子空间预测控制算法在主动噪声振动中的应用

Application of subspace predictive control in active noise and vibration control

为解决主动噪声和振动控制中的执行器饱和约束条件问题,在子空间系统辨识的基础上,研究了一种新颖的子空间预测控制方法。该控制方法联合了系统辨识和控制器设计,直接由输入-输出数据得到将来时刻的输出预测值;自动校正系统中的参数,克服了传统的模型预测控制中繁琐的系统辨识环节。同时子空间预测控制允许执行器机构出现饱和现象,在考虑由饱和现象导致的约束条件时,利用线性矩阵不等式将约束优化问题转化为无约束优化问题。采用椭球优化算法迭代地产生一系列体积逐渐减小的椭球序列,最终能收敛到一个最优解。在椭球算法的基础上推导了该算法达到收敛时所需要迭代次数的一个上界,这在智能优化算法中是很难求得到的。最后以直升机悬停状态时发生的颤振为例,利用本文中的子空间预测控制和椭球优化算法设计闭环系统的反馈控制器,验证闭环系统的输出响应能较好地跟踪期望值,从而得出本文方法的有效性。

A novel subspace predictive control algorithm based on subspace identification was studied to solve actuator saturation limitations in a range of active vibration and noise control problems.This algorithm not only combined system identification and control design,but also gave future predictive output values directly based on input-output data.This combination enabled antomatically tuning system parameters and avoided system identification procedures in traditional model predictive control.Meanwhile,the subspace predictive control permitted limitations on allowable actuator saturation.During considering the constraint conditions caused by saturation,a constrained optimization problem was converted to an unconstrained optimization problem using the linear matrix inequality technology.Then,an ellipsoid optimization algorithm was proposed to generate a sequence of ellipsoids with volume decreased.An upper bound on the maximum number of possible iteration steps was derived.This upper bound could not be obtained in all the intelligent algorithms.Finally,for an example of hellicopter flutter in hover mode,a closed loop feedback controller was designed using the subspace predictive control and the ellipsoid optimization algorithm.Simulation results showed that the output responses of the closed loop system can track the expected values well.So,the proposed method＇s efficiency was verified.