Automatic tuning of PID controllers using frequency sampling filters

This study proposes new proportional—integral—derivative (PID) controller auto‐tuners using frequency sampling filters (FSFs) for the estimation of plant frequency response information under relay feedback control. It differs from the existing auto‐tuners in the estimation of plant frequency response information and its utilisation in the frequency domain‐based PID controller design. A desired closed‐loop time constant is selected by the user as the scaling factor of the estimated open‐loop time constant. Simulation examples are used to demonstrate the efficacy of the auto‐tuner and its characteristics in disturbance rejection and reference following, indicating that the auto‐tuner produces satisfactory closed‐loop control performance for the commonly encountered systems in process control. In addition, Monte Carlo simulation studies are used to demonstrate that the FSF model‐based algorithm requires not only shorter experimental time to achieve higher accuracy in estimation but also provides much improvement over the traditional Fourier analysis‐based approaches when disturbances are encountered during the relay experiments.