A Novel Stable-Inverse Fractional-Order Predictive PID Control with Machine Learning-Based Performance Prediction for Non-Minimum Phase Systems

Non-minimum-phase behavior introduces an additional limitation in predictive process control because directly inverting a right-half-plane zero can result in an unstable controller. This study develops a Stable-Inverse Fractional-Order Predictive PID (SIFOPPID) controller for the non-minimum-phase operating configuration of a laboratory-scale quadruple-tank system. The proposed technique combines fractional-order PID dynamics with predictive dead-time compensation and a stable approximate inverse implemented through a fractional low-pass weighting function. This work evaluates three SIFOPPID variations in terms of transient response, inverse compensation, filtering, and implementation complexity. Experiments are performed on the real-time quadruple-tank system (QTS) under set-point changes, disturbance injection, and measurement noise, and the responses are compared with conventional PID and fractional-order PID controllers. Experimental results show that the proposed SIFOPPID provides various performance improvements. In Tank 1, SIFOPPID0.6 S3 yields the shortest rise time 38.741 s, while SIFOPPID0.8 S3 provides the lowest IAE, ISE, ITAE, and ITSE values. In Tank 2, SIFOPPID0.2 S2 provides the shortest rise time of 0.792 s, whereas SIFOPPID0.8 S1 provides the shortest settling time of 1289.204 s. To further evaluate the controller, this work developed machine learning-based models using Regression Tree and Ensemble Tree algorithms, with the Ensemble Tree achieving an RMSE of 0.78 and an R2 of 0.89. These results indicate that stable inverse compensation can improve predictive fractional-order control of NMP multivariable processes while providing a tunable trade-off among response speed, damping, and robustness.