Active disturbance rejection controller (ADRC) has achieved soaring success in motion controls featured by rapid dynamics. However, it turns obstreperous to implement it in the power plant process with considerable time-delay, largely because of the tuning difficulty. To this end, this article proposes a quantitative tuning rule for the time-delayed ADRC (TD-ADRC) structure based on the typical first order plus time delay (FOPTD) model. By compensating the FOPTD process as an integrator plus time delay in low frequencies, the gain parameter of TD-ADRC can be related to a scaled time constant which shapes the closed-loop tracking performance. Bandwidth parameter of extended state observer is scaled as a dimensionless parameter. A sufficient stability condition of TD-ADRC is theoretically derived in terms of the scaled parameter pair, the range of which falls within the practical interest. Relative delay margin is revealed as a critical robustness metric among others, a default pair of scaled parameter setting is recommended as well as an explicit retuning guideline according to the user's preference for performance or robustness. Simulation and laboratory water tank experiment validate the tuning efficacy and a coal mill temperature control test depicts a promising prospective of the proposed method in process control practice.

This paper introduces a new evidential clustering method based on the notion of "belief peaks" in the framework of belief functions. The basic idea is that all data objects in the neighborhood of each sample provide pieces of evidence that induce belief on the possibility of such sample to become a cluster center. A sample having higher belief than its neighbors and located far away from other local maxima is then characterized as cluster center. Finally, a credal partition is created by minimizing an objective function with the fixed cluster centers. An adaptive distance metric is used to fit for unknown shapes of data structures. We show that the proposed evidential clustering procedure has very good performance with an ability to reveal the data structure in the form of a credal partition, from which hard, fuzzy, possibilistic and rough partitions can be derived. Simulations on synthetic and real-world datasets validate our conclusions.

Active disturbance rejection control (ADRC) is widely applied in the motion control and the industrial process control for its merits of the uncertainty rejection, efficacy and ease of use. However, most process control models exist time-delay, which greatly deteriorates the closed-loop control performance of ADRC. Moreover, the controller gain tuning of ADRC is complex, laborious and time-consuming. Considering the above two difficulties, the key innovation of the paper is that aiming at the practical wet electrostatic precipitator (WESP) system with time-delay, a simple yet robust TD-ADRC gain tuning method is developed, which is mainly constructed by artificial time-delay block, observer and feedback control loop. The proposed gain tuning method is based on the bandwidth-parameterization technique, further using the scaling skill to simplify the gain tuning rule and stability analysis. Additionally, the exhaustive robustness metrics of closed-loop system are analyzed, which ensures that the gain tuning method maintains the controlled time-delay system with qualified robustness and well control performance. Alternatively, another robust stable region of TD-ADRC controller parameters are explored through the distinctively rigorous stability proof. Finally, plenty of simulations of WESP based on the practical operation data validate the effectiveness of the proposed method. Note to Practitioners — This paper was focused on gain tuning problem of the time-delay active disturbance rejection control (TD-ADRC) method. The controlled system is the first order plus time-delay (FOPTD) wet electrostatic precipitator (WESP) system. Thus, the novelties can be viewed from perspectives of method research and the combination of method and WESP model. From the perspective of the method research, time-delay in the process model is the obstacle to the most ADRC design or other kinds of controller design, and it always brings out lots of complexities to the gain tuning. In order to deal with the aforementioned problems, proposed TD-ADRC controller is designed for the purpose of simpler controller structure compared to the existing TD-ADRC method. Consequently, the simple gain tuning rule of proposed TD-ADRC method is explored by the exhaustive robustness analysis, which is under the pillar of the rigorous stability proof. Therefore, the engineer can avoid the laborious and time-consuming gain tuning procedure at the field and have the comprehensive hold to the robustness metric of time-delay system. From another perspective, proposed method can robustly regulate the WESP output in the presence of time-delay and disturbances in simulation, whose model is based on the practical data from the step response test. By the way, the proposed TD-ADRC is universal for higher order system which has the potential to apply in other system. It is promising that the proposed method could apply to the coal-fired station in the mid-term. In the future, more detailed researches about the versatile of the proposed method for the higher order system should be taken in an effort.

The Evidential K-Nearest Neighbor (EK-NN) classification rule provides a global treatment of imperfect knowledge in class labels, but still suffers from the curse of dimensionality as well as runtime and memory restrictions when performing nearest neighbors search, in particular for large and high-dimensional data. To avoid the curse of dimensionality, this paper first proposes a rough evidential K-NN (REK-NN) classification rule in the framework of rough set theory. Based on a reformulated K-NN rough set model, REK-NN selects features and thus reduces complexity by minimizing a proposed neighborhood pignistic decision error rate, which considers both Bayes decision error and spatial information among samples in feature space. In contrast to existing rough set-based feature selection methods, REK-NN is a synchronized rule rather than a stepwise one, in the sense that feature selection and learning are performed simultaneously. In order to further handle data with large sample size, we derive a distributed REK-NN method and implement it in the Apache Spark. The theoretical analysis of the classifier generalization error bound is finally presented. It is shown that the distributed REK-NN achieves good performances while drastically reducing the number of features and consuming less runtime and memory. Numerical experiments conducted on real-world datasets validate our conclusions.