Transfer Functions Of Linear Systems Research Articles

SINGLE-DEGREE-OF-FREEDOM VIBRATION ISOLATION SYSTEM WITH ONE ADDITIONAL SUPPORT

Vibration isolation is one of the most effective methods for reducing vibration levels of supporting structures when installing vibroactive equipment (active vibration isolation) or vibration levels of vibro-sensitive objects relative to foundation vibration levels (passive vibration isolation). Damping devices utilizing high-speed fluid flow through apertures have found wide applications in shock vibration isolation and vibration isolation systems in aerospace and defense sectors. Recent research has led to the development of viscous fluid dampers (VFDs) for use in civil engineering, particularly in earthquake-prone areas. Scientists conducted experiments aimed at determining the ability of viscous fluid dampers to reduce damages and displacements of structures without increasing stresses. Mathematical models have been developed and are applied in vibration isolation systems. When vibroactive equipment is installed on building and structure support systems, vibrations with sufficiently high vibration parameters may occur, potentially leading to loss of load-bearing capacity. In such cases, vibration isolation is considered one of the most effective methods for reducing these vibration levels. In this study, a calculation method has been developed, and calculation dependencies and algorithms for calculating vibration protection systems with nonlinear characteristics (additional support connections, viscous fluid damper) have been derived for both single-degree-of-freedom and two-degree-of-freedom systems. The research involved an analysis of normative and scientific-technical literature on the subject: types, structural solutions, calculation, and analysis of vibration protection systems. The main method selected was based on the use of transfer functions of linear systems (the non-traditional "normal form" method). Calculations were performed using computer mathematics systems- Matlab.

Investigating the limited performance of a deep-learning-based SPECT denoising approach: An observer-study-based characterization.

Multiple objective assessment of image-quality (OAIQ)-based studies have reported that several deep-learning (DL)-based denoising methods show limited performance on signal-detection tasks. Our goal was to investigate the reasons for this limited performance. To achieve this goal, we conducted a task-based characterization of a DL-based denoising approach for individual signal properties. We conducted this study in the context of evaluating a DL-based approach for denoising single photon-emission computed tomography (SPECT) images. The training data consisted of signals of different sizes and shapes within a clustered-lumpy background, imaged with a 2D parallel-hole-collimator SPECT system. The projections were generated at normal and 20% low-count level, both of which were reconstructed using an ordered-subset-expectation-maximization (OSEM) algorithm. A convolutional neural network (CNN)-based denoiser was trained to process the low-count images. The performance of this CNN was characterized for five different signal sizes and four different signal-to-background ratio (SBRs) by designing each evaluation as a signal-known-exactly/background-known-statistically (SKE/BKS) signal-detection task. Performance on this task was evaluated using an anthropomorphic channelized Hotelling observer (CHO). As in previous studies, we observed that the DL-based denoising method did not improve performance on signal-detection tasks. Evaluation using the idea of observer-study-based characterization demonstrated that the DL-based denoising approach did not improve performance on the signal-detection task for any of the signal types. Overall, these results provide new insights on the performance of the DL-based denoising approach as a function of signal size and contrast. More generally, the observer study-based characterization provides a mechanism to evaluate the sensitivity of the method to specific object properties, and may be explored as analogous to characterizations such as modulation transfer function for linear systems. Finally, this work underscores the need for objective task-based evaluation of DL-based denoising approaches.

Nonparametric modeling of self-excited forces based on relations between flutter derivatives

Unsteady self-excited forces are commonly represented by parametric models such as rational functions. However, this requires complex multiparametric nonlinear fitting, which can be a challenging task that requires know-how. This paper explores the alternative nonparametric modeling of unsteady self-excited forces based on relations between flutter derivatives. By exploiting the properties of the transfer function of linear causal systems, we show that damping and stiffness aerodynamic derivatives are related by the Hilbert transform. This property is utilized to develop exact simplified expressions, where it is only necessary to consider the frequency dependency of either the aeroelastic damping or stiffness terms but not both simultaneously. This approach is useful if the experimental data on aerodynamic derivatives that are related to the damping are deemed more accurate than the data that are related to the stiffness or vice versa. The proposed numerical models are evaluated with numerical examples and with data from wind tunnel experiments. The presented method can evaluate any continuous fitted table of interpolation functions of various types, which are independently fitted to aeroelastic damping and stiffness terms. The results demonstrate that the proposed methodology performs well. The relations between the flutter derivatives can be used to enhance the understanding of experimental modeling of aerodynamic self-excited forces for bridge decks.

FAST RATIONAL INTERPOLATION OF TRANSFER FUNCTIONS OF LINEAR DYNAMIC SYSTEMS WITH DISTRIBUTED PARAMETERS

Contex. Fast method of rational interpolation of the transfer function of linear dynamical systems with distributed parameters is described, the values of which can be found by numerical methods or by calculating the transcendental functions of the Laplace integral transform variable. The method makes it possible to determine explicitly the transfer function and, in particular, the characteristic equation of such a degree, which is sufficient to meet the accuracy requirements when calculating the root quality criteria for the dynamics of automatic control systems.Objective. According to the proposed method, rational interpolation is reduced to solving a system of linear equations, the order of which is much lower (more than twice) the order of similar systems used for rational interpolation of functions by known methods. The properties of this system are such that its solution can be obtained by special fast methods of the quadratic order of complexity.Method. An iterative algorithm for calculating the transfer function coefficients of a linear dynamic system with distributed parameters is carried out using the methods of complex variable functions theory using the discrete Laplace transform. The proposed approach made it possible to significantly speed up the calculations by decomposing the system of linear equations with respect to the coefficients of the transfer function to a system of approximately half the order, which allows a quick solution by the methods of Trench, Berlekamp-Massey, or Euclid.Results. An example of the practical use of an iterative algorithm for rational interpolation and calculation with a given accuracy of the root quality criteria for the dynamics of a support with gas lubrication is considered.Conclusions. The method allows to define explicitly the characteristic equation of such a degree, which is sufficient to meet the accuracy requirements when calculating the root quality criteria for the dynamics of automatic control systems. Rational interpolation is reduced to solving a system of linear equations, the order of which is much lower (more than twice) the order of similar systems used for rational interpolation of functions by known methods. The properties of the system are such that its solution can be obtained by special fast methods of the quadratic order of complexity.

Рациональная интерполяция передаточных функций линейных динамических систем с распределенными параметрами

Рациональная интерполяция передаточных функций линейных динамических систем с распределенными параметрами

V2V-Based Cooperative Control of Uncertain, Disturbed and Constrained Nonlinear CAVs Platoon

The longitudinal control of the platoon of connected and automated vehicles (CAVs) has gained extensive attention in recent transportation research. A majority of existing results are based on linearized third-order vehicular models, under the premise that a complete priori knowledge of vehicle dynamics is available. This article focuses on a general class of third-order nonlinear CAVs with parametric uncertainty and unknown external disturbance which cannot be linearized. A vehicle-to-vehicle (V2V) communication-based cooperative adaptive backstepping control scheme is proposed, in which unknown parameters and disturbance bounds are estimated on-line. Since the transfer function of linear systems cannot be applied to nonlinear systems to guarantee string stability, asymmetric time-varying constraints are employed to prevent the spacing errors from growing up. A realistic example is considered to verify the feasibility of the control algorithm.

Steady-state, harmonic response and moments of linear systems with periodic jumps

By relying on the recently introduced notion of transfer function for linear hybrid systems with periodic jumps, herein we extend, for the first time, frequency-domain analysis tools – well-known and extensively used in the context of purely continuous or discrete time systems – to such a class of hybrid systems. In fact, knowledge of the transfer function allows for the frequency-domain definition of the notion of 0-th momentof the underlying hybrid system, which is instrumental, e.g. for the solution to model reduction or input-output system identification problems. It is shown, in addition, that the notion of moment based on the hybrid transfer function possesses an interesting time-domain counterpart, hence extending the results obtained for purely continuous-time systems. To further substantiate the theoretical claims, the paper is concluded by the frequency-domain robustness analysis of the classical consensus protocol in the presence of sampled measurements.

Identification of differentially flat output of underactuated dynamic systems

This paper presents a data-driven algorithm for identification of locally differentially flat output from system output measurements. No detailed mathematical model of the system is needed. Trial output is written as a linear combination of measured outputs. An optimal linear combination is identified so that the trial output achieves the highest relative degree. When the relative degree is equal to the order of the system, the output is flat. The identification is done in the frequency domain by taking advantage of the asymptotic behaviour of transfer functions of linear systems. We have also developed data handling strategies to obtain the best estimate of the relative degree in the presence of measurement noise, high-frequency dynamics and Nyquist digitisation effect. The proposed algorithm is validated by numerical examples and an experimental study of a rotary crane system.

A Novel Nonlinear System Identification for Cerebral Autoregulation in Human: Computer Simulation and Validation.

Cerebral autoregulation in healthy humans was studied using a novel methodology adapted from Bendat nonlinear analysis technique. A computer simulation of a high-pass filter in parallel with a cubic nonlinearity followed by a low-pass filter was analyzed. A linear system transfer function analysis showed an incorrect estimate of the gain, cut-off frequency, and phase of the high-pass filter. By contrast, using our nonlinear systems identification, yielded the correct gain, cut-off frequency, and phase of the linear system, and accurately quantified the nonlinear system and following low-pass filter. Adding the nonlinear and linear coherence function indicated a complete description of the system. Cerebral blood flow velocity and arterial pressure were measured in six data sets. Application of the linear and nonlinear systems identification techniques to the data showed a high-pass filter, like the linear transfer function, but the gain was smaller. The phase was similar between the two techniques. The linear coherence was low for frequencies below 0.1Hz but improved by including a nonlinear term. The linear + nonlinear coherence was approximately 0.9 across the frequency bandwidth, indicating an improved description over the linear system analysis of the cerebral autoregulation system.

Inner–outer factorization for differential-algebraic systems

We consider transfer functions of linear time-invariant differential-algebraic systems. Based on the stabilizing solutions of certain differential-algebraic Lur’e equations, we will derive simple formulas for realizations of inner–outer factorizations. We show that the existence of a stabilizing solution only requires behavioral stabilizability of the system. We neither assume properness nor (proper) invertibility of the transfer function. We briefly discuss numerical aspects for the determination of such factorizations.

Minimal positive realizations of linear continuous-time fractional descriptor systems: Two cases of an input-output digraph structure

Abstract In the last two decades, fractional calculus has become a subject of great interest in various areas of physics, biology, economics and other sciences. The idea of such a generalization was mentioned by Leibniz and L’Hospital. Fractional calculus has been found to be a very useful tool for modeling linear systems. In this paper, a method for computation of a set of a minimal positive realization of a given transfer function of linear fractional continuous-time descriptor systems has been presented. The proposed method is based on digraph theory. Also, two cases of a possible input-output digraph structure are investigated and discussed. It should be noted that a digraph mask is introduced and used for the first time to solve a minimal positive realization problem. For the presented method, an algorithm was also constructed. The proposed solution allows minimal digraph construction for any one-dimensional fractional positive system. The proposed method is discussed and illustrated in detail with some numerical examples.

A Modified Frequency Domain Condition for the Physical Realizability of Linear Quantum Stochastic Systems

This paper is concerned with a modified version of the frequency domain physical realizability (PR) condition for linear quantum systems. We consider open quantum systems whose dynamic variables satisfy the canonical commutation relations of an open quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to physical quantum systems, these QSDEs must satisfy PR conditions. We provide a relatively simple proof that the PR condition is equivalent to the frequency domain $(J,J)$ -unitarity of the input–output transfer function and orthogonality of the feedthrough matrix of the system without the technical spectral assumptions required in previous work. We also show that the poles and transmission zeros associated with the transfer function of PR linear quantum systems are the mirror reflections of each other about the imaginary axis. An example is provided to illustrate the results.

Discrete-Time, Linear Periodic Time-Varying System Norm Estimation Using Finite Time Horizon Transfer Operators

The norm is one of the fundamental concepts of linear algebra and functional analysis. The notion of the norm is often employed in engineering, e.g. in control engineering, where main application is calculating the norm of the transfer function. Unfortunately existing methods are applicable for systems that can be described using Laplace transform, i.e. linear time-invariant (LTI) systems. An operational equivalent of the transfer function for linear time-varying systems is transfer operator. The transfer operator defined for finite time horizon can be described by finite dimensional matrix. Although for infinite time horizon the operator is infinite dimensional. In the paper a method for norm estimation of transfer operator defined on infinite time horizon is proposed. The method is applicable for linear time-varying, discrete-time systems given in general state-space form. The method take advantage of the properties of the transfer operator norm on a finite time horizon. Theoretical considerations are complemented by numerical examples.

Linear Quantum System Transfer Function Realization Using Static Networks for Input/Output Processing and Feedback

The realization of the transfer functions of linear quantum stochastic systems (LQSSs) is of fundamental importance for the practical applications of such systems, especially as coherent controllers for other quantum systems. So far, most works that have addressed this problem have used cascade realizations. In this paper, a new method is proposed, where the transfer function of an LQSS is realized by a series connection of two linear static networks, and a reduced LQSS. The introduction of pre- and postprocessing static networks leaves an intermediate reduced LQSS with a simple input/output structure, which is realized by a simple feedback network of single-mode LQSSs. The key mathematical tool that allows for the construction of this realization is an SVD-like decomposition for doubled-up matrices in Krein spaces. Illustrative examples are provided for the theory developed.

Realisation of Linear Continuous-Time Fractional Singular Systems Using Digraph-Based Method. First approach.

In this paper, a new method for computation of a minimal realisation of a given proper transfer function of fractional continuous-time singular one-dimensional linear systems using one-dimensional digraphs theory D has been presented. For the proposed method, an algorithm was constructed. The proposed solution allows minimal digraphs construction for any one-dimensional system. The proposed method was discussed and illustrated with numerical examples.

Vibration isolation systems, considered as systems with single degree of freedom

The research considers and analyzes vibration isolation systems, whose design schemes are single degree of freedom systems, including nonlinear elements - displacement limiter and viscous damper. Presented are calculation formulas in closed form for linear systems in operational modes (for harmonic and impulse loads), algorithms and examples of calculation of linear and nonlinear systems in operational and transient modes. The calculation method and the above dependences are written using the transfer (TF) and impulse response functions (IRF) of linear dynamical systems and dependencies that determine the relationship between these functions. The effectiveness of 2 options of vibration isolation systems in transient modes is analyzed. There is significant reduction of load from the equipment to the supporting structures in the starting-stopping modes by the use of displacement limiter.

The transfer function of generic linear quantum stochastic systems has a pure cascade realization

This paper establishes that generic linear quantum stochastic systems have a pure cascade realization of their transfer function, generalizing an earlier result established only for the special class of completely passive linear quantum stochastic systems. In particular, a cascade realization therefore exists for generic active linear quantum stochastic systems that require an external source of quanta to operate. The results facilitate a simplified realization of generic linear quantum stochastic systems for applications such as coherent feedback control and optical filtering. The key tools that are developed are algorithms for symplectic QR and Schur decompositions. It is shown that generic real square matrices of even dimension can be transformed into a lower 2×2 block triangular form by a symplectic similarity transformation. The linear algebraic results herein may be of independent interest for applications beyond the problem of transfer function realization for quantum systems. Numerical examples are included to illustrate the main results. In particular, one example describes an equivalent realization of the transfer function of a nondegenerate parametric amplifier as the cascade interconnection of two degenerate parametric amplifiers with an additional outcoupling mirror.

Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information

To control a quantum system via feedback, we generally have two options in choosing control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is the measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages/disadvantages, depending on the system and the control goal, hence their comparison in several situation is important. This paper considers a general open linear quantum system with the following specific control goals; back-action evasion (BAE), generation of a quantum non-demolished (QND) variable, and generation of a decoherence-free subsystem (DFS), all of which have important roles in quantum information science. Then some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand it is shown that, for each control goal, there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of BAE, QND, and DFS in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.

Static and Dynamic Characteristic Simulation of Feed System Driven by Linear Motor in High Speed Computer Numerical Control Lathe

In order to design the feed system of high speed Computer Numerical Control (CNC) lathe, the static and dynamic characteristics of feed system driven by linear motor in high speed CNC lathe were analyzed. The slide board was taking as the main moving part of the feed system, and the guide rail was the main support component of the linear motor feed system. The mechanical structure static stiffness of feed system is researched through the slide board statics analysis. The simulation results show that the maximum deformation of the slide board occurs in the middle of the slide board where the linear motor is placed. The linear motor feed system control model was established based on analysis of high-speed linear feed system control principle, and the linear motor feed system transfer function was established, and servo dynamic stiffness factors were analyzed. The control parameters of the servo system and actuating mechanism parameters of feed system on the effect of the linear motor servo dynamic stiffness were analyzed using MATLAB software. The simulation results show that the position loop proportional gain, speed loop proportional gain and speed loop integral response time are the biggest influence factors on servo dynamic stiffness. The displacement response is reduced under the cutting interference force step inputting, the servo dynamic stiffness is increased, the number of system oscillation is also reduced, and the system tends to be stable. DOI: http://dx.doi.org/10.11591/telkomnika.v11i7.2813 Full Text: PDF

Discuss about Linear System Transfer Function and Optical Transfer Function

Transfer function (TF) for linear time invariant system and optical transfer function (OTF) for linear space shaft invariant system are compared and contrasted. TF is the unilateral Laplace transform of system’s one-dimensional unit impulse response, dimensions of the input and output may be same or different, TF can be used to describe a variety of filter or to express solution of linear differential equations accurately. But OTF is the Fourier transform of system’s two-dimensional impulse response, dimensions of the input and output must be same, OTF can be used only to describe a low-pass filter or to express solution of the linear univariate partial differential equations approximately. Their eigenfunctions are similar complex exponential functions. OTF has stricter requirements and application conditions than TF. It is helpful to the readers’ understanding of TF and OTF.