Transfer Function Parameters Research Articles

Trajectory planning and tracking control for multiple-input multiple-output, linear time-invariant, sampled data systems in continuous time

In applications, usually sampled data controllers are employed. If the sampling time is sufficiently small, the sampled data structure may be neglected and the system is treated quasi-continuously. If the sampling time is longer, the system is treated in discrete time neglecting the behaviour in between the sample instances and the z-transform is used. This article combines these two approaches. The plant is driven by an input which consists of a sequence of values and a function forming the actuating variable. By use of the modified z-transform, the plant is modelled by a parametric transfer function matrix, whose additional parameter discloses the behaviour between sampling instances. Thus, the output signal is calculated not only at the points of sampling. A right co-prime matrix-fraction description is derived. Building on that description, basis variables are defined in the z-domain. The corresponding basis sequences can be chosen arbitrarily and with them the input sequences and the output functions are fixed and can be calculated without solving a differential or difference equation. This mathematical fact is applied to plan trajectories in continuous time. Hence, the entire output trajectory in continuous time can be taken into account. A tracking controller may be added to ensure that the disturbed system complies with the plan.

Fabrication of carbon films with ∼500nm holes for cryo-EM with a direct detector device

Single particle electron cryomicroscopy (cryo-EM) is often performed using EM grids coated with a perforated or holey layer of amorphous carbon. Regular arrays of holes enable efficient cryo-EM data collection and several methods for the production of micropatterned holey-carbon film coated grids have been described. However, a new generation of direct detector device (DDD) electron microscope cameras can benefit from hole diameters that are smaller than currently available. Here we extend a previously proposed method involving soft lithography with a poly(dimethylsiloxane) (PDMS) stamp for the production of holey-carbon film coated EM grids. By incorporating electron-beam (e-beam) lithography and modifying the procedure, we are able to produce low-cost high-quality holey-carbon film coated EM grids with ∼500nm holes spaced 4μm apart centre-to-centre. We demonstrate that these grids can be used for cryo-EM. Furthermore, we show that by applying image shifts to obtain movies of the carbon regions beside the holes after imaging the holes, the contrast transfer function (CTF) parameters needed for calculation of high-resolution cryo-EM maps with a DDD can be obtained efficiently.

Visualizing Power Frequency Dynamics Using D-Partitioning

In this paper we introduce D-Partitioning as a convenient direct method for visualizing the performance of power systems subjected to load changes. In Automatic Generation Control (AGC) schemes, such visualizations rely on manual calculations of the system stability limits. D-Partitioning obviates this reliance permitting a direct reading-off of the limits. The method assumes a test power system of known parameters embedding distributed solar power generation. The generated solar power injects discretely variable real power system disturbances. MATLAB/SIMULINK is used to mask the parameters of the system transfer function thus allowing for data entry or changes via a user interface. The system frequency behaviour is analyzed applying traditional methods within MATLAB and MATHEMATICA. Subsequent comparative results are established by applying D-Partitioning. Nyquist stability criterion and step frequency response results show that the system's stability limits cannot be discerned with certainty visually but only manually. In contrast D-Partitioning provides visually clearer stability limits. The paper provides an additional tool for the analysis of power systems described by transfer functions possibly with several variable parameters. The MATLAB User Interface used in the paper limits any flexible variation of the parameters. An improvement will be considered in ongoing studies by applying on the named parameters, MATHEMATICA's dynamic interactivity feature.

Parametric head-related transfer function modeling and interpolation for cost-efficient binaural sound applications

Parametric methods for modeling the perceptually relevant features of head-related transfer functions (HRTFs) are very important for the development of low-cost immersive sound applications. This letter describes an efficient method based on a low-order infinite impulse response filter implemented by a chain of second order sections of conventional shelving and peak audio filters. The parameters (central frequency, gain, and quality factor) are numerically adjusted by iteratively fitting the frequency response of the filter to the desired HRTF. Besides allowing for low-order binaural models, the proposed approach provides an efficient way to synthesize HRTFs for non-measured angles by applying a simple interpolation between the parameters from neighboring responses. Additionally, the HRTF database size is significantly reduced.

Fractional Order Butterworth Filter: Active and Passive Realizations

This paper presents a general procedure to obtain Butterworth filter specifications in the fractional-order domain where an infinite number of relationships could be obtained due to the extra independent fractional-order parameters which increase the filter degrees-of-freedom. The necessary and sufficient condition for achieving fractional-order Butterworth filter with a specific cutoff frequency is derived as a function of the orders in addition to the transfer function parameters. The effect of equal-orders on the filter bandwidth is discussed showing how the integer-order case is considered as a special case from the proposed procedure. Several passive and active filters are studied to validate the concept such as Kerwin-Huelsman-Newcomb and Sallen-Key filters through numerical and Advanced Design System (ADS) simulations. Moreover, these circuits are tested experimentally using discrete components to model the fractional order capacitor showing great matching with the numerical and circuit simulations.

The Hydrodynamic Response and Frequency Domain Analysis of Deep Sea Truss Spar Platform

With the development of marine oil going to the deeper water area, SPAR platform with its many advantages has gradually become the mainstream of the offshore oil and gas production facilities. In this paper, the Spar platform three-dimensional hydrodynamic model establish is established firstly, then the floating body hydrodynamic is calculated by using the three-dimensional flow theory to get Spar platforms transfer function and hydrodynamic parameters of its motion response. At last, the frequency domain for floating body and mooring system coupling calculation model is analyzed.

Frequency domain, parametric estimation of the evolution of the time-varying dynamics of periodically time-varying systems from noisy input–output observations

This paper presents a frequency domain, parametric identification method for continuous- and discrete-time, slow linear time-periodic (LTP) systems from input–output measurements. In this framework, the output as well as the input is allowed to be corrupted by stationary noise (i.e. an errors-in-variables approach is adopted). It is assumed that the system under consideration can be excited by a broad-band periodic signal with a user-defined amplitude spectrum (i.e. a multisine), and that the periodicity of the excitation signal Texc can be synchronized with the periodicity of the time-variation Tsys (i.e. Texc/Tsys∈Q), such that the system reaches a steady state (a periodic solution). Tsys is also known as the pumping period. Once the parametric estimation of the time-evolution of the system parameters has been performed, the system model is evaluated at the level of the instantaneous transfer function (also known as system function, or parametric transfer function), which rigorously characterizes LTP systems. If the dynamics of the LTP system are slowly varying or the system is linear parameter varying (LPV), a frozen transfer function approach is provided to easily visualize and assess the quality of the estimated model. To give the estimated quantities a quality label, uncertainty bounds on the model-related quantities (such as the time-periodic (TP) system parameters, the frozen transfer function, the frozen resonance frequency, etc.) are derived in this paper as well. Besides, a clear distinction between the instantaneous and the frozen transfer function concept is made, and both can be estimated with the proposed identification scheme. The user decides which transfer function definition suits best its purpose in practice. Finally, the identification algorithm is applied to a simulation example and to real measurements on an extendible robot arm.

Transient suppression in FRF measurement: Comparison and analysis of four state-of-the-art methods

This paper compares four well selected methods for computing the non-parametric Frequency Response Function (FRF) of a periodically excited linear time invariant system. The suppression of the transient is mandatory when its influence in the data is large. Better suppression of the transient leads to a better non-parametric FRF estimate. A good non-parametric FRF estimate can be used to validate the parametric transfer function model in a second step. The suppression of the transient will be highlighted using the mean squared error of the non-parametric FRF estimate. Temperature transients caused by heat diffusion are used as example. The selected methods consist of two standard windowing methods and two methods based on the Local Polynomial Method (LPM). LPM was designed to find a non-parametric FRF estimate in the presence of nonlinearities. This paper will modify LPM to find a non-parametric FRF estimate for linear systems using a single experiment. The mean squared error of the four non-parametric FRF estimates will be compared and analyzed, based on a simulation and a measurement example.

Dynamic displacement sensing, system identification, and control of a speaker-based tendon vibrator via accelerometers

In this paper, we develop a speaker-based tendon vibrator capable of applying vibrations with sustained amplitudes and desired time-frequency profiles to be used in inducing kinesthetic illusions. For modeling and control of the tendon vibrator, we propose and experimentally validate a method for real-time dynamic displacement sensing based on accelerometers. We tested the accuracy of displacement measurements by comparing the movements of the vibrator measured with differential accelerometers to those measured by a high resolution optical encoder. We completed frequency domain system identification of the vibrator and obtained a parametric transfer function model via displacements sensed by the encoder and by analog and digital integration. We show that within the frequency range of interest 20 -100 Hz, analog and digital integration methods were successful in capturing an accurate model of the vibrator. Under feedforward control, developed tendon vibrator is able to generate sustained 2-mm peak-to-peak vibrations throughout the frequency range of interest.

Assembly Sequence Planning Including Tool Check Based on Improved Ant-Colony Algorithm

According to the characteristics and demands of assembly sequence planning (ASP) of complicated electromechanical products, the improved Ant-Colony algorithm is presented to solve the problem. In order to plan assembly sequence, Precedence Graph, which is created based on assembly model, is created to record precedence relations between components. Several mechanisms are designed to make the precedence relations correct and compendious. To examine the feasibility of the sequences for tool’s operation, a quick checking method is proposed based on Potential Interference Information, which is created by simulating the tool’s movement and checking the interference information in entire assembly. Then, the Ant Colony Algorithm is improved to generate optimal assembly sequences with the guidance of precedence relations. Two important influence factors have been taken into account in the method. (1) A Penalty-Evaporation mechanism is proposed for the algorithm to punish unfeasible solutions. (2) Via analyzing the effects of the parameters in the state transfer function, the better solution is obtained while change the fixed parameters to transforming with time. Finally, an example illustrates the effectiveness of the strategy.

Advanced statistical analysis with guaranteed estimation of current performance for sampled-data systems with delay and generalized higher order hold

The paper provides the solution of the advanced statistical analysis problem for sampled-data systems, which is relevant for digitally controlled marine vehicles under water as well as on the surface. The difficult cases when the system has pure delay and a generalized digital to analog converter (DAC) of higher order are considered. The obtained solution is based on applying the parametric transfer function (PTF) concept, jointly with calculation of guaranteed estimation of the current performance. On the way to solution, we find general expressions for the PTF of sampled-data systems with pure delay and higher order hold. The intersample behavior of the current performance of the output signal is compared between sampled-data systems possessing traditional zero-order hold, and sampled data systems with extrapolator and interpolator of first order.

Analysis on Equivalence between Transfer Function and Equivalent Circuit Simulation in General Hamiltonian Modeling

Take generator system included AVR (automatic voltage regulator) and PSS (power system stabilizer) as an example, Using the time simulation method, Study the equivalence between the transfer function model and the equivalent circuit simulation, and establish the corresponding relations between the circuit structures, internal parameters and transfer function parameters, based on the energy of equivalent circuit, the Hamiltonian function of transfer function is derived indirectly, and the Hamiltonian model is established. The study in this paper provides a new way to establish generalized Hamiltonian model for linear system based on transfer function.

Quadratic L2-gain performance linear parameter-varying realisation of parametric transfer functions and state-feedback gain scheduling control

The study deals with the quadratic L2-gain performance linear parameter-varying realisation of parametric transfer functions and state-feedback gain scheduling control. It is shown that any parametric transfer function, which has L2-gain performance with a bound for all constant parameters values, admits a state space realisation guaranteeing quadratic L2-gain performance with the bound under arbitrary parameter variations. A reasonably general procedure is provided to find such a realisation with linear matrix inequality optimal technique. Furthermore, according to the realisation, the state-feedback gain scheduling control design is also dealt with. Finally, a simple numerical example is given to illustrate the efficiency of the proposed method.

Conjugate-order systems for signal processing: stability, causality, boundedness, compactness

The fundamental system theory is presented for a class of real systems whose derivative order is complex. It is demonstrated that these so-called conjugate-order systems have a scale-invariance property in both the time and frequency domains, which makes them useful for describing certain phenomena in continuous media. The conditions for which these systems are guaranteed to be causal and stable are reviewed. The compactness properties of their Hankel operators, which allow them to admit finite-order approximations, are also discussed. A procedure is developed for choosing appropriate transfer-function parameter values to design a stable conjugate-order system whose frequency response meets given bandwidth, resonance, and ripple specifications.

Retrieval of spinach crop parameters by microwave remote sensing with back propagation artificial neural networks: A comparison of different transfer functions

Back propagation artificial natural network (BPANN) is a well known and widely used machine learning methodology in the field of remote sensing. In this paper an attempt is made to retrieve the spinach crop parameters like biomass, leaf area index, average plant height and soil moisture content by using the X-band scattering coefficients with BPANN at different growth stages of this crop. The maturity age of this crop was found to be 45days from the date of sowing. After 45days from the date of sowing, this crop was cut at a certain height for production. Then, it is a point of interest to investigate the microwave response of variation in production. Significant variations in all the crop parameters were observed after cutting the crop and consequently made the problem more critical. Our work confirms the utility of BPANN in handling such a non-linear data set. The BPANN is essentially a network of simple processing nodes arranged into different layers as input, hidden and the output. The input layer propagates components of a particular input vector after weighting these with synaptic weights to each node in the hidden layer. At each node, these weighted input vector components are added. Each hidden layer computes output corresponding to these weighted sum through a non-linear/linear function (e.g. LOGSIG, TANSIG and PURLIN). These functions are known as transfer functions. Thus, each of the hidden layer nodes compute output values, which become inputs to the nodes of the output layer. At nodes of output layer also a weighted sum of outputs of previous layer (hidden layer) are obtained and processed through a transfer function. Thus, the output layer nodes compute the network output for the particular input vector. In this paper, output nodes use linear transfer function. Different transfer functions e.g. TANSIG, LOGSIG and PURELIN were used and the performance of the ANN was optimized by changing the number of neurons in the hidden layers. The present analysis suggests the need of critical analysis of the BPANN in terms of selection of the best transfer function and other network parameters for the better results.

The nonasymptotic confidence set for parameters of a linear control object under an arbitrary external disturbance

The problem is considered of developing the confidence sets for parameters of the transfer function of a control object (CO) on the basis of observable data. The assumptions as to disturbances (noises), affecting the CO, reduce to a minimum: noises can actually be arbitrary, but instead of them the user must have a chance of adding to the input signal a tentative disturbance independent of them. The procedure of solving this problem is suggested and substantiated, which is developed in the framework of the common diagram "leave-out sign-dominant correlation regions" (LSCR), actively progressed in the modern works of Marko Campi with co-authors, and using the approach, earlier suggested by the author, to the CO reparametrization. The procedure returns the confidence region, which for the finite set of observations with the probability selected by the user contains the parameters of the true transfer function.

Modeling Electromechanical Overcurrent Relays Using Singular Value Decomposition

This paper presents a practical and effective novel approach to curve fit electromechanical (EM) overcurrent (OC) relay characteristics. Based on singular value decomposition (SVD), the curves are fitted with equation in state space under modal coordinates. The relationships between transfer function and Markov parameters are adopted in this research to represent the characteristic curves of EM OC relays. This study applies the proposed method to two EM OC relays: the GE IAC51 relay with moderately inverse‐time characteristic and the ABB CO‐8 relay with inverse‐time characteristic. The maximum absolute values of errors of hundreds of sample points taken from four time dial settings (TDS) for each relay between the actual characteristic curves and the corresponding values from the curve‐fitting equations are within the range of 10 milliseconds. Finally, this study compares the SVD with the adaptive network and fuzzy inference system (ANFIS) to demonstrate its accuracy and identification robustness.

Model Order Reduction for Decentralized PID Control Design on TITO processes

The decentralized PID control design of multivariable processes is an appealing approach due to its practical applicability and the existence of a good theoretical basis. However, although industrial processes may be modeled using simple first order and second order models, in decentralized control, the models increase their complexity due to loop interaction, compromising the applicability of existing PID tuning rules. In fact, even inverse response behavior may appear due to loop interaction. The contribution of the article is twofold. First, we derive conditions to assess the inverse response behavior of reduced effective transfer functions. As a result, we know when tuning rules for first order and minimum phase second order models are suited for decentralized control tunning. Secondly, at the sight of matrix transfer function parameters, we derive simplified models in a straightforward way. The results are useful for decentralized MIMO process control design using simple tuning rules derived for first order and second order systems.

WYSIWYG (What You See is What You Get) Volume Visualization

In this paper, we propose a volume visualization system that accepts direct manipulation through a sketch-based What You See Is What You Get (WYSIWYG) approach. Similar to the operations in painting applications for 2D images, in our system, a full set of tools have been developed to enable direct volume rendering manipulation of color, transparency, contrast, brightness, and other optical properties by brushing a few strokes on top of the rendered volume image. To be able to smartly identify the targeted features of the volume, our system matches the sparse sketching input with the clustered features both in image space and volume space. To achieve interactivity, both special algorithms to accelerate the input identification and feature matching have been developed and implemented in our system. Without resorting to tuning transfer function parameters, our proposed system accepts sparse stroke inputs and provides users with intuitive, flexible and effective interaction during volume data exploration and visualization.

Determination of the most pertinent EUV proxy for use in thermosphere modeling

[1] Two major issues in the specification of the thermospheric density are the definition of proper solar inputs and the empirical modeling of thermosphere response to solar and to geomagnetic forcings. This specification is crucial for the tracking of low Earth orbiting satellites. Here we address both issues by using 14 years of daily density measurements made by the Stella satellite at 813 km altitude and by carrying out a multiscale statistical analysis of various solar inputs. First, we find that the spectrally integrated solar emission between 26–34 nm offers the best overall performance in the density reconstruction. Second, we introduce linear parametric transfer function models to describe the dynamic response of the density to the solar and geomagnetic forcings. These transfer function models lead to a major error reduction and in addition open new perspectives in the physical interpretation of the thermospheric dynamics.