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Robust Control of Rotary Inverted Pendulum Using Metaheuristic Optimization Techniques Based PID and Fractional Order P\({{\text{I}}}^{\uplambda }{{\text{D}}}^{\upmu }\) Controller

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Abstract

Purpose

Rotary inverted pendulum (RotIP) innates unstable and underactuated behaviour that is helpful in the realisation of many real-world problems. It is very challenging to identify and control the dynamics of RotIP system due to its nonlinear, complex, underactuated and unpredictable nature. The primary objective of this work is to improve the swing-up and stabilization performances of RotIP in comparison to the existing approaches. This paper aims to propose the modelling and optimal design of a PID and Fractional Order PID (\({{\text{PI}}}^{\uplambda }{{\text{D}}}^{\upmu }\)) controller with Integral ANTI-WINDUP technique along with variable velocity setpoints for the robust stabilization and control of the RotIP system by using metaheuristic optimization techniques.

Methods

Different controllers like PID, Fractional order PID with Integral ANTI-WINDUP technique with variable velocity setpoints (Vsw), are implemented over the RotIP system. The parameters P, I, λ, D and μ of the Fractional Order PID (\({{\text{PI}}}^{\uplambda }{{\text{D}}}^{\upmu }\)) controller are tuned by two optimization techniques i.e. genetic algorithm (GA) and particle swarm optimization (PSO) based on Integral Time Absolute Error (ITAE). Simulation and real-time experimentation analysis of the transient response and steady-state response has been done for both the controllers to see the overall control performances in comparison to conventional PID controller for RotIP system. The pendulum angle, rotary arm angle and controlled input voltage comparisons are executed with the developed control schemes for both simulation and real-time experimentation purpose.

Results

This study uses the QUARC target libraries in MATLAB to provide a hardware-in-loop structure to enable a real-time controller interface. Swing-up and balancing control responses of inverted pendulum have been carried out in simulation and real time with PID, Fractional Order PID controller and optimization using GA and PSO. The responses of rotary arm angle (\(\varnothing\)), pendulum angle (β) and controlled input voltage (ap) are observed in simulation and in real-time operation respectively. The responses and parametric data of State feedback Balance control, PID and FOPID controllers implied that when rotary arm angle (\(\varnothing\)) is tracking a ± 20° angle square wave in case of State feedback Balance control and ± 8° angle square wave in case of PID and FOPID, maximum pendulum angle (βmax) and maximum controlled input voltage (amax) for both Simulated and experimental responses are within the specified limits of |β| < 20 (deg) and maximum control effort \(\left({a}_{max}\right)=10v\).

Conclusion

The analysis of transient response and steady-state response of both simulation and real-time experimentation implies that Fractional Order PID (\({{\text{PI}}}^{\uplambda }{{\text{D}}}^{\upmu }\)) compensator provides overall better control performances as compared to conventional PID controller for RotIP system. Simulation and real-time experimentation results shows that GA & PSO tuned PID provides better optimized responses as compared to PID response but PSO tuned PID reduced the peak overshoot very significantly as compared to PID and GA tuned PID. In case of settling time, both GA & PSO tuned controllers gives somewhat similar results. GA & PSO tuned Fractional order PID controller reduced the peak overshoot and settling time very significantly as compared to fractional order PID controller. Between optimization algorithms, PSO tuned \({{\text{PI}}}^{\uplambda }{{\text{D}}}^{\upmu }\) controller provides overall better optimized results. PSO provides much better optimized results for both PID and \({{\text{PI}}}^{\uplambda }{{\text{D}}}^{\upmu }\) controllers as compared to the results provided by GA. The primary feature of the proposed controllers is that it resolves the issue of robustness, accuracy, dependability and complexity as compared to many existing algorithms.

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Data Availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Code Availability

Code is available.

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  1. Dept of Electrical Engineering, Delhi Technological University, Delhi, 110042, India

    Basant Tomar, Narendra Kumar & Mini Sreejeth

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Basant Tomar: Conceptualization and methodology, writing-original draft preparation, investigation, software, validation, editing; Narendra Kumar and Mini Sreejeth: Research design, formal analysis, guidance, and reviewing. All authors have read and approved the final manuscript.

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Correspondence to Basant Tomar.

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Tomar, B., Kumar, N. & Sreejeth, M. Robust Control of Rotary Inverted Pendulum Using Metaheuristic Optimization Techniques Based PID and Fractional Order P\({{\text{I}}}^{\uplambda }{{\text{D}}}^{\upmu }\) Controller. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-024-01399-9

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