An underactuated unmanned surface vessel (USV) is a nonholonomic system, in which trajectory tracking is a challenging problem that has drawn more and more attention from researchers recently. The control of trajectory tracking is of critical importance since it determines whether the task can be carried out successfully. In this paper, a non-singular terminal sliding model (NTSM) controller is proposed for the trajectory tracking control of the underactuated USV, with a nonlinear disturbance observer which is designed to measure complex environmental disturbances such as wind, waves, and currents. Exploratory simulations were carried out and the results show that the proposed controller is effective and robust for the trajectory tracking of underactuated USVs in the presence of environmental disturbances.

Piezoelectric actuators (PEAs), as a smart material with excellent characteristics, are increasingly used in high-precision and high-speed nano-positioning systems. Different from the usual positioning control or fixed frequency tracking control, the more accurate rate-dependent PEA nonlinear model is needed in random signal dynamic tracking control systems such as active vibration control. In response to this problem, this paper proposes a Hammerstein model based on fractional order rate correlation. The improved Bouc-Wen model is used to describe the asymmetric hysteresis characteristics of PEA, and the fractional order model is used to describe the dynamic characteristics of PEA. The nonlinear rate-dependent hysteresis model can be used to accurately describe the dynamic characteristics of PEA. Compared with the integer order model or linear autoregressive model to describe the dynamic characteristics of the PEA Hammerstein model, the modeling accuracy is higher. Moreover, an artificial bee colony algorithm (DE-ABC) based on differential evolution was proposed to identify model parameters. By adding the mutation strategy and chaos search of the genetic algorithm into the previous ABC, the convergence speed of the algorithm is faster and the identification accuracy is higher, and the simultaneous identification of order and coefficient of the fractional model is realized. Finally, by comparing the simulation and experimental data of multiple sets of sinusoidal excitation with different frequencies, the effectiveness of the proposed modeling method and the accuracy and rapidity of the identification algorithm are verified. The results show that, in the wide frequency range of 1–100 Hz, the proposed method can obtain more accurate rate-correlation models than the Bouc-Wen model, the Hammerstein model based on integer order or the linear autoregressive model to describe dynamic characteristics. The maximum error (Max error) is 0.0915 μm, and the maximum mean square error (RMSE) is 0.0244.

This paper proposes a continuous finite-time control scheme using a new form of terminal sliding mode (TSM) combined with a sliding mode disturbance observer (SMDO). The proposed controller is applied for nanopositioning of piezoelectric actuators (PEAs). Nonlinearities, mainly hysteresis, can drastically degrade the system performance. Same as the model imperfection, hysteresis can also be treated as uncertainties of the system. These uncertainties can be addressed by terminal sliding mode control (TSMC) for it is promising for positioning and tracking control. To further improve the robustness of the TSM controller, the SMDO is employed to estimate the bounded disturbances and uncertainties. The robust stability of the TSMC is proved through a Lyapunov stability analysis. Simulation results demonstrate the effectiveness of the proposed TSM/SMDO controller for both positioning and tracking applications. The fast response, few chattering, and high precision positioning and tracking performances can be achieved in finite time by the proposed controller.

Piezoelectric actuators (PEAs) have been widely used in aerospace, electronic communication and other high-accuracy manufacturing fields because of their high precision, low power consumption, fast response, and high resolution. However, piezoelectric actuators have very complicated hysteresis nonlinearity, which greatly affects their positioning and control accuracy. Particularly in the field of active vibration control, the control accuracy of piezoelectric actuators is easily affected by noise points. To address the problem, this paper proposes a hyperplane probability c-regression model (HPCRM) algorithm to establish its T-S fuzzy model of hysteresis nonlinearity. Firstly, an improved fuzzy c regression clustering algorithm is proposed to identify the antecedent parameters of T-S fuzzy model. This algorithm not only divides the fuzzy space better but also effectively avoids the influence of noise points generated by the external environment during data acquisition. Secondly, a new type of hyperplane membership function is introduced to solve the problem that the traditional Gaussian membership function does not match the hyperplane clustering algorithm. Finally, the accuracy of the modeling method is confirmed by several comparative experiments. Experimental results show that the proposed method is more precise than the traditional fuzzy c-regression models (FCRM) and probability c-regression models (PCRM) under the sine signals of 5 Hz–100 Hz.

This paper proposes an adaptive proportion‐integral (PI)‐based sliding mode control design (APISMC) used for nanopositioning of piezoelectric actuators (PEAs). Nonlinearities, mainly hysteresis, can drastically degrade the system performance. As well as the model imperfection, hysteresis can be treated as uncertainties of the system. These uncertainties can be addressed by sliding mode control (SMC) since SMC is promising for positioning and tracking control. To further improve the response speed, suppress chattering, and reduce the steady‐state error, the adaptive PI‐based SMC is employed to replace the discontinuous control. Actually, the adaptive PI‐based SMC offers a fast convergence of the sliding surface. Further, another advantage of the proposed controller lies in that its implementation only requires the online tuning PI parameters without acquiring the knowledge of bounds on system uncertainties. A linear second‐order system is utilized as the estimated model to compensate for the process nonlinearity and estimate the control gain. The robust stability of the APISMC is proved through a Lyapunov stability analysis. Simulation results demonstrate that the modified SMC is superior to the original one for both positioning and tracking applications. Compared with the original, the proposed controller provides better performance—less chattering, faster response, and higher precision.