Adaptive fuzzy observer and robust controller for a 2-DOF robot arm

Abstract

Adaptive fuzzy observers have been introduced in the recent past, which are capable of estimating uncertainties along with the states of a nonlinear system represented by an uncertain Takagi-Sugeno (TS) model. Application of such an observer to obtain estimates of the uncertainties in the state matrices and subsequently use them in the control of TS fuzzy models is the subject matter of this thesis. To demonstrate the adaptive observer and the controller design we use a 2-DOF robot arm model. The parameters of the robot arm are estimated for a laboratory-scale setup. The nonlinear model of the robot arm, consisting of six nonlinearities is simplified to contain only two nonlinearities. Then a four-rule TS fuzzy model is constructed using sector nonlinearity approach. The simplified nonlinear model and hence the fuzzy model almost exactly represent the complete nonlinear model. The mismatch in the plant and the nonlinear model is attributed to unmodelled dynamics in the state matrices. Assuming constant uncertainties in specific locations of the state matrices, an adaptive observer is used to estimate them and the simulation results are presented. The possibility to use the information about the structure of the uncertainties in the TS fuzzy model in designing the uncertainty estimation experiment is also presented. The uncertainty estimates provided by the adaptive observer are used to update the fuzzy model of the nonlinear system. The new model is used in the design of a robust state feedback stabilizing controller. Since the estimates obtained from the adaptive observer are used in controller design, the uncertainty distribution structure used in the design of both adaptive observer and the robust controller need to be same. Hence, a robust controller design is developed that uses the same uncertainty distribution structure as the adaptive observer. From the experimental results, it is concluded that stability can be guaranteed with a higher decay rate when using the updated model in robust controller design.