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Control-backup.py
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import numpy as np
import torch
import matplotlib.pyplot as plt
from PredictionModel import LSTM, device, LSTM2
# from pyomo.environ import *
from Kinetics import cstr_cascading_kinetics
from scipy.optimize import minimize, NonlinearConstraint
import ipyopt
# 如果使用神经网络，归一化没有考虑 ？？？？？？？？？？
#
# 控制量相关内容
# 目标函数： L = xT*Q*x + u1T*R*u1 + u2T*R*u2, Q= diag[2 × 103 1 2 × 103 1], R1 = R2 = diag[8e−13 0.001];
# x要改成输入 deltU 的累积量
# 李雅普诺夫函数: V = x1T*P1*x1 + x2T*P2*x2, P1=P2=np.array([[1060, 22], [22,0.52]])
# 约束条件： x in X,
# deltU in DELTU,
# dVdt * Fnn(x(tk), u1, u2) <= dVdt * Fnn(x(tk), Phi_nn1(tk), Phi_nn2(tk)) #在域外
# dVdt * Fnn(x(tk), u1, u2) <= rho_nn # 在域内
# parameters setting
Ea = 50000 # activation energy J/gmol
R = 8.314 # gas constant J/gmol/K
k0 = 8.46e6 # Arrhenius rate constant 1/min
V = 1 # Volume [m3]
rho = 1000.0 # Density [kg/m3]
Cp = 0.231 # Heat capacity [kJ/kg/K]
dHr = -1.15e4 # Enthalpy of reaction [kJ/kmol]
q = 5.0 # Flowrate [m3/h]
cAi = 1.0 # Inlet feed concentration [mol/L]
Ti = 350.0 # Inlet feed temperature [K]
cA0 = 0.5 # Initial concentration [mol/L]
T10 = 300.0 # Initial temperature of tank 1 [K]
T20 = 300.0 # Initial temperature of tank 2 [K]
controlInterval = 0.01 # 控制时间
sampleInterval = 0.0001 # 采样时间 - 微分时间
loopNum = 100
class controlMethod():
def __init__(self):
# 稳定点数值
self.CA1s = 1.954
self.CA2s = 1.954
self.CA10s = 4
self.CA20s = 4
self.Q1s = 0
self.Q2s = 0
self.T1s = 401.9
self.T2s = 401.9
self.rhonn = 10
self.rhomin = 12
self.rho_1_2 = 760
self.xs = np.array([self.CA1s, self.T1s, self.CA2s, self.T2s]) # 稳定点 ???????????????
self.P = np.array([[1060, 22],[22, 0.52]]) # size: 4x4
self.Q = np.diag([2e3, 1, 2e3, 1]) # size： 4x4
self.R = np.diag([8e-13, 0.001]) # size：2x2
self.PATH = "netModel/LSTM2_2_1_10epoch.pth" ## 两个子系统的运行合并到一个LSTM中来做
# self.PATH = "net/Model/LSTM_1_2_30epoch_1_windowSize.pth" ## 每个子系统的运行是一个LSTM
self.model =torch.load(self.PATH)
self.choice = 'FirstPrinciple' # or 'NN' 'FirstPrinciple'
# self.choice = 'NN'
self.fpModel = cstr_cascading_kinetics(Ea, R, k0, V, rho, Cp, dHr, q, Ti, cA0, T10, T20)
# for ipyopt used
self.seqSize = 5
self.initialConditions = np.zeros(1)
self.initialControls = np.zeros(1)
def nextStep(self, inputVar, method='NN'):
if method == 'NN':
output = self.model(inputVar)
output = output.data.cpu().numpy()
elif method == 'FirstPrinciple':
initialConditions = inputVar[0:6]
controlQuantity = inputVar[6:]
output = self.fpModel.nextState(initialState=initialConditions, controlQuantity=controlQuantity, timeInterval=sampleInterval, loopNum=loopNum)
return np.array(output)
def calSontag():
pass
def calObjective(self, controlSeq, seqSize, initialConditions, initialControls):
# 此函数为first-principle版本
# controlSeq, 4个一组，+0， +1， 为第一个控制器的 CA0 和 Q ， +2，+3，为第二个控制器的 CA0 和 Q
sum = 0
for i in range(0, seqSize):
deltU = np.array([controlSeq[4*i], controlSeq[4*i+1], controlSeq[4*i+2], controlSeq[4*i+3]])
nowControls = np.array(initialControls) + deltU # 当前控制量
u1Temp = nowControls[[0,1]]
u2Temp = nowControls[[2,3]]
nowConditions = np.array(initialConditions) # 当前状态量
nowInput = np.append(nowConditions, nowControls)
newOutput = self.nextStep(nowInput, method=self.choice)
initialConditions = newOutput
initialControls = nowControls
xTemp = newOutput[[0,1,3,4]] - self.xs # 只是取出来需要的两个状态
sum = sum + xTemp.T.dot(self.Q).dot(xTemp) + u1Temp.T.dot(self.R).dot(u1Temp) + \
u2Temp.T.dot(self.R).dot(u2Temp)
# sum = sum + xTemp.T*self.Q*xTemp + u1Temp.T*self.R*u1Temp + u2Temp.T*self.R*u2Temp
return sum
def calConstraints(self, controlSeq, seqNumNow, seqSize, initialConditions, initialControls, returnNum, modelType='NN'):
# 此函数为first-principle版本
# seqNumNow： 未来串口中的第几个
# controlSeqCA： 第一个控制量，CA，控制序列
# controlSeqQ：第二个控制量，Q， 控制序列
# seqSize： MPC窗口大小
# initialConditions：系统在MPC开始时候的系统状态
# initialControls： 系统在MPC开始时候的控制量
xTemp = np.array(initialConditions[[0,1,3,4]] - self.xs)
x1Temp = xTemp[[0,1]]
x2Temp = xTemp[[2,3]]
xkValue = x1Temp.T.dot(self.P).dot(x1Temp) + x2Temp.T.dot(self.P).dot(x2Temp)
# xkValue = x1Temp.T*self.P*x1Temp + x2Temp.T*self.P*x2Temp
if (xkValue <= self.rhonn) or (seqNumNow > 0): # 只需要判断第一个状态即可
for i in range(0,seqNumNow):
deltU = np.array([controlSeq[4*i], controlSeq[4*i+1], controlSeq[4*i+2], controlSeq[4*i+3]])
nowControls = np.array(initialControls) + deltU # 当前控制量
nowConditions = np.array(initialConditions) # 当前状态量
nowInput = np.append(nowConditions, nowControls)
newOutput = self.nextStep(nowInput, method=self.choice)
initialConditions = newOutput
initialControls = nowControls
xTemp = newOutput[[0,1,3,4]] - self.xs # 只是取出来需要的两个状态
# V = xTemp[0,1].T*self.P*xTemp[0,1] + xTemp[2,3].T*self.P*xTemp[2,3]
V1 = xTemp[[0,1]].T.dot(self.P).dot(xTemp[[0,1]])
V2 = xTemp[[2,3]].T.dot(self.P).dot(xTemp[[2,3]])
# return (V1 <= self.rhonn) and (V2 <= self.rhonn)
# return V1 - self.rhonn, V2 - self.rhonn, xTemp[[0,1]], xTemp[[2,3]]
if returnNum == 0:
return -(V1 - self.rhonn)
elif returnNum == 1:
return -(V2 - self.rhonn)
else:
print("wrong returnNumber!!!!!")
# elif (xkValue <= self.rho_1_2) :
else:
xTemp = initialConditions[[0,1,3,4]] - self.xs # x(k) 用于计算 dV(xk)/dx
# for i in range(seqNumNow):
# deltU = np.array([controlSeq[4*i], controlSeq[4*i+1], controlSeq[4*i+2], controlSeq[4*i+3]])
# nowControls = np.array(initialControls) + deltU # 当前控制量
# nowConditions = np.array(initialConditions) # 当前状态量
# nowInput = np.append(nowConditions, nowControls)
# newOutput = self.nextStep(nowInput, method=self.choice)
# initialConditions = newOutput
# initialControls = nowControls
# xTemp = newOutput[[0,1,3,4]] - self.xs # 只是取出来需要的两个状态
# sontag辅助控制率计算过程
dtvx1 = 2*self.P.dot(xTemp[[0,1]]) # 向量
dtvx2 = 2*self.P.dot(xTemp[[2,3]])
nowControls = np.array([0,0,0,0]) # 零输入
nowConditions = np.array(initialConditions) # 当前状态量
nowInput = np.append(nowConditions, nowControls)
outputTemp = self.nextStep(nowInput, method=self.choice) # 零输入响应
outputTemp = outputTemp[[0,1,3,4]] - self.xs
ftilde1 = outputTemp[[0,1]]
ftilde2 = outputTemp[[2,3]]
LfV1 = dtvx1.dot(ftilde1)
LfV2 = dtvx2.dot(ftilde2)
# 第一个罐子的控制量 # 这个地方用了动力学
g1 = np.array([q/V, 0])
Lg1V = dtvx1.dot(g1)
if Lg1V == 0:
h1_1xtk = 0
else:
h1_1xtk = -(LfV1 + np.sqrt(LfV1*LfV1 + np.power(Lg1V, 4)))/(Lg1V*Lg1V)
g2 = np.array([0, 1/(rho*Cp*V)])
Lg2V = dtvx1.dot(g2)
if Lg2V == 0:
h1_2xtk = 0
else:
h1_2xtk = -(LfV1 + np.sqrt(LfV1*LfV1 + np.power(Lg2V, 4))) / (Lg2V * Lg2V)
# 第二个罐子的控制量
g1 = np.array([q/V, 0])
Lg1V = dtvx2.dot(g1)
if Lg1V == 0:
h2_1xtk = 0
else:
h2_1xtk = -(LfV2 + np.sqrt(LfV2*LfV2 + np.power(Lg1V, 4)))/ (Lg1V * Lg1V)
g2 = np.array([0, 1/(rho*Cp*V)])
Lg2V = dtvx2.dot(g2)
if Lg2V == 0:
h2_2xtk = 0
else:
h2_2xtk = -(LfV2 + np.sqrt(LfV2*LfV2 + np.power(Lg2V, 4))) / (Lg2V * Lg2V)
# 辅助控制率计算Lyapunov上限
deltU = np.array([h1_1xtk, h1_2xtk, h2_1xtk, h2_2xtk])
nowControls = np.array(initialControls) + deltU # 当前控制量
nowConditions = np.array(initialConditions) # 当前状态量
nowInput = np.append(nowConditions, nowControls)
newOutput = self.nextStep(nowInput, method=self.choice)
xSontag = newOutput[[0,1,3,4]] - self.xs # 只是取出来需要的两个状态
xSontag1 = xSontag[[0,1]]
xSontag2 = xSontag[[2,3]]
V1Sontag = dtvx1.dot(xSontag1)
V2Sontag = dtvx2.dot(xSontag2)
# 优化控制率计算Lyapunov约束项值
deltU = np.array([controlSeq[0], controlSeq[1], controlSeq[2], controlSeq[3]])
nowControls = np.array(initialControls) + deltU # 当前控制量
nowConditions = np.array(initialConditions) # 当前状态量
nowInput = np.append(nowConditions, nowControls)
newOutput = self.nextStep(nowInput, method=self.choice)
optimalX = newOutput[[0,1,3,4]] - self.xs
optimalX1 = optimalX[[0,1]]
optimalX2 = optimalX[[2,3]]
V1Optimal = dtvx1.dot(optimalX1)
V2Optimal = dtvx2.dot(optimalX2)
# return (V1Optimal <= V1Sontag) and (V2Optimal <= V2Sontag)
# return V1Optimal - V1Sontag, V2Optimal - V2Sontag, xTemp[[0,1]], xTemp[[2,3]]
if returnNum == 0:
return -(V1Optimal - V1Sontag)
elif returnNum == 1:
return -(V2Optimal - V2Sontag)
else:
print("wrong returnNumber!!!!!")
def getConstraintJacVec(self, controlSeq, seqNum, seqSize, initialConditions, initialControls, returnNum, modelType='NN'):
# self, controlSeq, seqNumNow, seqSize, initialConditions, initialControls, returnNum
# seqNum 当前预测时间步
# seqSize MPC预测窗口大小
# initialConditions 当前时刻的未开始MPC的状态
# initialControls 当前时刻为开始MPC的控制量
# controlNum 控制器编号 输入为0，1，2，。。。分别对应1，2，3.。。号控制器
# modelType 预测模型类别
stepLen = 0.001 # 求微分时候的步长
controlSeq = np.array(controlSeq)
jacVec = np.zeros(controlSeq.shape) # 约束导数的大小
# 更新当前状态至第 seqNum 个预测时间窗口
for i in range(seqNum):
deltU = np.array([controlSeq[4*i], controlSeq[4*i+1], controlSeq[4*i+2], controlSeq[4*i+3]])
nowControls = np.array(initialControls) + deltU # 当前控制量
nowConditions = np.array(initialConditions) # 当前状态量
nowInput = np.append(nowConditions, nowControls)
newOutput = self.nextStep(nowInput, method=self.choice)
initialControls = nowControls
initialConditions = newOutput
# 计算当前约束条件的基础值，用于求解约束条件的倒数
controllerVarNum = int(len(controlSeq) / seqSize)
oringinPoint = self.calConstraints(controlSeq, seqNum, seqSize, initialConditions, initialControls, returnNum, modelType)
# 定位到第几个窗口 # 这个地方不对！！！！！！！！！！？？？？？？？？？？
for j in range(controllerVarNum):
controlPosition = j + seqNum * 4
controlSeqNew = controlSeq
controlSeqNew[controlPosition] = controlSeqNew[controlPosition] + stepLen
originPointNow = self.calConstraints(controlSeqNew, seqNum, seqSize, initialConditions, initialControls, returnNum, modelType)
jacVec[j] = (originPointNow - oringinPoint)/stepLen
return jacVec
def getConstraintJacVec_new(self, controlSeq, seqNum, seqSize, initialConditions, initialControls, returnNum, selectNum, modelType='NN'):
# self, controlSeq, seqNumNow, seqSize, initialConditions, initialControls, returnNum
# seqNum 当前预测时间步
# seqSize MPC预测窗口大小
# initialConditions 当前时刻的未开始MPC的状态
# initialControls 当前时刻为开始MPC的控制量
# controlNum 控制器编号 输入为0，1，2，。。。分别对应1，2，3.。。号控制器
# selectNum 输出当前窗口第几维数据，例如，如果是第二个 窗口的第三维度数据，则seqNum=1, selectNum=2
# modelType 预测模型类别
stepLen = 0.001 # 求微分时候的步长
controlSeq = np.array(controlSeq)
jacVec = np.zeros(controlSeq.shape) # 约束导数的大小
# 更新当前状态至第 seqNum 个预测时间窗口
for i in range(seqNum):
deltU = np.array([controlSeq[4*i], controlSeq[4*i+1], controlSeq[4*i+2], controlSeq[4*i+3]])
nowControls = np.array(initialControls) + deltU # 当前控制量
nowConditions = np.array(initialConditions) # 当前状态量
nowInput = np.append(nowConditions, nowControls)
newOutput = self.nextStep(nowInput, method=self.choice)
initialControls = nowControls
initialConditions = newOutput
# 计算当前约束条件的基础值，用于求解约束条件的倒数
controllerVarNum = int(len(controlSeq) / seqSize)
oringinPoint = self.calConstraints(controlSeq, seqNum, seqSize, initialConditions, initialControls, returnNum, modelType)
# 定位到第几个窗口
for j in range(controllerVarNum):
controlPosition = j + seqNum * 4
controlSeqNew = controlSeq
controlSeqNew[controlPosition] = controlSeqNew[controlPosition] + stepLen
originPointNow = self.calConstraints(controlSeqNew, seqNum, seqSize, initialConditions, initialControls, returnNum, modelType)
jacVec[j] = (originPointNow - oringinPoint)/stepLen
return jacVec
def get_sparsity_g_jac_matrix(self, varNum):
# varNum = x.shape()[0]
constraintNum = self.seqSize * 2 # 雅各比矩阵的长度 = MPC序列长度 * 变量个数
jacMatrix = np.ones([constraintNum, varNum])
row = []
col = []
# for i in range(0,constraintNum, 2):
# jacMatrix[i, 2*i] = 1
# jacMatrix[i, 2*i +1] = 1
# jacMatrix[i+1, 2*i +2] = 1
# jacMatrix[i+1, 2*i +3] = 1
# for i in range(0, constraintNum):
# for j in range(0, varNum):
# if jacMatrix[i,j] == 1:
# row.append(i)
# col.append(j)
for i in range(constraintNum): # 列
for j in range(varNum): # 行
if jacMatrix[i,j] == 1:
row.append(i)
col.append(j)
row = np.array(row)
col = np.array(col)
return (row, col)
def get_sparsit_hessian_matrix(self, varNum):
hessianMatrix = np.zeros([varNum, varNum])
for i in range(0,varNum,2):
hessianMatrix[i,i] = 1
hessianMatrix[i,i+1] = 1
hessianMatrix[i+1,i] = 1
hessianMatrix[i+1, i+1] = 1
# hessianMatrix = np.diag([1 for i in range(varNum)])
return hessianMatrix
def CentralizeLMPC(self, initialConditions, initialControls, seqSize):
# initialConditions: 初始状态
# initialControls: 初始控制量
# seqSize: MPC窗口长度
# return: CA, Q
###############################################################################################################
########## Pyomo方法 #############
###############################################################################################################
# OPmodel = ConcreteModel()
# OPmodel.deltCA = Var(range(0,2*seqSize), within=Reals, bounds=(-3.5,3.5)) # 入料量 优化变量
# OPmodel.deltQ = Var(range(0,2*seqSize), within = Reals, bounds=(-5e5,5e5)) # 加热器 优化变量
# OPmodel.f = Objective(rule= self.calObjective(OPmodel.deltCA, OPmodel.deltQ, seqSize, initialConditions, initialControls))
# for nowTime in range(0,seqSize):
# OPmodel.c1 = Constraint(expr= self.calConstraints(seqNumNow = nowTime, controlSeqCA=OPmodel.deltCA, controlSeqQ = OPmodel.deltQ, seqSize = seqSize,\
# initialConditions=initialControls, initialControls=initialControls))
# OPmodel.pprint()
# SolverFactory('ipopt').solve(OPmodel).write()
# print(OPmodel.deltCA)
# print(OPmodel.deltQ)
# # OPmodel.c1 = Constraint(OPmodel.nowTime, expr = self.calConstraints(seqNumNow = nowTime, controlSeqCA=OPmodel.deltCA, controlSeqQ = OPmodel.deltQ, seqSize = seqSize,\
# # initialConditions=initialControls, initialControls=initialControls) for nowTime in range(0,seqSize)) # using lambda function??????????????????????
# return OPmodel.deltCA, OPmodel.deltQ
###############################################################################################################
###############################################################################################################
###############################################################################################################
######## Scipy.optimize 方法
###############################################################################################################
# controlSeqInitial = np.tile(np.zeros(4), (1, seqSize)) # 4个一组，+0， +1， 为第一个控制器的 CA0 和 Q ， +2，+3，为第二个控制器的 CA0 和 Q
# # 优化项的初始值
# controlSeqInitial = np.squeeze(controlSeqInitial)
# bound = []
# for i in range(seqSize): # 计算输入约束
# bound.append((-3.4, 3.4))
# bound.append((-5e5,5e5))
# bound.append((-3.4,3.4))
# bound.append((-5e5, 5e5))
# bound = tuple(bound)
# def calCons(controlSeqInitial):
# cons = []
# jacs = []
# # n = int(len(controlSeqInitial)/4)
# n = seqSize
# for i in range(n): # 计算约束
# argrow0 = (i, seqSize, initialConditions, initialControls,0, self.choice)
# argrow1 = (i, seqSize, initialConditions, initialControls,1, self.choice)
# cons.append({'type':'ineq', 'fun': self.calConstraints, 'jac': self.getConstraintJacVec, 'args':argrow0})
# cons.append({'type':'ineq', 'fun': self.calConstraints, 'jac': self.getConstraintJacVec, 'args':argrow1})
# return cons
# def func(x):
# return self.calObjective(x, seqSize, initialConditions, initialControls)
# # res = minimize(self.calObjective, controlSeqInitial, args=(seqSize, initialConditions, initialControls), bounds=bound, method='trust-constr',constraints=calCons(controlSeqInitial), options={'disp':True})
# # res = minimize(self.calObjective, controlSeqInitial, args=(seqSize, initialConditions, initialControls), bounds=bound, method='BFGS',constraints=calCons(controlSeqInitial), options={'disp':True})
# res = minimize(self.calObjective, controlSeqInitial, args=(seqSize, initialConditions, initialControls), bounds=bound, method='SLSQP',constraints=calCons(controlSeqInitial), tol = 1e-10, options={'disp':True})
# return res.x
###############################################################################################################
######## ipopt 方法
###############################################################################################################
self.seqSize = seqSize
self.initialConditions = initialConditions
self.initialControls = initialControls
controlSeqInitial = np.tile(np.array([0.0,0.0,0.0,0.0]), (1, seqSize)) # 4个一组，+0， +1， 为第一个控制器的 CA0 和 Q ， +2，+3，为第二个控制器的 CA0 和 Q
# 优化项的初始值
controlSeqInitial = np.squeeze(controlSeqInitial)
x_l = np.tile(np.array([-3.5, -5e5, -3.5, -5e5]), (1,seqSize))
x_l = np.squeeze(x_l)
x_u = np.tile(np.array([3.5, 5e5, 3.5, 5e5]), (1,seqSize))
x_u = np.squeeze(x_u)
constraintsNum = seqSize * 2 # 约束的数量
g_l = np.tile(np.array([0.0, 0.0]), (1, seqSize))
g_l = np.squeeze(g_l)
g_u = np.tile(np.array([1e15,1e15]), (1,seqSize))
g_u = np.squeeze(g_u)
sparsity_indices_jac_g = self.get_sparsity_g_jac_matrix(controlSeqInitial.shape[0])
sparsity_indices_h = self.get_sparsit_hessian_matrix(controlSeqInitial.shape[0])
# 不知道怎么求 Hessian 矩阵 , ipyopt 说可以不用求
def func(x):
return self.calObjective(x, seqSize, initialConditions, initialControls)
def grad_f(x, out):
varNum = seqSize * 4
"""Return the gradient of the objective"""
for i in range(0,varNum,2):
out[i] = 2*self.R[0,0] * x[i]
out[i + 1] = 2 * self.R[1,1] * x[i + 1]
return out
def g(x, out):
n = seqSize
for i in range(n):
out[2*i] = self.calConstraints(x, i, seqSize, initialConditions, initialControls, 0, self.choice)
out[2*i + 1] = self.calConstraints(x, i, seqSize, initialConditions, initialControls, 1, self.choice)
return out
def jac_g(x, out):
varNum = seqSize * 4
for i in range(seqSize):
temp1 = self.getConstraintJacVec(x, i, seqSize, initialConditions, initialControls,0, self.choice)
temp2 = self.getConstraintJacVec(x, i, seqSize, initialConditions, initialControls,1, self.choice)
temp = np.append(temp1, temp2)
for j in range(0, varNum):
out[varNum*i + j] = temp[j]
return out
# nlp = ipyopt.Problem(
# n = 4*seqSize,
# x_l = x_l,
# x_u = x_u,
# m = constraintsNum,
# g_l = g_l,
# g_u = g_u,
# sparsity_indices_jac_g = sparsity_indices_jac_g,
# sparsity_indices_h=sparsity_indices_h,
# func, # 目标函数
# grad_f,
# g,
# jac_g,
# )
nlp = ipyopt.Problem(
4*seqSize,
x_l,
x_u,
constraintsNum,
g_l,
g_u,
sparsity_indices_jac_g,
sparsity_indices_h,
func,
grad_f,
g,
jac_g,
)
x, obj, status = nlp.solve(x0=controlSeqInitial)
return x
# model = ConcreteModel() # 创建模型对象
# # define model variables
# # domain = Reals(Default) / NonNegativeReals Binary
# model.x1 = Var(domain=Reals)
# model.x2 = Var(domain=Reals)
# # define objective function
# # sense = minimize(Default) / maximize
# model.f = Objective(expr = model.x1**2 + model.x2**2, sense=minimize)
# # define constraints, equations or inequations
# model.c1 = Constraint(expr = -model.x1**2 + model.x2 <= 0)
# model.ceq1 = Constraint(expr = model.x1 + model.x2**2 == 2)
# # use 'pprint' to print the model information
# model.pprint()
# SolverFactory('ipopt').solve(model).write()
# print(model.x1())
# print(model.x2())
# print(model.f())