有限时间控制的性能分析及参数选取

Performance analysis and parameter selection for finite-time control

相比于无幂函数的传统线性控制方法,有限时间控制器(finite-time controller, FTC)因具有指数参数而能实现更优的控制性能.以一阶系统为例,定性且定量地对FTC和线性控制器(linear controller, LC)性能进行较为全面的对比,共得出11个相关定理,重点研究如何选取FTC的控制参数,以获得比LC更优的控制性能.具体内容为:考虑一阶标称系统和受扰动系统,设定一系列能反映控制性能的评价指标,如最大控制量、能量消耗、收敛速度、稳态精度以及抗干扰能力等;相比于已给定的LC,通过计算求出每个指标所对应的FTC参数,并证明存在合适的参数范围使FTC在评价指标的约束下具有更优的控制性能;证明在同一评价指标约束下,相比于FTC,不存在具有更优性能的LC.该研究可为FTC优于LC提供理论支撑,也为如何选取或优化FTC参数提供理论依据.

Compared with the traditional linear control method without a power function,a finite-time controller(FTC)can achieve better control performance due to its exponential parameter.In this paper,we comprehensively compare the performance of the FTC and linear controller(LC)both qualitatively and quantitatively,for a first-order system.We have derived a total of 11 relevant theorems that focus on the selection of control parameters for the FTC to achieve superior control performance compared to the LC.The specific content is that a series of evaluation indicators are set for both the nominal system and the disturbed system to reflect their control performance.These indicators include the maximum control amplitude,energy consumption,convergence speed,steady-state accuracy,and anti-disturbance capability.Based on the given LC,the FTC parameters corresponding to each indicator are calculated.It has been proven that there is an optimal parameter range that can enhance the control performance of the FTC while still satisfying the constraints of the evaluation indicators.In addition,it is also important to demonstrate that,under the same evaluation index constraint,there is no LC with better performance than the FTC.The significance of the research is to provide theoretical support for improving the control performance of the FTC,and to establish a theoretical basis for selecting FTC parameters.