To overcome the detrimental effect of residual stress in welded joints, which affects the overall performance of the welded structure, this paper studies the magnitude and distribution of residual stress after welding and local post-weld heat treatment (PWHT). The coupled thermo-metallurgical-mechanical model for welding 6 mm thick Ti-6Al-4V (TC4) titanium alloy plates was established, the evolution of the SSPT and its effect on the residual stress were quantitatively analyzed, and a parametric analysis of local PWHT was performed. The results demonstrated that there was good agreement between the numerical results and the experimental data. Due to the cooling rate reaching 327 °C/s, the volume fraction of α^、 in the fusion zone (FZ) reached 0.218 after welding and decreased by 90.83% after PWHT when the heating temperature was 700 °C. The peak value of the longitudinal residual stress can reach 686.4 MPa after welding with SSPT, which was 11.38% lower than that without SSPT, and it decreased by 65.6% after PWHT when the heating temperature was 900 °C. The research results demonstrate that SSPT has a significant effect on residual stress, and PWHT can obviously reduce the residual stress, which provides a certain reference for welding TC4 titanium alloy plates.

Aiming at predefined-time synchronization for chaotic systems, a new predefined-time sliding mode control method is proposed. First, based on the definition of predefined-time stability, a novel predefined-time inequality is proposed, along with a detailed mathematical proof. This inequality differs from existing Lyapunov inequalities and offers greater flexibility. Second, a new sliding mode surface and sliding mode controller are proposed based on this inequality. Since the sliding mode controller introduced in this paper is tunable, the actual convergence time can be adjusted freely within the predefined time. Finally, two sets of numerical simulations demonstrate that the proposed method offers advantages in terms of short synchronization time and high regulatory performance compared to traditional predefined-time sliding mode control, finite-time sliding mode control, and fixed-time sliding mode control.

For the fixed-time nonlinear system control problem, a new fixed-time stability (FxTS) theorem and an integral sliding mode surface are proposed to balance the control speed and energy consumption. We discuss the existing fixed time inequalities and set up less conservative inequalities to study the FxTS theorem. The new inequality differs from other existing inequalities in that the parameter settings are more flexible. Under different parameter settings, the exact upper bound on settling time in four cases is discussed. Based on the stability theorem, a new integral sliding mode surface and sliding mode controller are proposed. The new control algorithm is successfully applied to the fixed-time control of chaotic four-dimensional Lorenz systems and permanent magnet synchronous motor systems. By comparing the numerical simulation results of this paper’s method and traditional fixed-time sliding mode control (SMC), the flexibility and superiority of the theory proposed in this paper are demonstrated. Under the same parameter settings, compared to the traditional FxTS SMC, it reduces the convergence time by 18%, and the estimated upper bound of the fixed time reduction in waiting time is 41%. In addition, changing the variable parameters can improve the convergence velocity.

In this paper, loss minimization control method of IPMSM based on approximate calculation is proposed. Firstly, according to the IPMSM mathematical model considering the equivalent iron loss, the loss minimization extreme value is solved by Lagrange equation, and the electromagnetic current variable is eliminated by the equivalent transformation method. Secondly, the relation of dq axis current is obtained by defining the virtual current. Considering the existence of the square term in the relation, a new approximate calculation method is proposed to eliminate the square term of the given current and obtain the dq axis current with the minimum loss. Finally, in order to further prove the performance of the proposed method, i d = 0 control, virtual current control method and torque approximation control method are analyzed and compared in MATLAB/SIMULINK. Simulation results show that the proposed control method is more perfect than the traditional virtual current method and has higher accuracy than the traditional approximate calculation method. Compared with the traditional three control methods, the total loss is reduced by 7.44% at least under rated working conditions.