Lightweight Modeling of Underwater Gliders and Nonlinear MPC Controller Design with Actuator Constraint
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摘要: 针对现有水下滑翔机模型非线性程度和维度过高以及难以设计有效的工程化控制器的问题, 首先根据水下滑翔机的运动机构组成及工作原理, 忽略建模过程中的次要影响因素, 对水下滑翔机进行轻量化建模以降低模型非线性度及复杂度, 并通过对比验证证明了轻量化模型的有效性。随后, 针对纵垂面运动进一步精简动力学方程, 发挥该模型维度低、计算量小的优点, 引入状态和控制量的实际约束, 设计了贴合实际的实时线性化模型预测姿态控制算法。数值仿真结果证明, 在±17.4°和±22.5°等水下滑翔机常见工况下, 所提出的基于轻量化模型的控制算法可有效快速追踪期望姿态, 且上升时间和稳态调节时间均比传统控制器提高70%以上。Abstract: In response to the problems of high nonlinearity and dimensionality of existing underwater glider models, as well as difficulty in designing effective engineering controllers, the composition and working principle of the motion mechanism of underwater gliders were first studied. By neglecting secondary influencing factors in the modeling process, lightweight modeling of underwater gliders was conducted to reduce model nonlinearity and complexity. The effectiveness of the lightweight model was demonstrated through comparative verification. Subsequently, according to the motion in the vertical plane, the dynamic equation was further simplified, and the advantages of low dimension and small calculation amount of the model were brought into play. The actual constraints of state and control variables were introduced, and a realistic predictive attitude control algorithm for a real-time linearized model was designed. The numerical simulation results show that under the two common working conditions of ±17.4° and ±22.5° for underwater gliders, the control algorithm based on the lightweight model proposed in this paper can quickly track the desired attitude, and the rise time and steady-state settling time are improved by more than 70% compared with traditional controllers.
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Key words:
- underwater glider /
- lightweight modeling /
- predictive control of model
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图 3 不同输入阶跃信号下俯仰角变化曲线
Figure 3. Change curves of pitch angle under different input step signals
表 1 实验参数列表
Table 1. List of experimental parameters
参数 数值 参数 数值 D/$ ( {{\text{m/}}{{\text{s}}^2}} ) $ 2.431 ${K_{M_0} }$/kg 0.28 $ {J_2} $/$( {{\text{kg}} \cdot {{\text{m}}^2}} )$ 25.430 $ {K_M} $/$( {{\text{kg/rad}}} )$ −65.84 $ {m_r} $/kg 11.000 $ {K_q} $/$( {{\text{kg}} \cdot {\text{s/ra}}{{\text{d}}^{\text{2}}}} )$ −205.64 g/$( {{\text{m/}}{{\text{s}}^{\text{2}}}} )$ 9.800 $ {m_s} $/kg 54.28 $ \tau $/s 0.200 $ {m_b} $/kg −0.5~0.5 $ {I_{s2}} $/$( {{\text{kg}} \cdot {{\text{m}}^{\text{2}}}} )$ 15.270 $ {I_{r2}} $/$( {{\text{kg}} \cdot {{\text{m}}^{\text{2}}}} )$ 10.16 $ {I_{A2}} $/$( {{\text{kg}} \cdot {{\text{m}}^{\text{2}}}} )$ 7.880 $\alpha $/(°) −7~7 
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表 2 RL-MPC与PID控制器性能指标对比
Table 2. Performance Index of RL-MPC and PID Controller
工作状态为$ \pm 17.4^\circ $ 时间/s 上升时间/s 调节时间/s PID RL-MPC PID RL-MPC 0~40 9.27 2.41 13.06 3.60 40~80 9.47 2.50 13.42 3.75 工作状态为$ \pm 22.5^\circ $ 时间/s 上升时间/s 调节时间/s PID RL-MPC PID RL-MPC 0~40 9.40 2.60 13.23 3.88 40~80 9.48 2.65 13.51 3.92
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