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Related Concept Videos

Linear time-invariant Systems01:23

Linear time-invariant Systems

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

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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....
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Stability01:28

Stability

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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...
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Pole and System Stability01:24

Pole and System Stability

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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...
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Second Order systems II01:18

Second Order systems II

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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Propagation of Uncertainty from Systematic Error01:10

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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A Tactile Automated Passive-Finger Stimulator TAPS
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A generalized smith predictor for unstable time-delay SISO systems.

R Sanz1, P García1, P Albertos1

  • 1Instituto de Automática e Informática Industrial Universitat Politècnica de València, 46020 València, Spain.

ISA Transactions
|October 8, 2017
PubMed
Summary
This summary is machine-generated.

A generalized Smith Predictor (SP) stabilizes linear time-invariant systems with time delays. This control method preserves performance and disturbance rejection, validated by simulations and experiments.

Keywords:
External disturbancesSingle-input single-output systemSmith PredictorTime delay

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Area of Science:

  • Control Systems Engineering
  • Automation and Robotics
  • Systems Theory

Background:

  • Linear time-invariant (LTI) systems with time delays present significant control challenges.
  • Traditional control methods often struggle to maintain stability and performance in the presence of time delays.
  • The Smith Predictor (SP) is a known technique for handling time delays in control systems.

Purpose of the Study:

  • To propose a generalized Smith Predictor (SP) for controlling single-input single-output (SISO) linear time-invariant (LTI) time-delay systems.
  • To demonstrate that combining a stabilizing output-feedback controller with the proposed predictor results in a stabilizing controller for the delayed system.
  • To show that the tracking performance and steady-state disturbance rejection are preserved compared to the delay-free equivalent.

Main Methods:

  • Generalization of the Smith Predictor (SP) structure for LTI SISO time-delay systems.
  • Analysis of controller stability and performance preservation.
  • Simulation studies comparing the proposed method with the ideal delay-free scenario.
  • Experimental validation on a laboratory platform.

Main Results:

  • The proposed generalized Smith Predictor (SP) effectively stabilizes LTI SISO time-delay systems.
  • The controller preserves the tracking performance and steady-state disturbance rejection capabilities of the equivalent delay-free system.
  • Simulation results confirm the effectiveness and compare favorably against the delay-free ideal.
  • Successful experimental implementation demonstrates practical feasibility.

Conclusions:

  • The generalized Smith Predictor offers a robust solution for controlling LTI time-delay systems.
  • The method maintains essential control loop characteristics, making it suitable for practical applications.
  • The approach is validated through both simulation and real-world experimental implementation.