Robust Adaptive Controller and Observer Design for a Class of Nonlinear Systems with Unknown Backlash-Like Hysteresis

This paper presents a controller and observer design for a class of nonlinear systems that have: i. the coupling of the unmeasured states and unknown parameters ii. unknown Backlash- Like Hysteresis (BLH) at its actuation. Firstly, we use a developed mathematical model of the BLH in which the BLH is cast into two terms; a linear term and a bound. Then a robust adaptive control law, unmeasured states observer, and unknown parameters estimator are designed such that global stability is achieved for all signals involved. Using the suggested scheme, simulation is carried on for a single- link mechanical system with a BLH exist at its actuation and dynamic friction torque exerts on the joint. We will see that excellent tracking performance is obtained and all closed loop signals are bounded.