Feedback Loop Structure Research Articles

Large-Signal Modeling and Experimental Design Automation of Self-Isolated Harmonic Oscillator for Pulling Effect Reduction

A class of self-isolated harmonic oscillator (SIHO) with a feedback-loop structure is able to significantly reduce the pulling effect without involving extra circuit complexity such as a buffer amplifier. In the first part of this paper, the operation principle of the SIHO is theoretically studied through equivalent circuit models and X-parameter techniques. Closed-form expressions are derived to represent the respective linear and nonlinear equivalent impedances of SIHO subnetworks perturbed by varied load and injected signals. A conventional feedback-loop oscillator structure delivering the fundamental tone is used for comparative study. Such a modeling technique reveals the physical principle and behavior parameters that have an impact on the pulling effect. The experimental verification of the SIHO operation principle and modeling is presented as the second part of this paper. To this end, a harmonic measurement and design system is proposed and implemented for the design of an exemplary SIHO, which delivers a 4-GHz signal with 16.6-dBm power, 28% dc-RF efficiency, and −136.5-dBc/Hz phase noise at 1-MHz offset. The design process does not rely on circuit simulation software packages or a prior knowledge of the large-signal model of transistors, thus demonstrating the concept of a model-free nonlinear circuit design automation based on the experimental optimization. The SIHO circuit model is validated with the measured X-parameters of its nonlinear subnetwork.

Robust track following in Hard Disk Drives with time delays: An infinite dimensional approach

Due to the existence of various sources of delays, the dynamical model of HDD (Hard Disk Drive) servo systems is actually infinite dimensional, although most of the existing algorithms simplified the model with Padé expansions or other finite dimensional approximations. In this paper, a robust loop shaping algorithm is developed for high accuracy track following of HDD servo systems with delays by using an H∞ synthesis approach for infinite dimensional systems. The H∞ controller is derived with a structure of an internal feedback loop including an FIR (Finite Impulse Response) filter and a first order IIR (Infinite Impulse Response) filter, which facilitates stable implementations. Digital implementation of the proposed control structure is further investigated by incorporating H∞ based sampled-data FIR filter design and approximation. Comparisons to other robust control methods are given, and the advantages of the proposed algorithm are demonstrated in terms of tracking TPI (Track-per-Inch) capability and transient responses using HDD factory measurement data.

A low-power low-noise amplifier with fully self-biased feedback loop structure for neural recording

This paper presents a fully self-biased, low-power LNA for neural recordings. Due to the capacitor coupling and low-supply voltage in LNA, the appropriate dc bias voltages for saturating the input transistors NMOS and PMOS of LNA should be separately provided. This paper focuses on the effects of different feedback ways to obtain input dc bias voltage, and proposes a completely self-biased structure to obtain the bias voltage directly from the inner nodes of the circuit. This connected way avoids using extra dc biasing circuit totally, saves capacitor area effectively and reduces the high-pass corner frequency greatly. Furthermore, the proposed method eliminates the likelihood for initial DC latch-up in the traditional way, making the circuit more stable. Simulated in a 0.18-µm CMOS process, the LNA consumes 1.2 µA from a 0.6 V supply, and achieves an input referred noise of 4.98 µVrms (1–10 kHz), corresponding to a noise efficiency factor of 2.13. Simulated CMRR and THD exceed 77 dB and 75 dB, separately.

Structural Loop Analysis of Complex Ecological Systems

Ecosystems are complex and dynamic making them challenging to understand. We urgently need to assess human impacts on ecosystems which cause changes in structural feedbacks producing large, hard to reverse changes in state and functioning. System dynamics has proven to be a useful and versatile methodology for modelling complex systems given the comparative ease with which feedback loops can be modelled. However, a common issue arises when models become too large and structurally complex to understand the causal drivers of system behaviour. There is a need for an intermediate level of analysis capable of identifying causal driving structures and dynamics, regardless of model complexity. This study investigates Loop Eigenvalue Elasticity Analysis, a structural analysis technique commonly used in business and economic system dynamics models, and evaluates its utility for identifying feedback loop structures responsible for behavioural changes in complex ecological systems. The approach is demonstrated by analysing a simple lake system model that has been extensively studied in the past for its capacity to undertake critical transitions between alternative stable states. We show how the dominance of feedback loops can be tracked through time building influence over the system's behaviour decades prior to the actual collapse in the system. We discuss our findings in the context of studying complex ecosystems and socio-ecological systems.

How to make better energy policy decisions? The stock and flow perspective

Energy policy issues and challenges abound. This paper addresses the energy policy as a complex, dynamic task whereby the planners and decision makers manage 'stocks' of limited resources. The stock and flow perspective provides a unique and powerful set of tools to better equip the policy decision makers to take on these challenges. By making use of various tools and techniques of system dynamics methodology such as causal loop diagrams, stock and flow diagrams, mathematical formulations, and structure-behaviour graphs of various energy system processes, it is shown how the stock and flow perspective can effectively address energy policy issues. With an understanding of the physics of underlying feedback loop structures of an energy system, and structure-behaviour graphs of various energy system processes including energy demand, policy incentives and inter-fuel substitution mechanism, and energy supply, the energy policy decision makers are expected to develop insights and make better decisions.

System dynamics archetypes for capacity management of energy systems

Energy systems are increasingly becoming more and more complex due to dynamic interactions of various supply-demand related variables in the systems. These variable interactions and the underlying feedback loop structures contribute to the realized overall system behavior. As a result, managing the capacity of energy systems is a complex task. The purpose of this paper is to present typical system dynamics archetypes for capacity management of energy systems. First, two archetypes are identified and modelled based on causal loop analysis: (i) limit to growth, and (ii) growth and underinvestment. The archetypes help the analyst to effectively visualize the entire system and forecast the reaction of the system. Second, stock flow analysis models are then presented. Third and finally, “what-if” simulation experiments are conducted to illustrate the key effects of limited capacity growth as well as growth with and underinvestment in the presence of time delays. The study demonstrates the importance of taking a systems thinking approach when managing the capacity of complex energy systems. Feedback loops and time delays must be considered seriously. By so doing, unwanted and unpredictable system fluctuations can be avoided when making capacity adjustment decisions.

Performance of Homeostatic Controller Motifs Dealing with Perturbations of Rapid Growth and Depletion.

An essential property of life is that cells and organisms have the ability to protect themselves against external disturbances/attacks by using homeostatic mechanisms. These defending mechanisms are based on negative feedback regulation and often contain additional features, such as integral control, where the integrated error between a controlled variable and its set-point is used to achieve homeostasis. Although the concept of integral control has its origin in industrial processes, recent findings suggest that biological systems are also capable of showing integral control. We recently described a basic set of negative feedback structures (controller motifs) where robust homeostasis is achieved against different but constant perturbations. As many perturbations in biology, such as infections, increase rapidly over time, we investigated how the different controller motifs equipped with different implementations of integral control perform in relation to rapidly changing perturbations, including exponential and hyperbolic changes. The findings show that the construction of an optimum biochemical controller design for time-dependent perturbations requires a certain match between the structure of the negative feedback loop, its signaling kinetics, and the kinetics of how integral control is implemented within the negative feedback loop.

Many roads to symmetry breaking: molecular mechanisms and theoretical models of yeast cell polarity.

Mathematical modeling has been instrumental in identifying common principles of cell polarity across diverse systems. These principles include positive feedback loops that are required to destabilize a spatially uniform state of the cell. The conserved small G-protein Cdc42 is a master regulator of eukaryotic cellular polarization. Here we discuss recent developments in studies of Cdc42 polarization in budding and fission yeasts and demonstrate that models describing symmetry-breaking polarization can be classified into six minimal classes based on the structure of positive feedback loops that activate and localize Cdc42. Owing to their generic system-independent nature, these model classes are also likely to be relevant for the G-protein–based symmetry-breaking systems of higher eukaryotes. We review experimental evidence pro et contra different theoretically plausible models and conclude that several parallel and non–mutually exclusive mechanisms are likely involved in cellular polarization of yeasts. This potential redundancy needs to be taken into consideration when interpreting the results of recent cell-rewiring studies.

Ultrahigh resolution fiber optic strain sensing system for crustal deformation observation

Due to the advantages of high resolution, low cost, small size, easy deployment and capability of multiplexed sensing, the recent developed optical fiber grating sensors provide powerful tools for crustal deformation monitoring. This paper reviews the development of several types of fiber-optic sensors with ultrahigh resolution in quasi-static domain. The fiber Bragg grating based Fabry-Perot interferometers and the -phase-shifted fiber Bragg gratings which are used as sensing components in the high resolution sensors are introduced. Some novel techniques such as interrogating the sensing components with intensity modulation sideband, dual feedback-loop structure for high bandwidth/large measurement range sensing, and the time-domain multiplexing of the high resolution quasi-static strain sensor are discussed in detail. Each sensing scheme with both operation process and achieved performances are given. The implementation of fiber grating sensors for in-situ measurement of crustal deformation and the results are also introduced. Compared with the traditional methods used in crustal deformation observation, the high-performance fiber optic strain sensors mentioned in the paper shows great potentials in providing wider measurement approaches in geophysical researches.

Properties of Boolean dynamics by node classification using feedback loops in a network.

BackgroundBiological networks keep their functions robust against perturbations. Many previous studies through simulations or experiments have shown that feedback loop (FBL) structures play an important role in controlling the network robustness without fully explaining how they do it. Hence, there is a pressing need to more rigorously analyze the influence of FBL structures on network robustness.ResultsIn this paper, I propose a novel node classification notion based on the FBL structures involved. More specifically, I classify a node as a no-FBL-in-upstream (NFU) or no-FBL-in-downstream (NFD) node if no feedback loop is involved with any upstream or downstream path of the node, respectively. Based on those definitions, I first prove that every NFU node is eventually frozen in Boolean dynamics. Thus, NFU nodes converge to a fixed value determined by the upstream source nodes. Second, I prove that a network is robust against an arbitrary state perturbation subject to a non-source NFD node. This implies that a network state eventually sustains the attractor despite a perturbation subject to a non-source NFD node. Inspired by this result, I further propose a perturbation-sustainable probability that indicates how likely a perturbation effect is to be sustained through propagations. I show that genes with a high perturbation-sustainable probability are likely to be essential, disease, and drug-target genes in large human signaling networks.ConclusionTaken together, these results will promote understanding of the effects of FBL on network robustness in a more rigorous manner.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0322-z) contains supplementary material, which is available to authorized users.

Shock Diffusion: Does Inter-Sectoral Network Structure Matter?

This paper introduces the concept of diffusion of shocks in a macroeconomic network consisting of inter-sectoral production linkages. I show that if sectors have different reaction horizons it would lead to diffusion of shocks through the network over time which prevents the inter-sectoral linkages to form the feedback loop structure essential to generate aggregate volatility. This result is different from other recent papers which have single period model with contemporaneous production linkages between different sectors thus generating sectoral shock amplification as one sector reacts to another contemporaneously resulting in bigger aggregate fluctuations. In contrast if sectors have different production horizons due to varying complexity of their production process or supply chain, it would break down the feedback architecture present in single period models. I further show that if the diffusion rate is varied for different sectors, the contribution of network structure to aggregate volatility can be insignificant. Also, it is no longer sufficient to characterize this contribution of inter-sectoral production network to aggregate volatility by just looking at input-output matrix or its summary statistics like degree distribution. The paper thus highlights the stark difference between the study of financial and inter-sectoral production networks because of the possibility of contemporaneous amplification and hence cascades in the case of financial networks. In the end, I propose lead time indicator as a possible proxy for measuring differential sectoral diffusion rates.

Moving horizon approach of integrating scheduling and control for sequential batch processes

Online integration of scheduling and control is crucial to cope with process uncertainties. We propose a new online integrated method for sequential batch processes, where the integrated problem is solved to determine controller references rather than process inputs. Under a two‐level feedback loop structure, the integrated problem is solved in a frequency lower than that of the control loops. To achieve the goal of computational efficiency and rescheduling stability, a moving horizon approach is developed. A reduced integrated problem in a resolving horizon is formulated, which can be solved efficiently online. Solving the reduced problem only changes a small part of the initial solution, guaranteeing rescheduling stability. The integrated method is demonstrated in a simulated case study. Under uncertainties of the control system disruption and the processing unit breakdown, the integrated method prevents a large loss in the production profit compared with the simple shifted rescheduling solution. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1654–1671, 2014

Interaction of NMDA receptor and pacemaking mechanisms in the midbrain dopaminergic neuron.

Dopamine neurotransmission has been found to play a role in addictive behavior and is altered in psychiatric disorders. Dopaminergic (DA) neurons display two functionally distinct modes of electrophysiological activity: low- and high-frequency firing. A puzzling feature of the DA neuron is the following combination of its responses: N-methyl-D-aspartate receptor (NMDAR) activation evokes high-frequency firing, whereas other tonic excitatory stimuli (-amino-3-hydroxyl-5-methyl-4-isoxazolepropionate receptor (AMPAR) activation or applied depolarization) block firing instead. We suggest a new computational model that reproduces this combination of responses and explains recent experimental data. Namely, somatic NMDAR stimulation evokes high-frequency firing and is more effective than distal dendritic stimulation. We further reduce the model to a single compartment and analyze the mechanism of the distinct high-frequency response to NMDAR activation vs. other stimuli. Standard nullcline analysis shows that the mechanism is based on a decrease in the amplitude of calcium oscillations. The analysis confirms that the nonlinear voltage dependence provided by the magnesium block of the NMDAR determine its capacity to elevate the firing frequency. We further predict that the moderate slope of the voltage dependence plays the central role in the frequency elevation. Additionally, we suggest a repolarizing current that sustains calcium-independent firing or firing in the absence of calcium-dependent repolarizing currents. We predict that the ether–a-go-go current (ERG), which has been observed in the DA neuron, is the best fit for this critical role. We show that a calcium-dependent and a calcium-independent oscillatory mechanisms form a structure of interlocked negative feedback loops in the DA neuron. The structure connects research of DA neuron firing with circadian biology and determines common minimal models for investigation of robustness of oscillations, which is critical for normal function of both systems.

A coherent feedforward loop design principle to sustain robustness of biological networks

Many studies have investigated the relationship between structural properties and dynamic behaviors in biological networks. In particular, feedback loop (FBL) and feedforward loop (FFL) structures have received a great deal of attention. One interesting and common property of FBL and FFL structures is their coherency of coupling. However, the role of coherent FFLs in relation to network robustness is not fully known, whereas that of coherent FBLs has been well established. To establish that coherent FFLs are abundant in biological networks, we examined gene regulatory and signaling networks and found that FFLs are ubiquitous, and are in a coherently coupled form. This result was also observed in the species-based signaling networks that are integrated from KEGG database. By using a random Boolean network model, we demonstrated that these coherent FFLs can improve network robustness against update-rule perturbations. In particular, we found that coherent FFLs increase robustness because these structures induce downstream nodes to be robust against update-rule perturbations. Therefore, coherent FFLs can be considered as a design principle of human signaling networks that improve network robustness against update-rule perturbations.

Feedback loop gains and system behavior (1996)

Kampmann C. E. (1996) Feedback loop gains and system behaviorProceedings of the 1996 International System Dynamics Conference. System Dynamics Society, Boston, MA, USAIn the past two decades, there has been a steady growth of analytical tools that can help the system dynamicist understand and test the behavior of large models. Without such tools, we must resort to simulation experiments and intuition developed from simple, low‐order, systems. While this traditional approach has served us well, there is always the danger that we overlook important mechanisms in larger systems or falsely attribute behavior patterns to particular structures.Among these new analytical tools, eigenvalue elasticity analysis (EEA) has received the most attention, perhaps because it rests on a consistent and comprehensive theoretical foundation. The approach involves decomposing system outcomes into characteristic behavior modes, each characterized by an eigenvalue of the linearized system matrix, and then examining how each eigenvalue or behavior mode is affected by small changes in the parameters of the system. The eigenvalue elasticity of a parameter change is a dimensionless number, defined as the fractional change in the eigenvalue resulting from a fractional infinitesimal change in that parameter. Parameters or structural links or loops in the model that have large elasticities are then interpreted as playing a dominant role in that behavior mode.EEA was first used by Nathan Forrester in his doctoral dissertation from 1982. However, it did not receive much attention in the field until the 1996 International System Dynamics Conference, where Christian Kampmann presented a rigorous analysis of the topology of feedback loop structures and how eigenvalue elasticities are related to the strength of individual feedback loops. Since then, an entire strand of research has been devoted to the development and application of EEA, where Kampmann's conference paper remains a seminal reference. Yet until now, the paper has never been published, and researchers have had to rely on private circulation of various drafts of the paper. With this archival publication, we wish to remedy this deficiency in the hope that the work will inspire others to continue developing EEA and further the high standards of analytical rigor that Kampmann's paper represents.AbstractLinking feedback loops and system behavior is part of the foundation of system dynamics, yet the lack of formal tools has so far prevented a systematic application of the concept, except for very simple systems. Having such tools at their disposal would be a great help to analysts in understanding large, complicated simulation models. The paper applies tools from graph theory formally linking individual feedback loop strengths to the system eigenvalues.The significance of a link or a loop gain and an eigenvalue can be expressed in the eigenvalue elasticity, i.e., the relative change of an eigenvalue resulting from a relative change in the gain. The elasticities of individual links and loops may be found through simple matrix operations on the linearized system.Even though the number of feedback loops can grow rapidly with system size, reaching astronomical proportions even for modest systems, a central result of the paper is that one may restrict attention to an independent subset which typically grows only linearly and at most as the square of system size. An algorithm for finding an independent loop set is presented, along with suggestions for how to augment it to select loops with large elasticities.For illustration, the method is applied to a well‐known system: the simple long‐wave model. Because this model exhibits highly nonlinear behavior, it sheds light on the usefulness of linear methods to nonlinear system. The analysis leads to a more thorough and deeper understanding of the system and sheds new light on conventional wisdom regarding the role of many of the system's feedback loops. Copyright © 2012 System Dynamics Society

A mechanism for robust circadian timekeeping via stoichiometric balance

Circadian (∼24 h) timekeeping is essential for the lives of many organisms. To understand the biochemical mechanisms of this timekeeping, we have developed a detailed mathematical model of the mammalian circadian clock. Our model can accurately predict diverse experimental data including the phenotypes of mutations or knockdown of clock genes as well as the time courses and relative expression of clock transcripts and proteins. Using this model, we show how a universal motif of circadian timekeeping, where repressors tightly bind activators rather than directly binding to DNA, can generate oscillations when activators and repressors are in stoichiometric balance. Furthermore, we find that an additional slow negative feedback loop preserves this stoichiometric balance and maintains timekeeping with a fixed period. The role of this mechanism in generating robust rhythms is validated by analysis of a simple and general model and a previous model of the Drosophila circadian clock. We propose a double-negative feedback loop design for biological clocks whose period needs to be tightly regulated even with large changes in gene dosage.

A Structural Model of Stress, Motivation, and Academic Performance in Medical Students

ObjectiveThe purpose of the present study was 1) to identify factors that may influence academic stress in medical students and 2) to investigate the causal relationships among these variables with path analysis.MethodsOne hundred sixty medical students participated in the present study. Psychological parameters were assessed with the Medical Stress Scale, Minnesota Multiphasic Personality Inventory, Hamilton Depression Scale, Beck Depression Inventory, and Academic Motivation Scale. Linear regression and path analysis were used to examine the relationships among variables.ResultsSignificant correlations were noted between several factors and Medical Stress scores. Specifically, Hamilton Depression Scale scores (β=0.26, p=0.03) and amotivation (β=0.20, p=0.01) and extrinsically identified regulation (β=0.27, p<0.01) response categories on the Academic Motivation Scale had independent and significant influences on Medical Stress Scale scores. A path analysis model indicated that stress, motivation, and academic performance formed a triangular feedback loop. Moreover, depression was associated with both stress and motivation, and personality was associated with motivation.ConclusionThe triangular feedback-loop structure in the present study indicated that actions that promote motivation benefit from interventions against stress and depression. Moreover, stress management increases motivation in students. Therefore, strategies designed to reduce academic pressures in medical students should consider these factors. Additional studies should focus on the relationship between motivation and depression.

The effects of feedback loops on disease comorbidity in human signaling networks

In general, diseases are more likely to be comorbid if they share associated genes or molecular interactions in a cellular process. However, there are still a number of pairs of diseases which show relatively high comorbidity but do not share any associated genes or interactions. This observation raises the need for a novel factor which can explain the underlying mechanism of comorbidity. We here consider a feedback loop (FBL) structure ubiquitously found in the human cell signaling network as a key motif to explain the comorbidity phenomenon, since it is well known to have effects on network dynamics. For every pair of diseases, we examined its comorbidity and length of all FBLs involved by the disease-associated genes in the human cell signaling network. We found that there is a negative relationship between comorbidity and length of involved FBLs. This indicates that a disease pair is more likely to comorbid if they are connected with FBLs of shorter length. We additionally showed that such a negative relationship is more obvious when the number of positive involved FBLs is larger than that of negative involved FBLs. Moreover, we observed that the negative relationship between comorbidity and length of involved FBLs holds especially for disease pairs that do not share any disease-associated genes. Finally, we proved all these results through intensive simulations, based on a Boolean network model. kwonyk@ulsan.ac.kr Supplementary data are available at BioInformatics online.

Inferring cell cycle feedback regulation from gene expression data

Feedback control is an important regulatory process in biological systems, which confers robustness against external and internal disturbances. Genes involved in feedback structures are therefore likely to have a major role in regulating cellular processes. Here we rely on a dynamic Bayesian network approach to identify feedback loops in cell cycle regulation. We analyzed the transcriptional profile of the cell cycle in HeLa cancer cells and identified a feedback loop structure composed of 10 genes. In silico analyses showed that these genes hold important roles in system’s dynamics. The results of published experimental assays confirmed the central role of 8 of the identified feedback loop genes in cell cycle regulation. In conclusion, we provide a novel approach to identify critical genes for the dynamics of biological processes. This may lead to the identification of therapeutic targets in diseases that involve perturbations of these dynamics.

Qualitative control of periodic solutions in piecewise affine models of genetic networks

Piecewise affine (PWA) systems are often used to model gene regulatory networks. In this paper we elaborate on previous work about control problems for this class of models, using also some recent results guaranteeing the existence and uniqueness of limit cycles, based solely on a discrete abstraction of the system and its interaction structure. Our aim is to control the transition graph of the PWA system to obtain an oscillatory behaviour, which is indeed of primary functional importance in numerous biological networks; we show how it is possible to control the appearance or disappearance of a unique stable limit cycle by qualitative action on the degradation rates of the PWA system, both by static and dynamic feedback, i.e. the adequate coupling of a controlling subnetwork. This is illustrated on two classical gene network modules, having the structure of mixed feedback loops.