﻿ 潜艇深度PD-模糊控制仿真研究
 舰船科学技术  2019, Vol. 41 Issue (1): 59-65 PDF

Simulation study on submarine depth PD-fuzzy control
LIU Xu-ming, HU Da-bin, XIAO Jian-bo, HU Jin-hui
Power Engineering College, Naval University of Engineering, Wuhan 430033, China
Abstract: Aiming at the problem that the single control method is ineffective to control depth of submarine, a compound control method combining PD control with fuzzy control was studied for keeping submarine depth. Based on vertical motion of submarine, PD-fuzzy controller for depth and fuzzy controller for pitch were designed. The three-degree-of-freedom simulation model of the submarine was established by using the Aerospace toolbox of Matlab/Simulink. The PID controller and the compound controller were used for simulation test under different working conditions. The simulation results show that, compared with the conventional PID controller, the compound controller has the characteristics of fast response, strong anti-interference ability and good robustness.
Key words: PID control     fuzzy control     three-degree-of-freedom
0 引　言

1 潜艇垂直面运动模型

 $\begin{split} &m(\dot u + wq - {x_G}{q^2} + {z_G}\dot q) =\\ & \frac{1}{2}\rho {L^4}{{X'}_{qq}}{q^2} + \frac{1}{2}\rho {L^3}({{X'}_{\dot u}}\dot u + {{X'}_{wq}}wq)+ \\ & \frac{1}{2}\rho {L^2}({{X'}_{uu}}{u^2} + {{X'}_{ww}}{w^2}) + \frac{1}{2}\rho {L^2}{u^2}({{X'}_{{\delta _b}{\delta _b}}}{\delta _b}^2 +\\ & {{X'}_{{\delta _s}{\delta _s}}}{\delta _s}^2) + \frac{1}{2}\rho {L^2}({a_T}{u^2} + {b_T}u{u_c} + {c_T}{u_c}^2) -\\ & (P - B)\sin \theta \text{，} \end{split}$ (1)

 $\begin{split} & m(\dot w - uq - {z_G}{q^2} - {x_G}\dot q) =\\ & \frac{1}{2}\rho {L^4}(Z_{\dot q}'\dot q + Z_{q\left| q \right|}'q\left| q \right|) + \frac{1}{2}\rho {L^3}Z_{\dot w}'\dot w +\\ & \frac{1}{2}\rho {L^3}(Z_q'uq + {{Z'}_{\left| q \right|{\delta _s}}}u\left| q \right|{\delta _s} + Z_{w\left| q \right|}'w\left| q \right|) +\\ & \frac{1}{2}\rho {L^2}(Z_0'{u^2} + Z_w'uw + Z_{w\left| w \right|}'w\left| w \right| + Z_{\left| w \right|}'u\left| w \right| + Z_{ww}'{w^2}) +\\ & \frac{1}{2}\rho {L^2}{u^2}(Z_{{\delta _b}}'{\delta _b} + Z_{{\delta _s}}'{\delta _s}) + (P - B)\cos \theta\text{，} \end{split}$ (2)

 $\begin{split} & {I_{yy}}\dot q + m\left[ {{z_G}\left( {\dot u + wq} \right) - {x_G}\left( {\dot w - uq} \right)} \right] =\\ & \frac{1}{2}\rho {L^5}(M_{\dot q}'\dot q + M_{q\left| q \right|}'q\left| q \right|) + \frac{1}{2}\rho {L^4}(M_{\dot w}'\dot w + M_q'uq +\\ & M_{\left| q \right|{\delta _s}}'u\left| q \right|{\delta _s} + M_{\left| w \right|q}'\left| w \right|q) + \frac{1}{2}\rho {L^3}(M_0'{u^2} + M_w'uw +\\ & M_{w\left| w \right|}'w\left| w \right| + M_{\left| w \right|}'u\left| w \right| + + M_{ww}'{w^2}) + \frac{1}{2}\rho {L^3}{u^2}(M_{{\delta _b}}'{\delta _b} +\\ & M_{{\delta _s}}'{\delta _s}) - Ph\sin \theta - \Delta P\Delta x\cos \theta - \Delta P\Delta z\sin \theta \text{。} \end{split}$ (3)

 $\dot \xi = u\cos \theta + w\sin \theta\text{，}$ (4)
 $\dot \zeta = - u\sin \theta + w\cos \theta \text{，}$ (5)
 $\dot \theta = q\text{。}$ (6)

2 潜艇深度与纵倾控制系统

 图 1 深度与纵倾控制系统框图 Fig. 1 Diagram of depth and pitch control system

 图 2 深度与纵倾控制系统仿真模型 Fig. 2 The simulation model of depth and pitch control system for submarine
 ${\delta _b} = {k_p}(\zeta - {\zeta _0}) + {k_d}\frac{{d(\zeta - {\zeta _0})}}{{d{\text{t}}}}\text{。}$ (7)

 图 3 舵机伺服系统仿真模型 Fig. 3 The simulation model of steering gear servo system
 $T\dot \delta = K({\delta _c} - \delta )\text{。}$ (8)

3 模糊控制器的设计

3.1 模糊化

 图 4 深度偏差e1的隶属函数 Fig. 4 Membership function of depth deviation e1

 图 5 深度偏差变化率ec1的隶属函数 Fig. 5 Membership function of depth deviation ratio ec1

 图 6 指令首舵角u1的隶属函数 Fig. 6 Membership function of ordered bow-rudder u1
3.2 知识库

 图 7 潜艇深度控制过程的典型阶跃响应 Fig. 7 The classic step response of submarine depth control process

3.3 模糊推理与清晰化

 图 8 深度模糊控制器的模糊推理输出特性曲面 Fig. 8 Fuzzy reasoning surface of depth fuzzy controller
4 仿真与分析

4.1 试验结果

1）在无干扰情况下，初始深度为80 m，分别给定目标深度120 m，40 m使其下潜和上浮，仿真结果如图9图10所示。

 图 9 下潜时各参数响应曲线 Fig. 9 The response curve of each parameter when diving

 图 10 上浮时各参数响应曲线 Fig. 10 The response curve of each parameter when floating

2）在有干扰情况下，初始深度为60 m，使其下潜至90 m，仿真结果如图11所示。图12为深度变化曲线局部放大图，图13为首舵变化曲线局部放大图。

 图 11 有干扰下各参数响应曲线 Fig. 11 The response curve of each parameter under interference

 图 12 深度响应曲线局部放大图 Fig. 12 Partial magnification of depth response curve

 图 13 首舵响应曲线放大图 Fig. 13 Partial magnification of bow-rudder response curve
4.2 分析

1）从图9（a）可以看出，PD-模糊控制相比于传统PID控制，具有响应速度更快，稳定时间更短，超调量更小的优点。这是由于在到达阈值之前不用考虑复合控制器的PD参数过大而引起超调，故其上升时间较短；而在到达阈值之后，复合控制器的模糊控制具有控制平缓的特点，故其稳定时间更短，超调更小。

2）通过图9图10对比可知，在不同工况下，PID控制器需要调整参数以使控制效果达到最优，而复合控制器不需要更改参数就可以满足控制要求，说明复合控制器具有较好的适应性和鲁棒性。

3）从图11图13可以看出，在有干扰条件下，PID控制的响应曲线震荡明显，尤其在打舵方面，这对潜艇的隐身性不利，同时也增加了舵机的磨损，而复合控制器的响应曲线变化平稳，受扰动影响较小。这说明复合控制器具有更好的抗干扰能力。

4）由于模糊控制器本质上属于PD控制，会产生静态偏差，但本文所设定的阈值很小，故其静态偏差可以忽略。若还需减小静态误差，则可以引入模糊积分环节。

5）在应用PD-模糊控制方法中，切换阈值 ${e_t}$ 的大小对控制效果有很重要的影响，如果选取过大，由于PD控制器作用时间短，无法发挥PD控制响应速度快的优点；选取过小，由于潜艇的惯性较大，模糊控制无法及时抑制潜艇运动而产生超调。因此，应该根据实际情况选择合适的切换阈值以兼顾系统的响应速度和控制超调。

5 结　语

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