The electrohydraulic elastic manipulator (EEM) includes an electro-hydraulic servo system (EHSS) and a variable stiffness mechanism (VSM). It is a complex system with the nonlinear elements, such as friction, parametric uncertainties, and modeling error as well as coupling torques in the elastic joint. This paper focuses on developing an equilibrium position controller for the EEM with the presence of the matched and unmatched uncertainties. The proposed controller is based on a backstepping scheme optimized using an adaptive sliding mode technique and an adaptive nonlinear PI structure. To estimate parameters of known functions in the system dynamics, the parametric learning laws are employed, while adaptive switching gain laws are used to adjust robust gains of discontinuous control terms. The robust switching gains increase or decrease as state control variables moves away or closes to the surfaces, respectively. Working together, these kinds of the adaptation laws can effectively deal with the problem of matched and unmatched uncertainties. Next, the Lyapunov approach is used to prove the robustness and stability of the whole system. The proposed method is practically implemented and compared with other controllers to demonstrate the effectiveness of the proposed method with the variant stiffness and the uncertainties.

We propose a gain-adaptive robust controller for position tracking of a brushless direct-current electric motor system. The controller has two design loops: an inner highly robust loop and an outer gain-adaptive loop. The inner loop is based on a backstepping framework to eliminate certainties in the system dynamics, while problem of internal and external disturbances is dealt with using a robust term directly synthesized from the tracking error. All control gains of the control signal produced by the robust loop are tuned online by a new gain-learning mechanism for the desired control performance. The gain dynamics are activated by special combinations of state control errors and deactivated by saturation functions. The stability of the closed-loop system is strictly proven by Lyapunov-based approaches. To verify the performance of the controller in a real-time system, a two degree-of-freedom robot leg was fabricated with the investigated motor system and experiments were carried out. The results obtained confirm the robustness, adaptation, fast response, and high accuracy of the proposed method.

This paper proposes an adaptive robust Jacobian-based controller for task-space position-tracking control of robotic manipulators. Structure of the controller is built up on a traditional Proportional-Integral-Derivative (PID) framework. An additional neural control signal is next synthesized under a non-linear learning law to compensate for internal and external disturbances in the robot dynamics. To provide the strong robustness of such the controller, a new gain learning feature is then integrated to automatically adjust the PID gains for various working conditions. Stability of the closed-loop system is guaranteed by Lyapunov constraints. Effectiveness of the proposed controller is carefully verified by intensive simulation results.