Data-Driven Modeling and Analysis of Transmission Error in Harmonic Drive Systems: Nonlinear Dynamics, Error Modeling, and Compensation Techniques

Harmonic drive systems (HDS) are high-precision robotic transmissions featuring compact size and high gear ratios. However, issues like kinematic transmission errors hamper their precision performance. This article focuses on data-driven modeling and analysis of an HDS to improve kinematic error compensation. The background introduces HDS mechanics, nonlinear attributes, and modeling approaches from literature. The HDS dynamics are derived using Lagrange equations. Experiments under aggressive conditions provide training data exhibiting deterministic patterns. Various linear and nonlinear models have been developed. The best-performing model, based on a nonlinear neural network, achieves over 98\% accuracy for one-step predictions on both the training and validation data sets. A phenomenological model separates the kinematic error into a periodic pure part and flexible part. Apart from implementation of estimated transmission error injection compensation, novel compensation mechanisms policies for the kinematic error are analyzed and proposed, including nonlinear model predictive control and frequency loop-shaping. The feedback loop is analyzed to select the controller for vibration mitigation. Main contributions include the nonlinear dynamics derivation, data-driven nonlinear modeling of flexible kinematic errors, repeatable experiment design, and proposed novel compensation mechanism and policies. Future work involves using physics-informed neural networks, sensitivity analysis, full life-cycle monitoring, and extracting physical laws directly from data.

Finite-Time Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems

This paper investigates the finite-time adaptive fuzzy tracking control problem for a class of pure-feedback system with full-state constraints. With the help of Mean-Value Theorem, the pure-feedback nonlinear system is transformed into strict-feedback case. By employing finite-time-stable like function and state transformation for output tracking error, the output tracking error converges to a predefined set in a fixed finite interval. To tackle the problem of state constraints, integral Barrier Lyapunov functions are utilized to guarantee that the state variables remain within the prescribed constraints with feasibility check. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions. In addition, all the signals in the closed-loop system are guaranteed to be semi-global ultimately uniformly bounded. Finally, two simulation examples are given to show the effectiveness of the proposed control strategy.

Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems With Input Delay via Dynamic Surface Technique

This brief constructs the adaptive backstepping control scheme for a class of pure-feedback systems with input delay and full state constraints. With the help of Mean Value Theorem, the pure-feedback system is transformed into strict-feedback one. Barrier Lyapunov functions are employed to guarantee all of the states remain constrained within predefined sets. By introducing the Pade approximation method and corresponding intermediate, the impact generated by input delay on the output tracking performance of the system can be eliminated. Furthermore, a low-pass filter driven by a newly-defined control input, is employed to generate the actual control input, which facilitates the design of backstepping control. To approximate the unknown functions with a desired level of accuracy, the fuzzy logic systems (FLSs) are utilized by choosing appropriate fuzzy rules, logics and so on. The minimal learning parameter (MLP) technique is employed to decrease the number of nodes and parameters in FLSs, and dynamic surface control (DSC) technique is leveraged to avoid so-called "explosion of complexity". Moreover, smooth robust compensators are introduced to circumvent the influences of external disturbance and approximation errors. By stability analysis, it is proved that all of signals in the closed-loop system are semi-globally ultimately uniform bounded, and the tracking error can be within a arbitrary small neighbor of origin via selecting appropriate parameters of controllers. Finally, the results of numerical illustration are provided to demonstrate the effectiveness of the designed method.