The Drazin inverse of matrices is applied to analysis of the pointwise completeness and of the pointwise degeneracy of the fractional descriptor linear discrete-time systems. Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of the fractional descriptor linear discrete-time systems are established. It is shown that every fractional descriptor linear discrete-time systems is not pointwise complete and it is pointwise degenerated in one step (for i = 1).
It is well known that the magnitudes of the coefficients of the discrete Fourier transform (DFT) are invariant under certain operations on the input data. In this paper, the effects of rearranging the elements of an input data on its DFT are studied. In the one-dimensional case, the effects of permuting the elements of a finite sequence of length N on its discrete Fourier transform (DFT) coefficients are investigated. The permutations that leave the unordered collection of Fourier coefficients and their magnitudes invariant are completely characterized. Conditions under which two different permutations give the same DFT coefficient magnitudes are given. The characterizations are based on the automorphism group of the additive group ZN of integers modulo N and the group of translations of ZN. As an application of the results presented, a generalization of the theorem characterizing all permutations that commute with the discrete Fourier transform is given. Numerical examples illustrate the obtained results. Possible generalizations and open problems are discussed. In higher dimensions, results on the effects of certain geometric transformations of an input data array on its DFT are given and illustrated with an example.
The main aim of this article is to survey and discuss the existing state of art concerning the assignability by a feedback of numerical characteristics of linear continuous and discrete time-varying systems. Most of the results present necessary or sufficient conditions for different formulation of the Lyapunov spectrum assignability problem. These conditions are expressed in terms of various controllability types and optimalizability of the controlled systems and certain properties of the free system such as: regularity, diagonalizability, boundness away, integral separation and reducibility.
The paper presents an interpretation of fractional calculus for positive and negative orders of functions based on sampled measured quantities and their errors connected with digital signal processing. The derivative as a function limit and the Grünwald-Letnikov differintegral are shown in chapter 1 due to the similarity of the presented definition. Notation of fractional calculus based on the gradient vector of measured quantities and its geometrical and physical interpretation of positive and negative orders are shown in chapters 2 and 3.
This work presents the results acquired during simulation studies done for a 3D free-floating satellite behaviour with input-output decoupling approach. The research object is a free-floating satellite with a 3 DoF rigid 3D manipulator where a noise disturbance was introduced. Different approaches are used to compensate the noise influence. Systems using a visual aid to determine the position of manipulator joints are not ideal and introduce some uncertainties. What is more, determining the position from joints encoders is not error-free while computing angular velocity from numerical differentiation introduces even greater disturbance to the system. A couple of scenarios were investigated where state of the manipulator, including its position and velocity, was disturbed with homogeneous noise. Also the control inputs of the manipulator were disturbed. Simulation results show that the biggest impact on the control quality has a scenario where the satellite’s state has been disturbed with additive noise.
Modern and innovative road spreaders are now equipped with a special swiveling mechanism of the spreading disc. It allows for adjusting a symmetrical or asymmetrical spreading pattern and provides for the possibility to maintain the size of the spreading surface and achieve an accurately defined spreading pattern with spreading widths. Thus the paper presents a modelling and control design methodology, and the concept is proposed to design high-performance and optimal drive systems for spreading devices. The paper deals with a nonlinear model of an electric linear actuator and solution of the new intelligent/optimal control problem for the actuator.
A simple robust cheap LQG control is considered for discrete-time systems with constant input delay. It is well known that the full loop transfer recovery (LTR) effect measured by error function ∆(z) can only be obtained for minimum-phase (MPH) systems without time-delay. Explicit analytical expressions for ∆(z) versus delay d are derived for both MPH and NMPH (nonminimum-phase) systems. Obviously, introducing delay deteriorates the LTR effect. In this context the ARMAX system as a simple example of noise-correlated system is examined. The robustness of LQG/LTR control is analyzed and compared with state prediction control whose robust stability is formulated via LMI. Also, the robustness with respect to uncertain time-delay is considered including the control systems which are unstable in open-loop. An analysis of LQG/LTR problem for noise-correlated systems, particularly for ARMAX system, is included and the case of proper systems is analyzed. Computer simulations of second-order systems with constant time-delay are given to illustrate the performance and recovery error for considered systems and controllers.
A comprehensive characterization of four selected fault distinguishability methods is presented herein. All considered methods are derived from structural residual approaches referring to model-based diagnostics. In particular, these methods are based on a binary diagnostic matrix, fault isolation system, sequences of symptoms, and their combinations. Fault distinguishability issues are discussed based on an example of four pressure vessel system. Substantial benefits are shown in fault distinguishability figures obtained by utilising extended knowledge regarding fault-symptom relation. Finally, the values of three fault distinguishability metrics are calculated for each method. For the case study, the highest score is achieved using the multivalued fault isolation method combined with a diagnosis utilising information regarding the antecedence of symptoms.
The process of synchronization of synchronous generators and power electronic converters with the power grid may take on quite different forms. This is due to their specific principles of operation and essential differences in energy conversion process. However, since synchronous generators and power converter often operate in the same utility network, coherent rules should be defined for them. Therefore, this paper aims at a formulation of the uniform and consistent interpretation of synchronization with the power grid for both types of aforementioned units. The author starts from the classic interpretation of synchronization for synchronous generators and power electronic converters, considered as micro-generators, specifies their mathematical and numerical models and then performs simulation tests. Selected synchronization algorithms are described in detail. Simulation tests are used for analysis of the elaboration of outcomes. The results of simulation tests are handled to formulate a uniform interpretation of synchronization for the micro-generation systems considered. Based on the results obtained, appropriate parallels are built between the two systems being compared. It is shown that the synchronization processes are identical regardless of the micro-generation unit considered. Nonetheless, they differ significantly due to their properties in transient states. Inverter systems have higher dynamics but their disadvantage lies in the relatively high sensitivity to disturbances and the complex selection process of the synchronization algorithm.
This paper discusses selected problems regarding a high-frequency improved current-fed quasi-Z-source inverter (iCFqZSI) designed and built with SiC power devices. At first, new, modified topology of the impedance network is presented. As the structure is derived from the series connection of two networks, the voltage stress across the SiC diodes and the inductors is reduced by a factor of two. Therefore, the SiC MOSFETs may be switched with frequencies above 100 kHz and volume and weight of the passive components is decreased. Furthermore, additional leg with two SiC MOSFETs working as a bidirectional switch is added to limit the current stress during the short-through states. In order to verify the performance of the proposed solution a 6 kVA laboratory model was designed to connect a 400 V DC source (battery) and a 3£400 V grid. According to presented simulations and experimental results high-frequency iCFqZSI is bidirectional – it may act as an inverter, but also as a rectifier. Performed measurements show correct operation at switching frequency of 100 kHz, high quality of the input and output waveforms is observed. The additional leg increases efficiency by up to 0.6% – peak value is 97.8%.
This paper proposes four different cost-effective configurations of a hybrid energy storage system (HESS) in an electric city bus. A comparison is presented between a battery powered bus (battery bus) and supercapacitor powered bus in two configurations in terms of initial and operational costs. The lithium iron phosphate (LFP) battery type was used in the battery bus and three of the hybrids. In the first hybrid the battery module was the same size as in the battery bus, in the second it was half the size and in the third it was one third the size. The fourth hybrid used a lithium nickel manganese cobalt oxide (NMC) battery type with the same energy as the LFP battery module in the battery bus. The model of LFP battery degradation is used in the calculation of its lifetime range and operational costs. For the NMC battery and supercapacitor, the manufacturers’ data have been adopted. The results show that it is profitable to use HESS in an electric city bus from both the producer and consumer point of view. The reduction of battery size and added supercapacitor module generates up to a 36% reduction of the initial energy storage system (ESS) price and up to a 29% reduction of operational costs when compared to the battery ESS. By using an NMC battery type in HESS, it is possible to reduce operational costs by up to 50% compared to an LFP battery ESS.
Designing, optimizing and analyzing optical systems as part of the implementation process into production of modern luminaires require using advanced simulation and computational methods. The progressive miniaturization of LED (light emitting diode) chips and growth in maximum luminance values, achieving up to 108 cd/m2, require constructing very accurate geometries of reflector and lens systems producing complex luminous intensity distributions while reducing discomfort glare levels. Currently, the design process cannot function without advanced simulation methods. Today’s simulation methods in the lighting technology offer very good results as far as relatively large conventional light sources such as halogen lamps, metal halide lamps and high pressure sodium lamps are concerned. Unfortunately, they often fail in the case of chip-on-board LED light sources whose luminous surface dimensions are increasingly often contained inside a cube of the side length below 1mm. With the high sensitivity of such small chips and lenses with dimensions ranging from a just a few to between 10 and 20 mm, which is presented in this paper, modern luminance distribution measurement methods, luminance modelling and ray tracing methods should be used to minimize any errors arising from incorrectly projecting the design in the final physical model. Also, very importantly, focus should be directed towards reducing a chance of making a mistake while collimating the position of the light source inside the optical system. The paper presents a novel simulation calculation method enriched with an analysis of optical system sensitivity to a light source position. The results of simulation calculations are compared with the results of laboratory measurements for corresponding systems.
The paper presents the authors’ concept of an adaptive road lighting that is concurrent with vehicles moving on roads. The lighting system is based on luminaires with light emitting diodes. The authors describe the operation of the adaptive road lighting system and point out benefits and limitations of the solution. The theoretical considerations are supported by an analysis of the installed and working system that was implemented at Bożeny street in Poznan, Poland. The system was also evaluated by the residents living near the street.
Grippers are routinely used to hold, lift and move organs in laparoscopic operations. They are generally toothed to prevent organs from slipping during retention. Organs held by grippers are always at risk of being damaged by the clamping force. In this study, noncontact grippers working with the Bernoulli principle and using air pressure were developed, and vacuum performance was compared in terms of maximum tissue weight holding capacity. For this purpose, Taguchi method was employed for experimental design and optimization, and Taguchi L16 orthogonal array was selected for experimental design. The experimental parameters were 4 gripper types, 4 air-pressure levels (3.5, 4.5, 5, and 5.5 bar), 4 flow rates (2.2, 2.6, 2.8 and 3 m3/h) and two animal tissue types (ventriculus/gizzard and skin). Values from the experimental procedures were evaluated using signal-to-noise ratio, analysis of variance and three-dimension graphs. An equation was obtained by using 3rd-order polynomial regression model for weight values. Optimization reliability was tested by validation tests and the revealed test results were within the estimated confidence interval. The results obtained from this study are important for future studies in terms of organ injury prevention due to traditional grippers in laparoscopic surgery.
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.
Calibration is necessary for dual manipulator to complete operational tasks. This paper proposes an effective robot-robot and hand-eye calibration method based on virtual constraints. Firstly, a rotational error model and a translational error model are established based on the relationships between the transformation matrices of the dual manipulator calibration system. Then a poses-alignment method is designed to make the poses of the two robots satisfy the constructed virtual constraints. At the aligned positions, the joint angles of the two robots are saved and used to calculate the values of the variables in the error models. Finally, the robot-robot and hand-eye rotational errors are estimated by an iterative algorithm. These errors are then used to calculate translational errors based on the SVD (singular value decomposition) method. To show the feasibility and effectiveness of the proposed method, experiments of robot-robot and hand-eye calibration for dual manipulators are performed. The experiment results demonstrate that the accuracy of the dual manipulator system is improved greatly.
The knowledge of the load in prestressed bolted connections is essential for the proper operation and safety of engineering structures. Recently, bolted joints have become an area of intensive research associated with non-destructive diagnostics, in particular in the context of wave propagation techniques. In this paper, a novel procedure of bolt load estimation based on the energy of Lamb wave signals was proposed. Experimental tests were performed on a single lap joint of two steel plates. Ultrasonic waves were excited and registered by means of piezoelectric transducers, while precise measurement of the bolt load was obtained by means of using the force washer transducer. Experimental tests were supported by the finite element method analysis based on Schoenberg’s concept. The results showed that the relationship between the bolt load and signal energy was strongly nonlinear and it depended on the location of acquisition points.
In this paper, the influence of biomodification of recycled concrete aggregate (RCA) on some properties of concrete was studied. Sporosarcina pasteurii strain was chosen for biodeposition process. The RCA came from parent concretes with varying w/c ratio. Recycled aggregate concrete (RAC) with two levels of w/c ratio, made from RCA not subjected to biomodification, was treated as reference. Compressive strength, water absorption and sorption of concretes were tested. The most significant influence of the aggregate biomodification was found in the case of sorption and this effect was highest for RAC made from the aggregate yielding from better quality parent concrete.
The paper concerns the problem of choosing a criterion for transmission line when lumped parameters analysis is required. First, the formal introduction of transmission line scheme is presented. Secondly, a new criterion for lumped-parameter analysis of transmission line is proposed. The criterion has clear physical meaning and simple mathematical form. The proposed criterion takes into account not only wave length, but also the dissipation of transmission line. The criterion can be easily adjusted to some requirements, such as needed level of no-load output voltage change.
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