2025.5.25 線形システムの過渡特性・定常特性

P-制御を適用した一次遅れシステムの過渡特性と定常特性を調べる。

状態ベクトル

$ \bf{x}(t) = \left[\begin{array}{c} y(t) \\ \dot{y}(t) \end{array} \right]

code:p1.py

import matplotlib.pyplot as plt

import torch as pt

import numpy as np

class Func_xd:

def __init__(self):

pass

def __call__(self, x, u):

return self.calc(x, u)

def calc(self, x, u):

return A@x + B@u

class Solver:

def __init__(self):

self.xd = Func_xd()

def solve_euler(self):

xd = self.xd

x = x0 # initial state

t = ts # start time

time = []

hist_x = []

hist_conv = []

loopflag = True

conv_count = 0

# start of iteration

while loopflag:

time.append(t)

hist_x.append(x.flatten())

#

y = C@x

err = ref - y

u = Kp@err

x = x + th*xd(x, u)

t = t + th

if t >= tf:

loopflag = False

hist_conv.append(conv)

if conv < conv_eps:

conv_count += 1

else:

conv_count = 0

if conv_count*th > conv_chk:

loopflag = False

# end of iteration

self.time = np.stack(time)

self.hist_x = pt.stack(hist_x, dim=0)

self.hist_conv = hist_conv

self.analyze()

return self.time, self.hist_x, hist_conv

def analyze(self):

hist_x = self.hist_x

time = self.time

chara = dict()

def get_time(val): # メソッド内関数

for i in range(len(hist_x) - 1):

def get_sett_time(grade):

print(rate, len(time))

for i in range(len(time)-1, 0, -1):

# 定常特性 #

# 定常値

# 定常偏差

# 過渡特性 #

# ピーク時間

# ピーク値

# 遅れ時間

# オーバーシュート

# 立ち上がり時間 (10% -> 90%)

time10 = get_time(val10)

time90 = get_time(val90)

# settime2 ... 整定時間２％

# settime5 ... 整定時間５％

self.chara = chara

return

def show(self):

for k, v in solver.chara.items():

print(k, v)

plt.grid()

plt.axhline(ref, c='b', lw=1)

plt.axhline(0, c='black', lw=0.7)

plt.axvline(0, c='black', lw=0.7)

plt.show()

def get_params():

return A, B, C, Kp, Ki, Kd, x0, ref

def trans_tensor(params):

trans = []

for arg in params:

x = pt.tensor(arg, dtype=pt.float)

trans.append(x)

return trans

# toplevel

params = get_params()

A, B, C, Kp, Ki, Kd ,x0, ref = trans_tensor(params) # グローバル変数に返す

print(str(dim_n) + '-input, ' + str(dim_m) + '-state, ' + str(dim_l)+ '-output')

print('# A:', A)

print('# B:', B)

print('# C:', C)

ts, tf, th = 0, 40, 0.01 # 初期、終端、刻み時刻

conv_eps = 0.0000001 # 収束判定の振幅

#

solver = Solver() # ソルバを生成

result = solver.solve_euler()

solver.show()

結果

code:result.txt

stead_val tensor(1.0000)

peak_index tensor(1478)

peak_time 14.77999999999973

peak_val tensor(1.0000)

delay_time 1.6700000000000013

overshoot tensor(0.)

rise_time 3.3399999999999612

sett_idx2 580

sett_time2 5.799999999999921

sett_idx5 472

sett_time5 4.719999999999944