This article studies an adaptive fault-tolerant approach with a fixed-time sliding mode for trajectory tracking of uncertain robot manipulators with actuator effectiveness faults. An equivalent system with an adaptive technique is developed to remove the effects of uncertainties on tracking performance, whereas an appropriate system transformation is accomplished to eliminate the effects of the actuator effectiveness faults. A significant feature of this study is that the fixed-time stability is guaranteed theoretically and practically in the presence of uncertainties and actuator effectiveness faults. Moreover, the appearing advantages are that the proposed approach yields an improved tracking performance without utilizing the overestimated control gain and prior knowledge of a robot and, then, overcomes the singularity and algebraic loop problems completely. The effectiveness of the proposed approach for tracking systems is accomplished on simulation and experimental results from a qualitative and quantitative analysis.

Thermal compensation control can correct errors caused by the thermal deformation of phased array antenna (PAA) panels. Thermal deformation of the panel is needed to calculate the compensation value. While the PAA is working, thermal deformation is unconditional to measure, but predicting it by temperature is feasible. However, thermal deformation is also affected by other factors, such as the structural shape, assembly method, and material parameters, and it is difficult to measure these parameters of PAA because of the complex structure. In contrast, the measurement method of the temperature and thermal deformation of the PAA in the laboratory is much easier. Therefore, a comprehensive influence parameters (CIPs)-finite element method (FEM) method was proposed in this study, it can extract the influence of above parameters on thermal deformation from temperature and thermal deformation measurement data and build a thermal deformation prediction model. Experiments have verified that the CIPs-FEM can greatly reduce the difficulty of thermal deformation modeling and have a high prediction accuracy.

The temperature-sensitive point is the input variable of the thermal error compensation model of computer numerical control (CNC) machine tools. At present, the most commonly used selection method is to measure the multipoint temperature and thermal error of the machine tool synchronously and select several temperature measurement points with the highest thermal error correlation as temperature-sensitive points according to the measurement data. This study reveals that this method sometimes has obvious mis-selection and causes the model to fail. The reason is that the weak correlation temperature measurement point away from the machine tool heat source amplifies the volatility of the correlation evaluation result, owing to the small overall change. If the calculated result exceeds the true strong correlation temperature measurement point, it will be incorrectly selected as the temperature-sensitive point. This scenario has been termed herein as the pseudocorrelation problem. With the gradual popularization of thermal error compensation technology for CNC machine tools, pseudocorrelation will seriously affect the mass production pass rate. Therefore, the study analyzes and rigorously proves the mathematical mechanism of this problem, and the temperature measurement point preselection algorithm based on the correlation coefficient volatility determination factor (CCVDF) is proposed to eliminate potential pseudocorrelation temperature points before selecting temperature-sensitive points. After 1000 random simulation experiments, the failure rate of Z-direction thermal error modeling after preselection decreased from 5.1% to 0.5%, and the Y-direction error decreased from 33.7% to 1.5%. This algorithm can greatly improve the qualification rate of large-scale equipment of thermal error compensation technology.

The thermal error of CNC machine tools can be reduced by compensation, where a thermal error model is required to provide compensation values. The thermal error model adaptive update method can correct the thermal error model by supplementing new data, which fundamentally solves the problem of model robustness. Certain problems associated with this method in temperature-sensitive point (TSP) selection and model update algorithms are investigated in this study. It was found that when the TSPs were selected frequently, the selection results may be different, that is, there was a variability problem in TSPs. Further, it was found that the variability of TSPs is mainly due to some problems with the TSP selection method, (1) the conflict between the collinearity among TSPs and the correlation of TSPs with thermal error is ignored, (2) the stability of the correlation is not considered. Then, a stable TSP selection method that can choose more stable TSPs with less variability was proposed. For the model update algorithm, this study proposed a novel regression algorithm which could effectively combine the new data with the old model. It has advantages for a model update, (1) fewer data are needed for the model update, (2) the model accuracy is greatly improved. The effectiveness of the proposed method was verified by 20 batches of thermal error measurement experiments in the real cutting state of the machine tool.

In the thermal-error compensation of CNC machine tools, temperature-sensitive points (TSPs) are used for predicting thermal error and need to have a high correlation with the thermal error. The stability of the correlation between TSPs and the thermal error is the key to long-term prediction accuracy. In this paper, the uncertainty-calculation method of the correlation coefficient is proposed to measure the stability of the correlation, and the reasons that affect the stability of the correlation of TSPs are analyzed. Then, the uncertainty-correlation coefficient is proposed, which can comprehensively evaluate the correlation and the stability of the correlation between TSPs and the thermal error. Through long-term experimental verifications, compared with the current TSP selection algorithm, the uncertainty-correlation coefficient can help to select a more stable TSP and improve the long-term prediction accuracy of the thermal error.

This paper develops a fault-tolerant tracking control (FTC) for robot manipulators with prescribed performance subject to uncertainties and partial loss in effectiveness of actuators (UPEAs). First, an integral sliding manifold without reaching phase is constructed for guaranteeing the prescribed performance in both the transient and steady states. With this integral sliding manifold, an FTC is proposed for uncertain robot manipulators to obtain advanced tracking performance with prescribed performance constraints under the effects of UPEAs. The stability analysis is guaranteed by the Lyapunov theory and a homogeneous technique. The primary contributions of our design are as follows: (i) the proposed approach removes the reaching phase completely for the sake of the prescribed performance and better chattering-restraining capability; (ii) the nominal control part is also removed in the formulation of the conventional integral sliding mode, and then the proposed approach eliminates the algebraic loop problem; (iii) a simple control structure is accomplished to eliminate the effects of time delay and computational burden. A simulation, along with experiments, is completed for verifying the effectiveness of the proposed approach.