Fuzzy Luenberger Observer Design for Nonlinear Flexible Joint Robot Manipulator

The process of controlling a Flexible Joint Robot Manipulator (FJRM) requires additional sensors for measuring the state variables of flexible joints. Therefore, taking the elasticity into account adds a lot of complexity as all the additional sensors must be taken into account during the control process. This paper proposes a nonlinear observer that controls FJRM, without requiring equipment sensors for measuring the states. The nonlinear state equations are derived in detail for the FJRM where nonlinearity, of order three, is considered. The Takagi-Sugeno Fuzzy Model (T-SFM) technique is applied to linearize the FJRM system. The Luenberger observer is designed to estimate the unmeasured states using error correction. The developed Luenberger observer showed its ability to control the FJRM by utilizing only the measured signal of the velocity of the motor. Stability analysis is implemented to improve the ability of the designed observer to stabilize the FJRM system. The developed observer is tested by simulation to evaluate the ability of the observer to estimate the unknown states. The results showed that the proposed control algorithm estimated the motor angle, gear angle, link angle, angular velocity of gear, and angular velocity of link with zero steady errors.