Data-Driven Virtual Setpoint P-Type Control with Prescribed Performance Function

In this letter, a prescribed performance function-based data-driven virtual setpoint P-type controller (PPF-DDVSPC) is proposed for single-input single-output (SISO) systems with nonlinear nonaffine dynamics. First, the original model with error constraint is converted into an unconstrained form using the prescribed performance function and error transformation technique. A virtual setpoint updating law, nested within the outer layer of the traditional P-type controller, is developed based on the newly defined unconstrained variable to limit the tracking error. Then, the unconstrained model and virtual setpoint law are converted into the available equivalent linear data models through dynamic linearization technology. The unknown pseudo-partial derivatives in the two models are estimated utilizing the modified projection algorithm. Finally, the P-type controller with prescribed performance is obtained by replacing the actual setpoint signal with the resulting virtual setpoint law. The bounded input and bounded output (BIBO) stability of the system is demonstrated by the contraction mapping principle, which ensures that the constraint conditions are satisfied. The effectiveness and robustness of the PPF-DDVSPC method are validated through a data-driven simulation of the blast furnace ironmaking process.