Pole Placement Method Research Articles

Load Frequency PID Controller Design Based on Pole Placement Method of an Islanded Microgrid

Load Frequency PID Controller Design Based on Pole Placement Method of an Islanded Microgrid

Real‐Time Implementation of Unknown Input Observer‐Based State and Unknown Disturbance Estimation for Series Active Filters

ABSTRACTSeries active filter (SAF) is generally utilized in compensating harmonic voltage source‐type loads. In this paper, a combined action of controller and observer is proposed for SAF. Full state feedback (SFB) and linear quadratic regulator (LQR) controllers are posited in order to estimate states, and fault. SFB utilizes the pole placement method, whereas LQR utilizes the tuning of matrices by Bryson's rule. Luenberger observer (LO), proportional–integral observer (PIO), and unknown input observer (UIO) were also designed. The efficacy of this scheme is illustrated through the simulations, in the presence of faults. The state dynamics of SFB‐ and LQR‐based control of SAF with LO, PIO, and UIO in different faulty cases are compared. It can be clearly seen through simulations that the state dynamic response of LQR‐based control of SAF is faster when compared to SFB‐based control of SAF in both cases. Further, LO and PIO established a steady‐state error between the actual state and its estimate, with reference to desired input, in the presence of a fault. UIO perfectly tracked the desired input, even in the presence of various unknown fault, when compared to LO and PIO. Furthermore, UIO also estimates the unknown faults better when compared to PIO. Finally, in a dynamic operating scenario, the effectiveness of the suggested control strategy has been assessed and verified using MATLAB/SIMULINK and the output of a real‐time simulator (OPAL‐RT OP4510).

A tracking control method with the fast finite-time command filter for four degrees of freedom tower cranes

Tower cranes are the main tool of the horizontal and vertical transportation for construction, which are always driven by operators slowly to prevent payloads from large swing, such that efficiency is low. To deal with the problem, a finite-time tracking control method based on fast command filters is proposed, which can eliminate the tracking error in finite time and restrain the swing at the same time. The asymptotic stability is proved by Lyapunov technique. Finally, the hardware experiment is carried out and compared with the existing methods on the self-built tower crane experimental platform, and the pole placement method is used to select control parameters. The effectiveness and superiority are verified by the experimental results.

Disturbance rejecting PID-FF controller design of a non-ideal buck converter using an innovative snake optimizer with pattern search algorithm

The optimal design of a proportional-integral-derivative controller with two cascaded first-order low-pass filters (PID-FF) for non-ideal buck converters faces significant challenges, including effective disturbance rejection, robustness to parameter variations, and the mitigation of high-frequency signal noise, with existing approaches often struggling and leading to suboptimal performance in practical applications. This study addresses these challenges by introducing a constraint on the open-loop crossover frequency to mitigate high-frequency noise and ensuring the controller prioritizes maintaining constant output voltage and robust responsiveness to input voltage and load current variations. This study also introduces an innovative metaheuristic algorithm, the opposition-based snake optimizer with pattern search (OSOPS), designed to address these limitations. OSOPS enhances the Snake Optimizer (SO) by integrating opposition-based learning (OBL) and Pattern Search (PS), thereby improving its exploration and exploitation capabilities. The proposed algorithm design includes a crossover frequency constraint aimed at counteracting high-frequency noise and ensuring robust performance under diverse disturbances. The efficacy of the OSOPS algorithm is demonstrated through rigorous statistical box plot analysis and convergence response comparisons with the original SO algorithm. Additionally, we systematically compare the performance of the OSOPS-based PID–FF–controlled non-ideal buck converter system against systems utilizing the original SO algorithm and the classical pole placement (PP) method. This evaluation encompasses transient and frequency responses, disturbance rejection, and robustness analysis. The results reveal that the OSOPS-based system outperforms the SO- and PP-based systems with 14.21 % and 32.10 % faster rise times, along with 15.38 % and 84.95 % faster settling times, respectively. The OSOPS and SO systems also exhibit higher bandwidths, exceeding the PP-based system by 18.74 % and 17.03 %, respectively. By addressing the key challenges in PID-FF controller design for non-ideal buck converters, this study provides a substantial advancement in control strategy, promising enhanced performance in practical applications.

Pole placement tuning of proportional integral derivative feedback controller for knee extension model

Functional electrical stimulation (FES) has shown potential in rehabilitative exercises for patients recovering from spinal cord injuries. In recent developments, conventional open-loop FES control techniques have evolved into closed-loop systems that employ feedback controllers for automation. However, closed-loop FES systems often face challenges due to muscle non-linear effects, such as fatigue, time delays, stiffness, and spasticity. Therefore, an accurate non-linear knee model is required during the design stage, and precise tuning of the feedback controller parameters is vital. A proportional– integral–derivative (PID) controller is commonly used as a feedback controller due to its simplicity and ease of implementation. However, most PID tuning methods are complex and time consuming. This paper investigates the viability of employing the pole placement technique for tuning a PID controller that regulates the non-linear knee extension model. The pole placement method aims to improve the control and adaptability of the PID controller in closed-loop FES systems, specifically by facilitating knee extension exercises. MATLAB Simulink was used to assess the effectiveness of this tuning approach. Results showed that the PID controller performed satisfactorily without non-linearities, but performance varied with the inclusion of specific non-linearities. The pole placement tuning method facilitated preliminary assessments of PID controller performance, preceding highly advanced optimization.

Disturbance observer based fixed-time control of stochastic systems

In this paper, the novel fixed-time anti-disturbance control scheme is proposed for a class of stochastic systems subjected to multiple disturbances and faults, and the disturbances consist of derivative-bounded disturbances and multiply noise. Based on the pole placement method, the fixed-time disturbance observer (Fixed-time DO) is devised to estimate derivative-bounded disturbances and an adaptive law is employed to approach the time-varying fault. Then a composite fixed-time controller is constructed to make the system converge to equilibrium position within a pre-specified time. At the same time, simulation examples illustrate that the proposed controller is effective and the convergence time is not related to the initial states of the system.

Indirect Measurement of Variables in a Heterogeneous Reaction for Biodiesel Production.

This research focuses on the development of a state observer for performing indirect measurements of the main variables involved in the soybean oil transesterification reaction with a guishe biochar-based heterogeneous catalyst; the studied reaction takes place in a batch reactor. The mathematical model required for the observer design includes the triglycerides' conversion rate, and the reaction temperature. Since these variables are represented by nonlinear differential equations, the model is linearized around an operation point; after that, the pole placement and linear quadratic regulator (LQR) methods are considered for calculating the observer gain vector L(x). Then, the estimation of the conversion rate and the reaction temperature provided by the observer are used to indirectly measure other variables such as esters, alcohol, and byproducts. The observer performance is evaluated with three error indexes considering initial condition variations up to 30%. With both methods, a fast convergence (less than 3 h in the worst case) of the observer is remarked.

Optimization of RST Controller for Speed Control of Linear Induction Motor Using Genetic Algorithm

Background: In this study, a new model of linear induction motor, along with the impact of end-effect on motor performance, is proposed. Moreover, a new strategy of control approach based on the polynomial RST controller is suggested and investigated. Objective: The proposed approach can provide a robust control strategy and overcome the limitations imposed by the proportional-integral (PI) regulator in the FOC technique. RST controller has a two-degree of freedom structure and consists of three polynomials, namely R, S and T, which are determined by the pole placement method and resolving of a Diophantine equation. Despite this, the implementation of this method is usually difficult and becomes more complicated with the complexity of the controlled plants. Methods: This study proposes the genetic algorithm (GA) optimization strategy for tuning RST controller parameters (adjust the controller coefficients) in order to achieve an adequate response time by minimizing the different objective functions, such as steady-state error, settling time, and rise time. Results: The accuracy and control performance of the proposed technique are checked and validated using Matlab /Simulink environment software tool. Simulation results reported that the proposed method (RST-GA) could provide robust solutions with perfect reference tracking and efficient disturbance rejection. Conclusion: These significant results make the proposed approach a promising technique for the design of a high-performance controller, which is highly suitable for industrial and electrical applications.

Pole-Placement-Based Calibration of an Electromagnetically Realizable Inerter-Based Vibration Absorber (IDVA) for Rotating Wind Turbine Blades

This paper deals with edgewise vibration mitigation of rotating wind turbine blades by means of inerter-based vibration absorber (IDVA), which can be realized both mechanically and electromagnetically. Introducing the electromagnetically-realizable IDVA to the blade forms a 3-degree-of-freedom (3-DOF) blade-IDVA system consisting of the rotating blade, an absorber, and a series inerter-dashpot-spring subsystem. Analytical optimal design formulas of the rotating blade-installed IDVA are then derived using a pole-placement method where the equal-modal-damping-ratio principle and the triple-root-bifurcation condition are applied. The analytical formulas show that the optimal parameters for the blade-IDVA system merely depend on the spinning speed of the rotor given the IDVA location and the absorber mass. Numerical results of the NREL 5 MW wind turbine with optimal IDVA show that optimal IDVA leads to superior performance than optimal TMD in mitigating the blade edgewise vibration and behaves nearly as same as optimal RIDTMD, along with slightly optimal damper parameters variation. This means that the inerter-dashpot-spring system can be deployed flexibly for damping edgewise vibrations of rotating blades.

Tuning of vibration absorbers by an effective modal coupling factor

The simplest family of vibration absorbers comprise inertia absorbers, with an inerter in series with a parallel or series dashpot–spring element, and stiffness absorbers, for which inerter and spring are interchanged. Vibration absorbers are tuned to a structure’s critical resonance, for which scalar structure-absorber equations are derived from an expansion in vibration modes with the absorber in either a free or clamped state. It is demonstrated that the influence from non-targeted residual modes is consistently represented by an effective modal coupling factor (EMCF), evaluated as the relative difference between free and clamped natural frequencies squared. While closely related to the coupling factor for shunted electromechanical transducers, the use of EMCFs determines an entirely new direction for the tuning of mechanical vibration absorbers on a flexible structure. For inertia and stiffness absorbers, the EMCF represents apparent mass or stiffness ratios that also account for the influence from residual modes. Therefore, analytical tuning expressions can be obtained from the derived modal frequency response functions, as demonstrated for a pole-placement method with the EMCF as a new governing absorber parameter. The accuracy of the proposed absorber tuning is validated by a simple numerical example, which shows that analytical tuning expressions can be used directly for vibration damping of flexible structures, provided that the EMCF is included correctly to compensate for the inherent modal interaction.

Wide area damping of electromechanical oscillations based on implicit reference model adaptive control

Assessing the stability of low-frequency inter-area oscillations remains an important issue in modern electrical power systems. The paper proposes a novel method for optimal tuning of power system stabilizers for wide area damping of electromechanical oscillations based on implicit reference model adaptive control. An implicit reference model of the system is formed on the basis of choosing the desired values of the roots of the characteristic polynomial of the system by computing the determinant of its characteristic matrix. An adaptive tuning procedure seeks to preserve the “reference” values of the coefficients in the characteristic polynomial of the swing equation model of the system identified at the current operating point. The proposed approach can be also considered as an adaptive pole placement method applied to the linearized swing equation model. Numerical experiments with the IEEE 30 bus test model confirm that the proposed method can be effective in maintaining dynamic and transient stability.

An Advanced Physiological Control Algorithm for Left Ventricular Assist Devices

Left ventricular assist devices (LVADs) technology requires developing and implementing intelligent control systems to optimize pump speed to achieve physiological metabolic demands for heart failure (HF) patients. This work aimed to design an advanced tracking control algorithm to drive an LVAD under different physiological conditions. The pole placement method, in conjunction with the sliding mode control approach (PP-SMC), was utilized to construct the proposed control method. In this design, the method was adopted to use neural networks to eliminate system uncertainties of disturbances. An elastance function was also developed and used as an input signal to mimic the physiological perfusion of HF patients. Two scenarios, ranging from rest to exercise, were introduced to evaluate the proposed technique. This technique used a lumped parameter model of the cardiovascular system (CVS) for this evaluation. The results demonstrated that the designed controller was robustly tracking the input signal in the presence of the system parameter variations of CVS. In both scenarios, the proposed method shows that the controller automatically drives the LVAD with a minimum flow of 1.7 L/min to prevent suction and 5.7 L/min to prevent over-perfusion.

Enhanced Control of Back-to-Back Converters in Wind Energy Conversion Systems Using Two-Degree-of-Freedom (2DOF) PI Controllers

The performance of a full-scale wind energy conversion system is dependent on the control system of the back-to-back power electronics converter. Different controllers have been proposed in the literature, many of which are variations of a generalized two-degrees-of-freedom (2DOF) PI controller. This paper presents a design method for the parameters of a 2DOF PI controller for the stator current, generator speed, grid current, and DC bus voltage control. The controller can be designed using a general independent zero and pole placement method. The proposed and conventional methods are analyzed based on their ability to track references, reject disturbances, and their sensitivity to noise. A tuning approach is proposed to enhance the controller’s bandwidth without sacrificing noise sensitivity or disturbance rejection capability. The conventional methods are shown to be special versions of the proposed design. Simulation results demonstrate the effectiveness of the proposed design.

Rich dynamics of a discrete two dimensional predator–prey model using the NSFD scheme

In this paper, we consider a two-species predator–prey model with Holling type III functional response and non-linear predator harvesting. The proposed model is discretized using a non-standard finite difference scheme (NSFD). The stability of different equilibrium points are analyzed. Also, the conditions of various types of bifurcations likely: Transcritical, Neimark–Sacker bifurcation (NSB), and Flip (Period doubling) bifurcation (PDB) have been established along with chaos control strategies. The numerical results indicate that the system exhibits different patterns of solutions, including single, two, and higher periodicity. Using Lyapunov exponents and bifurcation diagrams, chaotic solutions are verified. Two model parameters were drawn simultaneously in the attractor basin, which yielded different periodic solutions compared to the continuous dynamical system. Lastly, the pole placement method (PPM) has been used to control chaos in the proposed discrete ecological model.

STRONG ALLEE EFFECT AND EVOLUTIONARY DYNAMICS IN A SINGLE-SPECIES RICKER POPULATION MODEL

In this paper, a discrete-time Ricker population model with the strong Allee effect is proposed, and its complex dynamic behavior is analyzed. First, the existence and asymptotic stability of the unique positive equilibrium are studied. Second, Neimark–Sacker and period-doubling bifurcations of this discrete model were carried out, and corresponding bifurcation conditions were obtained. Third, the pole placement method and the hybrid control strategy have been used to control the chaos produced by these bifurcations. Finally, we use MATLAB software to carry out some numerical simulations to analyze the rich dynamics of the system as well as to verify our theoretical results.

Design of hvdc damping controller using pmu data

This paper describes a novel method to design a supplementary HVDC damping controller for damping the power oscillations in the electrical network. The electrical network of Karnataka and Tamil Nadu is the system under consideration and the Raigarh-Pugalur HVDC linkis taken for integrating the supplementary controller. PSSNETOMAC is used for Eigenvalue analysis to identify the oscillatory modes. The test signal method and pole placement method are used for designing and tuning the parameters of the supplementary controller. RTDSTM is utilized for the controller design and implementation. Dynamic analysis has been performed to validate the effectiveness of the designed controller.

Pole Placement-Based Current Control Method for CSI-Fed PMSM Drive With Eliminating Capacitor Voltage Sampling

This article proposes a pole placement based current control method for the current source inverter (CSI) fed permanent magnet synchronous machine (PMSM) drive with eliminating capacitor voltage sampling. Firstly, a generalized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -order feedback form of motor current and CSI output current is proposed in the stationary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha \beta$</tex-math></inline-formula> frame, for the arbitrary pole placement of the control plant. With the proposed pole placement method, the resonance frequency is moved closer to the Nyquist frequency and the resonance peak is damped. On this basis, a linear controller is proposed in the synchronous <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> frame for the high-performance current control of PMSM. Moreover, the control parameter selection method is presented based on the consideration of open-loop crossover frequency and phase margin (PM). In this way, the desired PM and enough gain margin (GM) can be achieved, thus guaranteeing the stability and robustness of the system. Finally, the effectiveness of the proposed method is verified by lab-scaled experiments.

An Investigation on the Stability of Dynamic Soaring Orbits

Dynamic soaring is a technique for extending flight times by utilising wind gradients. It was originally observed amongst birds like albatrosses and has huge potential for high-endurance UAV flights. In this paper, we investigate the stability of dynamic soaring orbits from a linear periodic system perspective and explore the feasibility of using a pole placement method for augmenting stability. Stability of dynamic soaring orbits is vital since the trajectories can get disturbed by a gust or crosswinds, causing the UAV to veer off-course. An open-loop stable orbit can reduce the control effort and power requirement. Variation of Phugoid damping values with wind shear has been studied for a qualitative appreciation of the stability of dynamic soaring orbits. For assessing the dependence of the stability of dynamic soaring orbits on wind shear, a Monte-Carlo based approach is used.

Development of magnetic levitation system with position and orientation control

This work demonstrates the design and development of a magnetic levitation (MagLev) system that is able to control both the position and orientation of the levitated object. For the position control, a pole placement method was exploited to estimate parameters of the proportional integral derivative (PID) controller. In addition, the MagLev was constructed using a pair of electromagnets, two infrared (IR) receiver-emitter pairs and a servo motor to allow the orientation of the object to be controlled. The proposed controller was programmed in a LabVIEW environment, which was then compiled and deployed into an embedded NI myRIO board. Experimental results demonstrated that the proposed method was able to achieve a zero steady-state orientation error when the object was rotated from 0 ◦ to ±90◦ , a steady-state position error of 0.3 cm without rotation, and steady-state position errors of no greater than 1.2 cm with rotation.

Sampled-Data Nonlinear Control of ECP-730 Magnetic Levitation System

Abstract This paper presents the idea of implementing various techniques related to sampled-data control for magnetic levitation systems. The control laws are designed to track time-varying signals and employ the feedback linearization technique based on the approximate discrete-time model. State feedback control is introduced with the gains adjusted via the pole placement method. A positional form proportional-integral-derivative (PID) control uses the trapezoidal summation for the integral term and the backward difference method for the derivative term. An input-output linearization feedback control is the most promising one, which incorporates the integrator in addition to the position error and velocity error. The integral action involves the manipulation of regulation error and reduces it with time to improve performance. Finally, controllers were tested in real time for practical demonstration along with a comparison for comprehensive analysis.