采样控制系统幅频特性的一种计算方法

Calculation for frame-frequency characteristics of sampling data control system

频率特性是描述控制系统性能的主要指标之一 ,在采样控制系统中 ,离散信号与连续信号并存 ,由于采样开关的存在 ,使得采样控制系统具有周期时变性 ,因而无法直接用传递函数来描述系统的频率特性 .基于采样控制系统直接设计理论 ,给出了采样控制系统幅频特性的计算方法 .首先应用提升技术 ,将周期时变系统转化为线性时不变系统 ,从而解决了采样控制系统周期时变、连续信号和离散信号共存的问题 ,并通过求解提升系统的幅频等效离散系统来求得采样控制系统的幅频特性 .最后用具体的计算实例验证了该方法的有效性 。

Frequency performance is one of the most important indexes describing the performance of the control systems. In sampled data control systems, the continuous signals and the discrete signals are concomitant. Because of the sampler, the sampled data control systems become the linear period time variant systems and we can not describe the frequency performance by the transfer function directly. In this paper, firstly, we use the lifting technique to transfer the period time variant systems into linear time invariant systems. By this way, we solve the time variant problem and the concomitant problem of the two time domain signals in sampled data control systems. Secondly, We compute the equivalent discrete systems of the lifted system. Then we can get the frequency response gain of sampled data system according to the equivalent discrete systems. In the end, a simulation example is given and the accuracy of the result is analized.