A novel auto-tuning PID control mechanism for nonlinear systems

Area of Science:

• Control Engineering
• Nonlinear System Dynamics
• Computational Mathematics

Background:

• Traditional PID controllers struggle with nonlinear and time-varying systems.
• Model Predictive Control (MPC) offers advanced control but can be computationally intensive.
• Existing auto-tuning methods may lack robustness for complex dynamics.

Purpose of the Study:

• Introduce a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative (RK-PID) controller.
• Enhance PID controller performance for continuous-time nonlinear systems.
• Improve parameter tuning using system prediction and error minimization.

Main Methods:

• Developed an RK-PID controller integrating Runge-Kutta discretization with model-predictive control principles.
• Tuned PID parameters via prediction error-square minimization using the RK system model.
• Implemented additive correction terms for adaptive PID parameter adjustments.
• Validated on unstable magnetic-levitation (SISO) and liquid-level (MIMO) systems.

Main Results:

• The RK-PID controller demonstrated effective auto-tuning and control performance.
• Achieved very small steady-state tracking errors and rapid parameter convergence.
• Showcased robustness and efficiency compared to standard PID, NMPC, RK-MPC, and SMC.

Conclusions:

• The proposed RK-PID controller offers a robust and efficient solution for controlling nonlinear systems.
• This approach provides superior tuning and performance over conventional methods.
• RK-PID is suitable for real-time applications requiring precise control of complex dynamics.