PIDm Control for IPDT Plants. Part 2: Setpoint Response

The paper continues in developing generalized two-degree-of-freedom (2DOF) proportional-integral-derivative (PID) control with the mth order derivative action, m[0,1] and with n ≥ mth order series binomial filters. By focussing on the setpoint responses, the explicit tuning formulas of a 1DOF PIDnm control for the integral-plus-dead-time (IPDT) plant models derived by the multiple real dominant pole method are augmented by the optimal prefilter enabling to cancel up to m + 1 of the m + 2 tuple dominant closed loop poles and thus to accelerate the setpoint step responses. Since in Matlab/Simulink, the simulative setpoint response evaluation of the PIDnm with m > 0 and IPDT plant is strongly limited by the numerical solver imperfections, the second part of the contribution brings also an experimental evaluation by real time control of a thermal plant. This fully confirms excellent properties of the novel type of control which, due to its high robustness, enables to simplify the plant identification and to work with the simple IPDTs model also in the case of selfregulating processes with significantly more complex dynamics.

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