State Feedback Control for Dual-inertia Servo Mechanisms With Performance Enhancement
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摘要: 为避免使用函数逼近器(神经网络或模糊系统), 并提高双惯量伺服系统的瞬态响应和稳态性能, 针对含外部扰动的双惯量伺服系统, 提出一种基于预设性能函数(Prescribed performance function, PPF)的类比例状态反馈控制策略. 首先, 提出一种改进的带有最大超调、收敛速率以及稳态误差的预设性能函数, 并将该函数融入控制器设计使二惯量伺服的跟踪误差保持在预定的边界之内. 其次, 基于预设性能函数设计了类比例状态反馈控制器实现跟踪控制. 与传统基于函数逼近控制方法相比较, 该方法可降低控制系统计算复杂度同时消除反演控制中存在的复杂度爆炸问题. 最后, 利用双惯量伺服系统实验平台开展了对比实验, 验证了所提出方法的有效性.Abstract: To avoid using the function approximation (neural networks or fuzzy logic systems) and enhance the transient and steady-state control performance, this paper proposes a proportional-integral feedback control strategy for dual-inertia servo systems with external disturbance based on prescribed performance functions (PPF). First, a modified prescribed performance function with guaranteed convergence rate, maximum overshoot and steady-state error boundary is employed, so that both the transient response and steady-state errors are retained within a predefined boundary. Second, a state-feedback control with this proposed PPF is suggested. Compared with the classical function approximation-based control approaches, the computational complexity of the developed control system is reduced and the explosion of complexity in the backstepping methods could be remedied. Finally, comparative experiments based on a dual-inertial test-rig are provided to show the effectiveness and superior performance of the proposed control scheme.
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图 2 改进的预设性能函数与原始预设性能函数比较
$(\varphi_{0}=2$ $\varphi_{\infty}=0.2)$ Fig. 2 Comparative profiles between the original PPF and the modified PPF with
$\varphi_{0}=2$ and$\varphi_{\infty}=0.2$ 
图 5 正弦
$x_d=3\sin(2\pi t/ 8)$ 跟踪性能:位置跟踪与跟踪误差Fig. 5 Tracking performance for
$x_d=3\sin(2\pi t/ 8)$ : Position tracking and tracking error
图 6 正弦
$x_d=8\sin(2\pi t/4)$ 跟踪性能:位置跟踪与跟踪误差Fig. 6 Tracking performance for
$x_d=8\sin(2\pi t/4)$ : Position tracking and tracking error
图 7 3种方法性能比较: 位置跟踪与跟踪误差
Fig. 7 Performance comparison: Position tracking and tracking error
表 1 系统参数
Table 1 System parameters
参数 数值 单位 电机惯量${J_m}$ 0.026 $ {\rm{kg \cdot {m^2}}}$ 负载惯量${J_l}$ 0.0113 ${\rm{kg \cdot {m^2}}}$ 弹性系数${K_l}$ 56 ${\rm{Nm/rad}}$ 
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表 2 性能指标
Table 2 Performance indexes
方法 $M_{e}$ $\mu_{e}$ $\sigma_{e}$ 本文方法 0.1587 0.0413 0.00004 动态面方法 0.3104 0.1171 0.00009 自适应神经控制 0.3081 0.0757 0.00007
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