A practical PID regulator with bounded torques for robot manipulators

Abstract

This paper proposes a saturated nonlinear PID regulator for industrial robot manipulators. Our controller considers the natural saturation problem given by the output of the control computer, the saturation phenomena of the internal PI velocity controller in the servo driver, and the actuator torque constraints of the robot manipulator. An approach based on the singular perturbations method is used to analyze the exponential stability of the closed-loop system. Experimental essays show the feasibility of the proposed controller. Furthermore, the theoretical results justify why the classical PID used in industrial robots preserves its exponential stability despite the saturation effects of the electronic control devices and the actuator torque constraints.

The New Design Strategy on PID Controllers

“…As been pointed out above, PID control is still being widely used in process control because of its robustness and with relatively simple structure, thousands of books and papers have been published (see (Åström & Hagglund, 1995), (Cong & Liang, 2009), (Datta et al, 2000), (Han, 2009), (Heertjes et al, 2009), (Hernandez-Gomez et al, 2010), (Leva et al, 2010), (Nusret & Atherton, 2006), (Santibanez et al, 2010), (Yaniv & Nagurka, 2004), etc.). However, the main problem in PID control is how to tune the parameters to adapt the controller to different situations ( (Han, 2009), (Leva et al, 2010), (Liu & Hsu, 2010), (Sekara et al, 2009), (Toscano & Lyonnet, 2009)).…”

Output-feedback proportional-integral-derivative-type control with multiple saturating structure for the global stabilization of robot manipulators with bounded inputs

“…(observe, from inequality (17) and the definition of 0 , that Pi (note that by inequality (21) and the definition of 0 : 0 < ð1 À g 0 Þk Pi À k g and q à i > 0); this is proven in Appendix 2 of Mendoza et al 16 From this, inequality (2) and item 5 of Lemma 1, we have…”

“…By inequality (21), W 11 ð q; _ qÞ is positive definite (since with " < " M " 1 , in accordance to inequality (17), any g 0 satisfying (21) renders Q 11 positive definite) and observe that W 11 ð0 n ; _ qÞ ! 1 as k _ qk !…”

“…Consider the closed-loop system in equations (20), under the satisfaction of inequalities (14), the conditions on the vector function s d stated through expressions (15), and Assumption 1 with suitable value of . Thus, for any positive definite diagonal matrices A, B, K I and K P such that inequalities (16) are fulfilled, and any " satisfying inequality (17), global asymptotic stability of the closed-loop trivial solution ð q; #; ÞðtÞ ð0 n ; 0 n ; 0 n Þ is guaranteed with j i ðtÞj ¼ ju i ðtÞj < T i , i ¼ 1; . .…”

On Saturated PID Controllers for Industrial Robots: the PA10 Robot Arm as Case of Study

“…In the practice, industrial robots are equipped with a position control computer which produces the commands of desired joint velocities to the joint actuator servo-drivers. In such a sense, Santibañez et al (2010) recently proposed a new saturated nonlinear PID regulator for robot manipulators that considers the saturation phenomena of both the control computer, the velocity servo-drivers and the torque constraints of the actuators. The structure of this controller is closer to the structure of the practical PID controllers used in the industry.…”