Real-time fractional order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> adaptive control strategy for fractional order two link manipulator

Abstract

Abstract Position controlled industrial robots are used for trajectory tracking with fast and precise motion. The modelling and control technique in such a case depends on manipulator structure, material, servo control and inertial force. This paper proposes a scheme of fractional order modelling of a two-link manipulator (TLM) system with non-linearities, parametric uncertainties and disturbances, in joint space. A newly developed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> adaptive control ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> AC) strategy is modified by introducing a fractional-order predictor and fractional order adaptation laws to achieve desired variations of joint angles of the TLM. The novelty of this paper lies in the fact that the proposed FO- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math> AC scheme works in synchronism with the FOTLM system to deal with the non-linearities, parametric uncertainties and disturbances during real-life experimentation. The stability of the overall close loop system is precisely guaranteed utilizing the Lyapunov theory, and all the closed-loop variables are bounded employing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> norm-based conditions. Real-life experimental studies demonstrate the superiority of the proposed control strategy.