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The purpose of this paper is to present the Galerkin method for analysis of steady-state processes in periodically time-varying circuits.

A converter circuit working on a time-varying load is often controlled by different signals. In the case of incommensurable frequencies, one can find a steady-state process only via calculation of a transient process. As the obtained results will not be periodical, one must repeat this procedure to calculate the steady-state process on a different time interval. The proposed methodology is based on the expansion of ordinary differential equations with one time variable into a domain of two independent variables of time. In this case, the steady-state process will be periodical. This process is calculated by the use of the Galerkin method with bases and weight functions in the form of the double Fourier series.

Expansion of differential equations and use of the Galerkin method enable discovery of the steady-state processes in converter circuits. Steady-state processes in the circuits of buck and boost converters are calculated and results are compared with numerical and generalized state-space averaging methods.

The Galerkin method is used to find a steady-state process in a converter circuit with a time-varying load. Processes in such a load depend on two incommensurable signals. The state-space averaging method is generalized for extended differential equations. A balance of active power for extended equations is shown.

This paper aims to overcome the main obstacle to compare the merits of the different control strategies for fixed-wing unmanned aerial vehicles (UAVs) to assess autopilot performances. Up to now, the published studies of control strategies have been carried out over disperse models, thus being complicated, if not impossible, to compare the merits of each proposal. The authors present a worked benchmark for autopilots studies, consisting of generalized models obtained by merging UAVs’ parameters gathered from selected literature (journals) with other parameters directly obtained by the authors to include some relevant UAVs whose models are not provided in the literature. To obtain them it has been used a dedicated software (from U.S. Air Force).

The proposed models have been constructed by averaging both the main aircraft defining parameters (model derivatives) and pole-zero locations of longitudinal transfer functions. The suitability of the used methodologies has been checked from their capability to fit the short period and the phugoid modes. Previous analytical model arrangement has been required to match a uniform set of parameters, as the inner state variables are neither the same along the different published models nor between the additional models the authors have here contributed. Besides, moving models between the space state representation and transfer function is not just a simple averaging process, as neither the parameters nor the model orders are the same in the different published works. So, the junction of the models to a common set of parameters requires some residual’s computation and transient responses assessment (even Fourier analysis has been included to preserve the dominance of the phugoid) to keep the main properties of the models. The least mean squares technique has been used to have better fittings between SISO model parameters with state–space ones.

Both the SISO (Laplace) and state-space models for the longitudinal transfer function of an “averaged” fixed-wing UAV are proposed.

More complicated situations, such as strong wind conditions, need another kind of models, usually based on finite element method simulation. These particular models apply fluid dynamics to study aerostructural aircraft aspects, such as flutter and other aerolastic aspects, the behavior under icing conditions or other distributed parameter problems. Even some models aim to control other aspects than the autopilot, such as the trajectory prediction. However, these models are not the most suitable for the basic UAV autopilot design (early design), so they are outside the objective of this paper. Obviously, the here-considered UAVs are not all the existing ones, but the number is large enough to consider the result as a reliable and realistic representation. The presented study may be seen as a stepping stone, allowing to include other UAVs in future works.

The proposed models can be used as benchmarks, or as a previous step to produce improved benchmarks, in order to have a common and realistic scenario the compare the benefits of the different control actions in UAV autopilots continuously presented in the published research.

A work with the scope of the presented one, merging model parameters from literature with other (often referred in papers and websites) whose parameters have been obtained by the authors has been never published.

This study aims to propose a new non-isolated Multi-Input Zeta-SEPIC (MIZS) dc–dc converter for renewable energy sources integration with different voltage levels (low-voltage source, high-voltage source). The chosen configuration of the converter is capable of performing bucking as well as boosting operations in various modes of operation.

Parameters of the selected MIZS converter are designed using the time-domain analysis. The selected converter belongs to the sixth-order family with two switches and six energy storage elements. State-space model of the converter is developed for each mode of operation, and using these individual state-space models, an average state-space model of the converter useful to carry out detailed analysis for different operating conditions is developed. Analysis related to operational stability of the converter is also carried out using Participation Factor (PaF)-based Eigen value analysis.

Using the PaF-based Eigen analysis, participation of the various state variables in different Eigen modes and vice versa is carried out. Performance of the converter for different parameter variations in the allowable range is determined and the same has been used to find the operational stability of the converter under different modes of operation. The selected converter has low inductor ripple currents and output voltage ripples when delivering the power to load.

Because operational stability of the converter under various operating conditions is one of the key performance indicators for selecting a particular type of converter, PaF-based Eigen value analysis has been carried out using the average state-space model developed for the selected MIZS converter. Operational stability analysis of the converter is carried out for parameter variations also. In addition, participation of the various states in each Eigen mode and vice versa have been analyzed for designed parameter values and also variation within the specified range of variations.

We compare methods to measure comovement in business cycle data using multi-level dynamic factor models. To do so, we employ a Monte Carlo procedure to evaluate model performance for different specifications of factor models across three different estimation procedures. We consider three general factor model specifications used in applied work. The first is a single-factor model, the second a two-level factor model, and the third a three-level factor model. Our estimation procedures are the Bayesian approach of Otrok and Whiteman (1998), the Bayesian state-space approach of Kim and Nelson (1998) and a frequentist principal components approach. The latter serves as a benchmark to measure any potential gains from the more computationally intensive Bayesian procedures. We then apply the three methods to a novel new dataset on house prices in advanced and emerging markets from Cesa-Bianchi, Cespedes, and Rebucci (2015) and interpret the empirical results in light of the Monte Carlo results.

Lalwani et al. devised a controllable state-space model for a general APVIOBPCS production and inventory system. However, their procedure did not cater for production delays of other than one time unit. The authors have sought to devise a model that allows for any value of production delay.

A discrete z transform model of APVIOBPCS inventory is obtained using conventional algebra and converted to a state-space model using a reachable control formulation. This is then analysed to produce an analytic expression for the eigenvalues and then the general stability solution is derived from the unit circle condition.

This model allows a state-space model conversion from a discrete time input-output model using an exponential production delay with no loss of generality and is fully controllable and observable. Stability of these models can be obtained from the system eigenvalues and agrees with the authors' previously published stability boundaries using transform models.

The system is described by a linear control model of the production process and does not include production limits or other resource limitations. It does not include any past history of sales demand and responses.

This work allows a model to be implemented in a spreadsheet of APVIOBPCS PIC that can be used for any production delay and can be modified to include different sales smoothing procedures.

This present model is an extension and improvement of the model devised by Lalwani, in that it allows more accurate modelling of inventory production systems by permitting a more flexible selection of delay parameter values, closer to those of real systems.

Recently, star variables and the post-crisis nature of cyclical fluctuations have attracted a great deal of interest. In this chapter, the authors investigate different methods of assessing business cycles (BCs) for the European Union in general and the euro area in particular. First, the authors conduct a Monte Carlo (MC) experiment using a broad spectrum of univariate trend-cycle decomposition methods. The simulation aims to examine the ability of the analysed methods to find the observed simulated cycle with structural properties similar to actual macroeconomic data. For the simulation, the authors used the structural model’s parameters calibrated to the euro area’s real gross domestic product (GDP) and unemployment rate. The simulation outcomes indicate the sufficient composition of the suite of models (SoM) consisting of popular Hodrick–Prescott, Christiano–Fitzgerald and structural trend-cycle-seasonal filters, then used for the real application. The authors find that: (i) there is a high level of model uncertainty in comparing the estimates; (ii) growth rate (acceleration) cycles have often the worst performances, but they could be useful as early-warning predictors of turning points in growth and BCs; and (iii) the best-performing MC approaches provide a reasonable combination as the SoM. When swings last less time and/or are smaller, it is easier to pick a good alternative method to the suite to capture the BC for real GDP. Second, the authors estimate the BCs for real GDP and unemployment data varying from 1995Q1 to 2020Q4 (GDP) or 2020Q3 (unemployment), ending up with 28 cycles per country. This analysis also confirms that the BCs of euro area members are quite synchronized with the aggregate euro area. Some major differences can be found, however, especially in the case of periphery and new member states, with the latter improving in terms of coherency after the global financial crisis. The German cycles are among the cyclical movements least synchronized with the aggregate euro area.

I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

The purpose of the paper is to introduce the dynamic phasor modelling (DPM) approach for stability investigation and control design of single-phase phase-locked loops (PLLs). The aim is to identify the system instabilities not predicted using the existent analysis and design methods based on the simplified average model approach.

This paper starts by investigating the performance of three commonly used PLL schemes: the inverse park-PLL, the second-order generalised integrators (SOGI)-frequency-locked loop and the enhanced-PLL, designed using the simplified average model and will show that following this approach, there is a mismatch between their actual and desired transient performance. A new PLL design method is then proposed based on the DPM approach that allows the development of fourth-order DPM models. The small-signal eigenvalues analysis of the fourth-order DPM models is used to determine the control gains and the stability limits.

The DPM approach is proven to be useful for single-phase PLLs stability analysis and control parameters design. It has been successfully used to design the control parameters and to predict the PLL stability limits, which have been validated via simulation and experimental tests consisting of grid voltage sag, phase jump and frequency step change.

This paper has introduced the use of DPM approach for the purpose of single-phase PLL stability analysis and control design. The approach has enabled accurate control gains design and stability limits identification of single-phase PLLs.

Purpose – Time-series regression models are applied to analyse transport safety data for three purposes: (1) to develop a relationship between transport accidents (or incidents) and various time-varying factors, with the aim of identifying the most important factors; (2) to develop a time-series accident model in forecasting future accidents for the given values of future time-varying factors and (3) to evaluate the impact of a system-wide policy, education or engineering intervention on accident counts. Regression models for analysing transport safety data are well established, especially in analysing cross-sectional and panel datasets. There is, however, a dearth of research relating to time-series regression models in the transport safety literature. The purpose of this chapter is to examine existing literature with the aim of identifying time-series regression models that have been employed in safety analysis in relation to wider applications. The aim is to identify time-series regression models that are applicable in analysing disaggregated accident counts.

Methodology/Approach – There are two main issues in modelling time-series accident counts: (1) a flexible approach in addressing serial autocorrelation inherent in time-series processes of accident counts and (2) the fact that the conditional distribution (conditioned on past observations and covariates) of accident counts follow a Poisson-type distribution. Various time-series regression models are explored to identify the models most suitable for analysing disaggregated time-series accident datasets. A recently developed time-series regression model – the generalised linear autoregressive and moving average (GLARMA) – has been identified as the best model to analyse safety data.

Findings – The GLARMA model was applied to a time-series dataset of airproxes (aircraft proximity) that indicate airspace safety in the United Kingdom. The aim was to evaluate the impact of an airspace intervention (i.e., the introduction of reduced vertical separation minima, RVSM) on airspace safety while controlling for other factors, such as air transport movements (ATMs) and seasonality. The results indicate that the GLARMA model is more appropriate than a generalised linear model (e.g., Poisson or Poisson-Gamma), and it has been found that the introduction of RVSM has reduced the airprox events by 15%. In addition, it was found that a 1% increase in ATMs within UK airspace would lead to a 1.83% increase in monthly airproxes in UK airspace.

Practical applications – The methodology developed in this chapter is applicable to many time-series processes of accident counts. The models recommended in this chapter could be used to identify different time-varying factors and to evaluate the effectiveness of various policy and engineering interventions on transport safety or similar data (e.g., crimes).

Originality/value of paper – The GLARMA model has not been properly explored in modelling time-series safety data. This new class of model has been applied to a dataset in evaluating the effectiveness of an intervention. The model recommended in this chapter would greatly benefit researchers and analysts working with time-series data.

This paper offers various state‐space representations in the context of applications of the system control theory to dynamic economic systems and examines interrelationships between the alternative representations in both economics literature and system control engineering literature. In particular, some characteristics of various state‐space forms are assessed with respect to the structural properties of each form, thereby demonstrating the relative advantages and disadvantages of different realization methods presented in this paper.