The double-holding water tank system is a common non-linear control system that plays a crucial role in process control in the chemical industry. It consists of two cylindrical glass containers: the preset tank and the main tank. The main challenge in controlling this system is adjusting the main control valve to ensure that the actual liquid level of the main tank tracks the desired liquid level. This paper explores the zeroing dynamics (ZD) method and its application in tracking control. A non-linear model is developed for the double-holding water tank system, and the ZD method is used to design an effective controller (called the ZD controller) for tracking control. Additionally, the robustness of the double-holding water tank system in the presence of time-varying perturbations is investigated. In order to substantiate the effectiveness and robustness of the ZD controller, simulation experiments on four different tracking trajectories corresponding to four different practical situations, as well as an extra simulation experiment considering time-varying perturbations, are conducted. Furthermore, a comparative simulation experiment based on the backstepping method is conducted. The presented results successfully illustrate the feasibility and effectiveness of the ZD method for the tracking control of double-holding water tank systems.

To address the problems of poor model diagnosis and poor noise immunity caused by inconsistent distribution of bearing fault features and difficulty in feature extraction in multi-condition environments, a multi-condition bearing fault diagnosis method based on a channel segmentation improved residual network is proposed. A channel segmentation mechanism is designed for channel information highlighting, by selecting one channel of the three-channel feature image as the main operation channel, stacking it with the secondary operation channel after convolution, and then inputting the stacked feature map into the convolutional neural network to realize the extraction and classification of bearing fault features. Four different network models were selected to verify the diagnostic performance of the channel segmentation mechanism on the Case Western Reserve University bearing dataset and the Jiangnan University bearing dataset, and noise immunity experiments were conducted on the Jiangnan University bearing dataset. The experiments show that the proposed diagnostic model on the Case Western Reserve bearing dataset has a minimum improvement of 6.8% compared to the comparison method for multi-case bearing fault diagnosis experiments. In terms of noise immunity, the diagnostic accuracy of the fault diagnosis model with the addition of the channel cut-off mechanism improves the diagnostic accuracy of the noisy data by an average of 4.3% compared to that without the addition. The proposed model still has excellent diagnostic performance when diagnosing variable speed bearing faults.

In the traditional iterative learning control (ILC) method, the operational time interval is conventionally fixed to facilitate a seamless learning process along the iteration axis. However, this condition may frequently be contravened in real-time applications owing to unknown uncertainties and unpredictable factors. In essence, replicating a control system at a consistent time interval proves challenging in practical scenarios. This paper proposes an adaptive iterative learning control (AILC) method for the multi-input–multi-output (MIMO) nonlinear system with nonuniform trial lengths and an invertible control gain matrix. Compared to the existing AILC research that features nonuniform trial lengths, the control gain matrix of the system in this paper is assumed to be invertible. Hence, the general requirement in the conventional AILC method that the control gain matrix of the system is positive-definite (or negative-definite) or even known is relaxed. Moreover, the tracking reference allows it to be iteration-varying. Finally, to prove the convergence of the system, the composite energy function is introduced and to verify the validity of the AILC method, a robot movement imitation with an uncalibrated camera system is used. The simulation results show that the actual output can track the desired reference trajectory well, and the tracking error converges to zero after 30 iterations.

This paper addresses the trajectory tracking control problem of underwater robots operating in uncertain underwater environments. An adaptive iterative learning control algorithm is proposed to handle external disturbances caused by environmental uncertainties, as well as system challenges including non-uniform trial lengths and unknown control gain matrices. To improve trajectory tracking accuracy, an external disturbance compensation term is introduced, and the controller parameters are updated online using the tracking error between the desired and actual trajectories. Furthermore, an adaptive learning rate strategy is developed to compensate in real time for errors induced by external disturbances and other uncertainties, enabling dynamic optimization of the controller parameters based on the actual system trajectory. The proposed method relaxes the stringent traditional assumptions that require the control gain matrix to be known and strictly a symmetric positive definite (or negative definite). Based on Lyapunov stability theory and finite-time control techniques, a composite energy function is constructed to rigorously prove the convergence of the closed-loop system. Simulation results demonstrate that the proposed algorithm ensures satisfactory trajectory tracking accuracy and robustness for the underwater robot in the presence of external disturbances and various uncertainties, effectively solving the stabilization control problem in uncertain underwater environments.