Linear proportional-integral-derivative (PID) controller stands for the most widespread technique in industrial applications due to its simple structure and easy tuning rules. Recently, considering fractional orders λ and μ, there has been studied the fractional-order PIλDμ (FPID) controller to provide salient advantages in comparison to the conventional integer-order PID, such as, a more flexible structure and a preciser performance. In addition, proportional and derivative (PD) and PID error manifolds have been classically proposed; however, there remains the question on how FPID-like error manifolds perform for the control of nonlinear plants, such as robots. In this paper, this problem is addressed by proposing a PD-IλDμ error manifold for novel vector saturated control. The 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.
Fractional PD-IλDμ Error Manifolds for Robust Tracking Control of Robotic Manipulators
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received September 25, 2017; final manuscript received September 23, 2018; published online November 8, 2018. Assoc. Editor: Srinivasa M. Salapaka.
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Muñoz-Vázquez, A. J., Parra-Vega, V., Sánchez-Orta, A., and Romero-Galván, G. (November 8, 2018). "Fractional PD-IλDμ Error Manifolds for Robust Tracking Control of Robotic Manipulators." ASME. J. Dyn. Sys., Meas., Control. March 2019; 141(3): 031006. https://doi.org/10.1115/1.4041605
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