Rapid Control Prototyping Simulation of Particle Swarm Optimization-Tuned Backstepping Tracking Control for A Rotary Inverted Pendulum

Summary

This protocol establishes a standardized rapid control prototyping procedure to evaluate Particle Swarm Optimization-tuned backstepping tracking control within a fixed-step real-time simulation environment.

Abstract

The primary objective of this protocol is to provide a reproducible fixed-step simulation framework for evaluating Particle Swarm Optimization (PSO)-based gain tuning in nonlinear control systems. The implementation begins with the formulation of a Furuta-type pendulum model, followed by the integration of a backstepping controller within a 2 ms fixed-step execution environment. The methodology involves a systematic four-stage process: characterizing non-ideal implementation constraints, defining a multi-objective Particle Swarm Optimization search space, executing automated offline tuning, and evaluating the resulting parameters through a standardized suite of trajectory-tracking and disturbance-rejection scenarios. This setup, utilizing high-performance industrial workstations and standardized signal interfaces, supports consistent repeated-trial comparisons within the same control architecture. The design compares a baseline manually tuned backstepping controller with a PSO-optimized variant that shares the exact same control structure, thereby isolating the impact of gain selection. Controller performance is assessed across three distinct operational scenarios: step-trajectory following, mixed-frequency sinusoidal tracking, and disturbance rejection. Statistical analysis of 10 repeated trials showed that PSO-based optimization reduced the step-tracking RMSE from 0.065 to 0.050 rad and attenuated peak pendulum excursions by 33.1%. These improvements were achieved alongside a 22.1% reduction in RMS control effort, indicating that the optimized parameters facilitated more efficient energy distribution within the Lyapunov-based framework. Ultimately, this methodology provides a structured simulation framework to evaluate nonlinear control strategies before any subsequent physical hardware implementation.

Introduction

The Furuta-type rotary inverted pendulum represents a fundamental benchmark for validating nonlinear control algorithms due to its open-loop instability and complex underactuated dynamics^1,2,3. Before implementation-oriented evaluation can be considered, these theoretical designs require rigorous simulation-based intermediary testing. Therefore, this protocol establishes a standardized, rapid control prototyping simulation framework to systematically evaluate the performance changes induced by Particle Swarm Optimization (PSO) on backstepping tracking controllers in a fixed-s....

Protocol

This protocol does not involve human subjects, animal testing, or clinical specimens. The procedures are executed entirely within a fixed-step simulation environment representing a nonlinear electromechanical control system. No physical rotary inverted pendulum experiment, physical hardware-in-the-loop validation, or physical deployment test was performed in this study.

1. Plant construction and signal convention establishment

1. Construct a high-fidelity simulation model of a Furuta-type rotary inverted pendulum. Define two generalized coordinates for the system: the rotary arm angle, θ, and the pendulum dev....

Results

The particle swarm optimization (PSO) algorithm demonstrated a rapid initial reduction in the composite objective function, followed by a period of gradual convergence. Specifically, the optimal fitness value decreased to 1.8757 within the first computational cycle, while the mean-swarm fitness dropped from 2.0573 to 1.2518 by the 35th iteration. The majority of this convergence occurred during the initial 15 to 20 iterations. Beyond this stage, the trajectory of the global-best solution converged, indicating that the sw.......

Discussion

The primary objective of this study is not merely to declare one controller superior to another under isolated conditions, but to demonstrate that the PSO-based gain optimization framework evaluated here can improve the performance of a backstepping controller across defined simulated non-ideal scenarios. The rotary inverted pendulum serves as an excellent benchmark for this evaluation due to its highly nonlinear, non-minimum phase, and underactuated characteristics²⁶. Beyond performance metrics, .......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
High-performance Workstation (Windows 11 Pro)	Various / Custom Build	N/A	Host machine for fixed-step real-time simulation and post-processing.
MATLAB (Version R2024a)	MathWorks	https://www.mathworks.com/products/matlab.html	Nonlinear plant modeling, controller coding, data export, and parameter management.
Simulink (Version R2024a)	MathWorks	https://www.mathworks.com/products/simulink.html	Block-diagram model construction for the Furuta-type pendulum and controller execution.
Simulink Desktop Real-Time (Version R2024a)	MathWorks	https://www.mathworks.com/products/simulink-desktop-real-time.html	Fixed-step real-time kernel for desktop execution of the control model.
Python (Version 3.11)	Python Software Foundation	https://www.python.org/	Secondary data processing, statistical handling, and figure preparation.
NumPy (Version 1.26)	NumPy Developers	https://numpy.org/	Numerical array operations for exported trial data.
pandas (Version 2.2)	pandas Developers	https://pandas.pydata.org/	Repeated-trial data organization and summary-table generation.
SciPy (Version 1.13)	SciPy Developers	https://scipy.org/	Statistical testing and signal-analysis utilities.
Matplotlib (Version 3.8)	Matplotlib Developers	https://matplotlib.org/	Plot generation for convergence, tracking, and distribution figures.