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## Inverse systems of linear systems

### Abstract

The concept of inverse systems for standard and positive linear systems is introduced. Necessary and sufficient conditions for the existence of the positive inverse system for continuous-time and discrete-time linear systems are established. It is shown that: 1) The inverse system of continuous-time linear system is asymptotically stable if and only if the standard system is asymptotically stable. 2) The inverse system of discrete-time linear system is asymptotically stable if and only if the standard system is unstable. 3) The inverse system of continuous-time and discrete-time linear systems are reachable if and only if the standard systems are reachable. The considerations are illustrated by numerical examples.
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## Study on Mine Ventilation Resistance Coefficient Inversion Based on Genetic Algorithm

### Abstract

The frictional resistance coefficient of ventilation of a roadway in a coal mine is a very important technical parameter in the design and renovation of mine ventilation. Calculations based on empirical formulae and field tests to calculate the resistance coefficient have limitations. An inversion method to calculate the mine ventilation resistance coefficient by using a few representative data of air flows and node pressures is proposed in this study. The mathematical model of the inversion method is developed based on the principle of least squares. The measured pressure and the calculated pressure deviation along with the measured flow and the calculated flow deviation are considered while defining the objective function, which also includes the node pressure, the air flow, and the ventilation resistance coefficient range constraints. The ventilation resistance coefficient inversion problem was converted to a nonlinear optimisation problem through the development of the model. A genetic algorithm (GA) was adopted to solve the ventilation resistance coefficient inversion problem. The GA was improved to enhance the global and the local search abilities of the algorithm for the ventilation resistance coefficient inversion problem.
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## Word Order and Composition of Lyrical Discourse

### Abstract

The paper is concerned with the most fundamental compositional divide to be found in lyrical discourse, consisting in that the latter one is normally split into an empirical part, presenting the author’s concrete experience, and a focal part, where the author discovers some signifi cant truth or/and changes her attitude towards the world. It is claimed in the paper that, more generally, one of the specifi c linguistic properties of focal fragments is their higher and/or specially underscored informativity, and, in particular, one of the means recruited to emphasize it is inverted word order.
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## Multi-Channel System for Sound Creation in Open Areas

### Abstract

There are typically two systems in use for sound reinforcement in open areas: the central, “wall of sound” system with speakers localized at the sides of the stage, and the zone system, in which additional speakers are introduced to obtain a uniform sound pressure level throughout the area of listening. In the past two decades the line array systems gained great popularity. The main purpose of their use is to obtain a uniformly distributed sound level throughout the listening area in order to achieve good speech intelligibility. The present paper aims to present an alternative and original method of sound reinforcement in open areas which is in contrast to the above solutions. This new method allows achieving a uniformly distributed sound pressure and good speech intelligibility in the area of interest, and also allows to gain spatial sound impression that accompanies sound reproduction in concert halls. Another advantage of the proposed system is the reduction of the sound level outside the area of interest, i.e. reduction of the noise level outside the area of listening.
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## Engineering design of the low-head Kaplan hydraulic turbine blades using the inverse problem method

### Abstract

The paper concerns the engineering design of guide vane and runner blades of hydraulic turbines using the inverse problem on the basis of the definition of a velocity hodograph, which is based on Wu’s theory [1, 2]. The design concerns the low-head double-regulated axial Kaplan turbine model characterized by a very high specific speed. The three-dimensional surfaces of turbine blades are based on meridional geometry that is determined in advance and, additionally, the distribution of streamlines must also be defined. The principles of the method applied for the hydraulic turbine and related to its conservation equations are also presented. The conservation equations are written in a curvilinear coordinate system, which adjusts to streamlines by means of the Christoffel symbols. This leads to significant simplification of the computations and generates fast results of three-dimensional blade surfaces. Then, the solution can be found using the method of characteristics. To assess usefulness of the design and robustness of the method, numerical and experimental investigations in a wide range of operations were carried out. Afterwards, the so-called shell characteristics were determined by means of experiments, which allowed to evaluate the method for application to the low-head (1.5 m) Kaplan hydraulic turbine model with the kinematic specific speed (»260). The numerical and experimental results show the successful usage of the method and it can be concluded that it will be useful in designing other types of Kaplan and Francis turbine blades with different specific speeds.
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## Inverse and forward surrogate models for expedited design optimization of unequal-power-split patch couplers

### Abstract

In the paper, a procedure for precise and expedited design optimization of unequal power split patch couplers is proposed. Our methodology aims at identifying the coupler dimensions that correspond to the circuit operating at the requested frequency and featuring a required power split. At the same time, the design process is supposed to be computationally efficient. The proposed methodology involves two types of auxiliary models (surrogates): an inverse one, constructed from a set of reference designs optimized for particular power split values, and a forward one which represents the circuit S-parameter gradients as a function of the power split ratio. The inverse model directly yields the values of geometry parameters of the coupler for any required power split, whereas the forward model is used for a post-scaling correction of the circuit characteristics. For the sake of illustration, a 10-GHz circular sector patch coupler is considered. The power split ratio of the structure is re-designed within a wide range of ��6 dB to 0 dB. As demonstrated, precise scaling (with the power split error smaller than 0.02 dB and the operating frequency error not exceeding 0.05 GHz) can be achieved at the cost of less than three full-wave EM simulations of the coupler. Numerical results are validated experimentally.
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## A robust model free controller for a class of SISO nonaffine nonlinear systems: Application to an electropneumatic actuator

### Abstract

This paper presents a robust model free controller (RMFC) for a class of uncertain continuous-time single-input single-output (SISO) minimum-phase nonaffine-in-control systems. Firstly, the existence of an unknown dynamic inversion controller that can achieve control objectives is demonstrated. Afterwards, a fast approximator is designed to estimate as best as possible this dynamic inversion controller. The proposed robust model free controller is an equivalent realization of the designed fast approximator. The perturbation theory and Tikhonov’s theorem are used to analyze the stability of the overall closed-loop system. The performance of the developped controller are verified experimentally in the position control of a pneumatic actuator system.
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