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Related Concept Videos

Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Time-Domain Interpretation of PD Control01:07

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...
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Transient and Steady-state Response01:24

Transient and Steady-state Response

In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state response.
Control Systems01:10

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...
Control System Problem01:21

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...

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Interactive and Visualized Online Experimentation System for Engineering Education and Research
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Published on: November 24, 2021

Stabilizing control for a class of delay unstable processes.

See Chek Lee1, Qing-Guo Wang, Le Binh Nguyen

  • 1Department of Electrical and Computer Engineering, National University of Singapore, 119260 Singapore, Singapore. seechek@nus.edu.sg

ISA Transactions
|April 27, 2010
PubMed
Summary
This summary is machine-generated.

This study details stabilizing unstable first-order plus time-delay processes using simple controllers. Explicit conditions and computational methods for controller parameters are provided with examples.

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Area of Science:

  • Control Engineering
  • Process Systems Engineering

Background:

  • First-order plus time-delay (FOPDT) processes are common in industrial applications.
  • Stabilizing these systems, especially when unstable and possessing a zero, presents significant control challenges.

Purpose of the Study:

  • To investigate the detailed stabilization of unstable FOPDT processes with a zero.
  • To develop explicit conditions for achieving system stability.
  • To present computational methods for designing stabilizing controllers.

Main Methods:

  • Analytical investigation of system dynamics.
  • Derivation of explicit mathematical conditions for stabilizability.
  • Development and application of computational algorithms for controller parameter determination.

Main Results:

  • Explicit stabilizability conditions for unstable FOPDT processes with a zero have been established.
  • Effective computational methods for determining stabilizing controller parameters were presented.
  • Illustrative examples demonstrated the practical application of the developed methods.

Conclusions:

  • The study provides a robust framework for stabilizing challenging FOPDT systems.
  • The presented methods offer practical tools for control engineers to design effective stabilizing controllers.