import control as ctrl
 
# 方式 1
s = ctrl.tf('s')
sys = 100 / (s ** 2 + 10 * s + 100)
 
# 方式 2
sys = ctrl.tf([100], [1, 10, 100])

# 求零點
sys.zero()
 
# 求極點
sys.pole()
 
# 特征參數、特征根
sys.damp()

# 階躍動態指標
step_info(sys)
# 階躍響應
t, response = step_response(sys, T)
 
# 脈沖響應
t, response = impulse_response(sys, T)
 
t, response = initial_response(sys, T)
t, response = forced_response(sys, T)

# Nyquist圖, 可傳入列表
nyquist_plot(sys)
 
# Bode圖, 可傳入列表
bode_plot(sys)
 
# 根軌跡圖
root_locus(sys)

import sympy
class Time_Response:
    ''' 時域響應'''
    s, t = sympy.symbols('s, t')
 
    def __init__(self, fun, doprint=False):
        ''' fun: 返回關于s的傳遞函數的 function
            doprint: 輸出公式'''
        sys = fun(self.s)
        self.f_t = sympy.integrals.inverse_laplace_transform(sys, s=self.s, t=self.t)
        if doprint:
            sympy.pprint(self.f_t)
 
    def __call__(self, time):
        ''' 使自身可作為函數被調用'''
        response = list(map(lambda i: float(self.f_t.subs({self.t: i})), time))
        return np.array(response)

import control as ctrl
import matplotlib.pyplot as plt
import numpy as np
 
# 自定義類所在的模塊
from mod.math_model import Time_Response
orange = 'orange'
blue = 'deepskyblue'
plt.rcParams['font.sans-serif'] = ['Microsoft YaHei']
f_t = Time_Response(lambda s: 100 / (s ** 2 + 10 * s + 100) / s, doprint=True)
t = np.linspace(0, 1, 100)
plt.subplot(1, 2, 1)
plt.title('sympy 計算')
plt.plot(t, f_t(t), c=orange)
s = ctrl.tf('s')
sys = 100 / (s ** 2 + 10 * s + 100)
t, response = ctrl.step_response(sys, T=1)
plt.subplot(1, 2, 2)
plt.title('control 計算')
plt.plot(t, response, c=blue)
plt.show()