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<p>Model-free design approaches are favoured for controller design when dealing with complex process models or models that lack accurate mathematical representation. This article presents a relay autotuning method for the PID controller for stable processes. By conducting a single ideal relay test, a limit cycle output is generated to aid in the Proportional–Integral–Derivative (PID) controller design. The design process involves two steps: initially, a zero-phase PID controller is derived to ensure a minimum gain margin; subsequently, the phase margin criterion is achieved using the indirect design method (IDA2). The proposed IDA2-relay autotuning method enables users to design a PID controller and adjust its robustness using a single tunable variable, which exhibits a monotonic relationship with robustness. The efficacy of the IDA2-<i>relay</i> PID autotuner is validated through two different simulations on higher-order plants. The experimental validation is also investigated for speed control of the DC motor with IDA2-relay autotuner implemented on Arduino microcontroller board. Under nominal conditions, the proposed method provides enhanced tracking and disturbance rejection, achieving up to 42% reduction in IAE and 29% in ISE compared to existing methods, while maintaining improved robustness. Similarly, in the DC motor experiment, the performance is improved by 3.13% in the presence of load changes.</p>

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Indirect-Relay Autotuning: A Model-Free Approach to Robust PID Controller Design and Implementation

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Dhiraj Shrivastava,
  • Bharat Verma,
  • Akash Gupta,
  • Prabin Kumar Padhy,
  • Anupam Kumar

摘要

Model-free design approaches are favoured for controller design when dealing with complex process models or models that lack accurate mathematical representation. This article presents a relay autotuning method for the PID controller for stable processes. By conducting a single ideal relay test, a limit cycle output is generated to aid in the Proportional–Integral–Derivative (PID) controller design. The design process involves two steps: initially, a zero-phase PID controller is derived to ensure a minimum gain margin; subsequently, the phase margin criterion is achieved using the indirect design method (IDA2). The proposed IDA2-relay autotuning method enables users to design a PID controller and adjust its robustness using a single tunable variable, which exhibits a monotonic relationship with robustness. The efficacy of the IDA2-relay PID autotuner is validated through two different simulations on higher-order plants. The experimental validation is also investigated for speed control of the DC motor with IDA2-relay autotuner implemented on Arduino microcontroller board. Under nominal conditions, the proposed method provides enhanced tracking and disturbance rejection, achieving up to 42% reduction in IAE and 29% in ISE compared to existing methods, while maintaining improved robustness. Similarly, in the DC motor experiment, the performance is improved by 3.13% in the presence of load changes.