Linear Time-invariant Transfer Functions Research Articles

Model-based optimal and robust control of renewable hydrogen gas production in a fed-batch microbial electrolysis cell

Microbial electrolysis cell (MEC) is a fundamental type of bio-electrochemical system. MEC is a novel and emerging renewable energy technology that is based on biomass. The behavior of the MEC system is highly nonlinear due to the complexity of its dynamics. For the desired optimal production of hydrogen, feedback control of MEC processes is necessary. Due to the novelty of MEC, limited research is available on its control. Studies on linear model-based robust control of MEC processes are missing. In this article, we develop a nonlinear dynamic model for MEC, linearize this model, and calculate a linear time-invariant transfer function. Based on this linearization, a fixed-structure, optimal and robust controller is proposed to achieve a fast-settling time exhibiting no overshoot and having zero steady-state error. The robustness of the developed controller is evaluated for parameter uncertainty, measurement noise, and disturbance rejection. Batch biomass processes are fed only at the start of each process cycle. The output does not follow the desired response when the substrate or biomass is consumed. Then, the error accumulates, and it causes the control effort to increase unboundedly. The existing literature on control of fed-batch MEC processes does not consider this integral windup phenomenon. In this article, we also develop an anti-windup control strategy to eliminate the integral windup error and to avoid any possible instability or destruction. The overall conclusion of our study is that the developed robust controller achieves a faster and more robust response than the existing controllers. We provide an anti-integral windup solution to eliminate windup errors in feedback control of fed-batch MEC processes.

Generating Arm-Swing Trajectories in Real-Time Using a Data-Driven Model for Gait Rehabilitation With Self-Selected Speed.

Gait rehabilitation is often focused on the legs and overlooks the role of the upper limbs. However, a variety of studies have demonstrated the importance of proper arm swing both during healthy walking and during rehabilitation. In this paper, we describe a method for generating proper arm-swing trajectories in real time using only measurements of the angular velocity of a person's thighs, to be used during gait rehabilitation with self-selected walking speed. A data-driven linear time-invariant transfer function is developed, using frequency-response methods, which captures the frequency-dependent magnitude and phase relationship between the thighs' angular velocities and the arm angles (measured at the shoulder, in the sagittal plane), using a data set of 30 healthy adult subjects. We show that the proposed method generates smooth trajectories for both healthy individuals and patients with mild to moderate Parkinson disease. The proposed method can be used in future robotic devices that integrate arm swing in gait rehabilitation of patients with walking impairments to improve the efficacy of their rehabilitation.

On the identifiability of dynamical networks * *Work supported by the Program Science Without Borders, CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnologico, Brazil, and by the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office.

Abstract The identification of networks from measured data has been studied for many years in computer science and statistics. Central to this topic is the identifiability of the network, also called reconstructibility or faithfulness in these communities. This paper examines a class of networks in which the node signals, assumed measurable, are connected by linear time-invariant transfer functions, and in which a noise signal and/or a known excitation signal may or may not be present at each node. The paper discusses the notion of network identifiability. It then proposes a definition that is shown to be efficient for the reconstruction of a dynamical network from measured data. This allows us to exhibit a parametrization of all equivalent network models that are consistent with the data, and thereby to produce a range of sufficient conditions for network identifiability. These conditions (in the form of prior knowledge on the structure of the excitations) show that for the identification of a dynamical network a trade-off exists between excitation from known external signals and excitation from the noise.

Sinusoidal Servocompensator Implementations With Real-Time Requirements and Applications

This brief solves critical long-standing numerical stability issues for solutions to the sinusoidal robust servomechanism problem implemented as discrete-time linear time-invariant transfer functions; new closed-form results for direct form I and direct form II implementations now enable such forms to be used indefinitely in open-loop autonomous, or feedforward, configuration, and also provide difference equation initialization and servocompensator output parameter estimation methods that can be quickly calculated and used to enhance transient system performance and to assess harmonic control components. Simulation and real-time experimental results presented, respectively, exhibit expected concordance and robust effectiveness, and therefore highlight the method whereby such linear configurations can be pragmatically applied to further reduce computational implementation requirements relative to their mathematically intensive nonlinear time-varying counterparts.

A Unified Frequency Domain Model to Study the Effect of Demyelination on Axonal Conduction.

Multiple sclerosis is a disease caused by demyelination of nerve fibers. In order to determine the loss of signal with the percentage of demyelination, we need to develop models that can simulate this effect. Existing time-based models does not provide a method to determine the influences of demyelination based on simulation results. Our goal is to develop a system identification approach to generate a transfer function in the frequency domain. The idea is to create a unified modeling approach for neural action potential propagation along the length of an axon containing number of Nodes of Ranvier (N). A system identification approach has been used to identify a transfer function of the classical Hodgkin–Huxley equations for membrane voltage potential. Using this approach, we model cable properties and signal propagation along the length of the axon with N node myelination. MATLAB/Simulink platform is used to analyze an N node-myelinated neuronal axon. The ability to transfer function in the frequency domain will help reduce effort and will give a much more realistic feel when compared to the classical time-based approach. Once a transfer function is identified, the conduction as a cascade of each linear time invariant system-based transfer function can be modeled. Using this approach, future studies can model the loss of myelin in various parts of nervous system.

A Closed-Loop Control Strategy for Air Conditioning Loads to Participate in Demand Response

Thermostatically controlled loads (TCLs), such as air conditioners (ACs), are important demand response resources—they have a certain heat storage capacity. A change in the operating status of an air conditioner in a small range will not noticeably affect the users’ comfort level. Load control of TCLs is considered to be equivalent to a power plant of the same capacity in effect, and it can significantly reduce the system pressure to peak load shift. The thermodynamic model of air conditioning can be used to study the aggregate power of a number of ACs that respond to the step signal of a temperature set point. This paper analyzes the influence of the parameters of each AC in the group to the indoor temperature and the total load, and derives a simplified control model based on the two order linear time invariant transfer function. Then, the stability of the model and designs its Proportional-Integral-Differential (PID) controller based on the particle swarm optimization (PSO) algorithm is also studied. The case study presented in this paper simulates both scenarios of constant ambient temperature and changing ambient temperature to verify the proposed transfer function model and control strategy can closely track the reference peak load shifting curves. The study also demonstrates minimal changes in the indoor temperature and the users’ comfort level.

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.

Designing time invariant repetitive controllers using frequency raising of periodic coefficient projection algorithm

Many control systems are subject to periodic disturbances. Spacecraft isolation mounts for fine pointing equipment, attempt to isolate from vibrations caused by imbalance in three or four reaction wheels or control moment gyros. Repetitive control (RC) is a type of control that specifically targets the frequencies of a disturbance aiming to achieve zero error in its presence. Typical approaches have difficulty with stability robustness to model errors at high frequency, and are difficult to use with multiple unrelated frequencies. The Matched Basis Function Repetitive Control (MBFRC) developed here specifically addresses both difficulties. It uses the projection algorithm from adaptive control to determine the error frequency components of interest. This results in linear equations with periodic coefficients. By using the frequency raising method, it is shown that there is an equivalent linear time invariant transfer function model for the repetitive control law. This process designs pole-zero configurations for RC compensators that would be very hard to create by other means.

A hybrid metric‐conceptual (HMC) model for monthly riverflow prediction in the semi‐arid Volta Basin of West Africa

Data‐based mechanistic modelling techniques have been applied to catchment monthly runoff, potential evaporation and rainfall time series to model monthly catchment runoff at selected gauging sites in the Volta Basin of West Africa. The aim of the study was to obtain a modelling framework that not only accounts for the rainfall‐runoff non‐linearity in the basin and provides acceptable predictions of the monthly catchment runoff for the sub‐basins studied, but also reveals the necessary insights for a plausible interpretation of the rainfall‐runoff mechanism in the basin. The rainfall‐runoff process was considered in two stages – a nonlinear transformation from rainfall to effective rainfall and then a linear transformation from effective rainfall to runoff. First a linear time varying, state dependent parameter (LTV‐SDP) transfer function model was applied to the monthly rainfall‐runoff calibration series of each sub‐basin to determine the form of the rainfall‐effective rainfall non‐linear transformation. The observed series (runoff or rainfall) that was significantly related to effective rainfall was then identified. Next, the functional form of this relationship was established and used to fit linear time invariant (LTI) transfer function models relating monthly runoff to monthly effective rainfall and potential evaporation. The best estimate of the monthly effective rainfall from the nonlinear modelling was obtained from the product of monthly rainfall and a fractional power of monthly runoff – the runoff acting as surrogate for catchment wetness. Since this form of effective rainfall cannot be used for simulation in validation mode (as the runoff series is unknown then), a non‐linear rainfall filter used in the Identification of unit Hydrographs And Component flows from Rainfall, Evaporation and Streamflow data (IHACRES) application was used to model effective rainfall in this mode. The study showed that monthly catchment runoff in the basin can be decomposed into two parallel flows, an instantaneous (within a month) and a slower (with one month delay) flow components. These results suggest that baseflow contribution to streamflow is insignificant in the Volta Basin.

Quantifying Cortical Activity During General Anesthesia Using Wavelet Analysis

This paper reports on a novel method for quantifying the cortical activity of a patient during general anesthesia as a surrogate measure of the patient's level of consciousness. The proposed technique is based on the analysis of a single-channel (frontal) electroencephalogram (EEG) signal using stationary wavelet transform (SWT). The wavelet coefficients calculated from the EEG are pooled into a statistical representation, which is then compared to two well-defined states: the awake state with normal EEG activity, and the isoelectric state with maximal cortical depression. The resulting index, referred to as the wavelet-based anesthetic value for central nervous system monitoring (WAV(CNS)), quantifies the depth of consciousness between these two extremes. To validate the proposed technique, we present a clinical study which explores the advantages of the WAV(CNS) in comparison with the BIS monitor (Aspect Medical Systems, MA), currently a reference in consciousness monitoring. Results show that the WAV(CNS) and BIS are well correlated (r = 0.969) during periods of steady-state despite fundamental algorithmic differences. However, in terms of dynamic behavior, the WAV(CNS) offers faster tracking of transitory changes at induction and emergence, with an average lead of 15-30 s. Furthermore, and conversely to the BIS, the WAV(CNS) regains its preinduction baseline value when patients are responding to verbal command after emergence from anesthesia. We conclude that the proposed analysis technique is an attractive alternative to BIS monitoring. In addition, we show that the WAV(CNS) dynamics can be modeled as a linear time invariant transfer function. This index is, therefore, well suited for use as a feedback sensor in advisory systems, closed-loop control schemes, and for the identification of the pharmacodynamic models of anesthetic drugs.

Active suspension for single wheel station of off‐road track vehicle

AbstractThe main objective of ground vehicle suspension systems is to isolate a vehicle body (sprung mass) from road irregularities in order to maximize passenger ride comfort, control the attitude of the vehicle on the road, and retain continuous road–wheel contact in order to provide vehicle holding quality. An appropriate active suspension design must resolve the inherent tradeoffs between ride comfort, road holding quality, and suspension travel. In this study, a robust controller for the active suspension of an off‐road, high‐mobility tracked vehicle is designed, for the first time, using quantitative feedback theory (QFT). A simulation model of a single suspension unit of the M‐113 armored personnel carrier vehicle was used to achieve a proper active suspension design. Two measured states of the 3‐degrees‐of‐freedom mathematical model were used as feedback signals in a cascaded SISO control system. The nonlinear dynamics of the tracked vehicle suspension unit was represented as a set of linear time invariant (LTI) transfer functions, which were identified with the Fourier integral method. Computer simulations of the vehicle with passive and active suspension systems over different terrain profiles are provided. A significant reduction of the vertical accelerations induced to the sprung mass (e.g., ride comfort improvement) was achieved while keeping the road‐arm between suspension travel limits (e.g., handling quality). Copyright © 2001 John Wiley & Sons, Ltd.

Active Control for Single Wheel Suspension of Off-Road Track Vehicle

The main objective of ground vehicles suspension system is to isolate a vehicle body (sprung mass) from road irregularities in order to maximize the passenger ride comfort and produce continuous road-wheel contact in order to provide vehicle holding quality. An appropriate active suspension design must resolve the inherent tradeoffs between ride comfort, road holding quality and suspension travel. In this study a robust controller for the active suspension of an off-road, high-mobility tracked vehicle is designed using Quantitative Feedback Theory (QFT). A simulation model of a single suspension unit of the armored personnel carrier vehicle M-113 was used to get a proper active suspension design. Two measured states of the 3 degrees-of-freedom mathematical model were used as feedback signals in a cascaded SISO control system. The nonlinear dynamics of the tracked vehicle suspension unit was represented as a set of linear time invariant (LTI) transfer functions which were identified with the Fourier integral method. Computer simulations of the vehicle with passive and active suspension systems over different terrain profiles are provided. Significant reduction of the vertical accelerations induced to the sprung mass (i.e. ride comfort improvement) was achieved while keeping the road-arm between suspension travel limits (i.e. handling quality). Hence a potential important improvement in cross-country mobility for a wide range of ride conditions could possibly be achieved by application of linear robust control for active suspension design for off-road tracked vehicles.