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ILC_sim_v3.2.py
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ILC_sim_v3.2.py
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import numpy as np
import scipy.signal
from common import *
from control_math import *
from numpy import pi
from scipy.signal import ss2tf, tf2ss, impulse, impulse2, step, butter, lsim, lsim2
from sympy import solve
from sympy.abc import a, b, c
from scipy.linalg import toeplitz
"""Plant"""
m = 0.03
k = 0
bb = 0
A = np.array([[0, 1], [-k / m, -bb / m]])
B = np.array([[0], [1 / m]])
C = np.array([1, 0])
D = np.array([0])
plant_num, plant_den = ss2tf(A, B, C, D)
res_freq = 200
anti_res_freq = 150
res_omega = res_freq * 2 * np.pi
anti_res_omega = anti_res_freq * 2 * np.pi
mass = 1
beta1 = 0.1
beta2 = 0.1
res_num = (
1
/ mass
* res_omega ** 2
/ anti_res_omega ** 2
* np.array([1, 2 * beta1 * anti_res_omega, anti_res_omega ** 2])
)
res_den = np.array([1, 2 * beta2 * res_omega, res_omega ** 2])
num = np.convolve(res_num, plant_num.flatten())
den = np.convolve(res_den, plant_den.flatten())
A, B, C, D = tf2ss(num, den)
sys_ss = StateSpaceModel(A, B, C, D, DT)
sys_tf = TransferFunc(num, den, DT)
# sys_tf = TransferFunc(res_num, res_den, DT)
"""Chirp信号初始化"""
start_freq = 10
end_freq = 2000
start_freq_ = 0.8 * start_freq
end_freq_ = 1.1 * end_freq
# 扫频时间
T4chirp = 1
T4chirp = (
int(((end_freq_ - start_freq_) / (end_freq - start_freq) * T4chirp) * SERVO_FREQ)
/ SERVO_FREQ
)
t4chirp = np.linspace(0, T4chirp, int(SERVO_FREQ * T4chirp) + 1)
u = np.sin(
2
* np.pi
* ((end_freq_ - start_freq_) / T4chirp * t4chirp ** 2 / 2 + start_freq_ * t4chirp)
)
# u = np.linspace(0, 1, len(t4dyn))
# u = np.sin(2 * pi * 500 * t4dyn)
"""计算Chirp响应"""
y = np.zeros_like(u)
for i in range(len(u)):
input_sig = u[i]
y_output, x_state = sys_ss.response(input_sig, method="zoh2")
y[i] = y_output
p = y
y = np.diff(y, 2) / DT / DT
y = np.pad(y, (2, 0), "constant", constant_values=(0, 0))
u_detrend = u - np.mean(u)
y_detrend = y - np.mean(y)
f_bode, fw_u = fft(hamm(u_detrend), DT)
f_y, fw_y = fft(hamm(y_detrend), DT)
resolution = 1 / DT / len(f_bode)
start_point = int(start_freq / resolution)
end_point = int(end_freq / resolution)
f_bode = f_bode[start_point:end_point]
fw = fw_y[start_point:end_point] / fw_u[start_point:end_point]
"""修正差分和离散化方法造成的伯德图误差"""
zoh_decay = (1 - np.e ** (-1j * 2 * pi * f_bode * DT)) / (1j * 2 * pi * f_bode * DT)
linear_decay = (
np.e ** (1j * 2 * pi * f_bode * DT)
* (1 - np.e ** (-1j * 2 * pi * f_bode * DT)) ** 2
/ (1j * 2 * pi * f_bode * DT) ** 2
)
fw = fw / zoh_decay / zoh_decay / zoh_decay
# 拟合传递函数
Bn, Am = fit(f_bode, fw, 2, 2)
sys_fit = TransferFunc(Bn, Am, DT)
print("num:", num, "\nden:", den[:-2])
print("Bn:", Bn, "\nAm:", Am)
# f_fit, fw_fit = sys_fit.bode(np.array(range(start_freq, end_freq)))
# fig, axes = plt.subplots(1, 2, figsize=(14, 5))
#
# axes[0].set_xlabel("f/[Hz]")
# axes[0].set_ylabel("Gain/[dB]")
# axes[0].semilogx(f_bode, 20 * np.log10(np.abs(fw)), label="Gain")
# axes[0].semilogx(f_fit, 20 * np.log10(np.abs(fw_fit)), label="Fit Gain")
#
# axes[1].set_xlabel("f/[Hz]")
# axes[1].set_ylabel("Phase/[deg]")
# axes[1].semilogx(f_bode, np.angle(fw, deg=True), label="Phase")
# axes[1].semilogx(f_fit, np.angle(fw_fit, deg=True), label="Fit Phase")
# plt.suptitle("sys id bode plot")
# plt.legend()
# plt.show()
"""设计PID"""
delay_num = np.array([1])
delay_den = np.array([0.00005, 1])
num_a_delay = np.convolve(delay_num, Bn)
den_a_delay = np.convolve(delay_den, Am)
sys_tf_delay = TransferFunc(num_a_delay, den_a_delay, DT)
# sys_tf = sys_tf_delay
f_fit4pid, fw_fit4pid = TransferFunc(num_a_delay, den_a_delay, DT).bode(
np.array(range(1, 500))
)
# f_fit4pid, fw_fit4pid = TransferFunc(num_a_delay, den_a_delay, DT).bode(
# np.array(range(1, 500))
# )
# f_fit4pid, fw_fit4pid = sys_fit.bode(np.array(range(1, 500)))
plant_gain = np.mean(20 * np.log10(np.abs(fw_fit4pid)))
kp, ki, kd = pole_placement(plant_gain, 80, 0, SERVO_FREQ)
# kp = 1000
# ki = 0.1
# kd = 1000
print(kp, ki, kd)
pid_controller = PID(kp, ki, kd, SERVO_FREQ)
pid_tf = TransferFunc([kd, kp, ki], [1, 0], DT)
# SPG
T4wait = 1 * DT
T4dyn = 0.5
T4settling = 0.03
T4move = T4wait + T4dyn + T4settling
y1 = 0.5
sol = solve(
[
a * T4dyn ** 5 + b * T4dyn ** 4 + c * T4dyn ** 3 - y1,
5 * a * T4dyn ** 4 + 4 * b * T4dyn ** 3 + 3 * c * T4dyn ** 2,
20 * a * T4dyn ** 3 + 12 * b * T4dyn ** 2 + 6 * c * T4dyn,
],
[a, b, c],
)
t4dyn = np.arange(0, T4dyn, DT)
set_p = sol[a] * t4dyn ** 5 + sol[b] * t4dyn ** 4 + sol[c] * t4dyn ** 3
set_v = 5 * sol[a] * t4dyn ** 4 + 4 * sol[b] * t4dyn ** 3 + sol[c] * 3 * t4dyn ** 2
set_a = 20 * sol[a] * t4dyn ** 3 + 12 * sol[b] * t4dyn ** 2 + sol[c] * 6 * t4dyn ** 1
t4move = np.arange(0, T4move, DT)
T4move = round(t4move[-1] + DT, 10)
set_p = np.append(np.zeros(int(T4wait / DT)), set_p).astype(float)
set_v = np.append(np.zeros(int(T4wait / DT)), set_v).astype(float)
set_a = np.append(np.zeros(int(T4wait / DT)), set_a).astype(float)
set_p = np.append(
set_p, y1 * np.ones(len(t4move) - len(t4dyn) - int(T4wait / DT))
).astype(float)
set_v = np.append(set_v, np.zeros(len(t4move) - len(t4dyn) - int(T4wait / DT))).astype(
float
)
set_a = np.append(set_a, np.zeros(len(t4move) - len(t4dyn) - int(T4wait / DT))).astype(
float
)
"""计算PS响应"""
# identity_tf = TransferFunc([1], [1], DT)
# closed_loop_tf = pid_tf * sys_tf / (identity_tf + pid_tf * sys_tf)
# ps_tf = sys_tf / (identity_tf + pid_tf * sys_tf)
# # ps_inv_tf = pid_tf + identity_tf / sys_tf
# # ps_inv_tf_scipy = scipy.signal.TransferFunction(ps_inv_tf.num, ps_inv_tf.den)
#
# T4ir = T4move
# t4ir = np.arange(DT, T4ir + DT, DT)
# # t4ir = np.arange(0, T4ir, DT)
# t4ir, process_sensitivity_ir = impulse(
# (ps_tf.num, ps_tf.den),
# T=t4ir,
# )
from scipy import signal
import control as ctrl
def inverse_toeplitz(an):
bn = np.zeros_like(an, dtype=float)
a0 = an[0]
bn[0] = 1 / a0
an_flip = np.flip(an)
for i in range(1, len(bn)):
bn[i] = -sum(bn[0:i] * an_flip[-i - 1 : -1]) / a0
return bn
iden_tf_ctrl = ctrl.TransferFunction([1], [1])
# sys_tf_ctrl = ctrl.TransferFunction(res_num, res_den)
sys_tf_ctrl = ctrl.TransferFunction(sys_tf.num, sys_tf.den)
pid_tf_ctrl = ctrl.TransferFunction(pid_tf.num, pid_tf.den)
ps_ctrl = sys_tf_ctrl / (iden_tf_ctrl + sys_tf_ctrl * pid_tf_ctrl)
t4move, process_sensitivity_ir = signal.impulse(
(ps_ctrl.num[0][0], ps_ctrl.den[0][0]), T=np.arange(DT, T4move + DT, DT)
)
# t4move = np.arange(0, T4move, DT)
process_sensitivity_ir = process_sensitivity_ir / SERVO_FREQ
import time
# T1 = time.time()
# ps_response_mat = np.mat(
# toeplitz(process_sensitivity_ir, np.zeros_like(process_sensitivity_ir)), dtype=float
# )
# ps_pinv_mat2 = np.linalg.pinv(ps_response_mat)
# T2 = time.time()
# print("直接求逆", T2 - T1, "秒")
T1 = time.time()
ps_pinv_t = inverse_toeplitz(process_sensitivity_ir)
ps_pinv_mat = np.mat(toeplitz(ps_pinv_t, np.zeros_like(ps_pinv_t)))
ps_pinv_mat = np.mat(np.roll(np.array(ps_pinv_mat), 2))
ps_pinv_mat[:, 0:2] = 0
ps_pinv_mat[-2:, :] = 0
T2 = time.time()
print("迭代求逆", T2 - T1, "秒")
# print(np.allclose(ps_pinv_mat, ps_pinv_mat2))
# plt.figure()
# plt.plot(t4move, process_sensitivity_ir)
# np.save("process_sensitivity_ir.npy", process_sensitivity_ir)
# np.save("ps_response_mat.npy", ps_response_mat)
# np.save("ps_pinv_mat.npy", ps_pinv_mat)
# Filter
Q_num, Q_den = butter(3, 5000, "low", analog=True)
# Q_num, Q_den = ([1], [1])
butter_filter = scipy.signal.TransferFunction(Q_num, Q_den)
# iteration
f_kp1 = np.zeros_like(set_p)
datalog = dict()
datalog["p_fbk"] = np.zeros_like(set_p, dtype=float)
datalog["err"] = np.zeros_like(set_p, dtype=float)
datalog["pid_output"] = np.zeros_like(set_p, dtype=float)
datalog["f_k"] = np.zeros_like(set_p, dtype=float)
datalog["plant_input"] = np.zeros_like(set_p, dtype=float)
print("Total Samples:", len(set_p))
plant_acc_tf = TransferFunc(
res_omega ** 2
/ anti_res_omega ** 2
* np.array([1, 2 * beta1 * anti_res_omega, anti_res_omega ** 2]),
np.array([1, 2 * beta2 * res_omega, res_omega ** 2]),
DT,
)
# plant_acc_tf = TransferFunc([0.045, 0.4, 2200], [0.000675, 0.024, 132], DT)
a2p_tf = TransferFunc([1], [1, 0, 0], DT)
plant_pos_tf = a2p_tf * plant_acc_tf
for k in range(15):
p_fbk = 0
sys_ss.reset()
pid_controller.reset()
f_k = f_kp1
for i in range(len(set_p)):
if i % 1000 == 0:
print(k + 1, i)
p_cmd = set_p[i]
a_cmd = set_a[i]
err = p_cmd - p_fbk
pid_output = pid_controller.response(err)
plant_input = pid_output + f_k[i]
p_fbk, x_state = sys_ss.response(
plant_input, method="zoh2"
) # +random.normal()/4/5
p_fbk = p_fbk[0, 0]
datalog["p_fbk"][i] = p_fbk
datalog["err"][i] = err
datalog["pid_output"][i] = pid_output
datalog["plant_input"][i] = plant_input
datalog["f_k"] = f_k
# current plant in as next ffc
# Le = np.zeros_like(set_p)
# Le_after_Q = np.zeros_like(set_p)
# current_ILC_after_Q = np.zeros_like(set_p)
# next_ILC = current_ILC + pid_output
# inverse plant
# Le = np.array(plant_pinv_mat * err.reshape(-1, 1)).reshape(-1)
# Le_after_Q = np.zeros_like(set_p)
# current_ILC_after_Q = np.zeros_like(set_p)
# next_ILC = current_ILC + pid_output + Le
# inverse ps (paper method)
# 矩阵计算方法
Le = np.array(ps_pinv_mat * datalog["err"].reshape(-1, 1)).reshape(-1)
# scipy库计算，行不通，因为非因果系统。Le = L * e = ps_inv * e
# t4move, Le, x_out = lsim2(ps_inv_tf_scipy, datalog["err"], t4move)
# without Q
f_k_after_Q = f_k
# with Q
# t4move, f_k_after_Q, x_out = lsim(butter_filter, f_k, t4move)
f_kp1 = f_k_after_Q + Le
fig, axs = plt.subplots(4, 2, figsize=(12, 12))
fig.suptitle("Iteration " + str(k + 1))
axs[0, 0].plot(t4move, set_p, label="cmd")
axs[0, 0].plot(t4move, datalog["p_fbk"], label="p_fbk")
axs[0, 0].legend(loc="upper left")
axs[0, 1].plot(t4move, datalog["err"], label="err")
axs[0, 1].legend(loc="upper left")
axs[1, 0].plot(t4move, datalog["pid_output"], label="pid out")
axs[1, 0].legend(loc="upper left")
axs[1, 1].plot(t4move, datalog["f_k"], label="f_k")
axs[1, 1].legend(loc="upper left")
axs[2, 0].plot(t4move, Le, label="Le")
axs[2, 0].legend(loc="upper left")
axs[2, 1].plot(t4move, f_k_after_Q, label="f_k_after_Q")
axs[2, 1].legend(loc="upper left")
axs[3, 0].plot(t4move, datalog["plant_input"], label="plant_input")
axs[3, 0].legend(loc="upper left")
axs[3, 1].plot(t4move, f_kp1, label="f_k+1 (f_k aft Q)")
axs[3, 1].legend(loc="upper left")
# plt.show()
# # 输入和加速度时域响应
# fig, axes = plt.subplots(1, 2, figsize=(14, 5))
#
# axes[0].set_xlabel("t4chirp/[s]")
# axes[0].set_ylabel("u/[N]")
# axes[0].plot(t4chirp, u, label="u")
#
# axes[1].set_xlabel("t4chirp/[s]")
# axes[1].set_ylabel("acc/[m/s**2]")
# axes[1].plot(t4chirp, y, label="acc")
# plt.suptitle("Input and Acc")
# # plt.legend()
#
# fig, axes = plt.subplots(1, 2, figsize=(14, 5))
#
# axes[0].set_xlabel("t4chirp/[s]")
# axes[0].set_ylabel("u/[N]")
# axes[0].plot(t4chirp, u, label="u")
#
# axes[1].set_xlabel("t4chirp/[s]")
# axes[1].set_ylabel("pos/[m]")
# axes[1].plot(t4chirp, p, label="pos")
#
# plt.suptitle("Chirp Response")
# # plt.legend()
#
# # 修正后和拟合的伯德图
# f_fit, fw_fit = sys_fit.bode(np.array(range(start_freq, end_freq)))
# fig, axes = plt.subplots(1, 2, figsize=(14, 5))
#
# axes[0].set_xlabel("f/[Hz]")
# axes[0].set_ylabel("Gain/[dB]")
# axes[0].semilogx(f_bode, 20 * np.log10(np.abs(fw)), label="Gain")
# axes[0].semilogx(f_fit, 20 * np.log10(np.abs(fw_fit)), label="Fit Gain")
#
# axes[1].set_xlabel("f/[Hz]")
# axes[1].set_ylabel("Phase/[deg]")
# axes[1].semilogx(f_bode, np.angle(fw, deg=True), label="Phase")
# axes[1].semilogx(f_fit, np.angle(fw_fit, deg=True), label="Fit Phase")
# plt.suptitle("sys id bode plot")
# plt.legend()
# #
# f_pid, fw_fit4pid = closed_loop_tf.bode(np.array(range(1, 2000)))
# fig, axes = plt.subplots(1, 2, figsize=(14, 5))
#
# axes[0].set_xlabel("f/[Hz]")
# axes[0].set_ylabel("Gain/[dB]")
# axes[0].semilogx(f_pid, 20 * np.log10(np.abs(fw_fit4pid)), label="Gain")
#
# axes[1].set_xlabel("f/[Hz]")
# axes[1].set_ylabel("Phase/[deg]")
# axes[1].semilogx(f_pid, np.angle(fw_fit4pid, deg=True), label="Phase")
# plt.suptitle("PID bode plot")
# plt.legend()
plt.show()