Linear And Time-invariant Research Articles

An Efficient Macromodel Extraction Strategy for Packaged MEMS Thermal Wind Sensor Considering Multiphysics

This work presents a novel strategy for efficiently extracting macromodels from multiphysics microelectromechanical system (MEMS) devices with weak coupling. To validate the strategy, the packaged thermal wind sensor is chosen to verify the feasibility of the strategy for the first time. Based on the characteristics of the packaged thermal wind sensor, it can be divided into three distinct energy fields: thermal field, fluid field, and electric field. The packaged thermal wind sensor is initially built as the finite element model, which represents a pure thermal system under no wind flow conditions. Then, the thermal system with linear and time-invariant (LTI) is identified as a state space model by its step response obtained by transient simulation of the finite element model. Other energy fields can be regarded as negative inputs for the state space model. Subsequently, the macromodel is constructed by describing the relationship among thermal field, fluid field and electric field with Verilog-A. Remarkably, the macromodel based on this strategy takes into account geometric factors and material parameters. The tests show that the error of far group thermistors between system-level simulation and experiment is less than 5% under the conventional wind speed range on constant power (CP) mode, and the results of wind direction between them also show a significant degree of overlap. In brief, the strategy of extracting macromodel enables the direct construction of connections between the finite element model of MEMS devices and integrated circuits.

Performance Analysis of an MLS-Based Interface for Impulse Response Estimation of Resistive and Capacitive Sensors

This paper presents a performance analysis of a system for electrochemical impedance spectroscopy (EIS). The system, composed by an analog front-end (AFE) and a custom microcontroller (MCU) board, performs the impulse response (IR) measurement of linear and time-invariant (LTI) systems with pseudo-random excitation signals. As a novelty, a specific AFE for the interfacing of two-terminal resistive and capacitive sensors is covered in detail. The paper proposes, for the first time, a mathematical model to predict the impact of the main noise sources in the measured IR. Thanks to the proposed approach, the AFE and the system’s parameters can be properly designed in order to reduce the error, thus, minimizing the energy-per-error figure of merit (FOM) as well. The AFE is realized as discrete-components circuit and it has been included in a custom MCU-based measurement system as an expansion module. The predicted results from the mathematical model, in terms of noise power, SNR, and measurement error are validated through system-level simulation and experimental measurements. The system performs the IR measurement with 1023 points, showing root-mean-square (RMS) measurement errors of 1% and 1.4% for the tested ADC sampling frequencies of 62.5 kHz and 125 kHz, respectively. These lead to excellent FOM values of 128.9 mJ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula> % <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and 252.6 mJ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula> % <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> that outstand the state of the art.

Risk-theoretic optimal design of output-feedback controllers via iterative convex relaxations

This work presents a framework to address the MIMO (multiple-input multiple-output) control design problem under model uncertainty. The plant is considered to be LTI (linear and time-invariant) and that it is parametrized by a random variable whose distribution may be unknown but can be sampled from. The objective is to design a dynamic LTI MIMO controller optimizing the closed-loop H2-performance. To account for the uncertainty in the plant, we employ measures of risk on the performance and discuss how coherent measures of risk are suitable to address this problem. In particular, we introduce a measure called Conditional Value-at-Risk (CVaR) and analyze its advantages and disadvantages regarding other traditional measures of risk. A simulation study complements the discussion.

Black-Box Modelling of Low-Switching-Frequency Power Inverters for EMC Analyses in Renewable Power Systems

Electromagnetic interference (EMI) from renewable power systems to the grid attracts more attention especially in the low-frequency range, due to the low switching frequency of high-power inverters. It is significantly important to derive EMI models of power inverters as well as to develop strategies to suppress the related conducted emissions. In this work, black-box modelling is applied to a three-phase inverter system, by implementing an alternative procedure to identify the parameters describing the active part of the model. Besides, two limitations of black-box modelling are investigated. The first regards the need for the system to satisfy the linear and time-invariant (LTI) assumption. The influence of this assumption on prediction accuracy is analysed with reference to the zero, positive and negative sequence decomposition. It is showing that predictions for the positive/negative sequence are highly influenced by this assumption, unlike those for the zero sequence. The second limitation is related to the possible variation of the mains impedance which is not satisfactorily stabilized at a low frequency outside the operating frequency range of standard line impedance stabilization networks.

Data-Driven Input-Passivity Estimation Using Power Iterations

Abstract In this work we develop a non-parametric method to estimate the input-passivity index of an unknown linear and time-invariant (LTI) system from iterative experiments based on the power method from numerical linear algebra. Inspired by the power method for estimating the H∞-norm (or L2-gain) from data, we propose an algorithm that time-reverses input-output data in order to emulate measurements of a virtual system whose L2-gain matches the passivity index of the original system under study. While the proposed method requires exciting the original system twice, we also introduce an improved sampling scheme where only one experiment per iteration is needed.

Data-driven model updating of an offshore wind jacket substructure

The present paper provides a model updating application study concerning the jacket substructure of an offshore wind turbine. The updating is resolved in a sensitivity-based parameter estimation setting, where a cost function expressing the discrepancy between experimentally obtained modal parameters and model-predicted ones is minimized. The modal parameters of the physical system are estimated through stochastic subspace identification (SSI) applied to vibration data captured for idling and operational states of the turbine. From a theoretical outset, the identification approach relies on the system being linear and time-invariant (LTI) and the input white noise random processes; criteria which are violated in this application due to sources such as operational variability, the turbine controller, and non-linear damping. Consequently, particular attention is given to assess the feasibility of extracting modal parameters through SSI under the prevailing conditions and subsequently using these parameters for model updating. On this basis, it is deemed necessary to disregard the operational turbine states—which severely promote non-linear and time-variant structural behaviour and, as such, imprecise parameter estimation results—and conduct the model updating based on modal parameters extracted solely from the idling state. The uncertainties associated with the modal parameter estimates and the model parameters to be updated are outlined and included in the updating procedure using weighting matrices in the sensitivity-based formulation. By conducting the model updating based on in-situ data harvested from the jacket substructure during idling conditions, the maximum eigenfrequency deviation between the experimental estimates and the model-predicted ones is reduced from 30% to 1%.

New results on the trade-off performance of LTI system with colored noise and encoder-decoder strategy

This paper studies the trade-off performance between tracking performance and control input energy of the multi-input multi-output(MIMO), linear and time-invariant(LTI) system over an additive coloured Gaussian noise(ACGN) channel and the encoder-decoder strategies. The restriction that filter in the encoder-decoder strategy must be diagonal matrix is not necessary. And some new results are derived according to the inner-outer factorization. The results show that the trade-off performance is correlated to the unstable pole, non-minimum phase zero of the system. Also new poles and zeros generated by the non-diagonal encoder-decoder strategies may affect the trade-off performance. At last, two examples with different filters and different encoder-decoder strategies are discussed to validate the conclusions. The various encoder-decoder strategies revealed by the simulations may enhance or deteriorate the trade-off performance proposed in this paper.

On the Use of the $Z$ Transform of LTI Systems for the Synthesis of Steered Beams and Nulls in the Radiation Pattern of Leaky-Wave Antenna Arrays

This paper addresses the use of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> transform to synthesize radiation patterns with prescribed nulls from a phased array of electronically reconfigurable leaky-wave antennas (LWAs). This approach provides the relationship between such antennas and linear and time invariant (LTI) systems. Using this signal processing perspective, the proper locations of the poles and zeros of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> transform of the associated LTI system provide a radiation pattern with prescribed specifications (mainly main lobes’ directions and surrounding radiation nulls). Then, these poles and zeros’ positions can be transformed into particular values of the LWA array control coefficients. The effectiveness of the proposed technique is demonstrated with the synthesis of various radiation patterns, with application to reconfigurable smart antennas. A comparison with more conventional uniform linear array architecture is also performed to evaluate the synthesis flexibility and system complexity of the proposed approach.

On the practical estimation of unknown inputs for polytopic LTI systems

Reconstruction of unknown inputs is an important issue in real-time monitoring when they cannot be directly measured. This study proposes a coupled robust observer to estimate both the state vector and the unknown input of uncertain linear and time invariant (LTI) systems. A Luenberger observer is first considered to estimate the state vector and then, a super-twisting observer uses the precedent estimations to reconstruct the unknown input. Two semi-definite optimisation problems are proposed to compute the observer gains. The feasibility of the strategy is illustrated by the two examples, one of them a non-linear biological system.

Testing a linear time invariant model for skin conductance responses by intraneural recording and stimulation.

Skin conductance responses (SCR) are increasingly analyzed with model‐based approaches that assume a linear and time‐invariant (LTI) mapping from sudomotor nerve (SN) activity to observed SCR. These LTI assumptions have previously been validated indirectly, by quantifying how much variance in SCR elicited by sensory stimulation is explained under an LTI model. This approach, however, collapses sources of variability in the nervous and effector organ systems. Here, we directly focus on the SN/SCR mapping by harnessing two invasive methods. In an intraneural recording experiment, we simultaneously track SN activity and SCR. This allows assessing the SN/SCR relationship but possibly suffers from interfering activity of non‐SN sympathetic fibers. In an intraneural stimulation experiment under regional anesthesia, such influences are removed. In this stimulation experiment, about 95% of SCR variance is explained under LTI assumptions when stimulation frequency is below 0.6 Hz. At higher frequencies, nonlinearities occur. In the intraneural recording experiment, explained SCR variance is lower, possibly indicating interference from non‐SN fibers, but higher than in our previous indirect tests. We conclude that LTI systems may not only be a useful approximation but in fact a rather accurate description of biophysical reality in the SN/SCR system, under conditions of low baseline activity and sporadic external stimuli. Intraneural stimulation under regional anesthesia is the most sensitive method to address this question.

Stability analysis of linear impulsive delay dynamical systems via looped-functionals

This article investigates the asymptotic stability of impulsive delay dynamical systems (IDDS) by using the Lyapunov–Krasovskii method and looped-functionals. The proposed conditions reduce the conservatism of the results found in the literature by allowing the functionals to grow during both the continuous dynamics and the discrete dynamics. Sufficient conditions for asymptotic stability in the form of linear matrix inequalities (LMI) are provided for the case of impulsive delay dynamical systems with linear and time-invariant (LTI) base systems (non-impulsive actions). Several numerical examples illustrate the effectiveness of the method.

Tracking Performance Bound with Finite Control Energy and Erasure Channel Energy Constraint

AbstractThis paper studies the tracking performance of the single‐input single‐output (SISO), finite dimensional, linear and time‐invariant (LTI) system under the channel input energy constraint over the Erasure channel. A new performance index is proposed which is minimized over all two‐degree‐of‐freedom stabilizing controllers. The explicit expressions of the lower bound of the performance index and the minimum of the signal‐to‐noise ratio are obtained. The results show that the performance bound is correlated to unstable poles, non‐minimum phase zeros and the packet loss probability. Finally, examples are given to validate the conclusions derived.

Lower bound of tracking performance with finite control energy and channel energy constraint

This paper studies the tracking performance of the single-input single-output (SISO), finite dimensional, linear and time-invariant (LTI) system over an additive white Gaussian noise (AWGN) channel with finite control energy and channel input energy constraint. A new performance index is proposed which is minimized over all stabilizing two-degree-of-freedom controllers. The explicit expressions of the lower bound of the tracking performance and the minimum of signal-to-noise required are obtained. The results show that the lower bound is correlated to the unstable pole, non-minimum phase zero and the channel scaling factor. Finally, one example is given to validate the conclusions by adopting the special inner-outer factorization.

Design of Reset Control Systems: The PI + CI Compensator

Reset compensation has been used to overcome limitations of linear and time invariant (LTI) compensation. In this work, a new reset compensator, referred to as proportional and integral (PI) + CI (Clegg integrator), is introduced. It basically consists of adding a Clegg integrator to a PI compensator, with the goal of improving the closed loop response by using the nonlinear characteristic of this element. It turns out that by resetting a percentage of the integral term in a PI compensator, a significant improvement can be obtained over a well-tuned PI compensator in some relevant practical cases, such as systems with dominant lag and integrating systems. The work is devoted to the development of PI + CI tuning rules for basic dynamic systems in a wide range of applications, including first and higher order plus dead time systems.

A Technique for Efficient Realization of Wide-Band FIR LTI Systems

This correspondence introduces a technique for efficient realization of wide-band finite-length impulse response (FIR) linear and time-invariant (LTI) systems. It divides the overall frequency region into three subregions through lowpass, bandpass, and highpass filters realized in terms of only one filter. The actual function to be approximated is in the low- and high-frequency regions realized using periodic subsystems. In this way, one can realize an overall wide-band LTI function in terms of three low-cost subblocks, leading to a reduced overall arithmetic complexity as compared to the regular realization. A systematic design technique is provided and a detailed example shows multiplication and addition savings of 62% and 48%, respectively, for a fractional-order differentiator with a 96% utilization of the bandwidth. Another example shows that the savings increase/decrease with increased/decreased bandwidth.

Dynamic behavior of BIS, M-entropy and neuroSENSE brain function monitors

The objective of this paper is to assess the suitability of brain function monitors for use in closed-loop anesthesia or sedation delivery. In such systems, monitors used as feedback sensors should preferably be Linear and Time Invariant (LTI) in order to limit sensor-induced uncertainty which can cause degraded performance. In this paper, we evaluate the suitability of the BIS A2000 (Aspect Medical Systems, MA), the M-Entropy Monitor (GE HealthCare), and the NeuroSENSE Monitor (NeuroWave Systems Inc, OH), by verifying whether their dynamic behavior conforms to the LTI hypothesis. We subjected each monitor to two different composite EEG signals containing step-wise changes in cortical activity. The first signal was used to identify Linear Time-Invariant (LTI) models that mathematically capture the dynamic behavior of each monitor. The identification of the model parameters was carried out using standard Recursive Least Squares (RLS) estimation. The second signal was used to assess the performance of the model, by comparing the output of the monitor to the simulated output predicted by the model. While a LTI model was successfully derived for each monitor using the first signal, only the model derived for NeuroSENSE was capable to reliably predict the monitor output for the second input signals. This indicates that some algorithmic processes within the BIS A2000 and M-Entropy are non-linear and/or time variant. While both BIS and M-Entropy monitors have been successfully used in closed-loop systems, we were unable to obtain a unique LTI model that could capture their dynamic behavior during step-wise changes in cortical activity. The uncertainty in their output during rapid changes in cortical activity impose limitations in the ability of the controller to compensate for rapid changes in patients' cortical state, and pose additional difficulties in being able to provide mathematically proof for the stability of the overall closed-loop system. Conversely, the NeuroSENSE dynamic behavior can be fully captured by a linear and time invariant transfer function, which makes it better suited for closed-loop applications.

Switching Between Controllers Using Replicator Dynamics

Abstract We propose replicator dynamics to design an alternative algorithm for switching control. We use a feedback control strategy with a finite set of commuting controllers, whose control action takes a linear and time-invariant (LTI) process output to a desired set point. Each controller represents a pure strategy of the evolutionary game, in which case the assigned resource is the time allowed for each controller to operate the process. Therefore, from an evolutionary game theoretical perspective, we give a higher payoff to those controllers with the best performances to control the process according to a specific fitness function. Our proposed control strategy is compared in simulation to an existing switching system strategy, and it preserves the stability conditions that have been developed for such systems.

A clarifying analysis of feedback error learning in an LTI framework

AbstractFeedback error learning (FEL) is a proposed technique for reference‐feedforward adaptive control. FEL in a linear and time‐invariant (LTI) framework has been studied recently; the studies can be seen as proposed solutions to a ‘feedforward MRAC’ problem. This paper reanalyzes two suggested schemes with new interpretations and conclusions. It motivates the suggestion of an alternative scheme for reference‐feedforward adaptive control, based on a certainty‐equivalence approach. The suggested scheme differs from the analyzed ones by a slight change in both the estimator and the control law. Boundedness and error convergence are then guaranteed when the estimator uses normalization combined with parameter projection onto a convex set where stability of the estimated closed‐loop system holds. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Feasibility study of time-intensity-based blood flow measurements using deconvolution.

Ultrasonic contrast agents have been used to enhance the acoustic backscattered intensity of blood and to assist the assessment of blood flow parameters. One example is the time-intensity method based on the indicator-dilution theory. In this case, a mixing chamber model can be employed to describe the concentration of the contrast agent as a function of time. By measuring the time intensities at both the input and output of the blood mixing chamber, blood flow information can be obtained if proper deconvolution techniques are applied. Note that most deconvolution techniques assume a linear and time invariant (LTI) system for the mixing of the contrast agent with blood. In this paper, the hypothesis that a blood mixing chamber is an LTI system was tested. Several aspects were studied. One aspect was the linear relationship between the concentration of the contrast agent and the backscattered intensity. The other aspect was the dependence of the derived time constants on the concentration. The concept of an effective mixing volume was also introduced and evaluated. Finally, the input and the output time constants were measured and compared to theory under the LTI assumption. Extensive experiments were performed. Two in vitro flow models were constructed and two contrast agents were used. Results indicated that the LTI assumption does not hold and quantitative flow estimation is generally not possible. Nonetheless, the indicator-dilution theory can still be applied if only relative measurements of the flow rate are required.

Plucked-String Models: From the Karplus-Strong Algorithm to Digital Waveguides and beyond

The emergence of what is called modeling and model-based sound synthesis is closely related to the development of computational simulations of plucked string instruments. Historically, the first approaches (Hiller and Ruiz 1971a, 1971b; McIntyre and Woodhouse 1979; McIntyre, Schumacher, and Woodhouse 1983) were followed by the Karplus-Strong (KS) algorithm (Karplus and Strong 1983). The KS algorithm was discovered as a simple computational technique that seemingly had nothing to do with physics. Soon thereafter, Julius Smith and David Jaffe showed a deeper understanding of its relation to the physics of the plucked string (Smith 1983; Jaffe and Smith 1983). Later, Julius Smith generalized the underlying ideas of the KS algorithm by introducing the theory of digital waveguides (Smith 1987). Digital waveguides are physically relevant abstractions yet computationally efficient models, not only for plucked strings, but for a variety of one-, two-, and three-dimensional acoustic systems (Van Duyne and Smith 1993; Savioja, Rinne, and Takala 1994; Van Duyne, Pierce, and Smith 1994). Further investigations embodied these ideas in more detailed synthesis principles and implementations, resulting in high-quality and realistic syntheses of plucked string instruments (Sullivan 1990; Karjalainen and Laine 1991; Smith 1993; Karjalainen, Valimaki, and Janosy 1993; Vilimaki, Huopaniemi, Karjalainen, and Jainosy 1996). A recent overview of research in this field is given by Smith (1996). The equivalence of Karplus-Strong and digital waveguide formulations in sound synthesis was already known when the waveguide theory appeared (Smith 1987, 1992, 1997); however, the relation has never been explicated in full detail. The first aim of this article is to show how the more physical waveguide model of a plucked string can be reduced to an extended form of the Karplus-Strong type that we call the single delay-loop (SDL) mod l. For a linear and time-invariant (LTI) case, this reduction is relatively straightforward, and results in a computationally more efficient digital filter structure. (Note that the historical order of the KS algorithm and digital waveguides is the reverse of their logical order, since the generalization was not developed until after the KS algorithm was designed. This article's title reflects the historical evolution: the beyond refers to recent generalizations and extensions of both concepts.) The second aim of this article is to discuss further extensions to the basic SDL models that make them capable of simulating plucking styles, beats in string vibration, sympathetic vibrations, and resonant strings. Such techniques have already been proposed and studied (Jaffe and Smith 1983; Smith 1993; Karjalainen, Vilimiki, and Janosy 1993). Here we discuss them in the context of our recent implementations of plucked-string models.