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Regarding a general class of integrating processes subject to uncertain delays, this paper investigates a two-degree-of-freedom (2-Dof) control scheme with a proportional-derivative (PD) controller and disturbance observer (DOB). Relative delay margin is introduced as a paramount metric to evaluate the delay robustness, with which a set of novel and explicit tuning formulae for PD controller is analytically derived under the single external loop. In this individual frame, the stability boundaries associated with the governing parameters are first studied, indicating the nominal stability conditions for the 2-Dof control system. Then the optimal tracking problem is formulated and addressed with such delay robustness constraints. For the design of the internal loop, the performance of DOB will be quantified by the trade-off between the external relative delay margin and the disturbance rejection, thus retaining the original PD controller design. Besides, the stability in the nominal delay range is primarily concerned when demarcating the low-pass filter in DOB, based on which a critical time constant is obtained through exhaustive testing. Following the route of combining analytical design with quantitative adjustment, the synthetic tuning rules can provide prescribed robustness against delay uncertainty for integrating processes. Through conducting illustrative simulations and a water tank experiment, the efficiency and merit of the proposed scheme are demonstrated. |
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