A Generalized Udwadia-Kalaba Control Design With Speed Inequality Constraints

Area of Science:

• Control Theory
• Mechanical Engineering
• Dynamical Systems

Background:

• Handling complex constraints in dynamical systems is challenging.
• Existing methods may not simultaneously address equality and speed inequality constraints.
• Robust control is crucial for system performance and safety.

Purpose of the Study:

• To propose a generalized Udwadia-Kalaba control method.
• To simultaneously manage equality and speed inequality constraints.
• To ensure uniform boundedness and ultimate boundedness of the dynamical system.

Main Methods:

• Establishing a dynamic model with both constraint types.
• Employing diffeomorphism state transition theory for state transformation.
• Designing a robust control strategy with state variable limitations.
• Utilizing the Lyapunov approach for stability analysis.

Main Results:

• The proposed method effectively handles simultaneous equality and speed inequality constraints.
• Uniform boundedness and uniform ultimate boundedness of the system were demonstrated.
• The control strategy ensures satisfaction of all imposed constraints.
• Feasibility was confirmed through simulations on an uncertain long-distance belt conveyor system.

Conclusions:

• The generalized Udwadia-Kalaba control method offers a robust solution for complex constrained systems.
• The approach enhances system stability and reliability.
• This method has practical implications for engineering applications like conveyor systems.