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摘要: 研究含有状态时延的严反馈非线性系统的跟踪控制问题, 充分考虑时延的时变性和任意性以及系统的未知动力学特性. 为解决该问题, 取代参数辨识、函数逼近、增益调节、指令滤波等常规技术, 提出基于导向函数的预设性能控制方法, 移除了控制器设计对于系统非线性、控制方向和虚拟控制信号导数等信息的依赖. 并且, 摆脱基于李雅普诺夫−克拉索夫斯基泛函或拉祖米欣函数的稳定性分析框架, 采用基于反证法的受限分析理论, 移除性能分析对于已知的时延上界、部分已知的时延非线性函数和时延导数小于1等常见约束. 因此, 形成无模型、低复杂度、高性能控制方法, 将跟踪误差限制于设计者预先选取的性能包络线内, 确保系统输出以预先设定的速度和精度跟踪上时变的设定值. 最后, 以具有延迟回收流的两级化学反应器为对象开展对比仿真, 实验结果验证了所提方法的有效性和优越性.Abstract: This paper is concerned with the tracking control problem for time-delay strict-feedback nonlinear systems, in which the time-varying arbitrary state delays and the completely unknown system dynamics are taken into full consideration. To address this problem, instead of parameter identification, function approximation, gain adaption and command filtering, an orientation function-based prescribed performance control approach is put forward. It eliminates the dependence of the control design on the system nonlinearities, the control directions and the virtual control signal derivatives. Moreover, in lieu of the stability analysis based on Lyapunov-Krasovskii functionals or Razumikhin functions, a framework for constraint analysis by contradiction is adopted. It excludes the commonly adopted assumptions on the known bounds of time-delays, the partially known time-delay nonlinearities and the time-delay derivatives less than 1. Therefore, a model-free low-complexity high-performance control scheme is obtained, which confines the tracking error inside the predefined performance envelop. In this way, it is achieved that the system output tracks the time-varying reference with the prescribed rate and accuracy. Finally, a comparative simulation on the two-stage chemical reactor with delayed recycle streams is conducted, and the simulation results substantiate the effectiveness and the superiority of the proposed approach.
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Key words:
- Model-free control /
- prescribed performance /
- reference tracking /
- time-delay /
- nonlinear systems
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表 1 模型参数
Table 1 Model parameters
$a_1$ $a_2$ $b_1$ $b_2$ $R_1$ $R_2$ $V_1$ $V_2$ $F$ 2 2 0.3 0.3 0.5 0.5 0.5 0.5 0.5 
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