Generalized proportional-integral extended state observer-based controller design for fully actuated systems.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics

Background:

• Fully actuated systems are susceptible to internal and external disturbances.
• Accurate state and disturbance estimation is crucial for effective control.

Purpose of the Study:

• To propose a novel feedback controller using an extended state observer for fully actuated systems.
• To ensure uniform ultimate boundedness of closed-loop system states despite disturbances.

Main Methods:

• Design of a generalized proportional-integral observer for simultaneous state and disturbance estimation.
• Utilization of linear parameter varying (LPV) approach and convexity principle for observer gain determination via linear matrix inequalities (LMIs).
• Development of a feedback controller leveraging estimated states and disturbances for compensation.

Main Results:

• The proposed observer effectively estimates system states and disturbances.
• The feedback controller ensures closed-loop system states are uniformly ultimately bounded.
• For constant or slow time-varying disturbances, observation errors and system states exhibit exponential convergence.
• Simulations confirm accurate disturbance estimation and significant reduction in state bounds.

Conclusions:

• The extended state observer-based feedback controller offers a robust solution for controlling fully actuated systems with disturbances.
• The LPV approach and LMIs provide a systematic way to design observer gains.
• The method demonstrates practical validity and effectiveness in simulation studies.