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Feedback control systems01:26

Feedback control systems

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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...
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Feedback in control systems plays a critical role in shaping various operational parameters, extending beyond simple error reduction to influence stability, bandwidth, gain, impedance, and sensitivity. Understanding these effects requires examining a basic feedback system characterized by defined input, output, error, and feedback signals.
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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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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.
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MTN output feedback tracking control for MIMO discrete-time uncertain nonlinear systems.

Hong-Sen Yan1, Qi-Ming Sun2

  • 1School of Automation, Southeast University, No.2 Sipailou, Nanjing, Jiangsu 210096, China; Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, No.2 Sipailou, Nanjing, Jiangsu 210096, China.

ISA Transactions
|November 30, 2020
PubMed
Summary

A new adaptive controller using multidimensional Taylor networks (MTN) offers improved real-time performance for complex systems. This novel approach demonstrates superior robustness compared to traditional neural networks in simulations.

Keywords:
Adaptive controlClosed-loop controlMIMO non-linear constant systemsMulti-dimensional Taylor network

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Area of Science:

  • Control Engineering
  • Nonlinear System Dynamics
  • Computational Intelligence

Background:

  • Multi-input and multi-output (MIMO) uncertain discrete-time nonlinear systems present significant control challenges.
  • Existing adaptive control methods, such as those based on neural networks, can be computationally intensive, limiting real-time applicability.

Purpose of the Study:

  • To develop a novel adaptive controller based on the multidimensional Taylor network (MTN) for MIMO uncertain discrete-time nonlinear systems.
  • To demonstrate the real-time control feasibility and enhanced performance of the MTN-based adaptive controller (MTNAC).

Main Methods:

  • The study introduces a new multidimensional Taylor network (MTN) architecture.
  • The controller design requires only multiplication and addition operations, simplifying real-time implementation.
  • Theoretical analysis confirms the convergence of output errors and boundedness of output signals.

Main Results:

  • The MTN-based adaptive controller (MTNAC) achieves semi-global, uniform, and ultimate boundedness of output signals.
  • Numerical simulations validate the controller's effectiveness.
  • Comparative analysis shows MNTAC exhibits better real-time performance and higher robustness than neural network-based controllers.

Conclusions:

  • The developed MTN-based adaptive controller is a viable and efficient solution for controlling complex nonlinear systems.
  • MTNAC offers significant advantages in real-time control and robustness over existing neural network approaches.