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Related Concept Videos

State Space Representation01:27

State Space Representation

645
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
645
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

387
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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State Space to Transfer Function01:21

State Space to Transfer Function

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
642
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

84
In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
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Transfer Function to State Space01:23

Transfer Function to State Space

892
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
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Linear time-invariant Systems01:23

Linear time-invariant Systems

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
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Related Experiment Video

Updated: Mar 11, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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Fitting state-space integral projection models to size-structured time series data to estimate unknown parameters.

J Wilson White1, Kerry J Nickols2, Daniel Malone3

  • 1Department of Biology and Marine Biology, University of North Carolina Wilmington, Wilmington, North Carolina, 28043, USA.

Ecological Applications : a Publication of the Ecological Society of America
|December 2, 2016
PubMed
Summary

A new Bayesian state-space integral projection model (SSIPM) accurately estimates population dynamics from size-structured survey data, even without individual-level demographic rates. This method improves local-scale monitoring for species like rockfish.

Keywords:
Sebastes carnatusSebastes mystinusfishing rateintegral projection modelparticle filterstate-space model

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Area of Science:

  • Ecology
  • Population Dynamics
  • Quantitative Biology

Background:

  • Integral projection models (IPMs) offer advantages over traditional matrix models for size-structured populations.
  • Parameterizing IPMs typically requires individual-scale demographic data, which is often unavailable.
  • Existing methods struggle with process and measurement error in time-series data.

Purpose of the Study:

  • To develop and test an alternative approach for estimating demographic parameters using size-structured survey data.
  • To introduce a Bayesian state-space IPM (SSIPM) that accounts for process and measurement error.
  • To demonstrate the SSIPM's utility with real-world fish population data.

Main Methods:

  • Developed a Bayesian state-space integral projection model (SSIPM).
  • Utilized time-series of size-structured survey data.
  • Tested the SSIPM with simulated data and applied it to nine years of rockfish survey data.

Main Results:

  • The SSIPM accurately estimated demographic parameters from simulated data.
  • The model provided reasonable fits to empirical data for blue and gopher rockfish.
  • Estimated fishing rates were higher than prior stock assessment estimates, highlighting local data value.

Conclusions:

  • The SSIPM provides a robust method for estimating demographic parameters from readily available survey data.
  • This approach enhances the value of local-scale monitoring for population dynamics.
  • The study outlines key decisions for SSIPM implementation in ecological research.