控制时滞与测量时滞采样系统的最优扰动抑制

Optimal Disturbance Rejection for Sampled-Data Systems with Control-Delay and Measurement-Delay

研究在持续外部扰动作用下,具有控制时滞和测量时滞的采样线性系统前馈-反馈最优扰动抑制控制器设计问题.首先将采样系统离散化为时滞离散系统,再利用模型转换将时滞离散系统转换为无时滞系统;对转换后的系统设计前馈-反馈最优控制器,证明其存在唯一性;通过求解Riccati矩阵方程和Stein方程,设计含控制记忆项的最优控制律,利用控制记忆项补偿时滞对系统产生的影响;然后通过构造降维状态观测器解决前馈控制物理不可实现以及状态不完全可测的问题.最后通过仿真示例,证实运用模型转换方法所设计的最优扰动抑制控制器,能够有效地补偿时滞给系统带来的影响,并实现扰动抑制.

The paper considers feedforward and feedback optimal disturbance rejection control design problem for sampled- data systems with control -delay and measurement -delay under persistent disturbances. Firstly, the sampled -data system is transformed into time- delay discrete -time system. Employing model transformation, it is converted into an equivalent nondelayed one. Then the control law of feedforwa^d and feedback optimal disturb- ance rejection is designed and its existence and uniqueness are proved. The optimal control law is derived from a Riccati equation and a Stein equation, which is combined with control memory terms. The terms compensate for the effect produced by time - delays. Further, the physical unrealization problem of feedforward control and the unmea- surement states problem are solved by constructing a reduced -order state observer. Finally, simulation examples illustrate that the designed optimal disturbance rejection controller by using model transformation approach can com- pensate effects produced by delays and damp disturbances.