Abstract：The traditional underwater launch device uses high-pressure gas to launch the load, and the structure and timing of the gas-generating mechanism are solidified. It operates in an open-loop mode according to the preset parameters, and cannot be accurately adjusted in time according to the load state, so meeting the increasing and diversified launch requirements is challenging. The thrust of the electromagnetic launcher is precisely adjustable, which makes it possible to launch underwater weapons using universal power. The resistance of the ground electromagnetic launcher is mainly nonlinear sliding friction and aerodynamic resistance. In addition, the resistance is considered small compared with the thrust at medium and low speeds. Thus, the model of the ground electromagnetic launcher can be simplified to a linear control system. However, the fluid resistance of the hydraulically balanced electromagnetic launch system is large and has a strong nonlinear relationship with the flow rate. The additional mass increases continuously during the launch process, and the system cannot be simplified into a linear system, which makes internal ballistic adjustment more difficult. Based on the principle and structure of the hydraulically balanced electromagnetic launch device, this paper first deduces the nonlinear dynamic analytical equation of the system, and gives a detailed derivation of key variables, which makes the nonlinear characteristics of the system clearer. A lumped loss coefficient is adopted to represent all fluid losses in the launch system and is directly calculated using easily measurable parameters such as thrust, mover, and load velocities. The system is transformed into a pseudo-linear system using state feedback linearization. Considering the practical engineering factors, the composite control strategies of "feedback linearization + proportion integration differentiation (PID) control" and "feedback linearization + sliding mode control (SMC)" are adopted respectively based on classical PID control and SMC. The launch performances are compared with the classic linear PID control. A set of underwater electromagnetic launch test devices has been developed, mainly including a cylindrical linear motor integrated launcher with a rated thrust of 200 tons, a 50 MV·A inverter, and a 30 MW lithium battery energy storage device. The launch device is installed beneath 40 meters of deep water. A series of launch tests were carried out. The results show that the PID control has an obvious lag error, and the combination of thrust feedforward can speed up the dynamic response. The composite control strategy of feedback linearization combined with PID or SMC has smaller tracking error, stronger anti-interference ability, and better adaptability. The linearized composite control method works well under typical conditions, abnormal conditions, strong disturbance conditions, and ballistics vary conditions. The muzzle velocity and position errors are both less than ±2 %. Sliding mode control suffers from chattering, the transient mutation in thrust will arouse noises that weaken the vehicle's acoustic stealth. Taking all factors into consideration, "feedback linearization + PID" is the most suitable for the requirements of an underwater electromagnetic launcher. The nonlinear factors are fully considered in the modeling and control algorithm, and high performance for inner ballistic control of the underwater electromagnetic launcher has been achieved. The modeling method is suitable for the hydraulically pressure-balanced launch application, and the control algorithm has a clear concept and strong versatility.
聂世雄. 集成式液压平衡电磁发射装置的非线性建模及控制[J]. 电工技术学报, 2023, 38(4): 852-864.
Nie Shixiong. Nonlinear Modeling and Control of Integrated Hydraulic Balanced Electromagnetic Launch System. Transactions of China Electrotechnical Society, 2023, 38(4): 852-864.
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2023, Vol. 38 
