如何使用python为简单的正弦波输入生成反冲信号？

Question

我正在使用下面的python代码，以便为简单的正弦波输入生成反向间隙信号。生成的输出不符合要求。输出应类似于Simulink中使用的反向间隙。

#Importing libraries 
import matplotlib.pyplot as plt
import numpy as np

#Setting upper limit and lower limit
LL = -0.5
UL = 0.5

#Generating the sine wave
x=np.linspace(0,10,1000)
y=(np.sin(x))

#phase shift of y1 by -pi/2
y1=(np.sin(x-1.571))

# plot original sine
plt.plot(x,y)

#setting the thresholds 
y1[(y1>UL)] = UL
y1[(y1<LL)] = LL

#Initializing at the input
y1[(y==0)]  = 0

y1[(y1>UL)] -= UL
y1[(y1<LL)] -= LL

#Plotting both the waves
plt.plot(x,y)
plt.plot(x,y1)

plt.grid()
plt.show()

Answer 1

我不认为对于强拆过程有一个简单的矢量化实现。第k个输出以非平凡的方式取决于先前的值。编写过程的简明方法（假设x是输入数组，y是输出数组）是

y[k] = min(max(y[k-1], x[k] - h), x[k] + h)

其中h是死亡的一半。

以下脚本包含使用Python for循环的backlash函数。 （该函数使用if语句而不是min和max函数。）它很简单，但速度不会很快。如果高性能很重要，您可以考虑重新实现Cython或numba中的函数。

import numpy as np


def backlash(x, deadband=1.0, initial=0.0):
    """
    Backlash process.

    This function emulates the Backlash block of Simulink
    (https://www.mathworks.com/help/simulink/slref/backlash.html).

    x must be a one-dimensional numpy array (or array-like).
    deadband must be a nonnegative scalar.
    initial must be a scalar.
    """
    halfband = 0.5*deadband

    y = np.empty_like(x, dtype=np.float64)
    current_y = initial

    for k in range(len(x)):
        current_x = x[k]
        xminus = current_x - halfband
        if xminus > current_y:
            current_y = xminus
        else:
            xplus = current_x + halfband
            if xplus < current_y:
                current_y = xplus
        y[k] = current_y

    return y


if __name__ == "__main__":
    import matplotlib.pyplot as plt

    t = np.linspace(0, 10, 500)
    x = np.sin(t)
    deadband = 1
    y = backlash(x, deadband=deadband)

    plt.plot(t, x, label='x(t)')
    plt.plot(t, y, '--', label='backlash(x(t))')
    plt.xlabel('t')

    plt.legend(framealpha=1, shadow=True)
    plt.grid(alpha=0.5)
    plt.show()