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Related Concept Videos

Linear time-invariant Systems01:23

Linear time-invariant Systems

262
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...
262
First Order Systems01:21

First Order Systems

93
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
93
PI Controller: Design01:24

PI Controller: Design

289
Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual...
289
Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

119
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...
119
Feedback control systems01:26

Feedback control systems

317
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...
317
Stability01:28

Stability

129
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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A robust finite-time model reference adaptive controller for arbitrary order disturbed LTI systems.

Héctor Ríos1, Roberto Franco2, Alejandra Ferreira de Loza3

  • 1Tecnológico Nacional de México/I.T. La Laguna, C.P. 27000, Torreón, Coahuila, Mexico; CONAHCYT, Investigadoras e Investigadores por México, C.P. 03940, Ciudad de México, Mexico.

ISA Transactions
|November 17, 2023
PubMed
Summary

A new adaptive controller achieves fast trajectory tracking for uncertain systems, even with disturbances. It guarantees rapid convergence of errors, demonstrating feasibility in simulations.

Keywords:
Adaptive controlLinear systemsModel reference adaptive control

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Area of Science:

  • Control Systems Engineering
  • Robotics
  • Adaptive Control Theory

Background:

  • Trajectory tracking is crucial for autonomous systems.
  • System uncertainties and external perturbations pose significant challenges.
  • Existing controllers may struggle with finite-time convergence under such conditions.

Purpose of the Study:

  • To develop a robust finite-time model reference adaptive controller.
  • To address trajectory tracking for linear time-invariant systems with uncertainties and perturbations.
  • To ensure finite-time convergence of tracking and parameter identification errors.

Main Methods:

  • Design of a robust finite-time model reference adaptive controller.
  • Application of Lyapunov and input-to-state stability theory for convergence proofs.
  • Simulation validation using an academic example and a robot manipulator.

Main Results:

  • Finite-time convergence to zero of tracking and parameter identification errors without external perturbations.
  • Finite-time convergence to a bounded region around the origin in the presence of time-dependent perturbations.
  • Demonstrated feasibility and effectiveness through simulation studies.

Conclusions:

  • The proposed adaptive controller effectively handles parameter uncertainties and external perturbations.
  • Finite-time convergence is achieved, offering improved performance over asymptotic methods.
  • The approach is validated for practical applications in robotics and control systems.