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Related Concept Videos

Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
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...
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
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...
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.
Stability of structures01:14

Stability of structures

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...

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Related Experiment Videos

Stability analysis of fuzzy parametric uncertain systems.

R J Bhiwani1, B M Patre

  • 1SGGS Institute of Engineering and Technology, Vishnupuri, Nanded, India. bhiwani_raju@rediffmail.com

ISA Transactions
|July 19, 2011
PubMed
Summary

This study simplifies stability margin calculations for fuzzy parametric uncertain systems (FPUS). A new method reduces the number of Kharitonov

Area of Science:

  • Control Systems Engineering
  • Fuzzy Systems
  • System Stability Analysis

Background:

  • Fuzzy parametric uncertain systems (FPUS) present challenges in stability analysis due to coefficient uncertainty.
  • Traditional methods for determining stability margins can be computationally intensive.

Purpose of the Study:

  • To propose a complexity-reduced technique for determining the stability margin of FPUS.
  • To analytically determine gain and phase margins for FPUS without graphical methods.

Main Methods:

  • The proposed method relies on the order of the characteristic polynomial.
  • It reduces the number of Kharitonov's polynomials required for stability margin determination, especially for lower-order systems.
  • The technique is extended to fuzzy interval polynomials.

Related Experiment Videos

Main Results:

  • For FPUS of order five, four, and three, only 3, 2, and 1 Kharitonov's polynomials are needed, respectively.
  • A complete set of Kharitonov's polynomials is only required for sixth-order and higher polynomials.
  • Analytical determination of gain and phase margins for FPUS is demonstrated.

Conclusions:

  • The proposed method significantly reduces computational load for stability margin analysis in lower-order FPUS.
  • This approach offers an efficient alternative to graphical techniques for gain and phase margin determination in FPUS.