Abstract
This study addressed the issues of providing an enhanced prescribed performance control technique and a finite–time convergence of the conventional robust integral of the sign of the error (RISE) control method and for Euler-Lagrange systems. An improved RISE control strategy blended with a novel sine hyperbolic function as the prescribed function technique was designed based on the finite-time convergence theorem. The unknown uncertainty due to unknown dynamics of Euler-Lagrange dynamics was estimated by the adaptive law comprised by the command trajectory signals. The stability of the closed-loop finite-time RISE control system was proved via the constructive finite-time Lyapunov function method. The outperformed results of the proposed control strategy over the conventional controls were demonstrated by the experimental verification for an articulated manipulator.
Highlights
High performance controller has been required to cope with the nonlinear behaviors found in numerous uncertain nonlinear industrial plants for responding to rapid technical developments during last two decades
To accomplish the desired tracking performance of the control system, numerous control methods have been utilized for a variety of uncertain nonlinear systems
The proposed control system is smaller to maximum 64% than that of the RISE controller. Both the RISE and finite-time RISE controller (FRISE) controllers violate the boundaries of the prescribed error performance
Summary
High performance controller has been required to cope with the nonlinear behaviors found in numerous uncertain nonlinear industrial plants for responding to rapid technical developments during last two decades. Adding the proposed sinh function multiplied by the defined error signal into the designed controller enables to obtain the desired prescribing performance without further aid of complicated transformation process. Remark 3: The proposed constraint method can be readily applied to controller without any complex transformation of error and prescribing functions. Remark 4: As the error approaches the prescribed boundary, ψcj(t) increases largely automatically as shown in Fig. 4 (b) This property can be readily applied in order to constrain the increase of the error by considering a reverse proportional control action against the error evolution. In (26), if the values of the prescribing parameters φj and δj are selected as ej(t)/φj(t) → ±1 or ej(t)/φj(t) → ±δj, ∂R → ∞, and the resulting error increases This problem results in violation of the prescribed constraint condition and the instability of the closed loop system, which are shown in Figure 4 (a).
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