled using successive trust region. Next, a DC-DC boost converter connected to the fuel cell is designed using interval analysis to boost and regulate the output voltage adhering to the changes in the temperature and loading conditions. To stabilize the output of PEMFC fed boost converter, double loop robust controllers are implemented which are designed by Coefficient Diagram Method (CDM). All the responses of the CDM controlled boost converter settle down smoothly at the desired settling time with zero overshoot. The proposed controller fair quite well as compared to other similar controllers in the existing literatures.

Virtual Inertia Control Methods in Islanded Microgrids

Although the deployment and integration of isolated microgrids is gaining widespread support, regulation of microgrid frequency under high penetration levels of renewable sources is still being researched. Among the numerous studies on frequency stability, one key approach is based on integrating an additional loop with virtual inertia control, designed to mimic the behavior of traditional synchronous machines. In this survey, recent works related to virtual inertia control methods in islanded microgrids are reviewed. Based on a contextual analysis of recent papers from the last decade, we attempt to better understand why certain control methods are suitable for different scenarios, the currently open theoretical and numerical challenges, and which control strategies will predominate in the following years. Some of the reviewed methods are the coefficient diagram method, H-infinity-based methods, reinforcement-learning-based methods, practical-swarm-based methods, fuzzy-logic-based methods, and model-predictive controllers.

Maximum sensitivity-constrained coefficient diagram method-based PIDA controller design: application for load frequency control of an isolated microgrid

This paper proposes an improved coefficient diagram method (CDM) for proportional integral derivative acceleration (PIDA) controller design. In the improved CDM, stability indices are obtained using a graphical approach based on the maximum sensitivity constraints. The stability indices play an important role in the designing of the controller and stability of the closed-loop control system. Further, the improved CDM is utilized to compute the analytical expressions for the coefficients gain of PIDA controller. From the application point of view, the proposed control approach is designed for load frequency control (LFC) of an isolated microgrid (IMG). In IMG, the generators cannot supply constant electrical power and sometimes cause an imbalance between power generation and demand. Thus, LFC scheme is applied to maintain the balance between power generation and demand. The effectiveness and robustness of proposed control approach are analyzed for IMG system under $$\pm 50$$ % parametric uncertainty, random load demand, random solar and wind power deviation profile. The efficacy and performance of proposed control approach are examined in comparison with the published PID, 2DOF-PID and PIDA control schemes.