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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...

Effects of feedback

Effects of feedback

Feedback in control systems plays a critical role in shaping various operational parameters, extending beyond simple error reduction to influence stability, bandwidth, gain, impedance, and sensitivity. Understanding these effects requires examining a basic feedback system characterized by defined input, output, error, and feedback signals.
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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...

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.
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Linear Momentum in Control Volume

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Time and frequency -Domain Interpretation of PI Control

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Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
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Quantum Fokker-Planck Master Equation for Continuous Feedback Control.

Björn Annby-Andersson¹, Faraj Bakhshinezhad¹, Debankur Bhattacharyya²

¹Physics Department and NanoLund, Lund University, Box 118, 22100 Lund, Sweden.

Physical Review Letters

|August 12, 2022

Summary

This summary is machine-generated.

We developed a new framework for quantum measurement and feedback control, enabling analysis of both linear and nonlinear protocols. This formalism simplifies complex quantum dynamics for applications in quantum technologies and thermodynamics.

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Area of Science:

Quantum physics
Quantum information science
Quantum thermodynamics

Background:

Measurement and feedback control are fundamental in quantum science and technology.
Existing theoretical models for quantum feedback are often limited to linear protocols or require complex numerical solutions.
Quantum information-to-work conversion is a key area in quantum thermodynamics.

Purpose of the Study:

To present a novel formalism for continuous quantum measurement and feedback control.
To extend the description of feedback control to include nonlinear protocols.
To provide a framework for analyzing quantum systems and detectors with finite bandwidth.

Main Methods:

Development of a quantum Fokker-Planck master equation for joint system-detector dynamics.
Derivation of a Markovian master equation for system dynamics under fast measurements.
Analytical treatment of quantum feedback control protocols.

Main Results:

A unified formalism for continuous quantum measurement and feedback (linear and nonlinear).
A quantum Fokker-Planck master equation describing system and detector dynamics.
An analytical Markovian master equation for system dynamics in the fast measurement limit.
Investigation of two basic information engines (quantum and classical) using the new formalism.

Conclusions:

The presented formalism offers a powerful tool for analyzing quantum feedback control beyond linear approximations.
The derived master equations facilitate analytical and numerical studies of quantum systems under continuous measurement.
This work advances the understanding of quantum information processing and thermodynamic engines.