Setpoint weighted PI-FOPD cascade controllers synthesis for unstable time-delayed processes satisfying prespecified safety margins

This article introduces a novel setpoint weighted PI-FOPD (SWPI-FOPD) cascade controller with a prefilter. It further describes a four-stage design strategy that sequentially enhances tracking responses, reduces overshoot, and ensures robustness for unstable time-delayed (UTD) processes. The controller applies to integrating and non-integrating UTD processes of any order and does not necessitate model order reduction or delay approximation. The strategy involves four stages, each targeting a specific aspect of performance improvement. The first stage designs the optimal and robust FOPD (ORFOPD) controller to accelerate tracking responses. In the second stage, the cascade optimal and robust PI (ORPI) controller ensures zero steady-state error. A gain and phase margin (GPM) tester determines the feasible specification-oriented regions (FSORs) on the K_P1-K_D1 and K_P2-K_I2 planes, aiding in selecting the ORFOPD and ORPI controllers to minimize the IAE or ISE index under ± 10% loop gain perturbations (LGPs). The third stage schedules setpoint weighting coefficients to reduce overshoot typically associated with UTD processes. The final stage uses a prefilter to refine the reference input signal and mitigate overshoot. A systematic design procedure is summarized to rapidly compute all controller gains in a step-by-step sequence. This SWPI-FOPD controller with a prefilter enhances robustness, provides rapid tracking response with zero steady-state error, and effectively reduces overshoot and IAE or ISE, even with ± 10% LGPs. Comparative simulations across three examples, along with a practical jacketed CSTR application, validate the feasibility and demonstrate the superior performance of the proposed controller.