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Minimization of the error based on integral performance criteria is performed to derive analytical rules using curve fitting techniques. Obtained analytical formulas may be used to determine the necessary tuning parameters of the I-PD controller from the known plant transfer function parameters. Advantages of the introduced tuning of I-PD controllers are shown by comparisons with other existing ones in terms of unit step responses, measurement noise, control signals, perturbations in plant transfer function parameters, and integral performance indices. 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