一种控制输入约束下的不确定离散系统非脆弱保性能控制器设计

Non-Fragile Guaranteed Cost Control for Uncertain Discrete System with Control input Constraints

【目的】针对考虑扰动及摄动情况下的控制输入约束的不确定离散系统,提出了非脆弱保性能的控制方法。【方法】首先,以最小化目标函数为性能指标、控制输入饱和范围为约束条件,从而推导出约束状态下的非脆弱保性能控制律。其次,使用李雅普诺夫方程来构造非线性矩阵不等式。再次,结合Schur补定理和布谷鸟群智能优化算法对不等式进行求解,得到控制输入约束下的非脆弱保性能控制律的参数。最后,通过Quanser三自由度陀螺仪平台进行试验验证。【结果】试验结果表明,本研究所提出方法的稳态误差浮动不超过0.07、跟踪误差不超过0.15。【结论】该方法在面对扰动及摄动情况时具有更高的鲁棒性,对提升三自由度陀螺仪的稳定性及控制精度具有重要意义。

[Purposes]In this paper,a non-fragile guaranteed performance control method is proposed for uncertain discrete systems with input constraints under perturbation.[Methods]In this method,By tak-ing the minimum objective function as the performance index and taking the saturation range of the con-trol input as the constraint condition,the non-fragile guaranteed performance control law under the con-straint state is derived.Secondly,the nonlinear matrix inequality is constructed by Lyapunov equation.Then,Schur's complement theorem and Cuckoo bird intelligent optimization algorithm are used to solve the inequality,and the non-fragile guaranteed performance control law parameters under the control in-put constraints are obtained.Finally,the experiment is verified by Quanser-3-DOF gyroscope platform.[Findings]The results show that the steady-state error of the proposed method is less than 0.07 and the tracking error is less than 0.15.[Conclusions]The method proposed in this paper has higher robustness in the face of disturbance and perturbation,and is of great significance for improving the stability and control accuracy of the 3-DOF gyroscope.