Frequency Response Of Plant Research Articles

Parasitic Component Small-Signal Modeling and Control of a Practical CLLC Resonant Converter

This article presents a comprehensive characterization of an asymmetric resonant CLLC dc/dc converter plant transfer function obtained using a generalized harmonic approximation (GHA)-based small-signal modeling approach. The effect of circuit parasitic components is comprehensively considered while deriving this model, and a quantified comparison of the resultant plant frequency response with a conventional first harmonic approximation (FHA)-based model is presented, which provides the designer insightful findings to design a robust and noise immune closed-loop compensator. Furthermore, a thorough explanation of a sliding mode control (SMC) along with detailed parameterization of the controller coefficients is provided by analyzing the system’s dynamic behavior and comparing the response with a conventional proportional–integral (PI)-based controller. In addition to the objective of designing a robust SMC controller, a phase shift-based secondary side modulation is introduced, which facilitates a significant reduction in the secondary side switching losses, thus enhancing the steady-state efficiency of the overall system. To validate and benchmark the open-loop plant response and controller dynamics, detailed steady-state results are elucidated for a 400–28- and 400–24-V voltage conversion at a rated load of 1 kW, with a resonant frequency of 500 kHz. Furthermore, a comprehensive experimental comparison between the proposed hybrid control scheme and the conventional PI controller is shown for two dynamic load changes corresponding to 10%–90% load step-up and 90%–10% load step-down. Quantification of dynamic response portrays a settling time reduction of 46.4% and an over/undershoot reduction of 33%, thus validating the robustness of the proposed control scheme.

Design of a closed-loop autotune PID controller for three-phase for power factor corrector with Vienna rectifier

A closed-loop auto-tuner proportional integral derivative (PID) controller for tuning the DC-link voltage, voltage neutral controllers, and DQ axis current for a power factor corrector with Vienna rectifier is developed and discussed in this study. In traditional tuning of these control loops, it is needed to tune one loop at a time manually, which tends to be a difficult and time-consuming process. In this work, we add a closed-loop PID auto-tuner in the control design will help to simplify and speed up this process by tuning all the 4 PID controllers in a single simulation running in a closed loop. Essentially, it runs auto-tuning experiments for the DQ axis -current, output voltage, and neutral point voltage loops by injecting perturbations; recording the output; estimating the plant frequency response, and tuning the PI controller parameters. In DQ-axis control, projections are used to convert time-based3-phase currents into a time invariant 2-coordinate vector. The results after adding the auto-tuner show that the response time improved considerably when the balanced load was introduced with the individual loads being connected. The results show that the neutral point voltage controller did a good job of keeping the voltage neutral point stable compared to the older controller gains.

Frequency regulation of wind energy integrated power system using a novel optimized type II fuzzy tilted integral derivative controller

Abstract The prime objective of the proposed research work is to study the frequency response of a wind plant integrated two area power system under sudden load disturbances when considered under deregulated market environment. The thermal power system has been modelled with suitable generation constraint and governor dead bands. Erratic behaviour of wind power makes the power system very sensitive to frequency deviations and proper frequency control is needed for stability. A new tilted integral derivative controller (TID) with type II fuzzy controller is considered as secondary controller for minimizing frequency fluctuations. The gains of the controller are set at an optimal value with the help of newly designed hybrid Dragonfly algorithm–Whale optimization algorithm for proper control action. System dynamic performance with and without renewable penetration is studied and robustness of the proposed controller is established under various market conditions and varying renewable power integration.

An Adaptive Control Scheme for Variable Speed Wind Turbines Providing Frequency Regulation in Isolated Power Systems with Thermal Generation

The lack of synchronous inertia, associated with the relevant penetration of variable speed wind turbines (VSWTs) into isolated power systems, has increased their vulnerability to strong frequency deviations. In fact, the activation of load shedding schemes is a common practice when an incident occurs, i.e., the outage of a conventional unit. Under this framework, wind power plants should actively contribute to frequency stability and grid reliability. However, the contribution of VSWTs to frequency regulation involves several drawbacks related to their efficiency and equipment wear due to electrical power requirements, rotational speed changes, and subsequently, shaft torque oscillations. As a result, wind energy producers are not usually willing to offer such frequency regulation. In this paper, a new control technique is proposed to optimize the frequency response of wind power plants after a power imbalanced situation. The proposed frequency controller depends on different power system parameters through a linear regression to determine the contribution of wind power plants for each imbalance condition. As a consequence, VSWTs frequency contribution is estimated to minimize their mechanical and electrical efforts, thus reducing their equipment wear. A group of sixty supply-side and imbalance scenarios are simulated and analyzed. Results of the case study are compared to previous proposals. The proposed adaptive control reduces the maximum torque and rotational speed variations while at the same time maintaining similar values of the load shedding program. Extensive results and discussion are included in the paper.

Robust output disturbance rejection control for anaerobic digestion processes

Anaerobic digestion (AD) is a powerful bioprocess used mainly in the treatment of highly polluted wastewaters with a valuable byproduct called biogas. However, the difficulties associated with the AD stable operation have prevented its worldwide application. The intrinsic complexity of the physicochemical and biological characteristics combined with the uncertain feedstock conditions, time lags and the lack of reliable measurements have hindered the application of a number of classical and advanced control strategies to deal with the control problem. On the other hand, robust H∞ theory offers a solid framework to handle feedback regulation of state variables on the plant frequency response in the face of disturbances and model uncertainties. This contribution presents a robust H∞ mixed sensitivity control design and tuning for output disturbances rejection and it is applied to an anaerobic digestion plant. This H∞ control holds the balance between robustness in the Chemical Oxygen Demand (COD) regulation and control effort. Simulation results show the effectiveness and benefits of the proposed design and tuning method. COD can effectively be regulated under: (i) load perturbations; (ii) model uncertainties and (iii) persistent output disturbances induced by COD measurement faults. The controller is applied to anaerobic digestion process but the approach can be implemented in distinct applications for organic matter degradation and other similar bioprocess and biological systems.

Introducing low‐order system frequency response modelling of a future power system with high penetration of wind power plants with frequency support capabilities

Wind power generation has reached a significant share in power systems worldwide and will continue to increase. As the converter-connected generation reduces the grid inertia, more and more interest has been given to exploiting the kinetic energy and controllability of variable-speed wind turbine generators (VSWTGs) for frequency support. Consequently, the grid frequency dynamics are changing. Thus, it is necessary to include the frequency response of wind power plants in the system frequency response (SFR) model. A novel approach to low-order SFR modelling of a future power system with a high share of frequency-support-capable VSWTGs has been presented. Low-order model of VSWTGs with primary frequency response and natural inertial response has been developed considering different wind turbine operating regimes and compared to the non-linear model for validation. Low-order model has been presented in a symbolic transfer function form. Model accuracy has been discussed and the impact of VSWTG parameters on frequency response has been analysed. The developed model facilitates studying power system frequency dynamics by avoiding the need for modelling complex VSWTG systems, while retaining a satisfying level of accuracy.

State-of-the-art review on frequency response of wind power plants in power systems

With an increasing penetration of wind power in the modern electrical grid, the increasing replacement of large conventional synchronous generators by wind power plants will potentially result in deteriorated frequency regulation performance due to the reduced system inertia and primary frequency response. A series of challenging issues arise from the aspects of power system planning, operation, control and protection. Therefore, it is valuable to develop variable speed wind turbines (VSWTs) equipped with frequency regulation capabilities that allow them to effectively participate in addressing severe frequency contingencies. This paper provides a comprehensive survey on frequency regulation methods for VSWTs. It fully describes the concepts, principles and control strategies of prevailing frequency controls of VSWTs, including future development trends. It concludes with a performance comparison of frequency regulation by the four main types of wind power plants.

Automatic tuning of PID controllers using frequency sampling filters

This study proposes new proportional-integral-derivative (PID) controller auto-tuners using frequency sampling filters (FSFs) for the estimation of plant frequency response information under relay feedback control. It differs from the existing auto-tuners in the estimation of plant frequency response information and its utilisation in the frequency domain-based PID controller design. A desired closed-loop time constant is selected by the user as the scaling factor of the estimated open-loop time constant. Simulation examples are used to demonstrate the efficacy of the auto-tuner and its characteristics in disturbance rejection and reference following, indicating that the auto-tuner produces satisfactory closed-loop control performance for the commonly encountered systems in process control. In addition, Monte Carlo simulation studies are used to demonstrate that the FSF model-based algorithm requires not only shorter experimental time to achieve higher accuracy in estimation but also provides much improvement over the traditional Fourier analysis-based approaches when disturbances are encountered during the relay experiments.

Shifting Method for Relay Feedback Identification

This paper introduces a method extending possibilities of the relay feedback identification of dynamic systems describable by their transfer function. The proposed “shifting” method enables to estimate three points on a plant frequency response from a single relay feedback test without using the FFT algorithm. The approach enables to estimate up to five parameters of the transfer function from sustained oscillations obtained by one relay test. For this purpose the method uses a biased relay. The introduced technique offers a tool for a large class of common control problems. The applicability of the proposed frequency-response identification method is demonstrated by estimating five parameters of the anisochronic model and by estimating three points on the frequency response of the physical model called “Air Aggregate”. All experiments were performed in Matlab/Simulink programming environment.

A novel accelerometer based feedback concept for improving machine dynamic performance

Abstract: Small size ultra-precision Computer Numerical Control (CNC) machines require high dynamic performance. Flexible frame phenomena can limit the machine dynamic performance, particularly in small size machines. A novel accelerometer based feedback concept for improving machine dynamic performance was developed and realised, a virtual metrology frame. It expends the limited techniques for improving dynamic performance of a small size machine by measuring the flexible frame displacement, and feeding it into the controller. The concept was implemented in a simplified linear motion system, and showed a 12dB reduction in the magnitude of the first resonance in the plant frequency response function. This allowed improving the servo bandwidth by 58% based on a PID controller. A new technique for real-time dynamic displacement measurements using accelerometer was developed. It shows a low sensor noise σ

The Sine Wave Tuning method: Robust PID controller design in the frequency domain

The paper presents a novel robust PID controller design method for nominal performance specified in terms of maximum overshoot and settling time. The PID controller design provides guaranteed gain margin GM. The parameter of the tuning rules is a suitably chosen point of the plant frequency response obtained by a sine-wave signal with excitation frequency ωn. Then, the designed controller moves this point into the phase crossover with the required gain margin GM. The couple (ωn;GM) is specified with respect to closed-loop performance requirements in terms of ηmax (maximum overshoot) and ts (settling time) according to developed parabolic dependences. The new approach has been verified on a vast batch of benchmark examples; subsequently, the developed algorithm has been extended to robust PID controller design for plants with unstable zero and unstructured uncertainties.

Frequency Response Estimation from Impulse or Step‐like Response by Virtual Experiments

AbstractThis paper considers the problem of estimating the frequency response of an unknown plant from impulse or step response measurements, possibly with non‐ideal step signals. The proposed method is direct (no model identification of the plant is needed) and it can be applied using a single set of data generated by the plant, with no need for specific experiments nor iterations. The frequency response of the plant, at a desired frequency, is estimated by a virtual experiment generating a filtered version of the data set. Numerical simulations show the effectiveness of the method.

Periodic disturbance rejection for fractional-order dynamical systems

Abstract This paper proposes a simple fractional-order derivative controller, based on an adaptive orthogonal signals generator, which permits both to reconstruct an unknown multi-sinusoidal disturbance and cancel its effect on the system output. An interesting feature is that the disturbance is removed by the generated internal signals with no additional dynamics in the cancellation algorithm. An opportune choice of the fractional-order controller guarantees the closed-loop stability of the system if the location of the plant frequency response at the estimated frequencies belongs to a halfplane passing through the origin of the complex plane, i.e. no information about the order of the system to be controlled, the relative degree, the nature of its poles and zeros, is required. The case of multi-sinusoidal disturbance is also analyzed. Simulations are presented that highlight the performances of the proposed method.

Stability and Performance Attainment with Fixed Order Controller Using Frequency Response

Recently, a new data driven controller synthesis is presented for calculating the family of stabilizing first, second and fixed order controllers using frequency respons. However, this method is applicable just for plants that can guarantee some smoothness at the boundary of the resulted high dimension LMI. This paper solve that issue and extends the approach to fixed order controllers guaranteeing some performance criteria which are applicable for the more general types of plants. It is shown that knowing the frequency response of plant is sufficient to calculate the stabilizing fixed order controllers from a set of convex linear inequalities. The H ∞ norm on sensitivity and complementary sensitivity functions are satisfied from some frequency domain inequalities (FDI) that could be examined from frequency response data. The usefulness of the proposed approach is illustrated by an academic example. doi: 10.5829/idosi.ije.2015.28.04a.09

Performance-guaranteed Robust PID Controller Design for Systems with Unstable Zero

The paper deals with the development of a new robust PID controller design method that guarantees designer-specified maximum overshoot and settling time for non-minimum phase processes with unstable zero. The PID controller design provides guaranteed gain margin GM. The parameter of the tuning rules is a suitably chosen point of the plant frequency response obtained by a sine-wave signal with excitation frequency ωn. Then, the designed controller moves this point into the phase crossover with the required gain margin GM. The couple (ωn;GM) is specified with respect to closed-loop performance requirements in terms of emax (maximum overshoot) and ts (settling time) according to developed parabolic dependences. The new approach has been verified on a vast batch of benchmark examples; subsequently, the developed algorithm has been extended to robust PID controller design for plants with unstable zero and unstructured uncertainties.

Gap Metric Bound Construction From Frequency Response Data

Motivated by the difficulty of designing low-order controllers for large-scale plants consisting of numerous interconnected subsystems, this paper addresses the issue of quantifying the ν-gap metric between the plant and a lower-order identified model, using only plant frequency response data. The main result of this paper is the construction of a bound on the ν-gap metric between plant and model that exploits the convergence properties of Chebyshev polynomial interpolants of point-wise in frequency system graph symbols. This bound subsequently informs the design of low-order robust controllers synthesised from the identified model. The techniques developed in this paper are demonstrated upon a semi-discretised 1D heat equation.

Biased Sinusoidal Disturbance Compensation With Unknown Frequency

This note combines an adaptive frequency estimation scheme with a fractional-order controller for unknown biased sinusoidal disturbance rejection. The disturbance is estimated via an adaptive orthogonal signals generator based on a third-order generalized integrator. A fractional-order controller is designed which guarantees the closed-loop stability of the system if the location of the plant frequency response, at the estimated frequencies, lies in an half-plane passing through the origin of the complex plane.

Periodic disturbance rejection with unknown frequency and unknown plant structure

This paper deals with asymptotic rejection of a multi-sinusoidal signal for linear single-input single-output stable systems with unknown structure. An adaptive orthogonal signals generator is used to both reconstruct the disturbance and cancel its effect on the system output. An interesting feature is that the disturbance is removed by the generated internal signals with no additional dynamics in the cancellation algorithm. A fractional-order controller is designed which guarantees the closed-loop stability of the system if the location of the plant frequency response at the estimated frequencies lies in a half-plane passing through the origin of the complex plane, i.e. no information about the order of the system to be controlled, the relative degree, the nature of its poles and zeros, is required. The case of multi-sinusoidal disturbance is also analyzed. Simulations and comparisons with existing approaches are presented that highlight the performances of the proposed method.

Theoretical and experimental determination of bandwidth for a two-axis fast steering mirror

Fast steering mirror (FSM) system is a precise beam steering mechanism which modulates the beam between a light source and a receiver using its reflecting surface. High bandwidth is an important property of FSM, which is associated with the response speed and stable precision. It is difficult to design the closed-loop bandwidth for FSM, which relies on the open-loop frequency response of the system and the design of the controller. A theoretical analysis, simulation, and testing method to determine an appropriate bandwidth designation for a two-axis FSM are developed in this paper. An ideal open-loop plant frequency response is compared to a final closed-loop bandwidth requirement, and then, stiffness of elastic support in each direction is researched and idea of stiffness design of elastic support is put forward. An integrated mechanical control simulation (IMCS) method is introduced to simulate the structural response and controller design synchronously to predict the final closed-loop control performance of the two-axis FSM system. Finally, the open-loop plant frequency response and closed-loop bandwidth of the assembled two-axis FSM system are tested with the results confirming the general validity of the analysis and simulation method presented in this paper.

Easy Tuning of PID Controllers for Specified Performance

The presented method allows achieving maximum overshoot and specified settling time of the closed-loop step response. It provides a simple way to control linear stable SISO systems even if the mathematical model is unknown. Tuning rule parameters are based on one suitably chosen point of the plant frequency response obtained by sine-wave signal with specified excitation frequency, and the required phase margin. The main result provided is construction of empirical charts used to convert time-domain performance specifications (maximum overshoot and settling time) into frequency domain performance measure (phase margin). The method is applicable for systematic shaping of the closed-loop response of the plant. The new approach has been verified on a set of benchmark examples and on a real plant as well.