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摘要: 设计了高阶全驱系统的一种无模型控制器. 首先, 将无模型控制问题转化为不确定系统的输出反馈半全局镇定问题; 随后, 基于参量Lyapunov设计方法, 构造基于观测器的动态输出反馈. 进一步地, 阐明由原系统与观测器误差系统构成的增广闭环系统是一类弱耦合互联系统, 通过分析该系统特性, 完成闭环系统渐近稳定性与吸引域分析. 最后, 论证该输出反馈控制器构成高阶全驱系统的无模型控制器. 与传统基于模型的控制器相比, 所设计控制器不仅能够适应系统存在未建模动态及控制增益未知的情形, 还具有显式表达式, 且参数调节简便(对于n阶系统, 仅需调整3个参数). 通过船舶航向控制系统与柔性关节机械臂系统的仿真, 验证所设计无模型控制器的有效性.
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关键词:
- 无模型控制器 /
- 高阶全驱系统 /
- 参量Lyapunov设计 /
- 输出反馈 /
- PD反馈
Abstract: A model-free controller for high-order fully actuated (HOFA) systems is designed. First, the model-free control problem is transformed into a semi-global output feedback stabilization problem for uncertain systems. Next, an observer-based dynamic output feedback controller is derived via parametric Lyapunov design. Furthermore, the resulting augmented closed-loop system, composed of the original system and the observer error system, is shown to be weakly coupled and interconnected. Then, a rigorous analysis confirms the asymptotic stability and region of attraction of the closed-loop system. Finally, the output feedback controller is proven to be a verifiable model-free solution for the HOFA system. Compared to model-based alternatives, the proposed controller handles unmodeled dynamics and unknown control gains, offers an explicit analytical expression, and simplifies parameter tuning to only three parameters for an $n$-th order system. Simulations on ship course control and a flexible-joint robot confirm its effectiveness. -
图 3 柔性关节机械臂(22)的仿真结果
Fig. 3 Simulation results for the flexible-joint manipulator (22)
图 4 转化后系统(23)的状态及估计
Fig. 4 States of the transformed system (23) and their estimations
表 1 P和$ Q(\gamma) $的显式解
Table 1 Explicit solutions for P and $ Q(\gamma) $
系统阶数 A b c P $ Q(\gamma) $ $ n=1 $ 0 1 1 1 γ $ n=2 $ $ \left[\begin{array}{*{20}{c}} {0}&{1}\\{0}&{0 }\end{array} \right] $ $ \left[\begin{array}{*{20}{c}} {0}\\{1} \end{array} \right] $ $ \left[\begin{array}{*{20}{c}} {1}\\{0 }\end{array} \right] ^{{\rm{T}}} $ $ \left[\begin{array}{*{20}{c}} {1}&{1}\\{1}&{2 }\end{array} \right] $ $ \left[\begin{array}{*{20}{c}} {2\gamma}&{\gamma ^{2}}\\{\gamma ^{2}}&{\gamma ^{3} }\end{array} \right] $ $ n=3 $ $ \left[\begin{array}{*{20}{c}} {0}&{I_{2}}\\{0}&{0_{1\times 2} }\end{array} \right] $ $ \left[\begin{array}{*{20}{c}} {0}\\{0}\\{1 }\end{array} \right] $ $ \left[\begin{array}{*{20}{c}} {1}\\{0}\\{0 }\end{array} \right] ^{{\rm{T}}} $ $ \left[\begin{array}{*{20}{c}} {1}&{2}&{1}\\{2}&{5}&{3}\\{1}&{3}&{3 }\end{array} \right] $ $ \left[\begin{array}{*{20}{c}} {3\gamma}&{3\gamma ^{2}}&{\gamma ^{3}}\\{3\gamma ^{2}}&{5\gamma ^{3}}&{2\gamma ^{4}}\\{\gamma ^{3}}&{2\gamma ^{4}}&{\gamma ^{5} }\end{array} \right] $ $ n=4 $ $ \left[\begin{array}{*{20}{c}} {0}&{I_{3}}\\{0}&{0_{1\times 3}} \end{array} \right] $ $ \left[\begin{array}{*{20}{c}} {0}\\{0}\\{0}\\{1} \end{array} \right] $ $ \left[\begin{array}{*{20}{c}} {1}\\{0}\\{0}\\{0} \end{array} \right] ^{{\rm{T}}} $ $ \left[\begin{array}{*{20}{c}} {1}&{3}&{3}&{1}\\{3}&{10}&{11}&{4}\\{3}&{11}&{14}&{6}\\{1}&{4}&{6}&{4 }\end{array} \right] $ $ \left[\begin{array}{*{20}{c}} {4\gamma}&{6\gamma^{2}}&{4\gamma^{3}}&{\gamma^{4}}\\{6\gamma^{2}}&{14\gamma^{3}}&{11\gamma^{4}}&{3\gamma^{5}}\\{4\gamma^{3}}&{11\gamma^{4}}&{10\gamma^{5}}&{3\gamma^{6}}\\{\gamma^{4}}&{3\gamma^{5}}&{3\gamma^{6}}&{\gamma^{7}} \end{array} \right] $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ 
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表 2 船舶航向控制系统的参数
Table 2 Parameters of the ship course control system
参数 $T$ $K$ $\alpha_{1}$ $\alpha_{2}$ $\alpha_{3}$ 数值 1 a 0.25/s 0.01 s2/rad2 0.2 s/rad 0.3
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表 3 柔性关节机械臂的参数
Table 3 Parameters of the flexible-joint manipulator
参数 G K m L $ J_{1} $ $ J_{2} $ 数值 9.8 m/s2 3 N m/rad 0.2 kg 0.2 m 2 kg m2 5 kg m2
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