The paper introduces generalized PID control with the derivative action degrees m ∈ [0, 4] and with n ≥ mth order series binomial filters. Together with the traditional PI (m=0) and PID control (m=1), this setup covers also solutions with higher order derivatives denoted previously as the PIDD², or PIDD²D³ controllers and remains open to more complex combinations. The novel contribution includes explicit tuning formulas for the integral-plus-dead-time (IPDT) plant models with m=3 and m=4 as well as the systemic approach to design of such a long sequence of controllers. Derived by the multiple real dominant pole method they enable to significantly reduce the measurement noise impact by simultaneously speeding up transients and increasing the closed loop robustness against plant uncertainties. With respect to the necessary extent of the problem description, solution and of the corresponding performance evaluation, the contribution has been split into two parts. The first part focuses on the disturbance response evaluation by simulation. This is limited to some degree by the numerical problems of the available Simulink solvers. To overcome the simulation problems, the second part dealing with design and evaluation of the setpoint responses will consider also real time experiments.