Mechanical design and robust tracking control of a class of antagonistic variable stiffness actuators based on the equivalent nonlinear torsion springs

Abstract

The novel conceptual model of the antagonistic variable stiffness actuator based on the equivalent nonlinear torsion spring and the friction damper is demonstrated. For the dynamic model of the antagonistic variable stiffness actuator in the presence of parametric uncertainties, unknown bounded friction torques, unknown bounded external disturbance, and input saturation constraints, using the coordinate transformation, the state space model of the antagonistic variable stiffness actuator with composite disturbances and input saturation constraints is transformed into an extended integral chain-type pseudo-linear system with input saturation constraints. Subsequently, a combination of the linear extended state observer, sliding mode control, and adaptive input saturation compensation law is adopted for the design of the robust tracking controller that simultaneously regulates the position and stiffness of the antagonistic equivalent nonlinear torsion spring-based variable stiffness actuator. Under the proposed controller, the semi-global uniformly ultimately bounded stability of the closed-loop system has been proved via Lyapunov stability analysis. Simulation studies demonstrate the effectiveness and the robustness of the proposed robust adaptive tracking control method for the antagonistic variable stiffness actuator.

Robust tracking control for two classes of variable stiffness actuators based on linear extended state observer with estimation error compensation

“…Finally, the simulation results show the effectiveness, robustness, and good adaptability of the designed controller. The proposed design idea of reducing the tracking error can be extended to the tracking control of other types of systems [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] to improve the tracking accuracy and disturbance rejection performance of the controller.…”

“…[29][30][31][32][33][34][35][36][37][38][39] For the antagonistic VSAs based on equivalent nonlinear torsion springs (ENTSs) in the presence of parametric uncertainties, unknown friction torques, unknown external disturbance, and input saturation constraints, a combination of the LESO, the sliding mode control (SMC), and the adaptive input saturation compensation (ISC) is designed to achieve the simultaneous position and stiffness tracking control of the VSAs. 40 However, in the above studies, 21,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] the estimation errors were not considered explicitly in the DOB-based control or the LESO-based control.…”

“…Similar to the gain settings of the LESO in many other types of control systems, [29][30][31][32][33][34][35][36][37][38][39][40] the LESO with fixed preset observation gains is used in the tracking control of the antagonistic VSA based on ENTS. 40 However, the LESO with fixed preset observation gains always has estimation errors, especially when the reference trajectories change abruptly (i.e. the tracking errors are large), or the timevarying disturbances are imposed on the system, or the disturbances in the system are large, or the disturbances imposed on the system suddenly change.…”

“…Dv cq and Dv ckej ), there exist unknown bounded positive constants b q and b k such that Dv cq b q , and Dv ckej b k . The inequality 0 h j j À htanh h e À Á0:2785e holds for any e > 0 and for any h 2 R 40.…”

Hysteresis modeling of piezoelectric micro-positioning stage based on convolutional neural network

“…They use hysteresis operators and differential equations to characterize hysteresis, respectively. For example, the Preisach model 4,5 and the Prandtl–Ishlinskii (PI) model 6–8 are operator-based models and the Bouc–Wen model 9–11 is a differential model. PI model is widely used for hysteresis modeling because it is relatively simple, and its analytical inverse model can be obtained.…”