楼主scgbb你好。只有公式是不够的，公式中的变量必须有值。

PEN

首先，您必须知道您正在尝试建模的系统类型。起初你不知道模型的系数，所以你做了一个很好的猜测。该算法使用该猜测的值计算反馈位置和估计位置之间的平方误差之和。
这个平方误差值之和是上面＃2中的ERR。首先，ERR值会很高，因为猜测不是那么好，但计算机将尝试许多不同的值，直到误差平方和尽可能低。这可能需要几秒甚至几分钟。在＃2之上，平方误差之和非常小。模型的估计响应之间的误差几乎与实际响应相同。在＃2和＃4的示例中，估计的模型几乎是完美的。在＃4中，估计的速度比从反馈计算的速度更准确。请注意，还会估算加速度。如果你继续解决闭环主题的问题，你会明白为什么估计加速度很重要。今天的计算机可以尝试开环增益，固有频率和阻尼因子的数百种组合，直到误差平方和非常小。这是RMCTools使用的方法。

我已经发布了我的阀门建模程序的结果。该程序计算15个参数的值。我听说有人计算最多40个参数的值。我认为这很少见。


另一种方法是使用VCCM方程计算开环增益。使用自然频率的等式计算固有频率。阻尼因子是估计，直到可以使开环移动测量过冲。

系统识别和放置极点是控制理论中最重要的两个部分。对我来说很明显，液压和机械人员并没有学会如何控制他们设计的系统。这就是为什么有这么多糟糕的设计。

First you must know what kind of system you are trying to model. At first you do not know the coefficients for the model, so you make a good guess. The algorithm computes the sum of squared errors between the feedback position and the estimated position using the values of this guess.
This sum of squared errors value is the ERR in #2 above. At first the ERR value will be high because the guess is not that good, but the computer will try many different values until the sum of squared errors is as low as it can be. This may take many seconds or even minutes. In #2 above the sum of square error is very small.  The error between the model’s estimated response is almost the same as the actual response.  In the example in #2 and #4 the estimated model is almost perfect.   In #4 the estimated velocity is more accurate than the velocity computed from the feedback.  Notice that the acceleration is also estimated.  You will see why it is important to estimate the acceleration if you keep solving problems on the closed loop topic. Todays computers can try many hundreds of combinations of open loop gain, natural frequency and damping factor until the sum of squared errors is very small.   This is the method RMCTools uses.

I have posted the results of my valve modeling program.  This program calculates the value for 15 parameters.   I have heard of people calculating the values for up to 40 parameters.  I think this is rare though.


The other way is to compute the open loop gain by using the VCCM equation.  The natural frequency is calculated using the equation for natural frequency.   The damping factor is an estimate until it is possible to make a open loop move an measure the overshoot.

System identification and placing poles are two of the most important parts of control theory.  It has been apparent to me that hydraulic and mechanical people are not taught how to control the systems they design.  This is why there are so many bad designs.