来自该系列:使用Bode图
Carlos Osorio, MathWorks
了解如何通过在此MATLAB中塑造开环频率响应来实现所需的闭环特性®Tech Talk by Carlos Osorio.
所以考虑到现在我们有了一个大致的shapes, we would like for those two main closed-loop transfer functions T and S, the question becomes, how can we make sure that our controller will make the closed-loop system have a response that is anywhere close to having those frequency characteristics? To answer that, let us start by taking a look at the bode plot of a generic open-loop transfer function. Because this is just the product of P times C on a logarithmic scale, the frequency trace PC will be the superposition of the trace of the given plant and the trace of the controller we're trying to design.
The big advantage of dealing with the open-loop transfer function is that we can directly design the shape of C in such a way that, when superimposed with our plan, P, the resulting PC will have somewhat desirable characteristics. So now we might ask, what kind of shape should we give to our open-loop transfer function in order for it to make the closed-loop system have the frequency characteristics we are looking for?
Let me first highlight the 0 dB line on the magnitude trace and the minus 180 degrees on the phase trace. And remember, the crossover frequency is located where the magnitude trace crosses that 0 dB line. We want to see how the complementary sensitivity transfer function T=PC/(1+PC), relates to the open-loop transfer function.
请注意,我们不能直接使用叠加,因为分母中有一个求和。因此,我们需要使用我们的渐近近似方法来尝试从给定的开环传递函数推断t的形状。如果我们在交叉频率之前查看区域方式,并且开路传输函数的大小大于1或绘图上0 dB,则PC将主导分母,T将大约为PC/PC,或1。因此,t的幅度和相位都将保持在Bode图上的大约0。
如果我们查看交叉后的区域方式,并且开放环传递函数的大小远小于1,现在,1将主导分母,t将近似PC/1,这意味着T的迹线该区域将遵循PC的轨迹。
请注意,t的实际痕迹非常紧密地遵循我们的渐近近似。以类似的方式,如果我们查看灵敏度传递函数,那么当PC大于1时,它将大约1/PC,在对数尺度上,这意味着PC的负数。因此,在低频区域中,S的痕迹将相对于0。
当PC小于1时,S将大约1/1。因此,在高频区域的身体图上,S的幅度和相位大约为0。再次,S的实际痕迹非常接近我们的渐近近似。
因此,总而言之,如果我们想要在T中良好的跟踪性能特征和S中的良好干扰拒绝,我们需要确保我们的开环设计在低频率下具有足够的收益 - 换句话说,PC需要是远高于零dB,至少比交叉频率低十年。实际上,如果我们想达到零稳态误差,我们的增益需要在DC处为无穷大,这意味着我们的开路传输函数需要在低频上类似于纯积分器。
如果我们想要良好的噪声排斥特性,我们的开路设计应该具有良好的速率卷,并在交叉频率上方提供良好的衰减。因此,正如我们刚刚看到的那样,在我们开放环设计的高频和低频端情况下,弄清楚将发生什么。能够预测我们闭环系统在交叉频率周围的区域中的行为有点棘手。交叉频率的位置和我们越过的方式不仅会影响控制器的性能,而且对闭环系统的稳定性也至关重要。
您还可以从以下列表中选择一个网站:
选择中国网站(中文或英语)以获得最佳场地性能。其他Mathworks乡村网站未针对您所在的访问进行优化。