Two-degree-of-freedom proportional integral control of inverse response second-order processes

The aim of this paper is to present a robust tuning method for two-degree-of-freedom (2DoF) proportional integral (PI) controllers for inverse response controlled processes modeled by a second-order plus a right-half plane zero (SOPRHPZ) transfer function. This is based on the use of a servo and regulatory control closed-loop model reference optimization procedure. The robustness of the control system is analyzed for model right-half plane zero relative positions in the range from 0.1 to 4.0. It is found that the non-minimum phase zero position affects the achievable control system robustness level. Controller tuning equations that guarantee the design robustness level are provided for inverse response second-order models with right-half plane zero relative positions in ranges that depend of the target robustness level. The designer is allowed to deal with the performance/robustness trade-off of the closed-loop control system by specifying the desired robustness level through selecting the desired maximum sensitivity in the range from 1.4 to 2.0. In addition, a smooth servo/regulatory performance combination is obtained by forcing both closed-loop transfer functions to perform as closely as possible to non-oscillatory dynamic targets. Comparative examples show the effectiveness of the proposed robust tuning method and its exact achievement of the control system robustness target for the inverse response controlled process models considered.