In [1]:
# Import the needed Packages
# FMU Simulation
import MoBASimulator as mb
# Numpy
import numpy as np
# Bokeh for Plotting
#import bokeh.plotting as bk
#import bokeh.io as bi
#from bokeh.io import export_svgs
#bi.output_notebook()
# select a palette
#from bokeh.palettes import Spectral10 as palette
#from bokeh.models import Legend, LabelSet, Label, BoxAnnotation
# Matplotlib for Plotting
import matplotlib.pyplot as plt
# Algorithms
import Algorithms as alg
from Algorithms import TUBScolorscale
from Algorithms import cm2in
# Make the relevant Inputs
export_folder = "../Latex/Graphics/"
model_name = "Approximation_Limits"
# Plot width and heigth in cm
plot_width = 19.
plot_height = 7.5
# Model Parameter
k = [[1,.3],[.3,1]]
t = [[99.,101.],[102.,98.]]
l = [[.1,.1],[50,.1]]
# Rosenbrock
#k = [[1.,2./3.],[1.,1.]]
#t = [[1.,1./3.],[1.,1.]]
#l = [[1e-10,1e-10],[1e-10,1e-10]]
# Woodberry
#k = [[12.8,-18.9],[6.6,-19.4]]
#t = [[16.7,21.0],[10.9,14.4]]
#l = [[1,3],[7,3]]
# Make variable storage
yl = []
ul = []
timel = []
TApprox = np.zeros((2,2,10))
LApprox = np.zeros((2,2,10))
TReal = np.zeros((2,2,10))
LReal = np.zeros((2,2,10))
# Show log window
sim = mb.Simulator()
sim.showLogWindow()
for delay in range(10,110,10):
# Make variable storage
yex = []
uex = []
timex = []
# The needed Parameter
K = np.zeros((2,2))
T = np.zeros((2,2))
L = np.zeros((2,2))
# Load a Model
sim.clear()
sim.loadModel("C:/Users/juliu/Documents/Thesis/Modelica/FMU/2_2/Masterthesis_Models_mimo_0processmodel.fmu")
# Parameter Values
params = {}
# Loop over system size
for outputs in range(1,3):
for inputs in range(1,3):
# Process Parameter
# System Gain
params.update({"fmu.num["+str(outputs)+","+str(inputs)+",1]": k[outputs-1][inputs-1]})
# System Lag
params.update({"fmu.den["+str(outputs)+","+str(inputs)+",2]": 1})
# System Lag
params.update({"fmu.den["+str(outputs)+","+str(inputs)+",2]": 1})
# System Delay
params.update({"fmu.delay["+str(outputs)+","+str(inputs)+"]": (delay/100.0)*l[outputs-1][inputs-1]})
params.update({"fmu.den["+str(outputs)+","+str(inputs)+",1]":t[outputs-1][inputs-1] - (delay/100.0)*l[outputs-1][inputs-1]})
# Set Parameter and show for checking
sim.set(params)
#sim.showParameterDialog()
#print(params)
# First run, Input 1 -> Output 1 & 2
sim.set({"fmu.u[1]": 1,"fmu.u[2]": 0})
# Set timestep = 1e-2, endtime = 100
sim.resetModelState()
res = sim.simulate(0.01, 500)
# Get the signals
y = res["fmu.y[1]"]
y2 = res["fmu.y[2]"]
u = res["fmu.u[1]"]
time = res["time"]
# Get TF from Input 1 to Output 1
K[0][0],T[0][0],L[0][0]=alg.Integral_Identification(y,u,time)
# Get TF from Input 1 to Output 2
K[1][0],T[1][0],L[1][0]=alg.Integral_Identification(y2,u,time)
# Second run, Input 2 -> Output 1 & 2
# Reload the Model to set everything to zero
sim.resetModelState()
sim.set({"fmu.u[1]":0, "fmu.u[2]":1})
# Set timestep = 1e-2, endtime = 100
res=sim.simulate(0.01, 500)
# Get the signals
y = res["fmu.y[1]"]
y2 = res["fmu.y[2]"]
u = res["fmu.u[2]"]
time = res["time"]
# Get TF from Input 2 to Output 1
K[0][1],T[0][1],L[0][1] = alg.Integral_Identification(y,u,time)
# Get TF from Input 2 to Output 2
K[1][1],T[1][1],L[1][1] = alg.Integral_Identification(y2,u,time)
# Loop over the methods for controller design
for methods in range(0,3):
if methods == 0:
# Make a decentralized controller
KY,B,D = alg.Control_Decentral(K,T,L)
elif methods == 1:
# Make a decoupled controller with Astrom
KY,B,D = alg.Control_Astrom(K,T,L,0.01*np.eye(2,2))
else:
# Make a decoupled controller with modified Astrom
KY,B,D = alg.Control_Decoupled(K,T,L,0.01*np.eye(2,2))
# Make zeros to 1e-10 for numerical stable process
KY[KY==0] = 1e-10
B[B==0] = 1e-10
D[D==0] = 1e-10
# Load the closed loop model
sim.clear()
sim.loadModel("C:/Users/juliu/Documents/Thesis/Modelica/FMU/2_2/Masterthesis_Models_mimo_0closedloop.fmu")
# Parameter Valuess
params = {}
# Loop over system size
for outputs in range(1,3):
for inputs in range(1,3):
# Controller Parameter
# Proportional Gain
params.update({"fmu.kp["+str(outputs)+","+str(inputs)+"]": KY[outputs-1][inputs-1][0]})
# Integral Gain
params.update({"fmu.ki["+str(outputs)+","+str(inputs)+"]": KY[outputs-1][inputs-1][1]})
# Decoupler
params.update({"fmu.d["+str(outputs)+","+str(inputs)+"]": D[outputs-1][inputs-1]})
# Set Point Weight
params.update({"fmu.b["+str(outputs)+","+str(inputs)+"]": B[outputs-1][inputs-1]})
# Process Parameter
# Process Parameter
# System Gain
params.update({"fmu.num["+str(outputs)+","+str(inputs)+",1]": k[outputs-1][inputs-1]})
# System Lag
params.update({"fmu.den["+str(outputs)+","+str(inputs)+",2]": 1})
# System Delay
params.update({"fmu.delay["+str(outputs)+","+str(inputs)+"]": (delay/100.0)*l[outputs-1][inputs-1]})
params.update({"fmu.den["+str(outputs)+","+str(inputs)+",1]":t[outputs-1][inputs-1] - (delay/100.0)*l[outputs-1][inputs-1]})
# Set Parameter Values
sim.set(params)
# First run, Input 1 -> Output 1 & 2
sim.resetModelState()
sim.set({"fmu.u[1]": 1.,"fmu.u[2]": 0.})
res=sim.simulate(1, 1500)
# Second run, Input 2-> Output 1 & 2
sim.set({"fmu.u[1]": 1.,"fmu.u[2]": 1})
res=sim.simulate(1, 3000)
# Store the output
yex.append([res["fmu.y[1]"],res["fmu.y[2]"]])
uex.append([res["fmu.u[1]"],res["fmu.u[2]"]])
timex.append([res["time"],res["time"]])
yl.append(yex)
ul.append(uex)
timel.append(timex)
In [2]:
from bokeh.layouts import gridplot
p1 = bk.figure(title = "Influence of the Approximation", height= 300, width = 800)
p2 = bk.figure(height= 300, width = 800)
for i in range(0,10):
y = yl[i]
time = timel[i]
p1.line(time[0][0],y[0][0], color = "red")
p1.line(time[1][0],y[1][0], color = "blue")
p1.line(time[2][0],y[2][0], color = "green")
p2.line(time[0][1],y[0][1], color = "red")
p2.line(time[1][1],y[1][1], color = "blue")
p2.line(time[2][1],y[2][1], color = "green")
p = gridplot([[p1],[p2]])
bk.show(p)
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