Optimal PID controller design with adjustable maximum sensitivity

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Abstract
In this work, the exponential weighted square‐of‐error functions are exploited for controller design. It is reported that the exponential weight in square‐of‐error objective function is related to the maximum sensitivity of the process. Therefore, it is possible to control the maximum sensitivity of the process without measuring the frequency response. Moreover, the existing integral‐square‐error‐ and integral‐time‐square‐error‐based proportional‐integral‐derivative (PID) tuning rule is modified with the proposed exponential weighted square‐of‐error functions that allow the user to further tune the maximum sensitivity of the process. The proposed theory is corroborated with the help of a gain optimisation example by the traditional minimisation approach and a PID controller design example by the proposed tuning rule (for the stable/unstable process) and stochastic optimisation approach.

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