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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 and...

Control System Problem

Control System Problem

In an open-loop system, such as a basic thermostat, the poles of the transfer function influence the system's response but do not determine its stability. However, when feedback is introduced to form a closed-loop system, such as an advanced thermostat that adjusts heating based on room temperature, stability is governed by the new poles of the closed-loop transfer function.
When forming a closed-loop system, issues can arise if the poles cross into the unstable region, leading to potential...

Conservation of Energy in Control Volume

Conservation of Energy in Control Volume

Consider a turbine operating under steady-flow conditions. The control volume is drawn around the turbine, with fluid entering at one point and exiting at another. The turbine extracts energy from the fluid, which performs mechanical work (shaft work).
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to:

Time-Domain Interpretation of PD Control

Time-Domain Interpretation of PD Control

Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...

Frequency-Domain Interpretation of PD Control

Frequency-Domain Interpretation of PD Control

Proportional-Derivative (PD) controllers are widely used in fan control systems to improve stability and performance. A fan control system can be effectively represented using a Bode plot to illustrate the impact of a PD controller through its transfer function. The Bode plot visually conveys how PD control modifies the fan's response across various frequencies, providing a frequency domain interpretation of the controller's behavior.
The proportional control gain, combined with the system's...

Control Systems

Control Systems

Control systems are everywhere in contemporary society, influencing diverse applications from aerospace to automated manufacturing. These systems can be found naturally within biological processes, such as blood sugar regulation and heart rate adjustment in response to stress, as well as in man-made systems like elevators and automated vehicles. A control system is essentially a network of subsystems and processes that collaboratively convert specific inputs into desired outputs.
At the heart...

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Related Experiment Video

Updated: Jun 18, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

A pseudospectral method for optimal control of open quantum systems.

Jr-Shin Li¹, Justin Ruths, Dionisis Stefanatos

¹Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA. jsli@seas.wustl.edu

The Journal of Chemical Physics

|November 10, 2009

Summary

A new computational method uses pseudospectral approximations for designing optimal pulse sequences in open quantum systems. This approach accurately designs pulse sequences for nuclear magnetic resonance spectroscopy, offering flexibility for various quantum system manipulations.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Last Updated: Jun 18, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum Physics
Computational Chemistry
Spectroscopy

Background:

Optimal pulse design in quantum systems is crucial for precise control.
Open quantum systems present unique challenges due to environmental interactions.
Existing methods for pulse design can be computationally intensive or limited in scope.

Purpose of the Study:

To develop a unified computational method for designing optimal pulse sequences in open quantum systems.
To transform continuous-time optimal control problems into solvable finite-dimensional nonlinear programming problems.
To validate the method's efficacy using nuclear magnetic resonance (NMR) spectroscopy examples.

Main Methods:

Utilizing pseudospectral approximations, specifically the Legendre pseudospectral method.
Reformulating the optimal pulse design as a constrained nonlinear programming problem.
Employing standard numerical optimization suites to solve the transformed problem.

Main Results:

Achieved excellent agreement between computational results and analytical solutions for maximum transfer efficiency in NMR.
Demonstrated the method's capability to handle practical aspects like smoothing discontinuous controls.
Successfully derived minimum-energy and time-optimal controls for open quantum systems.

Conclusions:

The pseudospectral method provides an efficient and accurate approach for optimal pulse design in open quantum systems.
This unified computational framework is broadly applicable to various quantum systems, both open and closed.
The method facilitates the analysis of practical control considerations beyond theoretical optima.