Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Linear Approximation in Time Domain

Linear Approximation in Time Domain

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, the...

Feedback control systems

Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...

Open and closed-loop control systems

Open and closed-loop control systems

Control systems are foundational elements in automation and engineering. They are broadly categorized into open-loop and closed-loop systems. These classifications hinge on the presence or absence of feedback mechanisms, significantly influencing the system's performance, complexity, and application.
An open-loop control system operates without feedback from the output. It consists of two primary elements: the controller and the controlled process. The controller receives an input signal and...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

Calibration Curves: Linear Least Squares

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...

Linearization and Approximation

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Discrete-time model of an adaptive optics systems.

Journal of the Optical Society of America. A, Optics, image science, and vision·2007

Same author

Minimum variance control structure for adaptive optics systems.

Journal of the Optical Society of America. A, Optics, image science, and vision·2006

Same author

Fast calibration of high-order adaptive optics systems.

Journal of the Optical Society of America. A, Optics, image science, and vision·2004

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 26, 2026

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

Linear-quadratic-Gaussian control for adaptive optics systems using a hybrid model.

Douglas P Looze¹

¹Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA 01003, USA. looze@ecs.umass.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|December 26, 2008

Summary

This study introduces an improved adaptive optics (AO) controller using a linear-quadratic-Gaussian (LQG) design. The new method enhances AO system performance by simplifying calculations for complex dynamics.

More Related Videos

Bringing the Visible Universe into Focus with Robo-AO

Bringing the Visible Universe into Focus with Robo-AO

Published on: February 12, 2013

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Related Experiment Videos

Last Updated: Jun 26, 2026

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

Bringing the Visible Universe into Focus with Robo-AO

Bringing the Visible Universe into Focus with Robo-AO

Published on: February 12, 2013

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

Optics and Photonics
Control Systems Engineering
Astronomy Instrumentation

Background:

Adaptive optics (AO) systems are crucial for high-resolution imaging by correcting wavefront distortions.
Existing AO control designs often face challenges with computational complexity and system dynamics.
Accurate modeling of deformable mirror dynamics, wavefront sensing, and signal processing is essential for effective AO control.

Purpose of the Study:

To develop a novel linear-quadratic-Gaussian (LQG) controller for adaptive optics systems.
To design the controller based on an equivalent discrete-time model that accurately represents system dynamics.
To reduce the computational burden associated with controller design by leveraging the discrete-time model structure.

Main Methods:

Formulated a discrete-time model of the AO system, including deformable mirror dynamics, asynchronous wavefront sensing, and zero-order hold operation.
Integrated a continuous-time model of the incident wavefront into the discrete-time framework.
Reduced the dimensions of the Riccati equations required for the LQG controller design by exploiting the discrete-time model's structure.

Main Results:

The proposed LQG design effectively models key components of an AO system.
Significant reduction in the computational complexity of solving Riccati equations was achieved.
The developed LQG controller demonstrated improved performance of the AO system under various operating conditions.

Conclusions:

The LQG design based on the equivalent discrete-time model offers a computationally efficient approach for AO systems.
This method enhances the performance and robustness of adaptive optics control.
The findings provide a valuable framework for advancing AO system design and implementation in demanding applications.