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The purpose of this paper is to examine the impact of applying two classical controller strategies, including two proportional (P) controllers with two feedback loops and one proportional–integral–derivative (PID) controller with one feedback loop, on the order and inventory performance within a production-inventory control system.

The simulation experiments of the dynamics behaviour of the production-inventory control system are conducted using a model based on control theory techniques. The Laplace transformation of an Order–Up–To (OUT) model is obtained using a state-space approach, and then the state-space representation is used to design and simulate a controlled model. The simulations of each model with two control configurations are tested by subjecting the system to a random retail sales pattern. The performance of inventory level is quantified by using the Integral of Absolute Error (IAE), whereas the bullwhip effect is measured by using the Variance ratio (Var).

The simulation results show that one PID controller with one feedback loop outperforms two P controllers with two feedback loops at reducing the bullwhip effect and regulating the inventory level.

The production-inventory control system is broken down into three components, namely: the forecasting mechanism, controller strategy and production-inventory process. A state-space approach is adopted to design and simulate the different controller strategy.

Focuses on steady state modelling of basic unipolar non‐isolated PWM AC line matrix‐reactance choppers (MRC). Their single‐phase topologies are similar to well‐known basic DC/DC converter ones. The MRC are built up through the adaptation of DC/DC converter topologies, which are based on the substitution of self‐commutated unidirectional switches by bi‐directional ones.

Presents an approach to modelling of the MRC with averaging operator different to the one used in averaged modelling of the DC/DC converters. There is running averaging of each switching period in the proposed approach. Following this, there is a demonstration of the solutions convergence of the state space and averaged state space equations for infinitive switching frequency.

The running averaging of each switching period should be used if averaged state space method is applied to the analysis of presented choppers. A circuit averaged model build‐up procedure of the presented choppers is the same as for the DC/DC ones.

Presents a quantitative assessment of accuracy for the averaged models of the presented MRC for finite switching frequency.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion). The dynamic model of VSI-PMSMs is multivariable and exhibits complicated nonlinear dynamics. The inverters’ currents, which are generated through a pulsewidth modulation process, are used to control the stator currents of the PMSM, which in turn control the rotational speed of this electric machine. So far, several nonlinear control schemes for VSI-PMSMs have been developed, having as primary objectives the precise tracking of setpoints by the system’s state variables and robustness to parametric changes or external perturbations. However, little has been done for the solution of the associated nonlinear optimal control problem. The purpose of this study/paper is to provide a novel nonlinear optimal control method for VSI-fed three-phase PMSMs.

The present article proposes a nonlinear optimal control approach for VSI-PMSMs. The nonlinear dynamic model of VSI-PMSMs undergoes approximate linearization around a temporary operating point, which is recomputed at each iteration of the control method. This temporary operating point is defined by the present value of the voltage source inverter-fed PMSM state vector and by the last sampled value of the motor’s control input vector. The linearization relies on Taylor series expansion and the calculation of the system’s Jacobian matrices. For the approximately linearized model of the voltage source inverter-fed PMSM, an H-infinity feedback controller is designed. For the computation of the controller’s feedback gains, an algebraic Riccati equation is iteratively solved at each time-step of the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control for this system, the H-infinity Kalman filter is proposed as a state observer. The proposed control method achieves fast and accurate tracking of the reference setpoints of the VSI-fed PMSM under moderate variations of the control inputs.

The proposed H-infinity controller provides the solution to the optimal control problem for the VSI-PMSM system under model uncertainty and external perturbations. Actually, this controller represents a min–max differential game taking place between the control inputs, which try to minimize a cost function that contains a quadratic term of the state vector’s tracking error, the model uncertainty, and exogenous disturbance terms, which try to maximize this cost function. To select the feedback gains of the stabilizing feedback controller, an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. To analyze the stability properties of the control scheme, the Lyapunov method is used. It is proven that the VSI-PMSM loop has the H-infinity tracking performance property, which signifies robustness against model uncertainty and disturbances. Moreover, under moderate conditions, the global asymptotic stability properties of this control scheme are proven. The proposed control method achieves fast tracking of reference setpoints by the VSI-PMSM state variables, while keeping also moderate the variations of the control inputs. The latter property indicates that energy consumption by the VSI-PMSM control loop can be minimized.

The proposed nonlinear optimal control method for the VSI-PMSM system exhibits several advantages: Comparing to global linearization-based control methods, such as Lie algebra-based control or differential flatness theory-based control, the nonlinear optimal control scheme avoids complicated state variable transformations (diffeomorphisms). Besides, its control inputs are applied directly to the initial nonlinear model of the VSI-PMSM system, and thus inverse transformations and the related singularity problems are also avoided. Compared with backstepping control, the nonlinear optimal control scheme does not require the state-space description of the controlled system to be found in the triangular (backstepping integral) form. Compared with sliding-mode control, there is no need to define in an often intuitive manner the sliding surfaces of the controlled system. Finally, compared with local model-based control, the article’s nonlinear optimal control method avoids linearization around multiple operating points and does not need the solution of multiple Riccati equations or LMIs. As a result of this, the nonlinear optimal control method requires less computational effort.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion), The solution of the associated nonlinear control problem enables reliable and precise functioning of VSI-fd PMSMs. This in turn has a positive impact in all related industrial applications and in tasks of electric traction and propulsion where VSI-fed PMSMs are used. It is particularly important for electric transportation systems and for the wide use of electric vehicles as expected by green policies which aim at deploying electromotion and at achieving the Net Zero objective.

Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system’s state vector and by the last sampled value of the control input vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation, which is used for computing the feedback gains of the controller, is new, as is the global stability proof for this control method. Comparing with nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems that can be transformed to the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions.

This paper estimates a Nelson-Siegel model under the state-space representation in order to circumvent the shortcomings of the conventional Nelson-Siegel model and evaluates the predictive ability of the estimated model. The results indicate that the estimated Nelson-Siegel time-varying three factors have close relations to their counterparts : level, slope and curvature and the inflection of the Korean yield curve is located around the maturity of 55-month. Meanwhile, each factor is found to have unit-root but differenced-factors do not show signs of unit-roots, hence proved I (1) series. In order to assess the efficacy of the estimated model, we compare the yield prediction from our model with several natural competitors : random walk, Fama-Bliss, and Cochrane-Piazzesi. With respect to out-of-sample performance, Fama-Bliss model proves to be the worst in term structure forecasts in Korea. The predictive performance differs between the random walk and the state-space Nelson-Siegel model depending on the forecast horizon lengths. At the shorter horizon, the state-space Nelson-Siegel model outperforms the random walk, but the table is turned in the longer horizon

The purpose of this paper is to investigate a control engineering-based system model that allows for any value of production delay for a three-tier supply chain with information delays between tiers or systems with epos.

A discrete z transform model of automatic pipeline, variable inventory and order based production control system three-tier supply chain is obtained using a state-space model using a reachable control formulation. This model provides a discrete time state-space model conversion using an exponential production delay with no loss of generality.

This work allows a three-tier supply chain model to be computed via a spreadsheet using any production delay and can be modified to include different sales smoothing procedures. The model is fully controllable and observable. Stability of these models is obtained from the system eigenvalues and agrees with our previously published stability boundaries.

The system is described by a linear control model of the production process and does not include production limits or other resource limitations, including history of sales demand and response.

This present model is an extension of the model devised by White and Censlive, in that it allows accurate modelling of multi-tier inventory production systems by permitting flexible selection of delay parameter values for real systems.

This paper aims to consider a problem of assembly sensitivity in a multi-station assembly process. The authors focus on the assembly process of aircrafts, which includes cabins and inertial navigation system (INSs), and establish the assembly process state space model for their assembly sensitivity research.

To date, the process-related errors that cause large variations in key product characteristics remains one of the most critical research topics in assembly sensitivity analysis. This paper focuses on the unique challenges brought about by the multi-station system: a system-level model for characterizing the variation propagation in the entire process, and the necessity of describing the system response to variation inputs at both station-level and single fixture-level scales. State space representation is used to describe the propagation of variation in such a multi-station process, incorporating assembly process parameters such as fixture-locating layout at individual stations and station-to-station locating layout change.

Following the sensitivity analysis in control theory, a group of hierarchical sensitivity indices is defined and expressed in terms of the system matrices in the state space model, which are determined by the given assembly process parameters.

A case study of assembly sensitivity for a multi-station assembly process illustrates and validates the proposed methodology.

The purpose of this paper is to consider the stochastic differential equation of the RL electrical circuit as the dynamic model of a state space system when the current in the circuit is hidden and corrupted by the measurement noise. Estimation of the corrupted current and the values of missing or unknown parameters (resistance, the observed current variance in the measurement model, the mean and variance of the current prior distribution) which are the main concern in electrical engineering is considered.

Optimal filtering is proposed for estimation of the hidden current from the noisy observations. Also, the problem of analyzing this model based on estimation of the unknown parameters is addressed from the likelihood‐based and Bayesian perspective.

Computational techniques for parameter estimation are carried out by the Maximum likelihood (ML) approach using Expectation‐Maximization type optimization and Bayesian Monte Carlo perspective using Metropolis‐Hastings scheme. The explicit formulas for the ML estimator are obtained and it is shown that the smoothers, the filters and the predictions for the current have the best confidence intervals, respectively. Some numerical simulation examples which are performed by R programming software are considered to show the efficiency and applicability of the proposed approaches. Results show an excellent estimation of the parameters based on these approaches.

Due to the fact that in an empirical situation of electrical engineering, observing the current in the circuit regardless of the measurement noise and knowing the exact value of the parameters are unrealistic assumptions, this paper can be used in various types of real time projects.

To the best of the authors' information, the problem of analyzing the state space model of RL electrical circuit has not been studied before. Furthermore, the estimation of the hidden current as the state of the system and estimation of the unknown parameters of the model via both ML and Bayesian approaches have been investigated for the first time in the present study.

The purpose of this paper is to investigate the influence of time steps, integration methods, and saturation modeling on the accuracy of the synchronous machine model. This model is compared with the PSCAD built‐in synchronous machine model in order to compare the accuracy of one of the most used synchronous machine models in a commercially available software versus a well‐documented and widely accepted state‐space synchronous machine model.

In the paper, a synchronous condenser with the saturation phenomenon is modeled using state‐space equations in the rotating dq‐reference frame and is implemented both in Matlab/Simulink and PSCAD. Integration methods of up to the fifth order are implemented for increased accuracy. The saturation modeling includes modeling of the saturation in both d‐ and q‐axis. A steady‐state and dynamic performance comparison towards the built‐in PSCAD synchronous machine model is performed. The saturation modeling does not include the saturation of the leakage fluxes.

When the forward Euler method is used, in order to obtain less than 5 percent error, the time step should not exceed 5 μs. The third‐order Runge‐Kutta method is the preferred choice and it provides desired accuracy when the time step is equal or smaller than 1,000 μs. The built‐in PSCAD model satisfies the error criteria for time steps smaller than 300 μs. A small discrepancy of 2 percent is found during the steady‐state test.

The paper presents the performance of the higher order integration methods in an EMTP‐type software environment where the trapezoidal integration method is most often used. It provides a good guide for building an owner‐defined model. A comparison of a dynamic performance between the publicly documented state‐space and a synchronous machine models commonly used for power system transient studies is presented.

This article reviews the literature on the econometric relationship between DSGE and VAR models from the point of view of estimation and model validation. The mapping between DSGE and VAR models is broken down into three stages: (1) from DSGE to state-space model; (2) from state-space model to VAR( ∞ ); (3) from VAR( ∞ ) to finite-order VAR. The focus is on discussing what can go wrong at each step of this mapping and on critically highlighting the hidden assumptions. I also point out some open research questions and interesting new research directions in the literature on the econometrics of DSGE models. These include, in no particular order: understanding the effects of log-linearization on estimation and identification; dealing with multiplicity of equilibria; estimating nonlinear DSGE models; incorporating into DSGE models information from atheoretical models and from survey data; adopting flexible modeling approaches that combine the theoretical rigor of DSGE models and the econometric model’s ability to fit the data.

The purpose of this article is to treat the nonlinear optimal control problem in EV traction systems which are based on 5-phase induction motors. Five-phase permanent magnet synchronous motors and five-phase asynchronous induction motors (IMs) are among the types of multiphase motors one can consider for the traction system of electric vehicles (EVs). By distributing the required power in a large number of phases, the power load of each individual phase is reduced. The cumulative rates of power in multiphase machines can be raised without stressing the connected converters. Multiphase motors are also fault tolerant because such machines remain functional even if failures affect certain phases.

A novel nonlinear optimal control approach has been developed for five-phase IMs. The dynamic model of the five-phase IM undergoes approximate linearization using Taylor series expansion and the computation of the associated Jacobian matrices. The linearization takes place at each sampling instance. For the linearized model of the motor, an H-infinity feedback controller is designed. This controller achieves the solution of the optimal control problem under model uncertainty and disturbances.

To select the feedback gains of the nonlinear optimal (H-infinity) controller, an algebraic Riccati equation has to be solved repetitively at each time-step of the control method. The global stability properties of the control loop are demonstrated through Lyapunov analysis. Under moderate conditions, the global asymptotic stability properties of the control scheme are proven. The proposed nonlinear optimal control method achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

Comparing to other nonlinear control methods that one could have considered for five-phase IMs, the presented nonlinear optimal (H-infinity) control approach avoids complicated state-space model transformations, is of proven global stability and its use does not require the model of the motor to be brought into a specific state-space form. The nonlinear optimal control method has clear implementation stages and moderate computational effort.

In the transportation sector, there is progressive transition to EVs. The use of five-phase IMs in EVs exhibits specific advantages, by achieving a more balanced distribution of power in the multiple phases of the motor and by providing fault tolerance. The study’s nonlinear optimal control method for five-phase IMs enables high performance for such motors and their efficient use in the traction system of EVs.

Nonlinear optimal control for five-phase IMs supports the deployment of their use in EVs. Therefore, it contributes to the net-zero objective that aims at eliminating the emission of harmful exhaust gases coming from human activities. Most known manufacturers of vehicles have shifted to the production of all-electric cars. The study’s findings can optimize the traction system of EVs thus also contributing to the growth of the EV industry.

The proposed nonlinear optimal control method is novel comparing to past attempts for solving the optimal control problem for nonlinear dynamical systems. It uses a novel approach for selecting the linearization points and a new Riccati equation for computing the feedback gains of the controller. The nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations.