This paper describes the adaptive control design to solve the trajectory tracking problem of a Delta robot with uncertain dynamical model. This robot is a fully actuated, parallel closed-chain device. The output-based adaptive control was designed within the active disturbance rejection framework. An adaptive nonparametric representation for the uncertain section of the robot model was obtained using an adaptive least mean squares procedure. The adaptive algorithm was designed without considering the velocity measurements of the robot joints. Therefore, a simultaneous observer-identifier scheme was the core of the control design. A set of experimental tests were developed to prove the performance of the algorithm presented in this paper. Some reference trajectories were proposed which were successfully tracked by the robot. In all the experiments, the adaptive scheme showed a better performance than the regular proportional-integral-derivative (PID) controller with feed-forward actions as well as a nonadaptive active disturbance rejection controller. A set of numerical simulations was developed to show that even under five times faster reference trajectories, the adaptive controller showed better results than the PID controller.

A field-oriented armature-input-voltage output-feedback control approach is proposed for the robust linear controller design on an induction motor. The scheme simultaneously solves an angular-velocity reference-trajectory tracking task and a flux magnitude regulation in the presence of arbitrary time-varying load torques and unknown nonlinearities. The field-oriented input-voltage scheme is combined with linear high-gain asymptotic observers, of the generalized proportional-integral type, and linear active-disturbance-rejection output-feedback controllers. The linear observers online estimate, in a simultaneous manner, the output phase variables and the lumped effects of the following: 1) unknown time-varying load torques and unmodeled frictions and 2) rather complex state-dependent nonlinearities present in the electric and magnetic circuits. The field-oriented part of the scheme uses the classical flux observer or simulator. The proposed control laws naturally decouple, while linearizing, the extended second-order dynamics for the angular velocity and the squared flux magnitude. The proposed control scheme is here tested on an experimental induction motor setup.