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As the percentage of renewable energy source within the energy production mix has expanded, it is become gradually difficult to determine the appropriate values for controller gains and model parameters. Controlling system frequency of interconnected power system during sudden load disturbance requires careful consideration of the controller gain values and small signal stability model parameters. This study proposes an innovative methodology for ascertaining controller gain values and model parameters for plug-in electric vehicles (PEVs) in load frequency control (LFC) applications. Proposed method uses the root locus (RL) approach to find the suitable controller gain values and model parameters for PEVs. This paper offers a thorough mathematical description of the proposed RL approach. Routh approximation method is used for reduced-order modelling (ROM), which comprises thermal and PEV systems, to reduce complexity of higher-order system while designing controllers. Fractional-order proportional-integral-derivative controller (FO-PID) is proposed, and its parameters are adjusted using particle swarm optimization (PSO) tool. To validate the efficacy of suggested method, a comprehensive comparison of time response parameters and performance indices (PI) is carefully carried out. Also, the various PEVs state of charge (SOC) levels is investigated, and effects of these levels are studied in LFC with robustness analysis of controller. The proposed method for determining gain value is highly reliable and efficient, outperforming existing methodologies in the literature. [ABSTRACT FROM AUTHOR]

In this short note, the relative stability results (based on root locus and Bode analyses) reported in "Optimal tuning of sigmoid PID controller using nonlinear sine cosine algorithm for the automatic voltage regulator system" (Suid and Ahmad, 2022) are analyzed. It is shown that the use of closed-loop transfer functions (CLTFs) should be avoided in relative stability analysis since they may lead to less accurate stability results. The present study affirms that the results of relative stability analysis obtained using loop transfer functions (LTFs) are more reliable and accurate. • Relative stability results reported in [ISA Trans 128(B) (2022) 265–86] are analyzed. • It is found that instead of LTF, CLTF was used for relative stability analysis. • The use of CLTF led to less accurate relative stability results. • Relative stability analysis is more reliable and accurate with LTF. [ABSTRACT FROM AUTHOR]

The rise of deep reinforcement learning in recent years has led to its usage in solving various challenging problems, such as chess and Go games. However, despite its recent success in solving highly complex problems, a question arises on whether this class of method is best employed to solve control problems in general, such as driverless cars, mobile robot control, or industrial manipulator control. This paper presents a comparative study between various classes of control algorithms and reinforcement learning in controlling an inverted pendulum system to evaluate the performance of reinforcement learning in a control problem. A test was performed to test the performance of root locus-based control, state compensator control, proportional-derivative (PD) control, and a reinforcement learning method, namely the proximal policy optimization (PPO), to control an inverted pendulum on a cart. The performances of the transient responses (such as overshoot, peak time, and settling time) and the steady-state responses (namely steady-state error and the total energy) were compared. It is found that when given a sufficient amount of training, the reinforcement learning algorithm was able to produce a comparable solution to its control algorithm counterparts despite not knowing anything about the system’s properties. Therefore, it is best used to control plants with little to no information regarding the model where testing a particular policy is easy and safe. It is also recommended for a system with a clear objective function.

In this paper, we compare two different kinds of position controllers, namely PD (both compensated and uncompensated PD) and Cascade controller (both compensated and uncompensated Cascade). SIMULINK software is used to implement lumped parameters estimation with UKF. The Proportional-Derivative (PD) controller design by root locus and Cascade controller design have been chosen for our feedback system, and coulomb friction as disturbance is taken into account in the estimation model. The aim of this paper is to find out which controller is better (both compensated and uncompensated PD controller vs. both compensated and uncompensated Cascade controller). Therefore, the objective is to show how useful the parameter estimation for controller design with compensation. Through comparing two position controller designs, the experiment results show that both Compensated Proportional Derivative (PD) controller and Cascade controller Design have much better performance than the Uncompensated ones. [ABSTRACT FROM AUTHOR]

The purpose of this report is to explain the design and implementation process of a PID controller with a lead network to control the tilt angle of an aerodynamic rocker. For this, the mathematical model of the plant was built and the physical and electrical parameters that characterize the plant were identified experimentally. By linearizing the model around a defined operating point, the transfer function of the system was obtained, which was validated by means of simulations in MATLAB®-Simulink. With this, the PID controller and the lead network were designed considering the performance and robustness requirements. Subsequently, the plant was physically built, and the control system was implemented in a Microchip® brand PIC18 microcontroller. Finally, tests were carried out on the physical implementation to verify the performance and robustness attained. As a result, a controller was obtained whose implementation is fast, has a good follow-up to a wide range of references, rejects disturbances, and is robust to changes in the plant. It is concluded that the implementation in the proposed microcontroller was successful and other researchers are invited to experiment with this project in different ways. [ABSTRACT FROM AUTHOR]

The main goal of the paper is to achieve the structural reliability of the failure components in the system that can be modelled as a Transfer Function (TF). The classical reliability of the power system has been a major field for research in the past decades, which has resulted in the reliability of the power grid by integrating the failure rates of the system components. As a result, a gap analysis is carried out by modelling the failure components into TF, and a comparison of structural and classical reliability is explained in the paper. The paper expands on methodology of the mapping technique for transforming a system from one domain to another. By doing so, the transformation of the Complex Coefficients Integer Order (CCIO) and the Complex Coefficients Fractional Order (CCFO) system transfer function becomes the Non-complex Coefficients Integer Order (NCCIO) in nature. Therefore, the root locus plot for the transformed system is observed as the symmetrical structure about the real axis. Therefore, the plane transformation becomes advantageous in the field of structural reliability analysis. The root locus plot for the transformed system into a w-plane becomes reliable as per the symmetrical structure. The reliability index Loss of Load Probability (LOLE) has been evaluated with different forced outage rates of the system components to analysis the classical reliability of the system.

This study evaluates the performance of three control systems, namely the root locus method, type-1 Mamdani fuzzy logic system (FLS), and interval type-2 Mamdani FLS, in noise-free and noisy ball and beam systems. The main contribution of this study is enabling improved design and implementation of control systems in real-world applications by offering a comprehensive understanding of each control system's performance. The methodology involves conducting four tests focusing on various input types, including a 0.8-meter step input and sine wave function, and assessing the presence of noise in the system. The performance of each control system is analyzed using parameters such as rise time, settling time, and percentage overshoot, with the interval type-2 Mamdani FLS further examined by varying footprint of uncertainty values. Results from noisefree tests reveal that the root locus method has a shorter rise time and settling time but a higher percentage overshoot compared to the type-1 Mamdani FLS and type-2 Mamdani FLS. In noisy environments, the type-2 Mamdani FLS with varying Footprint of Uncertainty values outperforms the type-1 Mamdani FLS with reduced rise time, settling time, and percentage overshoot. The root locus method shows a significantly higher percentage overshoot in noisy conditions compared to the other two control systems. In conclusion, the type-2 Mamdani FLS control system demonstrates superior capability under changing conditions compared to the type-1 Mamdani FLS, with its performance varying based on the footprint of uncertainty values. This study highlights the importance of selecting the appropriate control system depending on specific needs and environmental factors. [ABSTRACT FROM AUTHOR]

The three-phase voltage-source grid-connected inverters suffer from grid-connected current quality problems due to system resonance caused by the under-damping characteristics of the filter and grid impedance, on the one hand, and the grid-connected current distortion caused by the high content of low harmonics in the grid voltage, on the other hand. To resolve this problem, a current quality improvement control strategy, combining capacitor-current feedforward active damping and harmonic virtual impedance reshaping, is proposed by analyzing the mechanisms of system resonance and grid-connected current distortion. In addition, the proposed control strategy allows determining the virtual impedance parameters by using the root locus method, so as to achieve the purpose of improving the output grid-connected current quality of the three-phase voltage-source grid-connected inverter under weak grid conditions. Finally, the correctness and effectiveness of the proposed control strategy are verified by simulation and experiment.

Copyright of Experimental Technology & Management is the property of Experimental Technology & Management Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Based on the principle of Lagrange mechanics, especially considering the effects of rotation damping and nonsynchronous damping, a radial 4-dimensional dynamic model of the flywheel bearing rotor system is proposed. Applying the Laplace eigenvalue method, the stability effects of rotational damping, nonsynchronous damping, and their coupling effects are investigated by means of root locus method. Under the control of the linear quadratic regulator, dynamical characteristics of the flywheel bearing rotor system with varied rotational damping and nonsynchronous damping are also studied. The results show that the rotation damping, nonsynchronous damping, and their coupling effects have vast and complex instability effects on high-speed flywheel bearing rotor system. However, there are three exceptions. The tiny proportional rotational damping, remaining below 12%, and the minuscule proportional co-nonsynchronous damping; the product of the nonsynchronous damping and the speed ratio below 5% both can enhance the stability of the system. Furthermore, in the situation that the counter-nonsynchronous damping is coupled with the large proportion of rotational damping, the stability of the system can also be boosted distinctly. On the other hand, the numerical experimental results show that the rotational damping and nonsynchronous damping have a beneficial effect on the flywheel system controlled by linear quadratic regulator. In addition, under the control of linear quadratic regulator, the transient dynamical behavior of the flywheel rotor system with rotational damping or co-nonsynchronous damping performed better than the flywheel rotor system with the coupled damping. The numerical simulations of the transient response of the flywheel rotor system under active control are consistent with some of the derived stability analysis results. The results about the stability analysis and the performance in vibration control give the suggestions for the instability control and fault detection of the system. [ABSTRACT FROM AUTHOR]

It is shown how a stability test, alternative to the classical Routh test, can profitably be applied to check the presence of polynomial roots inside half-planes or even sectors of the complex plane. This result is obtained by exploiting the peculiar symmetries of the root locus in which the basic recursion of the test can be embedded. As is expected, the suggested approach proves useful for testing the stability of fractional-order systems. A pair of examples show how the method operates. It is believed that the suggested geometric approach can also be of some didactic value in introducing basic control-system tools to engineering students.

The Z -source inverter is a desirable power converter topology for voltage source and current source converter applications, which is an exciting alternative for replacing the popular conventional type. This paper presents a novel method for designing voltage-type Z -Source inverters that are innovated based on good voltage source and D C -Link prerequisites such as its current and voltage value. This method is caused to reduce the size of the capacitor and inductor as well as the total cost of the converter, which is applicable in hybrid electric vehicle development. Z -Source inverter's output based on its input variables and effects has been investigated to propose to optimize the design/control method. State space equations are obtained, and its model is analyzed to illustrate how the undesired effects of these changes can be omitted or compensated. It has been used to optimize the designed parameters. A prototype experimental Z-Source inverter with a rated power of 500 W and switching frequency of 20 kHz is developed to demonstrate the validity of the design process. The Simulation and experimental results verify that the proposed method successfully optimizes the x-shape Impedance design. • An effective design method for fewer values of C and L in the voltage type ZSI • Effect of LC of X-shape in voltage type ZSI on dynamic behavior versus input changes • A new strategy for healing dynamic behavior of voltage type ZSI versus input changes • Simulation and excremental results are presented To prove the mathematical theory. [ABSTRACT FROM AUTHOR]

This paper concerns the development and analysis of multigeneration systems based on hybrid sources such as biomass and wind. Industry requires different types of sources to provide several outputs, so the goal of this research was to fulfill the industrial requirement with optimization. The multigeneration cycle supplies enough power to satiate energy demands, i.e., power, cooling, hydrogen, air conditioning, freshwater, hot water, and heating. For this, the multigeneration cycle was modeled in the Engineering Equation Solver (EES) and Simulink to obtain optimized results for the industry. Energy and exergy for the multigeneration cycle were determined to assess the performance of the cycle and to investigate the optimized results for the overall system. This study shows that for configuration selection and design, different thermodynamic, economic, and environmental aspects should be considered. Based on the results, the selection of the best location for this multigeneration system was made. Power output from the wind turbine was around 7 MW and from biogas 0.6 MW. The overall exergy efficiency of the multigeneration system was found to be 0.1401.

This paper aims to investigate the critical stability of a multi-degree-of-freedom (multi-DOF) real-time hybrid simulation (RTHS). First, the critical time-delay analysis models are developed using the continuous- and discrete-time root locus (RL) techniques, respectively. A bilinear transform is introduced into the first-order Padé approximation while conducting the discrete RL analysis. Based on this technique, the time delay can be explicitly used as the gain factor and thus the instability mechanism of the multi-DOF RTHS system can be analyzed. Subsequently, the critical time delays calculated by the continuous- and discrete-time RL techniques, respectively, are compared for a 2-DOF RTHS system. It is shown that assuming the RTHS system to be a continuous-time system will result in overestimating the critical time delay. Finally, theoretically calculated critical delays are demonstrated and validated by numerical simulation and a set of RTHS experiments. Parametric analysis provides a glimpse of the effects of time step, frequency and damping ratio in a performing partitioning scheme. The constructed analysis model proves to be useful for evaluating the critical time delay to predict stability and performance, therefore facilitating successful RTHS. [ABSTRACT FROM AUTHOR]

The process involved is a pilot scale packed distillation column that separates a mixture of methanol and water. The performances of two discrete time controllers that different parameter tuning techniques were used for each of them were examined in the face of the set point tracking of the overhead product composition. The success of the discrete time controllers were assessed by means of the rise time and integral of the square error (ISE) criteria. A discrete time proportional integral controller with two terms was obtained by using the velocity form of controller law. For this controller, the proportional sensitivity term (Kc) and the other term were determined by creating root locus diagram and replacing the closed loop poles to the appropriate location in unit circle of z-plane. The most successful proposed controller action was obtained with Kc of 0.95 and integral time constant of 2.375 min according to rise time of 3.7 min and ISE criteria of 1.08. The discrete time proportional integral derivative (PID) controller with six parameters as P=0.009185, I=0.01835, D=0, N=100, b=1, c=1 that were tuned by using Simulink control design and 1 min sampling time was applied to the process. The same controller performance with six parameters of P=1.164, I=0.5319, D=-0.01481, N=3.783, b=0.1233, c=0.01017 was investigated by choosing 0.5 min sampling time. By comparing all the performances obtained, it can be said that the discrete time controller with two terms tuned by the suggested approach can easily be applied to obtain the most desired performance.

In this study, an optimal Tree-Seed Algorithm (TSA) algorithm-based Proportional-Integral-Derivative (PID) controller is proposed for automatic voltage regulator (AVR) system terminal tracking problem. PID controller gains Kp, Ki, and Kd are optimized with the proposed TSA algorithm based on different objective functions. The TSA-based optimal PID controller's performance is compared with numerous PID controllers, which were developed using different meta-hermetic optimization algorithms in the literature. Several analysis methods including root locus, bode analysis, robustness, and disturbance rejection are studied and compared with reported works in the literature. It is shown that there is still a research gap to improve the tracking performance of the AVR system due to its importance in electrical systems. According to the obtained comparison results, it has been revealed that the proposed TSA-based PID controller improves tracking properties under load change thus it can be effectively used for synchronous generator automatic voltage regulator terminal voltage stability.

Background: The first objective for realizing and handling biological systems is to choose a suitable model prototype and then perform structure and parameter identification. Afterwards, a theoretical analysis is needed to understand the characteristics, abilities, and limitations of the underlying systems. Generalized Michaelis–Menten kinetics (MM) and S-systems are two well-known biochemical system theory-based models. Research on steady-state estimation of generalized MM systems is difficult because of their complex structure. Further, theoretical analysis of S-systems is still difficult because of the power-law structure, and even the estimation of steady states can be easily achieved via algebraic equations. Aim: We focus on how to flexibly use control technologies to perform deeper biological system analysis. Methods: For generalized MM systems, the root locus method (proposed by Walter R. Evans) is used to predict the direction and rate (flux) limitations of the reaction and to estimate the steady states and stability margins (relative stability). Mode analysis is additionally introduced to discuss the transient behavior and the setting time. For S-systems, the concept of root locus, mode analysis, and the converse theorem are used to predict the dynamic behavior, to estimate the setting time and to analyze the relative stability of systems. Theoretical results were examined via simulation in a Simulink/MATLAB environment. Results: Four kinds of small functional modules (a system with reversible MM kinetics, a system with a singular or nearly singular system matrix and systems with cascade or branch pathways) are used to describe the proposed strategies clearly. For the reversible MM kinetics system, we successfully predict the direction and the rate (flux) limitations of reactions and obtain the values of steady state and net flux. We observe that theoretically derived results are consistent with simulation results. Good prediction is observed (> 9 9. 7 % accuracy). For the system with a (nearly) singular matrix, we demonstrate that the system is neither globally exponentially stable nor globally asymptotically stable but globally semistable. The system possesses an infinite gain margin (GM denoting how much the gain can increase before the system becomes unstable) regardless of how large or how small the values of independent variables are, but the setting time decreases and then increases or always decreases as the values of independent variables increase. For S-systems, we first demonstrate that the stability of S-systems can be determined by linearized systems via root loci, mode analysis, and block diagram-based simulation. The relevant S-systems possess infinite GM for the values of independent variables varying from zero to infinity, and the setting time increases as the values of independent variables increase. Furthermore, the branch pathway maintains oscillation until a steady state is reached, but the oscillation phenomenon does not exist in the cascade pathway because in this system, all of the root loci are located on real lines. The theoretical predictions of dynamic behavior for these two systems are consistent with the simulation results. This study provides a guideline describing how to choose suitable independent variables such that systems possess satisfactory performance for stability margins, setting time and dynamic behavior. Conclusion: The proposed root locus-based analysis can be applied to any kind of differential equation-based biological system. This research initiates a method to examine system dynamic behavior and to discuss operating principles. [ABSTRACT FROM AUTHOR]

In this study, phase lead and phase lead-lag controller design, which are among the classical control methods, was implemented by root locus and Bode diagram methods for real-time DC motor position control. Since a model-based controller will be designed, the mathematical model has been obtained by calculating from experimental data with the black box system identification method. The implementation was developed using the STM32F4 development kit and the Waijung block set supported by Matlab. Controller performance has been tested by observing real-time results on the experimental setup as a result of giving reference inputs to the system. The functioning of the design process of both methods and the practicability of the methods were introduced in real-time and it was observed that the designed controllers achieved successful performance. The experimental setup and methods used in the application offer both reliable operation and economical solutions for control applications. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to show how Lyapunov theory and the root locus technique, widely known as powerful tools for control design, can be used to provide a characterization of the convergence properties of the celebrated continuous-time Newton and Householder methods. In particular, a Lyapunov analysis is carried out to characterize the local and global properties of these methods and it is shown how techniques to qualitatively draw the root locus of a polynomial with complex coefficients can be used to determine the boundaries of the basin of attraction of each root of the polynomial to be zeroed, which is an equilibrium of a suitably designed dynamical system. Finally, by leveraging on the properties of the root locus, an algorithm is proposed to approximate all the complex roots of a given polynomial, tackling the key issue of choosing complex initial guesses even when only real roots are sought. [ABSTRACT FROM AUTHOR]

With the electronization process of mobile hydraulics moving forward, the basic demand of power limitation control is increasingly fulfilled by electronic pump controllers to replace hydro-mechanical regulators. However, the nonlinear power controller introduces additional dynamics and potential oscillations into the electrohydraulic system. In this paper, the dynamic performance of the electrohydraulic system is analyzed using the linearized mathematical model and root locus tool, considering the factors of pump dynamic, actuator dimension, power setting point, and so on. A pump-based virtual leakage compensator is designed to reduce oscillations due to low damping excited by the power controller. The stability and parameter selection are then discussed to obtain optimal dynamic behavior. Using the traditional power controller as a comparison, the boom lifting motion test of a 2-ton excavator was carried out to validate the proposed compensator. The test result indicates that the proposed controller with optimized parameters has the ability to suppress pressure fluctuations and velocity oscillations.

Autonomous underwater vehicles (AUVs) are widely used in the field of ocean engineering. Steady state analysis of a AUV is considered a necessary part in the design process. A rear dual propeller vector propulsion AUV is developed in this paper. Motivated by improving the AUV stability, a washout filter-based feedback optimization methodology for AUV is presented. First, with the AUV structural parameters, a AUV four degree-of-freedom mathematical model of the motion space is calculated to provide a mathematical basis for rock-bottom steady state control systems. Second, the transfer function of the filter is derived according to the pole-zero and root locus map of the AUV system. The washout filter correction model is established based on the root locus map and is connected in series with the AUV space-state model. The simulation analysis result shows that the stability of a system is greatly increased after the whole system is connected to the filter. Finally, the AUV thrust pool test and sailing test are carried out. The experimental results show that the proposed method can improve the thrust stability of a system. This method can be applied to AUV thrust control systems.

In order to study the effect of different gust durations on the safety of a high-speed train passing by a wind-break breach at a speed of 120 km/h, the root locus method is used to analyze the suspension modes of the train under different speeds. The original gust is obtained based on the Unsteady Reynolds-averaged Navier-Stokes (URANS) model when the train passes by a 12 m breach between two windbreaks with a normal crosswind speed of 32 m/s. A group of scaling factors for stretching and compressing the time windows is applied to change the gust duration without changing the amplitude. The results show that when the gust duration is close to the natural period of the suspension system, the train responses and derailment coefficient of the train can be amplified. As the attack angles of the first and second wheelset are still in the clockwise direction when overlooking the wheelset, the first wheelset is more vulnerable than the second wheelset. When the gust duration is longer than the natural period of lower sway, the initial fluctuation of the train response can be relieved. [ABSTRACT FROM AUTHOR]

It is shown how a stability test, alternative to the classical Routh test, can profitably be applied to check the presence of polynomial roots inside half-planes or even sectors of the complex plane. This result is obtained by exploiting the peculiar symmetries of the root locus in which the basic recursion of the test can be embedded. As is expected, the suggested approach proves useful for testing the stability of fractional-order systems. A pair of examples show how the method operates. It is believed that the suggested geometric approach can also be of some didactic value in introducing basic control-system tools to engineering students. [ABSTRACT FROM AUTHOR]

Different from other references that use Ziegler-Nichols method or another trial and error method to design the proportional-integral-derivative (PID) controller, this paper is based on the precise controller design in combination with the root locus criterion. According to the system properties and the task requirements, we applied the model reduction method, root locus criterion, root contour, pole-zero placement, frequency response, and orthodox PID criterion to design various controllers. Besides, we analyzed the system responses in a time domain to obtain the optimal controller parameters. We also designed a robust controller to give the system better relative stability through the comparisons of system performances in the frequency domain. Furthermore, in this paper, we also created the reverse gain PID controller to deal with the negative effects of the non-minimum phase system. Not only does this controller improve both the transient response and steady-state error but also enhance the relative stability of the system at the same time. Finally, according to the system properties, this paper can make the controllability of UAV much better by a variety of design methods and flexible controller applications, and then expand the application fields and scopes of UAVs. In sum, the research content is academic, practical, and very efficient as it can be used as reference material that can be applied in further follow-up research.

This work investigates the dynamics of the Chua circuit with cubic polynomial nonlinearity using methods for stability analysis based on linearization and frequency response. Root locus technique maps eigenvalues of the linearized system in order to analyze the local stability, which allows to verify dynamic features, motion patterns, and attractor topologies. The method based on describing functions allows analyze effects of the cubic nonlinearity in the system, as well as predict equilibrium and fixed points, periodic and chaotic orbits, limit cycles, multistability and hidden dynamics, unstable states, and bifurcations. The stability of the Chua circuit with cubic polynomial nonlinearity is analyzed using both approaches in order to identify and map dynamics in parameter spaces. Numerical investigations based on computational simulations corroborate the theoretical results obtained using this stability analysis. This theoretical analysis and the numerical investigations present interesting insights about the dynamics of the Chua circuit with cubic polynomial nonlinearity and provides a design tool for electro-electronic implementations. [ABSTRACT FROM AUTHOR]

The dynamic analysis of induction motors is supported by well-known theories: the two-axes transformation, and the space vector theory. Yet some inconsistencies with the theory of dynamic systems exist. The machine eigenvalues suggest the existence of two damped oscillators, physically not understandable. The respective eigenfrequencies change with the angular velocity of the reference frame. This contradicts the understanding that eigenfrequencies are inherent system properties. Physically, the dynamics depend on the continuous distribution of magnetic energy and its spatial displacement during transient processes. Information on the system dynamics is lost when dividing the continuum of magnetic energy into discrete portions. Complex state variables associate the dynamics to the propagation in space of distributed magnetic fields. The dynamic analysis reveals the existence single-complex eigenvalues. These define a novel class of system identifiers. They are characterized by having only one imaginary part instead of a conjugate complex pair. The use of complex state variables conveys insight and physical understanding of the dynamic processes within the machine. The approach constitutes an extension to the theory of dynamic systems. [ABSTRACT FROM AUTHOR]

Motor arus searah (DC) menjadi populer karena fleksibilitas dan kemudahan dalam pengoperasiannya. Namun motor DC perlu diatur agar mempunyai kecepatan serta respon transien yang diinginkan terlebih ketika diberi beban. Penelitian ini bertujuan untuk merancang dan mensimulasikan alternatif pengendalian motor DC. Pengendalian yang digunakan adalah dengan metode Proporsional Integral Derivatif (PID) melalui root locus. Pada artikel ini akan dipaparkan pemodelan motor DC yang akan diperoleh fungsi alih antara kecepatan sudut dan input tegangan jangkar. Kemudian akan dilihat dan dirancang skema pengendalian dengan respon transien dan steady state yang diinginkan melalui root locus dengan menambahkan pole dan zero. Setelah disimulasikan, hasil perancangan kendali PID yang diperoleh telah sesuai spesifikasi yang diinginkan serta stabil dengan uji kestabilan Routh Hurwitz.

In this paper, a controller has been presented by the root locus method based on the state space average model of the boost switching regulator with all of the converter’s parameters and uncertainties. In this model, the load current is unknown and the inductor, capacitor, diode and active switch are non ideal and have an on-state resistance. Furthermore, an on-state voltage drop has been considered for diode and active switch. By neglecting the load current and assuming the ideal elements the simplified model of the regulator has been caddied out. By these complete and simplified models, a step by step method has been proposed to design a single input single output (SISO), second order controller based on roots locus method. In this regard the controller's electronic circuit has been introduced by operational amplifiers. At the end, by simulation of the complete closed-loop system in MATLAB Simulink environment and comparing its results by the results of the regulator and controller circuits in PLECS, the accuracy of the designed controller performance has been shown.

This study introduces a proposed control method for microgrids (MGs) in islanded (off-grid) mode. The proposed control method is developed by modifying the droop control method using H-infinity controller. In this control method, the droop control loop, current and voltage control loops are adjusted to respond to system load variation. The proposed method is an adaptive control one as it regulates the system voltage and frequency to their nominal values after system load variations. Also, it is a repetitive control method as it depends on the internal model principle that provides good performance for voltage and current error tracking. To prove the applicability and effectiveness of the proposed method, it is applied to a test system using MATLAB/Simulink under three different loading conditions. The results are compared with those of droop control and they prove the effectiveness of the proposed method in adjusting MGs under the off-grid mode of operation. Also, a system stability analysis is performed based on root locus and system step response. Robustness analysis is performed to prove the ability of the proposed controller to restore the system performance after the fault clearance.