时滞离散系统正弦扰动的最优抑制

Optimal damping of sinusoidal disturbances in discrete-time systems with time-delays

研究状态和控制都含时滞的线性离散系统在正弦扰动下的减振控制问题.首先提出一种变量代换,并利用此代换将原系统转换为不含控制时滞的系统.然后利用逐次逼近法将最优控制问题转化为求解一族无时滞的线性两点边值序列问题.得到的最优控制律由解析的状态反馈,前馈和具有记忆的控制项以及时滞补偿序列的极限组成.通过截取时滞补偿序列的有限项,可以得到系统的次优减振控制律.仿真结果表明,该方法容易实现,设计的控制器对正弦扰动有较强的抑制能力.

We consider the damping of sinusoidal disturbances in discrete-time systems with time-delays in states and inputs. Through a variable substitution, the original system is transformed into a form without time-delay in inputs. Then, by using the successive approximation approach, the optimal control problem is transformed into a sequence of linear two- point-boundary-value problems. The optimal control law consists of the analytic state feedback, feedforward, control with memory terms, and the limit of a sequence of vectors for time-delay compensation. By carrying out a finite-step iteration of a compensation sequence, a suboptimal damping control law is also obtained. Simulations demonstrate the easy realization of the algorithm, and the strong ability in sinusoidal disturbances rejection.