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Proportional-Integral-Derivative (PID) controllers are widely used in various control systems to enhance stability and performance. In a thermostat, it adjusts heating or cooling based on the temperature difference between the actual and desired levels. They are often used in automotive speed systems, effectively managing sudden speed changes while maintaining a constant speed under varying conditions. On the other hand, PI controllers, commonly employed in voltage regulation, enhance stability...
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Three-Dimensional Force System:Problem Solving01:30

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A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
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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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PD Controller: Design01:26

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In automotive engineering, car suspension systems often employ Proportional Derivative (PD) controllers to enhance performance. PD controllers are utilized to adjust the damping force in response to road conditions. A controller, acting as an amplifier with a constant gain, demonstrates proportional control, with output directly mirroring input.
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Stability of Equilibrium Configuration: Problem Solving01:13

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The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
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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...
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Optimal nonlinear PID TSK3DCMAC controller based on balancing composite motion optimization for ballbot with external

Van-Truong Nguyen1, Dai-Nhan Duong1, Duc-Hung Pham2

  • 1Faculty of Mechatronics, SMAE, Hanoi University of Industry, Hanoi, Viet Nam.

ISA Transactions
|January 24, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a novel nonlinear PID controller-based Takagi-Sugeno-Kang 3D Cerebellar Model Articulation Controller (NPID-TSK3DCMAC) for enhanced ballbot stability. The new controller significantly reduces errors and improves robustness against external disturbances.

Keywords:
Balancing Composite Motion Optimization algorithmBallbotNPID controlTSK3DCMAC

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Area of Science:

  • Robotics
  • Control Systems Engineering
  • Artificial Intelligence

Background:

  • Conventional Proportional Integral Derivative (PID) controllers struggle with the nonlinear dynamics and external forces inherent in ballbot systems.
  • Existing control methods often exhibit performance degradation under dynamic and varying operational conditions.

Purpose of the Study:

  • To develop an innovative control strategy for improving dynamic balance and disturbance rejection in ballbot systems.
  • To overcome the limitations of traditional PID controllers in handling complex, real-time dynamic systems.

Main Methods:

  • A nonlinear PID controller-based Takagi-Sugeno-Kang 3D Cerebellar Model Articulation Controller (NPID-TSK3DCMAC) was designed.
  • The controller integrates nonlinear PID control, TSK3DCMAC, and the Balancing Composite Motion Optimization (BCMO) algorithm.
  • The TSK3DCMAC was trained iteratively, and the BCMO algorithm optimized controller gains, with stability analyzed via Lyapunov techniques.

Main Results:

  • The NPID-TSK3DCMAC controller demonstrated significant error reduction: 45.84% MSE and 25.68% MAE reduction compared to PID (without external force).
  • Compared to NPID, it achieved 99.87% MSE and 63.91% MAE reduction (without external force).
  • Under external force, it surpassed NPID by 64.94% in MSE and 17.67% in MAE, proving robustness.

Conclusions:

  • The proposed NPID-TSK3DCMAC controller effectively regulates ballbot motion and maintains stability amidst external disturbances.
  • The approach offers a robust and precise solution for applications demanding agile motion control in challenging environments.
  • Simulation and experimental results validate the controller's superior performance and robustness.