Fractional PD-I?D? Error Manifolds for Robust Tracking Control of Robotic Manipulators

[+] Author and Article Information
Aldo Jonathan Muñoz-Vázquez

CONACYT Research Fellow, School of Engineering, Autonomous University of Chihuahua, Campus II, Chihuahua, Chihuahua, Mexico

Vicente Parra Vega

Full Professor, Robotics and Advanced Manufacturing, Center for Research and Advanced Studies, Saltillo, Coahuila, Mexico

Anand Sanchez-Orta

Full Professor, Robotics and Advanced Manufacturing, Center for Research and Advanced Studies, Saltillo, Coahuila, Mexico

Gerardo Romero-Galván

Full Professor, Electrical and Electronic Engineering, Autonomous University of Tamaulipas, Reynosa - Rodhe, Tamaulipas, Mexico

1Corresponding author.

ASME doi:10.1115/1.4041605 History: Received September 25, 2017; Revised September 23, 2018


Linear PID controller stands for the most widespread technique in industrial applications due to its simple structure and easy tuning rules. Recently, considering fractional orders ? and µ, there has been studied the fractional-order PI? Dµ (FPID) controller to provide salient advantages in comparison to the conventional integer-order PID, such as, a more flexible structure and preciser performance. In addition, PD and PID error manifolds have been classically proposed, however, there remains the question on how FPID error manifolds perform for the control of nonlinear plants such as robots. In this paper, this problem is addressed by proposing a PD-I? Dµ error manifold for novel vector saturated control. Stability analysis shows convergence into a small vicinity of the origin wherein such hybrid combination of integer- and fractional-order error manifolds provides further insights into the closed-loop response of the nonlinear plant. Simulations studies are carried out to illustrate the feasibility of the proposed scheme.

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