PID在Simulink中以正弦波为参考 [英] PID working with sine wave as reference in simulink

问题描述

我看到了使用PID控制器控制DC到DC buck转换器的输出dc电压的示例.

我想实现DC到AC转换器.

我尝试使用PID控制器.

由于我正在将输出交流信号(连续变化)与参考正弦信号进行比较，因此PID控制器未提供预期的输出.

在DC到DC的情况下，两个参考信号都是恒定的.

在我的情况下，它是不断变化的正弦波.

有人可以提出任何方法来获得准确的DC到AC转换吗?

P.S. PID控制器可以与连续变化的高频(100Hz)参考信号一起使用吗?

解决方案

如果您希望正弦波参考的误差为零，则有两种选择:

DQ0控制器

您需要将参考信号和控制(测量)值转换(使用 dq0变换也称为 Park变换)到具有相同频率的旋转帧.您的正弦波(在这种情况下为100Hz).

这样做时，您的参考信号和测量值将变为100 Hz的恒定值，并且您可以使用常规的PID控制器(实际上，您需要两个-一个用于 d 框架，另一个用于 q 框架).

然后，您将使用PID控制器输出的逆变换来驱动转换器调制器的占空比.

请注意，如果您的系统是单相的，则必须滤除dq0转换结果中的二阶谐波.

谐振控制器

在PID控制器中，积分作用负责零误差常数参考跟踪，因为它实际上是零频率下的无限增益(即常数).在使用拉普拉斯形式的传递函数中，积分部分与控制器函数中的1/s相对应.

要跟踪正弦波，您需要使用(1/w²+s²)形式的控制器，该控制器将保证在参考正弦波的频率(w=2*pi*f)处具有无限的增益.

实际上，我们可以用数学方法证明DQ0 PID控制器等效于谐振控制器.

I have seen example of controlling output dc voltage of DC to DC buck converter using PID controller.

I want to implement DC to AC converter.

I tried using PID controller.

Since i am comparing output AC signal(continuously varying) with reference sinusoidal signal, PID controller is not providing expected output.

In case of DC to DC, both reference signal was constant.

In my case, it is continuously varying sine wave.

Can anyone suggest any way to get accurate DC to AC conversion?

P.S. Can PID controller work with continuously varying reference signal with high frequency(100Hz)?

解决方案

If you want to have zero error for a sine wave reference you have two alternatives:

DQ0 Controller

You need to transform (using the dq0 transform also known as Park transform) your reference signal and controlled (measured) values to a rotating frame with the same frequency of your sine wave (in this case 100Hz).

When doing that, your reference signal and measured values will become constant values at 100 Hz and you can use a regular PID controller (actually you will need two - one for the d frame and other for the q frame).

Then you use the inverse transform of the PID controller output that will drive the duty cycle of your converter modulator.

Just notice that if your system is single-phase, there will be 2nd order harmonics in the result of the dq0 transform that have to be filtered out.

Resonant Controller

In the PID controller, the integral action is responsible for zero error constant reference tracking, because it is effectively a infinite gain at zero frequency (i.e. constant). In the transfer function using Laplace form the integral part corresponds to 1/s in the controller function.

To track sine waves, you need a controller in the form of (1/w²+s²), that will guarantee a infinite gain at the frequency of the reference sine wave, where w=2*pi*f.

In fact, we can proof mathematically that a DQ0 PID Controller is equivalent to the Resonant Controller.

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