Super-twisting sliding mode differentiation for improving PD controllers performance of second order systems

Area of Science:

• Control Systems Engineering
• Nonlinear System Dynamics
• Robotics

Background:

• Designing proportional derivative (PD) controllers is challenged by noise in derivative calculations.
• High-frequency noise corrupts the output error signal, hindering accurate derivative estimation.
• Existing methods struggle with robust differentiation in the presence of significant noise.

Purpose of the Study:

• To develop a robust exact differentiator for proportional derivative (PD) controllers.
• To apply the supertwisting algorithm (STA) within a PD structure for nonlinear systems.
• To validate the effectiveness of STA-enhanced PD controllers for multi-input multi-output (MIMO) systems.

Main Methods:

• Integration of the supertwisting algorithm (STA) as a differentiator in a closed-loop PD controller.
• Analysis of stability conditions using non-smooth Lyapunov functions and Riccati equations.
• Numerical simulations including an inverted pendulum stabilization and a two-link robot manipulator tracking task.

Main Results:

• The supertwisting algorithm (STA) successfully acted as a robust exact differentiator.
• PD controllers utilizing STA demonstrated significant advantages in handling noisy signals.
• Successful stabilization of an inverted pendulum and accurate tracking for a robot manipulator were achieved.

Conclusions:

• The supertwisting algorithm (STA) provides a robust solution for derivative estimation in noisy environments.
• STA-enhanced PD controllers offer improved performance for second-order nonlinear MIMO systems.
• This approach is effective for practical applications in robotics and control engineering.