## 1 Introduction
This is typically applicable to applications that require a MAS to rapidly converge to a consensus state within a specified time frame [13], such as obstacle avoidance conditions, decision-making in emergencies [14], and so on. Reference [15] introduces and analyzes two distributed control protocols based on finite-time stability to address the first-order nonlinear MASs problem with rapid convergence. The initial state typically affects the convergence time of the finite-time consensus. When the initial state of the system is large, the convergence time will correspondingly increase, and the effectiveness of achieving finite-time convergence may not be as pronounced [16]. Therefore, the fixed-time consistency theory was developed to address this issue. The fixed-time consensus requires that a MAS reaches a consensus synchronization state within a predetermined fixed time, regardless of the initial state. The fixed-time consensus is typically applicable to applications with strict performance and robustness requirements for MASs, such as formation control of aircraft, and synchronization in satellite networks. Reference [17] proposed a fixed-time consistency protocol to achieve convergence of the system within a fixed time. The results show that the system performance is significantly better than the finite-time consistency protocol. In multi-motor speed regulation systems, the accuracy of speed synchronization control depends not only on the speed loop controller structure and control algorithms but also heavily on the design of the current loop controller. Sliding mode control (SMC) is widely utilized in the design of controllers for speed regulation systems due to its significant advantages such as high precision, strong robustness, and simple structure [18]. In traditional SMCs, a high switching control gain is typically employed to ensure system robustness. However, this high switching gain strategy often leads to chattering phenomena [19]. Complementary sliding mode control (CSMC), compared to other control methods, not only effectively reduces the chattering phenomenon but also offers improved control precision [20]. Through this approach, it can be ensured that the velocity/position error of the motor is reduced by at least 50% when compared to traditional SMC [21]. Reference [22] proposes a disturbance-observer-based CSMC, which endows the entire PMSM control system with excellent capabilities for suppressing chattering and ensuring tracking performance. Additionally, the conventional SMC method cannot guarantee the robustness of the servo system in the approaching phase [23]. Therefore, the TISMC method has been developed [24]. Compared with traditional SMC, TISMC can set the initial value of the integral term to place the system in the sliding phase at the beginning, eliminating the approaching phase and enhancing system robustness. The main contributions are as follows:  
1. This paper innovatively considers the multi-PMSM speed control system as a MAS, transforming the problem of coordinated speed control of multi-PMSMs into a consensus problem of MASs. 2. The designed consensus protocol enables the system to converge within a fixed time. Additionally, a terminal integral sliding mode observer (TISMO) is designed to observe disturbances and compensate for them, thereby obtaining the desired q-axis current. 3. Within the framework of PMSM vector control, a CSMC current loop controller is designed for each PMSM system, effectively suppressing system chattering and enhancing the robustness of the system. The structure of this paper is as follows: Section 2 presents the mathematical model of the multi-PMSM system, and some used lemmas are given. In Section 3, a consensus protocol and a disturbance observer are designed, and their stability is proven using the Lyapunov function. In Section 4, a CSMC current loop controller is designed. In Section 5, comparative experimental validation is carried out and the results are analyzed. This paper is summarized in Section 6.