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Physical Pendulum01:06

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When a rigid body is hanging freely from a fixed pivot point and is displaced, it oscillates similar to a simple pendulum and is known as a physical pendulum. The period and angular frequency of a physical pendulum are obtained by using the small-angle approximation and drawing parallels with a spring-mass system. The small-angle approximation (sinθ=θ) is valid up to about 14°.
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Torsional Pendulum01:09

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Physiological models in pharmacokinetics are instrumental in understanding the distribution and elimination of drugs within the body. These models describe the drug concentration within target organs, influenced by factors such as drug uptake, tissue volume, and blood flow. Drug uptake is governed by the partition coefficient, which signifies the drug concentration ratio in tissue to that in the blood. The blood flow rate to a specific tissue is expressed as Qt, and the rate of change in tissue...
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RBF-ARX model-based fast robust MPC approach to an inverted pendulum.

Xiaoying Tian1, Hui Peng1, Feng Zhou2

  • 1School of Automation, Central South University, Changsha, Hunan 410083, China.

ISA Transactions
|March 17, 2019
PubMed
Summary

This study introduces an efficient robust predictive control (RBF-ARX-ERPC) method for systems like inverted pendulums. It reduces computation for robust model predictive control (RMPC) using a novel RBF-ARX model.

Keywords:
Efficient RMPCInverted pendulumOffline computationRBF-ARX modelReal-time control experiment

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Area of Science:

  • Control Engineering
  • Artificial Intelligence
  • Robotics

Background:

  • Robust Model Predictive Control (RMPC) faces heavy online computation burdens and challenges with precise plant model acquisition in industrial settings.
  • These limitations hinder the widespread practical application of RMPC.
  • Existing methods struggle to balance robustness with computational efficiency.

Purpose of the Study:

  • To propose an efficient robust predictive control (RBF-ARX-ERPC) approach integrating Radial Basis Function network-based Auto-Regressive models with eXogenous input (RBF-ARX) and fast RMPC.
  • To address the computational burden and modeling inaccuracies associated with traditional RMPC.
  • To demonstrate the effectiveness of the proposed method on a nonlinear inverted pendulum system.

Main Methods:

  • Offline identification of an RBF-ARX model without an offset term to capture nonlinear system behavior.
  • Construction of convex polytopic sets to represent the system's global nonlinear dynamics.
  • Formulation and offline solution of a quasi-min-max MPC optimization problem using linear matrix inequalities (LMIs) to generate explicit control laws and stable invariant ellipsoids.
  • Implementation of a look-up table for storing offline optimization results.
  • Online control involving simple state-vector computation and bisection search.

Main Results:

  • The proposed RBF-ARX-ERPC approach successfully synthesized explicit control laws.
  • The controller achieved asymptotic stability through invariant ellipsoids.
  • Real-time control experiments on a linear one-stage inverted pendulum (LOSIP) validated the method's effectiveness.
  • Significant reduction in online computation compared to traditional RMPC was achieved.

Conclusions:

  • The RBF-ARX-ERPC approach provides a complete and systematic solution for designing efficient robust MPC controllers.
  • The integration of RBF-ARX modeling and fast RMPC significantly alleviates the computational burden of RMPC.
  • The method is effective for controlling fast-responding, nonlinear plants like inverted pendulums, enhancing RMPC's practical applicability.