# Ref:
import numpy as np
from cpsim import Simulator
from cpsim.controllers.PID import PID
# system dynamics
state_num = 45
A = np.zeros((state_num, state_num))
tmp = np.array([[1], [-2], [1]])
A[0:2, 0:1] = tmp[1:3, 0:1]
for i in range(state_num - 2):
A[i:i + 3, i + 1:i + 2] = tmp
A[state_num - 2:state_num, state_num - 1:state_num] = tmp[0:2, 0:1]
if state_num == 2:
A = np.array([[-2, 1], [1, -2]])
B = np.zeros((state_num, 1))
u_point = (state_num + 1) // 3 - 1
B[u_point, 0] = 1
C = np.zeros((1, state_num))
y_point = (state_num + 1) // 3 * 2 - 1
C[0, y_point] = 1
D = np.zeros((1, 1))
x_0 = np.zeros((state_num))
# utils parameters
# KP = 0.00000099 * state_num * state_num * state_num * state_num
# KI = 0
# KD = 0
KP = 10
KI = 0.23
KD = 0
control_limit = {'lo': [-0.5], 'up': [50]}
R = np.eye(1) * 0.0008
Q = np.eye(state_num)
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class Controller:
def __init__(self, dt):
self.dt = dt
self.pid = PID(KP, KI, KD, current_time=-dt)
self.pid.setWindup(100)
self.pid.setSampleTime(dt)
self.set_control_limit(control_limit['lo'], control_limit['up'])
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def update(self, ref: np.ndarray, feedback_value: np.ndarray, current_time) -> np.ndarray:
self.pid.set_reference(ref[0])
cin = self.pid.update(feedback_value[0], current_time)
return np.array([cin])
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def set_control_limit(self, control_lo, control_up):
self.control_lo = control_lo
self.control_up = control_up
self.pid.set_control_limit(self.control_lo[0], self.control_up[0])
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def clear(self):
self.pid.clear(current_time=-self.dt)
# class Controller:
# def __init__(self, dt, control_limit=None):
# self.lqr = LQR(A, B, Q, R)
# self.lqr.set_control_limit(control_limit['lo'], control_limit['up'])
#
# def update(self, ref: np.ndarray, feedback_value: np.ndarray, current_time) -> np.ndarray:
# self.lqr.set_reference(ref)
# cin = self.lqr.update(feedback_value, current_time)
# return cin
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class Heat(Simulator):
"""
States: (N,)
x[i]: temperature on the i'th field
Control Input: (1,)
heat source to heat the a point of the rod located at 1/3 of the length
Output: (1,)
record the temperature at 2/3 of the length
Output Feedback
Controller: PID
"""
def __init__(self, name, dt, max_index, noise=None):
super().__init__('Aircraft Pitch ' + name, dt, max_index)
self.linear(A, B)
controller = Controller(dt)
settings = {
'init_state': x_0,
'feedback_type': 'state',
'controller': controller
}
if noise:
settings['noise'] = noise
self.sim_init(settings)
if __name__ == "__main__":
max_index = 1000
dt = 1
ref = [np.array([15])] * (max_index + 1)
noise = {
'process': {
'type': 'white',
'param': {'C': np.eye(state_num) * 0.01}
}
}
heat = Heat('test', dt, max_index, noise)
for i in range(0, max_index + 1):
assert heat.cur_index == i
heat.update_current_ref(ref[i])
# attack here
heat.evolve()
# print results
import matplotlib.pyplot as plt
t_arr = np.linspace(0, 10, max_index + 1)
ref = [x[0] for x in heat.refs[:max_index + 1]]
y_arr = [x[0] for x in heat.outputs[:max_index + 1]]
plt.plot(t_arr, y_arr, t_arr, ref)
plt.show()
# u_arr = [x[0] for x in heat.inputs[:max_index + 1]]
# plt.plot(t_arr, u_arr)
# plt.show()