Selection Of Weighting Functions Research Articles

Multi-Objective Optimisation-based Robust H∞ Controller Design Approach for a Multi-Level DC-DC Voltage Regulator

In case an analytical approach to the selection of any weighting function is not possible, the selection process is usually a random and time-consuming process. In robust H∞ control theory, the selection of scalar, time, or frequency-dependent weighting functions is the main issue to shape the amplitude-frequency characteristic curve of the feedback controller. Therefore, we propose a robust H∞ control approach which utilises the multi-objective grey wolf optimisation algorithm (MOGWO) to obtain the optimal performance weighting functions in the presence of right half-plane zeros and limited bandwidth constraints. A trade-off design flowchart is proposed, providing Pareto optimal solutions to choose the optimal configuration of the robust feedback controller. The control method is structured by combining the robust H∞ optimal technique and the multi-objective algorithm. The effectiveness of the approach is compared with the non-convex single-objective heuristic solutions like the multi-verse optimisation algorithm (MVO), whale optimisation algorithm (WOA), and grey wolf optimisation algorithm (GWO). The focus of this design is to track and stabilise the output voltage of the DC-DC converter in the presence of external disturbances and parameter uncertainties. The optimised controllers are implemented using a digital signal processor (DSP) on a 200 W interleaved boost converter. The simulation results and experimental findings show that the proposed control method provides supreme disturbance rejection along with maintaining the stability of the system.

Modelling publication bias and p-hacking.

Publication bias and p-hacking are two well-known phenomena that strongly affect the scientific literature and cause severe problems in meta-analyses. Due to these phenomena, the assumptions of meta-analyses are seriously violated and the results of the studies cannot be trusted. While publication bias is very often captured well by the weighting function selection model, p-hacking is much harder to model and no definitive solution has been found yet. In this paper, we advocate the selection model approach to model publication bias and propose a mixture model for p-hacking. We derive some properties for these models, and we compare them formally and through simulations. Finally, two real data examples are used to show how the models work inpractice.

Robust tracking system design for a synchronous reluctance motor – SynRM based on a new modified bat optimization algorithm

This paper discusses optimal controller structure design for a Synchronous Reluctance Motor (SynRM). Optimization of controller parameters is based on a new modified BAT optimization algorithm (mBAT). SynRM is represented with a nonlinear dynamic model of a synchronous machine. All gathered nonlinearities of SynRM are taken into account in the controller’s design and optimization procedure with mBAT. A novel SynRM controller structure with a modified robust disturbance observer (mRDO) is presented. The modified mRDO ensures a higher level of stability margin, efficient disturbance rejection, and enables transparent controller parametrization and optimization. Controller synthesis is based on robust ℋ∞ pole-placement technique. The ℋ∞ robust criteria are presented in the form of spectral polynomials and their strong positivity conditions. Spectral polynomials (SP) can be directly used as objective functions in the mBAT optimization procedure. The mBAT algorithm, in terms of the derived SP introduces a novel approach to adaptive weighting function selection and modification of BAT velocity in the position formula. The new modification of the BAT algorithm is inspired by feedback control theory and Lyapunov exponential stability property. The proposed modification of the mBAT significantly increases the efficiency of the given optimization problem.

Influence of Type of Frequency Weighting Function On VDV Analysis

Transport vibrations are the subject of many research, mostly their influence on structural elements of the building is investigated. However, nowadays, especially in the centres of large cities were apartments, residential buildings are closer to the transport vibration sources, an increasing attention is given to providing vibrational comfort to humans in buildings. Currently, in most countries, two main methods of evaluation are used: root mean squared method (RMS) and vibration dose value (VDV). In this article, VDV method is presented and the analysis of the weighting functions selection on value of VDV is made. Measurements required for the analysis were made in Krakow, on masonry, residential, two storey building located in the city centre. The building is subjected into two transport vibration sources: tram passages and vehicle passages on very close located road. Measurement points were located on the basement wall at ground level to control the excitation and in the middle of the floor on the highest storey (in the place where people percept vibration). The room chosen for measurements is located closest to the transport excitation sources. During the measurements, 25 vibration events were recorded and analysed. VDV values were calculated for three different weighting functions according to standard: ISO 2631-1, ISO 2631-2 and BS-6841. Differences in VDV values are shown, but also influence of the weighting function selection on result of evaluation is also presented. VDV analysis was performed not only for the individual vibration event but also all day and night vibration exposure were calculated using formulas contained in the annex to the standard BS-6841. It is demonstrated that, although there are differences in the values of VDV, an influence on all day and night exposure is no longer so significant.

Application of Coordinated SOFC and SMES Robust Control for Stabilizing Tie-Line Power

Wind power causes fluctuations in power systems and introduces issues concerning system stability and power quality because of the lack of controllability of its discontinuous and intermittent resources. This paper presents a coordinated control strategy for solid oxide fuel cells (SOFCs) and superconducting magnetic energy storage (SMES) to match the intermittent wind power generation and compensate for the rapid load changes. An optimal H∞ control method, where the weighting function selection is expressed as an optimization problem, is proposed to mitigate tie-line power fluctuations and the mixed-sensitivity approach is used to deal with the interference suppression. Simulation results show that the proposed method significantly improves the smoothing effect of wind power fluctuations. Compared with the conventional control method, the proposed method has better anti-interference performance in various operating situations.

Weighting Function Selection Problem in the Galerkin Method

When a problem contains more than one unknown function and a corresponding number of differential equations, the contents of the Galerkin method are not necessarily completely clear. This theme is discussed in the paper by considering four example cases: one-dimensional heat conduction, the bending of an Euler–Bernoulli beam, a regenerator problem and an axially moving string problem. A strategy for selection of the proper weighting function is proposed. Some numerical results are presented. Suggestions regarding how a basic finite element course for engineering students might proceed in its initial stages are given.

Mixed ${\cal H}_{2}/{\cal H}_{\infty}$ Observer-Based LPV Control of a Hydraulic Engine Cam Phasing Actuator

In this paper, a family of linear models previously obtained from a series of closed-loop system identification tests for a variable valve timing cam phaser system is used to design a dynamic gain-scheduling controller. Using engine speed and oil pressure as the scheduling parameters, the family of linear models was translated into a linear parameter varying (LPV) system. An observer-based gain-scheduling controller for the LPV system is then designed based on the linear matrix inequality technique. A discussion on weighting function selection for mixed H2/H∞ controller synthesis is presented, with an emphasis placed on examining various frequency responses of the system. Test bench results show the effectiveness of the proposed scheme.

Muti‐Objective Nonlinear Model Predictive Control of Semibatch Polymerization Reactors

AbstractA novel control system for semibatch polymerization reactors based on nonlinear MPC is proposed that is aimed to deal with more than one control objective. Commonly, multi‐objective control problems are reduced to single objective problems, but better control can be achieved by solving the problem as a true multi‐objective optimization problem because the interactions among the control goals are taken into account. Moreover, the selection of subjective weighting functions is avoided. The procedure is based on computing a trade‐off solution among the control objectives that features the minimum distance from a given point on the Pareto front to the Utopia region. To illustrate the application of the multi‐objective nonlinear MPC strategy two complex reaction systems are deployed. magnified image

ℋ ∞ Robust control of a T1DM model

Abstract The control of physiological systems is usually a highly demanding task. The requirements are strict and there is a little margin of error, since failure can directly endanger the patient's life. In the same time the performance of the available sensors and actuators are limited in most cases, leaving even higher burden on the control algorithm. Finally the available mathematical models themselves are rather complex and nonlinear in nature. Modern robust control theory can be a potential solution and provide a mathematically proven stability of the controlled loop. However, being a linear control methodology, the direct use is not a simple task. The current paper presents a case study of the nowadays widely used ℋ∞ robust control methodology's applicability on physiological control systems, specifically on type 1 diabetes. The most important challenges and problems to take into account are discussed (like weighting function selection, robust performance investigation) together with nonlinear control extension possibilities. The case study is done on the well known and widely used type 1 diabetes mellitus (T1DM) model of Hovorka et al. (2004).

Intelligent robust control design of a precise positioning system

This paper addresses an intelligent uncertainty function to improve the robust stability and performance of H∞ controlled system in terms of reduced conservatism. The system is identified, output performance and control signal requirements are controlled by proper selection of performance and control weighting functions. Adaptive Neuro Fuzzy Inference System (ANFIS) learns the uncertainty bounds of model uncertainty that results from unmodeled dynamics and parameter variations, then the developed uncertainty weighting function will be included in the synthesis of the H∞ controller. ν-gap measure is utilized to validate the intelligent identified uncertainty bounds and measure the stability of the designed H∞ controlled system as well. Experimental results on a servo motion system reveal the advantages of combining intelligent uncertainty identification and robust control. Improved performance is achieved. The proposed approach also allows for iterative experiment design.

Mu‐Synthesis for Magnetic Bearings of Flywheel

AbstractIn this paper, the μ‐Synthesis Control method is applied to control Active Magnetic Bearings (AMBs) Flywheel. The dynamics of the open‐loop system is influenced by external disturbances, nonlinearities, uncertainties and signal limits. Thus, a design methodology, which covers the practical issues of optimal robust control like the modelling of uncertainties, selection of optimal weighting functions is presented. The goal of this paper is the experimental evaluation robust performance of the AMBs system. The laboratory stand with the high speed rotor supported magnetically was built and presented. The stable operation, good stiffness of the rotor suspension and robust performances of the closed‐loop AMBs is reached. Finally, the success of the robust control is demonstrated through results of computer simulations and experimental results. The experimental results show the effectiveness of the control system as well as good vibrations reduction of the designed controllers. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Robust Control Scheme for Medium-Voltage-Level DVR Implementation

In this paper, a robust control scheme with an outer Hinfin voltage control loop and an inner current control loop is designed and implemented on a medium-voltage (MV)-level dynamic voltage restorer (DVR) system. Through a simple selection of weighting functions, the synthesized Hinfin controller would exhibit significant gains in the vicinity of positive- and negative-sequence fundamental frequencies, and therefore, it would be able to regulate both positive- and negative-sequence components effectively, with explicit robustness in the face of system parameter variations. A detailed discussion of Hinfin controller weighting function selection, inner current loop tuning, and system disturbance rejection capability is presented. Finally, the designed control scheme is extensively tested on a laboratory 10-kV MV-level DVR system with varying voltage sag (balanced and unbalanced) and loading (linear/nonlinear load and induction motor load) conditions. It is shown that the proposed control scheme is effective in both balanced and unbalanced sag compensation and load disturbance rejection, as its robustness is explicitly specified.

Partial pole placement of H∞ based PSS design using numerator-denominator perturbation representation

A new H∞ PSS design method which uses the numerator-denominator perturbation representation and includes the partial pole placement technique and a new weighting function selection method is proposed. This overcomes certain conventional H∞ PSS design algorithm limitations. A sixth-order machine model is used to increase the accuracy of selected weighting functions. A robust PSS has been successfully designed for single and two-machine systems by treating the highly nonlinear characteristic of the power system as model ‘uncertainty’. The design is verified to have better performance for a wide range of system operating conditions when compared with the conventional PSS designs.

Systematic H∞ weighting function selection and its application to the real-time control of a vertical take-off aircraft

In this paper, the selection of H ∞ weighting functions for general practical applications is investigated. It is shown that an H ∞ weighting function for a single-input–single-output ( SISO) plant can be obtained by considering a series of connections of elementary low-order plants. For a constrained control effort, an explicit weighting function expression is derived for the first time. A novel method for the selection of weighting functions in H ∞ mixed sensitivity design is proposed to control the percentage overshoot directly. An example illustrating how the transient response of a standard H ∞ design is improved by using the proposed weighting functions is provided. Finally, real-time experimental results are presented for the roll-angle control of a laboratory-scale physical model of a vertical take-off aircraft.

Spiral interpolation algorithm for multislice spiral CT--part I: theory.

This paper presents the adaptive axial interpolator (AAI), a novel spiral interpolation approach for multislice spiral computed tomography (CT) implemented in a clinical multislice CT scanner, the SOMATOM Volume Zoom (Siemens Medical Systems, Forchheim, Germany). The method works on parallel-beam data generated from the acquired fan-beam data by azimuthal rebinning. Spiral interpolation is performed by distance-dependent weighting; i.e., for each ray, its distance to the image plane is evaluated and serves as an argument to a freely selectable weighting function, resulting in a weight factor. A normalization step is applied to the weight factors to ensure that the sum of all corresponding weights (i.e., the weights applied to rays that contribute to the same ray in the interpolated sinogram) is 1. By selection of appropriate weighting functions and suitable adjustment of the tube current, it is possible to keep the slice sensitivity profiles (SSP) as well as the pixel noise constant for all pitch values in the relevant range. Also, a large range of slice-thickness can be reconstructed from a given collimation. The method is, thus, very versatile. Further advantages are that it uses the entire applied dose for imaging and allows for efficient implementation using a table lookup approach.

A new H∞ based PSS design using numerator–denominator perturbation representation

Abstract A new H∞ PSS design method which uses the numerator–denominator perturbation representation and includes the partial pole placement technique and a new weighting function selection method is proposed. This overcomes certain conventional H∞ PSS design algorithm limitations. A robust PSS has been successfully designed by treating the highly non-linear characteristic of the power system as model ‘uncertainty’. The design is verified to have better performance for a wide range of system operating conditions when compared with the conventional PSS design.

Applying H∞ optimisation method to power system stabiliser design Part 2: Multi-machine power systems

The application of the H ∞ optimisation method to power system stabiliser design is studied in this paper. The weighting function selection and the application to multi-machine power systems are investigated in two separate parts. In this second part, it is shown that PSS design for multi-machine power systems can be translated into a problem of a series of sequential stabiliser designs. Each of them is for a very high order Single—Input Single—Output (SISO) ‘plant’ and can be formulated as an H ∞ mixed-sensitivity optimisation problem. The method developed in the first part for the selection of weighting functions is also used in this second part. Applying these to a model of a 10 machine 39 bus-bar power system shows a satisfactory performance.

Applying H∞ optimisation method to power system stabiliser design Part 1: Single-machine infinite-bus systems

The application of the H ∞ optimisation method to power system stabiliser design is studied in this paper. The weighting function selection and the application to multi-machine power systems are investigated in two separate parts. In this first part, it is shown that the PSS design for single-machine infinite-bus systems can be formulated as an H ∞ mixed-sensitivity optimisation problem. A new method of selecting weighting functions and an extended conventional PSS structure are presented in the paper. The example system used by deMello and Concordia (IEEE Transactions, 1969, PAS-88, 316–325) and other researchers is also used in the paper to illustrate the proposed design method.

Weighting function selection in the H∞ design process

The theory of H∞-norm optimisation is well known, and the technique has been applied to numerous design examples. Although simple rules exist for the selection of weighting functions used in the controller synthesis, the process is still subjective in nature. This paper is concerned with two aspects of the determination of weighting functions: firstly, guidelines for the initial selection of weighting functions and secondly tuning the performance weighting function to achieve the required closed-loop performance. The theory is illustrated with reference to the design of a do servo system controller.

Experimental design of H-infinity weighting functions for flight control systems

This paper introduces an experimental solution for H weighting function selection by exploiting an experimental planning method that has been used in quality control. Conducting matrix experiments using special matrices, called orthogonal arrays, allows the effects of several weighting parameters to be determined efficiently so that the resulting H* controller can satisfy many design specifications simultaneously in the environment for which the controller is designed. To show the feasibility and efficiency of this methodology, a flight control system for an airplane is designed to satisfy 11 performance specifications simultaneously, when the airplane is undergoing a large shift in c.g. position.