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

• Published in: ISA transactions 2012-11, Vol.51 (6), p.792-800
• Main Authors: Huang, C.Q., Xie, L.F., Liu, Y.L.
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Computer science; control theory; systems; Computer Simulation; Control system synthesis; Control theory. Systems; Controllers; Drives; Equipment Failure Analysis; Exact sciences and technology; Feedback; Jacobi matrix method; Jacobian matrix; Linkage mechanisms, cams; Manipulators; Mathematical models; Mechanical engineering. Machine design; Models, Theoretical; Nonlinear Dynamics; Nonlinear PID; Proportional integral derivative; Robot arms; Robot manipulator; Robotics; Robotics - instrumentation; Robotics - methods; Robots; Uncertain Jacobian
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2012.06.003

In framework of traditional PID controllers, there are only three parameters available to tune, as a result, performance of the resulting system is always limited. As for Cartesian regulation of robot manipulators with uncertain Jacobian matrix, a scheme of PID controllers with error-dependent integral action is proposed. Compare with traditional PID controllers, the error-dependent integration is employed in the proposed PID controller, in which more parameters are available to be tuned. It provides additional flexibility for controller characteristics and tuning as well, and hence makes better transient performance. In addition, asymptotic stability of the resulting closed-loop system is guaranteed. All signals in the system are bounded when exogenous disturbances and measurement noises are bounded. Numerical example demonstrates the superior transient performance of the proposed controller over the traditional one via Cartesian space set-point manipulation of two-link robotic manipulator. ► The architecture of traditional PID controller limits the potential for performance improving. ► The proposed nonlinear PID is developed to break through this limit. ► The proposed controllers possess the superior transient performance over the traditional one. ► Asymptotic stability of the resulting system is guaranteed. ► All signals keep bounded when the system is subjected to bounded exogenous disturbances.