## 1 Introduction
The main contributions of this work can be summarized in the following aspects: (a) in practice, based on engineering applications, a new type of additional motor drive design is adopted in the LSJ damping system, accompanied by a centralized lubrication system, effectively improving the stability of the system. (b) In theory, an iterative algorithm based on a PD controller is used to control nonlinear LSJ systems. By utilizing large-step simulation algorithms and hardware sampling, the running time of iterative algorithms is shortened, making them more suitable for engineering applications. (c) In terms of combining theory and practice, by utilizing the C-HITL platform, i.e., the software and hardware combination method by way of OLE (object linking and embedding) for process control (OPC) communication, any complex intelligent algorithm can be indirectly applied to conventional controller hardware, which actually proposes an engineering application approach for complex intelligent algorithms. (d) The LSJ vibration control is a rarely studied topic, but its harmfulness is becoming increasingly apparent under extreme working conditions. At present, the LSJ control in some studies is based on a qualitative control method established on the basis of constant speed, slowly varying the yaw angle control. The LSJ control in the present study is an integrated control method based on a nonlinear LSJ displacement and nonlinear yaw angle, which has more engineering practical significance and is convenient for dealing with extreme working conditions. The knowledge gap that this study intends to bridge is also related to the following aspects. The types of yaw systems are mainly divided into two categories [28]: one is the sliding bearing yaw system, as shown in this study, and the other is the rolling bearing system. At present, neither of these commercial systems has established or matched LSJ suppression system methods, and both are simplified through the intermittent application of lubricating oil [29]. Therefore, another advantage of this study is the design of an intelligent algorithm for performing matching [30; 31], which not only drives the auxiliary motor, but also achieves dynamic lubrication, characterized by dynamic changes in the rolling friction coefficient. In the traditional jitter control method, a performance balance method between worm gear self-locking and yaw braking mechanisms was also used to achieve limited LSJ suppression [32], which is a local and passive suppression method. The characteristics of this passive suppression method include stiffness adjustment design, finite element analysis method, and linear LSJ amplitude suppression based on the assumption of a constant yaw rate [33; 34; 35]. However, the active dynamic control method adopted in the present study not only achieves amplitude suppression, but also frequency suppression, and it can directly handle nonlinear systems, which has a positive significance for engineering applications. Of course, in the end, this design also explores the theoretical method [36; 37] of handling nonlinear systems based on a linear analysis with linear matrix inequality (LMI), as a purely theoretical discussion compared to engineering application methods.