PD plus error-dependent integral nonlinear controllers for robot manipulators with an uncertain Jacobian matrix

Area of Science:

• Robotics
• Control Systems Engineering
• Mechatronics

Background:

• Traditional PID controllers offer limited tuning parameters, restricting system performance.
• Cartesian regulation of robot manipulators presents challenges due to uncertain Jacobian matrices.

Purpose of the Study:

• To propose an enhanced PID controller scheme with error-dependent integral action for robot manipulator Cartesian regulation.
• To improve transient performance and ensure system stability in the presence of uncertainties and disturbances.

Main Methods:

• Implementation of an error-dependent integral action within the PID controller framework.
• Analysis of controller flexibility and tuning capabilities.
• Guaranteeing asymptotic stability of the closed-loop system.
• Boundedness analysis for all system signals under external disturbances and noise.

Main Results:

• The proposed PID controller offers more tunable parameters compared to traditional ones.
• Enhanced flexibility in controller characteristics and tuning leads to superior transient performance.
• Asymptotic stability of the closed-loop system is mathematically guaranteed.
• All system signals remain bounded when disturbances and noise are bounded.

Conclusions:

• The novel PID controller with error-dependent integral action significantly enhances transient performance for robot manipulator control.
• The proposed scheme provides greater flexibility and guarantees system stability, outperforming traditional PID controllers.