﻿ 基于VFFRLS的水下协同作业ROV自校正滑模控制
 舰船科学技术  2022, Vol. 44 Issue (16): 89-93    DOI: 10.3404/j.issn.1672-7649.2022.16.017 PDF

Self-tuning sliding mode control of ROV for underwater cooperative operation based on VFFRLS
LI Guo-dong, WANG Xu-yang
Institute of Underwater Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China
Abstract: The recovery of fuel oil from deep-sea sunken ships is of great significance to the protection of the marine environment. Remote operated vehicle are required to connect large equipment such as inner and outer hull perforating machines and pumping machines to complete the perforation of the inner and outer ship plates and inner pumping and other underwater meticulous process. After the ROV is docked with large equipment, the dynamic parameters of the entire system will change significantly, resulting in the original controller being no longer suitable for the new system. It may even diverge when controlling the heading angle, making it impossible to perform meticulous process. For this reason, a self-tuning sliding mode control based on the recursive least squares method with variable forgetting factor is proposed, and the sliding mode control parameters are updated in real time through online identification of changing system dynamics parameters to improve the adaptive performance of the controller, thereby satisfying the specific motion control accuracy requirements of ROV cooperative operation, and the effectiveness of the method is verified by the simulation experiment of Matlab/Simulink heading angle tracking sine curve.
Key words: ROV     model identification     self-tuning control     sliding mode control     underwater cooperative operation
0 引　言

1 ROV动力学模型

 图 1 固定坐标系 ${O_n} - XYZ$ 与随体坐标系 $O - xyz$ Fig. 1 Fixed coordinate system ${O_n} - X Y Z$ and satellite coordinate system $O - xyz$

 $M\dot v + C(v)v{\text{ + }}D(v)v + g(\eta ) = \tau 。$ (1)

 $M\dot v + D(v)v + g(\eta ) = \tau ，$ (2)
 $M = {\rm{diag}}\{ m - {X_{\dot u}}{\text{ }}0{\text{ }}m - {Z_{\dot w}}{\text{ }}0{\text{ }}{M_{\dot q}}{\text{ }}{I_z} - {N_{\dot r}}\}，$ (3)
 $D = - {\rm{diag}}\{ {X_u}{\text{ 0 }}{Z_w}{\text{ 0 }}{M_q}{\text{ }}{N_r}\}，$ (4)
 $g(\eta ) = {[0{\text{ }}0{\text{ }} - W{\text{ }}0{\text{ }} - WB{G_z}\sin (\theta ){\text{ }}0]^{\rm{T}}}。$ (5)

 $({I_z} - {N_{\dot r}})\dot r - {N_r}r = {\tau _N}，$ (6)

 $\tau \dot r(t) + r(t) = Ku(t - {T_d}) , \dot \varphi (t) = r(t)，$ (7)

 $G(s) = \frac{{{\varphi _s}}}{{{u_s}}} = \frac{K}{{\tau {s^2} + s}}{e^{ - {{{T}}_d}s}} 。$ (8)

2 水下机器人基于VFFRLS的自校正滑模控制 2.1 可变遗忘因子的递推最小二乘法

VFFRLS算法是基于最小二乘法原理的一种改进算法，具有对于参数的识别速度较快，对于参数的变化敏感，计算量较最小二乘法小，适合于工程使用，且对于噪声的抗扰能力较强的特点，其算法原理如下[9-10]

 $e(n) = d(n) - {x^{\rm{T}}}(n)w(n - 1) ，$ (9)
 $k(n) = \frac{{p(n - 1)x(n)}}{{\lambda (n) + {x^{\rm{T}}}(n)p(n - 1)x(n)}}，$ (10)
 $w(n) = w(n - 1) + k(n)e(n)，$ (11)
 $p(n) = \frac{1}{{\lambda (n)}}\left[ {p(n - 1) - k(n){x^{\rm{T}}}(n)p(n - 1)} \right]，$ (12)
 $\lambda (n) = {\lambda _{\min }} + (1 - {\lambda _{\min }}){2^{L(n)}} ，$ (13)
 $L(n) = - {\rm{round}}[\mu {e^2}(n)] 。$ (14)

2.2 控制系统结构

ROV在对接特殊装置后系统动力学参数会发生较大改变，由于滑模控制参数与ROV系统水动力参数具有较强的相关性，所以需要实时调整滑模控制器的参数，才能够获得满足工程精度要求的控制性能。ROV基于VFFRLS的自校正滑模控制器结构设计如图2所示，当系统动力学参数发生较大变化后，VFFRLS算法的遗忘因子会先趋向于最小值，当辨识参数稳定后，遗忘因子会趋向于最大值，此时的自校正滑模系统的控制率能取得最佳控制效果。

 图 2 基于VFFRLS的自校正滑模控制系统结构 Fig. 2 The structure of an underwater vehicle adaptive sliding model control system based on VFFRLS
2.3 自校正滑模控制

 $\ddot \varphi = \frac{{{N_r}}}{{{I_z} - {N_{\dot r}}}}\dot \varphi + \frac{1}{{{I_z} - {N_{\dot r}}}}{\tau _N}，$ (15)

 $s = c\dot \varphi + (\varphi - {\varphi _d}) = c\dot \varphi + {\varphi _e} ，$ (16)

 $\dot s = c\ddot \varphi + {\dot \varphi _e} = \left(c\frac{{{N_r}}}{{{I_z} - {N_{\dot r}}}} + 1\right){\dot \varphi _e} + c\frac{1}{{{I_z} - {N_{\dot r}}}}{\tau _N} ，$ (17)

 $\dot s = - \varepsilon {{\rm{sgn}}} (s) - ks{\text{ }}(\varepsilon > 0,k > 0)，$ (18)

 ${\tau _N} = \frac{{{I_z} - {N_{\dot r}}}}{c}\left( - \varepsilon {{\rm{sgn}}} (s) - ks\right) - \left({N_r} + \frac{{{I_z} - {N_{\dot r}}}}{c}\right){\dot \varphi _e} ，$ (19)

${\tau _N}$ 即控制输入。

 $V(s,t) = \frac{1}{2}{s^2} ，$ (20)

 $V'(s,t) = s\dot s = s( - \varepsilon {{\rm{sgn}}} (s) - ks)。$ (21)

3 首向角速度跟踪仿真对比

 ${K_p} = \frac{{w_n^2\tau }}{K} ，$ (22)
 ${K_d} = \frac{{2\xi \sqrt {K{K_p}\tau } - 1}}{K} = \frac{{2\xi {w_n}\tau - 1}}{K}，$ (23)
 ${K_i} = \frac{{{w_n}}}{\text{π} }{K_p} = \frac{{w_n^3\tau }}{{\text{π} K}} 。$ (24)

VFFRLS在仿真实验过程中识别出来的参数如图3所示，平均误差率如表3所示。可以看出，基于该种方法得到的在线辨识参数准确且迅速，误差率在5%以下，在采样率为100 Hz的条件下2 s内可以得到较稳定结果。在角度跟踪的仿真中，60 s的时候ROV对接了重量为1050 kg的内层开孔机，并改变了其系统特性，即系统动力学参数。传统PID控制、基于VFFRLS的自校正PID控制、传统滑模控制与基于VFFRLS的自校正滑模控制效果见图4

 图 3 VFFRLS参数辨识图 Fig. 3 Recursive least square method parameter identification diagram with variable forgetting factor

 图 4 PID控制、滑模控制、自校正PID控制与自校正滑模控制效果对比 Fig. 4 Comparison of the effects of PID control, sliding mode control, self-tuning PID control and self-tuning sliding mode control

1）当ROV系统动力学参数发生比较大改变后，对于传统PID控制器与传统滑模控制的影响比较大，PID控制器跟踪首向角时甚至出现了发散，但自校正滑模控制与自校正PID控制在跟踪角度正弦信号仍然保持着良好的跟踪效果。

2）在模型变换前，自校正滑模控制参考输入与输出的标准差比自校正PID参考输入与输出的标准差小68.57%，模型变换后，自校正滑模控制参考输入与输出的标准差比自校正PID控制参考输入与输出的标准差小34.80%。所以自校正滑模控制比自校正PID控制效果更好。

3）在模型变换后，自校正滑模控制参考输入与输出的标准差比传统滑模控制参考输入与输出的标准差要小72.31%，所以基于VFFRLS的在线辨识算法可以有效地提升滑模控制的跟踪效果。

4 结　语

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