文章信息
- 吕成兴, 于海生, 周忠海, 臧鹤超, 张风丽, 张照文. 2018.
- Lü Cheng-xing, YU Hai-sheng, ZHOU Zhong-hai, ZANG He-chao, ZHANG Feng-li, ZHANG Zhao-wen. 2018.
- 端口受控哈密顿方法的电力双推进无人船航向航速控制
- Speed and heading control of unmanned surface vehicles system based on port-controlled hamiltonian (PCH) control method control method
- 海洋科学, 42(1): 134-138
- Marina Sciences, 42(1): 134-138.
- http://dx.doi.org/10.11759/hykx20171011023
-
文章历史
- 收稿日期:2017-10-11
- 修回日期:2017-12-30
2. 齐鲁工业大学(山东省科学院), 山东省科学院 海洋仪器仪表研究所, 山东 青岛 266033;
3. 山东省海洋环境监测技术重点实验室, 山东 青岛 266033;
4. 国家海洋监测设备工程技术研究中心, 山东 青岛 266033
2. Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Sciences), Qingdao 266033, China;
3. Shandong Provincial Key Laboratory of Ocean Environmental Monitoring Technology, Qingdao 266033, China;
4. National Engineering and Technological Research Center of Marine Monitoring Equipment, Qingdao 266033, China
无人船作为多用途的观测平台, 具有隐身性好、操纵灵活、自动驾驶等特点, 适合在各种恶劣环境下, 搭载多种海洋测量传感器用于相关海洋测量领域, 将成为海洋观测领域的一种重要技术手段[1-2]。
随着通信、人工智能等新兴技术的发展, 各国加大了无人船的研发力度。早在2000年美国MIT的无人艇研究小组已经针对自主海岸勘探系统设计出“Auto Cat”号双体无人艇。随后国内相关单位也对无人船进行了相应的研究。
无人船需要在复杂的海洋环境中自主航行和作业, 并且作业时要求系统在保持与期望的轨迹跟踪精度同时, 又能够具有良好的机动性能, 对操纵性、控制性能和可靠性均提出了苛刻的要求。目前无人船航向航速的控制方法主要包括: PID控制、Backstepping控制、Lyapunov控制等控制算法。在文献[3-5]中使用了李雅普诺夫直接法和反步法相结合的方法对无人船的轨迹进行跟踪控制, 张晓杰等[6]进行了直流电机驱动固定双桨的无人水面艇行运动仿真工作, 万磊等[7]设计了非完全对称欠驱动无人艇的轨迹跟踪控制器, 实现了非完全对称欠驱动高速无人艇的任意参考轨迹的跟踪控制。
近年来, 具有实际物理意义的互联和阻尼配置无源性控制方法在非线性系统的控制中得到广泛使用[8-10]。本文以电力双推进无人船自主运动控制为研究对象, 其中航速航向为无人船完成复杂航行任务的关键问题。使用永磁同步电机作为无人船的驱动电机, 采用基于端口受控哈密顿(PCH)方法, 使系统的能量损耗较小, 有效提高了无人船的电力续航能力。
1 系统硬件平台设计本文所搭建了USV实验平台如图 1所示。无人船由固定在艇体尾部左右的螺旋桨产生的推力进行驱动, 螺旋桨由永磁同步电机驱动。
无人船实验平台硬件包括:
(1) 嵌入式计算平台, 用于综合处理数据信号和控制信号, 运行控制算法, 向操纵执行机构发送控制信号;
(2) 传感器测量模块, 用于测量船体的速度、位置、信息以及航向、航姿信息的采集;
(3)推进驱动模块, 驱动航向、航速控制的执行机构, 如螺旋桨、喷水推进器。
2 系统模型由于无人艇航行的阻力, 螺旋桨的推力和电动机的特性都是非线性的, 因此所建立的模型也是非线性的。无人船的运动控制主要研究在艏摇、纵荡和横荡3个方向上的运动, 我们采用广泛应用的Fossen[11-12]动力学和运动学模型分别为(1)和(2):
$\left\{ {\begin{array}{*{20}{l}} {{m_{11}}\dot u - {m_{22}}vr + {d_{11}}u = f} \\ {{m_{22}}\dot v + {m_{11}}ur + {d_{22}}v = 0} \\ {{m_{33}}\dot r + \left( {{m_{22}} - {m_{11}}} \right)uv + {d_{33}}r = T} \end{array}} \right.$ | (1) |
$ \left\{ \begin{gathered} \dot x = u\cos \psi-v\sin\psi \hfill \\ \dot y = u\sin \psi + v\cos \psi \hfill \\ \dot \psi = r \hfill \\ \end{gathered} \right. $ | (2) |
其中, u为纵荡速度, v为横摇速度, r艏摇角速度。
$\begin{gathered} M\dot \upsilon + C\left( \upsilon \right)\upsilon + D\left( \upsilon \right)\upsilon = \tau \hfill \\ \dot \eta = R(\eta )\upsilon \hfill \\ \end{gathered} $ | (3) |
其中,
永磁同步电机驱动螺旋桨所产生的推进力可以表述为[6]:
${T_p} = {K_p}\rho {\omega ^2}{d^4}$ | (4) |
永磁同步电机在d-q坐标轴下的数学模型为[13]:
$\left\{ \begin{gathered} {L_d}d{i_d}/dt = - {R_s}{i_d} + {n_p}\omega {L_q}{i_q} + {u_d} \hfill \\ {L_q}d{i_q}/dt = - {R_s}{i_q} - {n_p}\omega {L_d}{i_d} - {n_p}\omega \Phi + {u_q} \hfill \\ {J_m}d\omega /dt = {n_p}\left[{\left( {{L_d}-{L_q}} \right){i_d}{i_q} + \Phi {i_q}} \right] - {\tau _L} \hfill \\ \end{gathered} \right.$ | (5) |
隐极式永磁同步电机的内部损耗可以表示为:
${P_{loss}} = {P_{Cu}} = \frac{3}{2}{R_s}\left( {i_d^2 + i_q^2} \right)$ | (6) |
本文采用基于端口受控哈密顿(PCH)方法, 有效降低了永磁同步电机系统的能量损耗(6), 提升了无人船的电力续航能力。
3 端口受控哈密顿方法的航速航行控制器设计电力双推进无人船可被看作是一种二端口的能量变换装置, 并且能量守恒, 利用端口受控哈密顿(PCH)控制方法的能量成形、互联配置和阻尼注入来确定该系统的行为。端口受控耗散哈密顿系统模型为[8]:
$\left\{ \begin{gathered} \left[{\begin{array}{*{20}{c}} {\dot q} \\ {\dot p} \end{array}} \right] = [J(q, p)-R(q, p)]\left[{\begin{array}{*{20}{c}} {\frac{{\partial H}}{{\partial q}}} \\ {\frac{{\partial H}}{{\partial p}}} \end{array}} \right] + G(q)\tau \hfill \\ y = {G^{\rm{T}}}(q)\frac{{\partial H}}{{\partial p}} \hfill \\ \end{gathered} \right.$ | (7) |
其中,
$\begin{aligned} H(q, p) = & K(q, p) + V\left( q \right) \\ = & \frac{1}{2}{p^T}{M^{ - 1}}(q)p + V(q) \\ \end{aligned} $ | (8) |
为将无人船系统(1)和(2)渐进地稳定在期望的平衡点附近, 构造一个加入控制后的闭环期望能量函数
$\left\{ \begin{gathered} \left[{\begin{array}{*{20}{c}} {\dot q} \\ {\dot p} \end{array}} \right] = \left[{\begin{array}{*{20}{c}} 0&{{M^{-1}}{M_d}} \\ {-{M_d}{M^{-1}}}&{{J_2} - {D_d}} \end{array}} \right]\left[{\begin{array}{*{20}{c}} {\frac{{\partial {H_d}}}{{\partial q}}} \\ {\frac{{\partial {H_d}}}{{\partial p}}} \end{array}} \right] \hfill \\ {y_d} = {G^T}(q)\frac{{\partial {H_d}}}{{\partial p}} \hfill \\ \end{gathered} \right.$ | (9) |
其中,
${H_d}(q, p) = \frac{1}{2}{p^T}{M_d}^{ - 1}(q)p + {V_d}(q)$ | (10) |
IDA-PBC控制方法通过寻找反馈控制
${\tau _{ida}} = {\tau _{es}}(q, p) + {\tau _{di}}(q, p)$ | (11) |
${\tau _{es}} = {({G^T}G)^{ - 1}}{G^T}[\frac{{\partial H}}{{\partial q}}-{M_d}{M^{-1}}\frac{{\partial {H_d}}}{{\partial q}} + {J_2}{M_d}^{-1}p]$ | (12) |
${\tau _{di}} = - {K_v}{G^T}\frac{{\partial {H_d}}}{{\partial p}}$ | (13) |
其中, 通过第一步设计
$\left[{\begin{array}{*{20}{c}} {\dot q} \\ {\dot p} \end{array}} \right] = \left\{ {\left[{\begin{array}{*{20}{c}} \mathbf{0}&{K(q)} \\ {-{K^T}(q)}&{-C(p)} \end{array}} \right] - \left[{\begin{array}{*{20}{c}} \mathbf{0}&\mathbf{0} \\ \mathbf{0}&D \end{array}} \right]} \right\}\left[{\begin{array}{*{20}{c}} {\frac{{\partial H}}{{\partial q}}} \\ {\frac{{\partial H}}{{\partial p}}} \end{array}} \right] + \left[{\begin{array}{*{20}{c}} \mathbf{0} \\ {G(q)} \end{array}} \right]\tau $ | (14) |
$\begin{gathered} q \triangleq \eta \hfill \\ p \triangleq M\upsilon \hfill \\ \end{gathered} $ | (15) |
系统的哈密顿函数表示为:
$ \begin{gathered} H\left( {q, p} \right) = \frac{1}{2}{p^T}{M^{-1}}\left( q \right)p \hfill \\ \;\;\;\;\;\;\;\;\;\;\; = \frac{1}{2}\left( {{m_{11}}{u^2} + {m_{22}}{v^2} + {m_{33}}{r^2}} \right) \hfill \\ \end{gathered} $ | (16) |
其中,
无人船数学模型的闭环系统可以表示为如下形式:
$\left[{\begin{array}{*{20}{c}} {\dot q} \\ {\dot p} \end{array}} \right] = \left\{ {\left[{\begin{array}{*{20}{c}} {\rm{0}}&{K(q)} \\ {-{K^T}(q)}&{{J_2}} \end{array}} \right] - \left[{\begin{array}{*{20}{c}} {\rm{0}}&{\rm{0}} \\ {\rm{0}}&{{D_d}} \end{array}} \right]} \right\}\left[{\begin{array}{*{20}{c}} {\frac{{\partial {H_d}}}{{\partial q}}} \\ {\frac{{\partial {H_d}}}{{\partial p}}} \end{array}} \right]$ | (17) |
公式(17)也可以表示为:
$\left[{\begin{array}{*{20}{c}} {\dot q} \\ {\dot p} \end{array}} \right] = [{J_d}(q, p)-{R_{d(}}q, p)]\left[{\begin{array}{*{20}{c}} {\frac{{\partial {H_d}}}{{\partial q}}} \\ {\frac{{\partial {H_d}}}{{\partial p}}} \end{array}} \right]$ | (18) |
其中,
$\begin{gathered} {J_d}(q, p) = - {J_d}^T(q, p) = \left[{\begin{array}{*{20}{c}} {\rm{0}}&{K(q)} \\ {-{K^T}(q)}&{{J_2}} \end{array}} \right]; \hfill \\ {R_d} = {R_d}^T = \left[{\begin{array}{*{20}{c}} 0&0 \\ 0&{{D_d}} \end{array}} \right] \geqslant 0 \hfill \\ \end{gathered} $ | (19) |
${D_d} = \left[{\begin{array}{*{20}{c}} {{d_{d1}}}&0&0 \\ 0&0&0 \\ 0&0&{{d_{d3}}} \end{array}} \right]$ | (20) |
闭环系统的哈密顿函数为:
$\begin{aligned} {H_d}(p, q) = & \frac{1}{2}[{m_{11}}{\left( {u-{u_d}} \right)^2} + {m_{22}}{v^2} + {m_{33}}{r^2}] & \\ + \frac{1}{2}k{}_\psi {(\psi - {\psi _d})^2} \\ \end{aligned} $ | (21) |
定义
${\left[{{u_*}, {v_*}, {r_*}, {\psi _*}} \right]^T} = {[{u_d}, 0, 0, {\psi _d}]^T}$ | (22) |
为了使公式(14)与公式(17)相等, 可以选择参数矩阵:
${J_2}{\rm{ = }} - C(p)$ | (23) |
由公式(11)、(12)和(13)可以得到电力双推进无人船的航速航向控制器为:
$\left\{ \begin{gathered} f = {d_{11}}u - {d_{d1}}(u - {u_d}) \hfill \\ T = {k_\psi }({\psi _d} - \psi ) - {m_{22}}v{u_d} + {d_{33}}r - {d_{d3}}r \hfill \\ \end{gathered} \right.$ | (24) |
其中,
我们选择闭环PCH系统的哈密顿函数为李雅普诺夫参考函数
$\begin{aligned} \dot V = {{\dot H}_d}(p, q) = & \frac{{{\partial ^T}{H_d}}}{{\partial p}}\dot p + \frac{{{\partial ^T}{H_d}}}{{\partial q}}\dot q \\ = & - \frac{{{\partial ^T}{H_d}}}{{\partial p}}{D_d}\frac{{\partial {H_d}}}{{\partial p}} \leqslant 0 \\ \end{aligned} $ | (25) |
根据李雅普诺夫稳定性理论和拉萨尔不变集定理, 如果该闭环系统包括在集合, 即
电力双推进无人船长1.2 m, 重量为17.5 kg, 模型参数经过计算可以得到[14]:
控制器参数选择
损耗随时间变化曲线如图 5所示, 与廖煜雷等在文献[5]提出李雅普诺夫直接法和反步法相结合得到的航速航向控制器进行能耗对比, 可以得到PCH控制器的能量损耗较小。
6 结论本文研究了基于端口受控哈密顿方法的电力双推进无人船航向、航速控制方法, 将电力双推进无人船看作是二端口的能量变换装置, 并且能量守恒, 利用端口受控哈密顿(PCH)控制方法的能量成形、互联配置和阻尼注入来确定该系统的行为。采用基于端口受控哈密顿(PCH)方法, 使系统的能量损耗较小, 有效提高了无人船的电力续航能力。通过试验平台的仿真系统进行仿真及优化设计, 为进一步的试验研究提供了理论基础。
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