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This proposed work is presenting the approximation of higher-order (HO) underwater robotic vehicle (URV) controller with the help of multi-point matching technique by incorporating greywolf optimization algorithm (GWOA). The performance of URV system is affected by external and internal dynamics. The proper momentum of URV system is achieved by designing a controller. The URV can be effectively operated by control action of controller. The URV controller is approximated to comparatively lower-order (LO) to propose an efficient, effective and economical controller for HOURV system. The approximation is accomplished with the help of expansion parameters of HOURV controller and its desired LOURV controller. The errors between these expansion parameters of HOURV controller and its desired LOURV controller are minimized using multi-point matching. The multi-point matching is depicted in the form of objective function (OF). The constructed OF is minimized by exploiting GWOA by fulfilling the steady-state matching condition and Hurwitz stability criterion, as constraints. The effectiveness of proposed approach of multi-point matching is verified by comparing the proposed LOURV model with LOURV models obtained with the help of other approximation approaches. The applicability of proposed LOURV controller is evaluated and validated by analyzing responses and tabulated data obtained in the results. Additionally, the statistical data of performance error values (PEVs) are provided in tabulated form along with its bar plot.

This research article deals with a new stable approximation (SA) technique for the approximation of higher order system (HOS) into its corresponding lower order model (LOM). The proposed approximation technique is a mixed scheme of time moment (TM) matching and integrated stability equation (ISE) method. Numerator as well as denominator coefficients of corresponding LOM are computed by using TM and ISE method respectively. Further, it is observed that LOM retains the fundamental characteristics of HOS. This proposed method is verified by considering two standard test cases. From simulated results, the performance accuracies of the corresponding LOM are evaluated by comparing its step and frequency response with HOS.

AbstractA novel mathematical expression for time moments (TMs) of discrete time interval system is introduced in this paper. Based on these TMs, the model of DIS is also derived. For computing the lower-order model for DIS, modified integrated derivative (MID) technique along with matching of TMs are adopted. To demonstrate this technique, a DIS is exemplified through test systems. The simulated results are compared with various existing techniques to evaluate the accuracy of the proposed technique.

A mathematical model is a virtual entity that uses mathematical language to describe the behavior of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines like physics, biology, and electrical engineering as well as in the social sciences like economics, sociology and political science. Physicists, Engineers, Computer scientists, and Economists use mathematical models most extensively. With the advent of high performance processors and advanced mathematical computations, it is possible to develop high performing simulators for complicated Multi Input Multi Ouptut (MIMO) systems like Quadruple tank systems, Aircrafts, Boilers etc. This paper presents the development of the mathematical model of a 500 MW utility boiler which is a highly complex system. A synergistic combination of operational experience, system identification and lower order modeling philosophy has been effectively used to develop a simplified but accurate model of a circulation system of a utility boiler which is a MIMO system. The results obtained are found to be in good agreement with the physics of the process and with the results obtained through design procedure. The model obtained can be directly used for control system studies and to realize hardware simulators for boiler testing and operator training.

This paper presents reduced integer order models of fractional differentiators. A two step procedure is followed. Using the Carlson method of approximation, approximated second iteration models of fractional differentiators are obtained. This method yields transfer function of high orders, which increase the complexity of the system and pose difficulty in realization. Hence, three reduction techniques, Balanced Truncation method, Matched DC gain method and Pade Approximation method are applied and reduced order models developed. With these models, fractional Proportional-Derivative and fractional Proportional-Integral-Derivative controllers are implemented on a fractional order plant and closed loop responses obtained. The authors have tried to reflect that the Carlson method in combination with reduction techniques can be used for development of good lower order models of fractional differentiators. The frequency responses of the models obtained using the different reduction techniques are compared with the original model and with each other. Three illustrative examples have been considered and their performance compared with existing systems.

Abstract This article is concerned with comparing the position controllers designed for an elastic system using its complete and deficient dynamic models. The system considered here as an application example consists of three rotors connected with two elastic shafts. Three kinds of controller are designed and compared. Controller-3 is designed using the complete dynamic model of the system. Therefore, it works perfectly, satisfying all the specified requirements. Controller-2 is designed based on a deficient model that consists of two rotors connected with a single elastic shaft. Therefore, it works with an acceptable performance only for limited magnitudes of its gains. If its gains are increased too much to improve the steady-state accuracy, the closed-loop system becomes unstable owing to the spillover effect induced by the unmodelled dynamic feature, which is the inertia at the midpoint of the shaft. Controller-1 is designed based on a more deficient model that consists of a single rotor mounted on a rigid shaft. Therefore, it also works with an acceptable performance only for limited magnitudes of its gains. With too large gains, it also suffers from the spillover effect induced by the unmodelled dynamic feature, which is the elasticity of the shaft. However, with the increasing gains, the spillover effect caused by controller-1 makes the closed-loop system increasingly oscillatory but never unstable. In other words, controller-1 is robust against the destabilizing tendency of the spillover effect. From this point of view, controller-1 is better than controller-2, even though the model used for controller-1 is more deficient than that used for controller-2. Another prominent feature of controller-1 is that it is highly sensitive to the location where the position and velocity sensors are placed to acquire the necessary feedback signals. If this location is different from the location where the controlling torque is applied, controller-1 destabilizes the closed-loop system.

In this paper, a new model reduction technique for the large-scale continuous time systems is proposed. The proposed technique is a mixed method of Routh approximation and factor division techniques. In this technique, the Routh approximation method is applied for determining the denominator coefficients of the reduced model and the numerator coefficients are calculated by the factor division method. The proposed technique has two main advantages as it gives the stable reduced-order model if the original model is stable and ensures the retention of first “r” number of time moments of the actual system in the rth-order reduced system. This method is also applicable for those systems for which Routh approximation method fails. To illustrate the proposed method, a real-time system model is reduced where the reduced model retains the fundamental properties of the actual model. In order to examine the efficiency, accuracy and comparison to other existing standard model reduction methods, the presented technique has been verified on two standard numerical examples taken from the literature.

The application and development of smart classroom (SC) have improved the teaching quality. The teacher–student interaction (TSI) is the core element of the SC. The research on TSI is insufficient due to the lack of evaluation models. The objective of this study was to construct a TSI evaluation model to guide teachers in building high-quality SC. The hierarchical evaluation model of TSI was constructed by literature analysis, video analysis, and other methods. The Lag sequence analysis method was used to verify that the hierarchical model of TSI evaluation in SC had the needs of lower-order interaction to support higher-order interaction and higher-order interaction to expand lower-order interaction. This research constructed a hierarchical evaluation model of TSI in SC by analyzing the connotation and characteristics of TSI and coding analysis of SC teaching videos. The evaluation hierarchy model was divided into four first-level dimensions from low to high and from specific to abstract (operational interaction, behavioral interaction, cognitive interaction, and creative interaction). Each first-level dimension contained four second-level dimensions. The support of lower-order interaction and the expanding role of higher-order interaction reflected the characteristics of progressive level by level.

This paper proposes a reverberation suppression algorithm utilizing fractional lower-order moments based on statistical properties. As fractional lower-order moments can only be applied on symmetric α-stable random variables, the energy redistribution method is used, so reverberation signals can obtain the characteristic exponents of the symmetric α-stable distribution. To evaluate the proposed algorithm, an experiment involving simulated linear frequency modulation reverberation with the proposed method and comparison methods is performed and discussed. Moreover, an experiment is conducted using reverberation as measured from the lake. The results show that the proposed algorithm can achieve better reverberation suppression and signal enhancement performance compared with other methods.

Risk quantification for cryptocurrency assets is a challenging task due to their speculative nature and strongly heavy-tailed returns. Existing measures of tail risk are based primarily on the variability of extreme returns, whilst ignoring the multiple biases occurring at distinct frequencies other than the original sampling frequency. As such, they often fail to adapt to specific investment horizons and also account for the inherent microstructure frictions of cryptocurrency returns. To address this problem, we propose a novel extreme risk measure which (i) regularizes the variability of extreme returns with a confidence interval where they have a likelihood of occurring, and (ii) adapts precisely to a predefined investment horizon. To this end, we leverage the power of alpha-stable models for defining a proper confidence interval with the effectiveness of wavelet analysis for decomposing the returns at multiple frequencies. An empirical evaluation with major cryptocurrencies demonstrates improved performance of our extreme risk measure against commonly used measures based on extreme expectiles and light-tailed models.