Nonlinear adaptive control using the Fourier integral and its application to CSTR systems

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Chemical Process Control

Background:

• Time-variant nonlinear systems present significant control challenges due to unpredictable dynamics.
• Traditional controllers struggle with both random and deterministic disturbances.
• Adaptive control strategies are crucial for enhancing system robustness and performance.

Purpose of the Study:

• To introduce a new nonlinear adaptive tracking controller for general time-variant nonlinear systems.
• To address challenges posed by both random and deterministic disturbances.
• To ensure asymptotic convergence and stability of the control system.

Main Methods:

• A two-loop control architecture: an inner fuzzy sliding mode control (FSMC) for feedback and an outer Fourier integral control for feedforward.
• Sliding mode control (SMC) principles ensure the stability of the inner loop.
• Lyapunov direct method guarantees the asymptotic convergence of the adaptive control system.

Main Results:

• The proposed controller effectively handles random disturbances via FSMC and deterministic disturbances via Fourier integral control.
• The controller demonstrates asymptotic convergence, ensuring system stability.
• Successful application to composition control in a continuously stirred tank reactor (CSTR) validates its effectiveness.

Conclusions:

• The developed nonlinear adaptive tracking controller offers a robust solution for complex time-variant systems.
• The hybrid control strategy effectively mitigates diverse disturbance types.
• The controller's efficacy is proven through its successful application in a CSTR system.