Finite-time PID control for nonlinear nonaffine systems

This article proposes a finite-time proportional-integral-derivative (FT-PID) control method to fast stabilize the control system to achieve the desired performance within the predesignated time instants. For a considered nonaffined nonlinear system, we develop a new dynamic linearization approach to reformulate the system model as a linear data model (LDM) whose arguments are consistent with that used in the PID control law. Then, a projection algorithm is presented to estimate the unknown pseudo gradient vector of the LDM. Subsequently, an adaptive tuning algorithm is designed to update the three PID parameters by solving linear matrix inequalities in terms of the predesignated error precision and the finite-time instant. The finite-time convergence of the proposed FT-PID control system is shown mathematically, which guarantees a pre-specified error precision to be achieved within the predesignated finite-time instants. As a result, not only can the proposed FT-PID control save the control cost but it also improves the production efficiency. The simulation study verifies the results.