Continuous Finite-Time Terminal Sliding Mode IDA-PBC Design for PMSM with the Port-Controlled Hamiltonian Model

Finite-time control scheme for speed regulation of permanent magnet synchronous motor (PMSM) is investigated under the port-controlled Hamiltonian (PCH), terminal sliding mode (TSM), and fast TSM stabilization theories. The desired equilibrium is assigned to the PCH structure model of PMSM by maximum torque per ampere (MTPA) principle, and the desired Hamiltonian function of state error is constructed in the form of fractional power structure as TSM and fast TSM, respectively. Finite-time TSM and fast TSM controllers are designed via interconnection and damping assignment passivity-based control (IDA-PBC) methodology, respectively, and the finite-time stability of the desired equilibrium point is also achieved under the PCH framework. Simulation results validate the improved performance of the presented scheme

Sliding Mode Control Design for a Class of SISO Systems with Uncertain Sliding Surface

The problem of designing a sliding mode controller with uncertain sliding surface for a class of uncertain single-input-single-output systems is studied. The design case is handled by using the invariant transformation first in order to separate the sliding mode and the reaching mode of the sliding mode control system. It is shown that the sliding mode design needs not to consider the uncertainties of the sliding surface, which can be handled in the reaching phase design. The results generalize the robust design of the reaching phase such that one specific reaching phase design may agree with several sliding surfaces

Evaluating Structural, Chlorophyll-Based and Photochemical Indices to Detect Summer Maize Responses to Continuous Water Stress

his study evaluates the performance of structural, chlorophyll-based, and photochemical indices to detect maize water status and to assess production based on five years of field experiments (2013–2017) during the primary growth stages. We employed three categories of indicators, including water condition and productive and thermal indicators, to quantify the responses of summer maize under continuous water stress from drought to waterlogging conditions. Furthermore, we adopted several spectral indices to assess their sensitivity to three categories of metrics. The results showed the association is the best between the treatment level and Leaf Water Content (LWC). The waterlogging treatment influenced Leaf Water Potential (LWP) in moderate drought stress. Severe drought stress caused the strongest reduction in productivity from both Leaf Area Index (LAI) and chlorophyll content. In terms of sensitivity of various indices, red-edge-position (REP) was sensitive to maize water conditions LWP, LAI and chlorophyll content. Photochemical Reflectance Index (PRI) and Normalized Difference Vegetation Index (NDVI) were the most and second most sensitive indices to productive indicators, respectively. The results also showed that no indices were capable of capturing the information of Crop Water Stress Index (CWSI)

Fixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems

Abstract The paper devotes to study fixed‐time stability of stochastic nonlinear systems and fixed‐time consensus of stochastic multi‐agent systems (SMASs). Firstly, a new fixed‐time stability theorem is established and a high‐precise estimation of settling time is provided. Secondly, as an application, the fixed‐time consensus problem of SMASs is discussed in virtue of the established theorem. A new class of fixed‐time nonlinear consensus protocols with stochastic perturbation is designed by employing the neighbour's information. Based on graph theory, matrix theory and fixed‐time stability theorem, we prove that fixed‐time consensus of SMASs is achieved under the designed protocol. Moreover, some sufficient conditions are proposed to guarantee fixed‐time consensus of SMAS. It is shown that the settling time is not only independent of the initial conditions, but also it has higher precise. In the end, three numerical examples are provided to illustrate correctness of our theoretical results

Sliding mode control of a piezoelectric actuator with neural network compensating rate-dependent hysteresis

Piezoelectric actuators (PEA) are the fundamental elements for high-precision high-speed positioning/tracking task in many nanotechnology applications. However, the intrinsic hysteresis observed in PEAs has impaired their potential, specially, the motion accuracy. In this paper, the complicated nonlinear dynamics of PEA including hysteresis, creep, drift and time-delay etc. are treated as a black-box system exhibited as rate-dependent hysteresis. The multi-valued hysteresis is analyzed as a single-valued function so that a neural network (NN) can be built to model the hysteresis and its inversion. A sliding mode controller (SMC) augmented with inverse hysteresis model is then developed to compensate the hysteretic behavior, modeling error and disturbance to improve the positioning/tracking stability and accuracy. The effectiveness of this algorithm experimentally verified through the actual tracking control of a PEA

Robust global fast terminal sliding mode controller for rigid robotic manipulators

A global fast terminal sliding mode controller (GFTSMC) is proposed for a-link rigid robot manipulators by employing the fast terminal sliding mode control concept" in both the reaching phase and the sliding phase. Under the control, the system states will reach the terminal sliding manifold in a desired finite time and then converge to the origin along the sliding manifold in a specified finite time, resulting in reduced steady tracking error in comparison with the linear sliding mode controller. The proposed sliding mode controller is continuous and therefore is chattering-free. An example is shown to demonstratethe effectiveness of the controller

Indirect adaptive fuzzy control of nonlinear systems with terminal sliding modes

A global fast terminal sliding mode controller with fast terminal adaptive fuzzy approximator is proposed for general single input single output nonlinear systems. The finite time convergence property of the fast terminal sliding mode is used in the design of the controller. It is applied not only in the reaching phase and the sliding phase of the sliding mode control system, but also in the adaptive fuzzy approximator for the unknown nonlinear system. Stability of the control system and convergence of the approximation are proved

A fuzzy neural network approximator with fast terminal sliding mode and its applications

This paper presents a new training method for fuzzy neural network (FNN) systems to approximate unknown nonlinear continuous functions. Fast terminal sliding mode combining the finite time convergent property of terminal attractor and exponential convergent property of linear system has faster convergence to the origin in finite time. The proposed training algorithm uses the principle ofthe fast terminal sliding mode into the conventional gradient descent learning algorithm. The Lyapunov stability analysis in this paper guarantees that the approximation is stable and converges to the optimal approximation function with improved speed instead of finite time convergence to unknown function. The proposed FNN approximator is then applied in the control of an unstable nonlinear system and the Duffing system. The simulation results demonstrate the effectiveness of the proposed method