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, LogTickFormatter
# 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 = "Rosenbrock_Testing"
# Plot width and heigth in cm
plot_width = 19.
plot_height = 7.5
# Simulation Parameter
hmax = .3
# Model Parameter
#k = np.random.uniform(-10,10,(2,2))
#t = np.random.uniform(1,20,(2,2))
#l = np.random.uniform(10,20,(2,2))
# 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]]
# The needed Parameter
K = np.zeros((2,2))
T = np.zeros((2,2))
L = np.zeros((2,2))
# Load a Model
sim = mb.Simulator()
sim.clear()
sim.loadModel("C:/Users/juliu/Documents/Thesis/Modelica/FMU/2_2/Masterthesis_Models_mimo_0processmodel.fmu")
sim.setOperationMode('FMU for ModelExchange')
# Show log window
sim.showLogWindow()
# 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)+",1]": t[outputs-1][inputs-1]})
params.update({"fmu.den["+str(outputs)+","+str(inputs)+",2]": 1})
# System Delay
params.update({"fmu.delay["+str(outputs)+","+str(inputs)+"]": l[outputs-1][inputs-1]})
# Set Parameter and show for checking
sim.set(params)
#sim.showParameterDialog()
#print(params)
# Get the state space
ss = sim.analyser_getStateSpaceForm()
# 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, 40)
# 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, 80)
# 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)
In [2]:
# Make variable storage
y = []
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)
print("RGA")
print(KY,B,D)
elif methods == 1:
# Make a decoupled controller with Astrom
KY,B,D = alg.Control_Astrom(K,T,L,hmax*np.eye(2,2))
print("Aström")
print(KY,B,D)
else:
# Make a decoupled controller with modified Astrom
KY,B,D = alg.Control_Decoupled(K,T,L,hmax*np.eye(2,2))
print("R2D2")
print(KY,B,D)
# 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)+",1]": t[outputs-1][inputs-1]})
params.update({"fmu.den["+str(outputs)+","+str(inputs)+",2]": 1})
# System Delay
params.update({"fmu.delay["+str(outputs)+","+str(inputs)+"]": 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(0.1, 100)
# Second run, Input 2-> Output 1 & 2
sim.set({"fmu.u[1]": 1.,"fmu.u[2]": 1})
res=sim.simulate(0.1, 200)
# Store the output
y.append([res["fmu.y[1]"],res["fmu.y[2]"]])
u.append([res["fmu.u[1]"],res["fmu.u[2]"]])
time.append([res["time"],res["time"]])
# Make Aström Reference from Paper
KY = np.array([ [[0.245, 0.248, 0], [0,0,0]], [[0,0,0], [-0.452,0.075,0]] ])
B = np.array([[0,0],[0,0]])
D = np.linalg.inv(k)
# 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")
sim.reloadModel()
# Parameter Values
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
# 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)+",1]": t[outputs-1][inputs-1]})
params.update({"fmu.den["+str(outputs)+","+str(inputs)+",2]": 1})
# System Delay
params.update({"fmu.delay["+str(outputs)+","+str(inputs)+"]": l[outputs-1][inputs-1]})
# Set Parameter Values
sim.set(params)
#sim.showParameterDialog()
# First run, t<40
sim.resetModelState()
sim.set({"fmu.u[1]": 1,"fmu.u[2]": 0})
res=sim.simulate(0.01, 100)
# t>=40
sim.set({"fmu.u[1]": 1,"fmu.u[2]": 1})
# Set timestep = 1e-2, endtime = 100
res=sim.simulate(0.01, 200)
In [3]:
plt.rcParams['svg.fonttype'] = 'none'
plt.style.use('seaborn-whitegrid')
fig, ax = plt.subplots(2, sharex=True,figsize = cm2in(plot_width,2.*plot_height))
ax[0].plot(res["time"],res["fmu.y[1]"], color = TUBScolorscale[0], linewidth = 1., linestyle = "dashed")
ax[0].plot(time[0][0],y[0][0], color = TUBScolorscale[9], linewidth = 1.)
ax[0].plot(time[1][0],y[1][0], color = TUBScolorscale[1], linewidth = 1.)
ax[0].plot(time[2][0],y[2][0], color = TUBScolorscale[3], linewidth = 1.)
ax[0].grid(True)
ax[0].set_ylabel('$y_1$')
ax[1].plot(res["time"],res["fmu.y[2]"], color = 'k', linewidth = 1., linestyle = "dashed", label="Reference")
ax[1].plot(time[0][1],y[0][1], color = TUBScolorscale[9], linewidth = 1., label="RGA")
ax[1].plot(time[1][1],y[1][1], color = TUBScolorscale[1], linewidth = 1., label="Astrom")
ax[1].plot(time[2][1],y[2][1], color = TUBScolorscale[3], linewidth = 1., label = "R2D2")
ax[1].grid(True)
ax[1].set_ylabel('$y_2$')
ax[1].set_xlabel('Time [s]')
plt.legend(loc="lower right")
plt.savefig(export_folder+model_name+".svg")
plt.show()
In [9]:
plt.style.use('seaborn-whitegrid')
# Define Functions
S = lambda omega : alg.compute_sensitivity(ss,KY,B,D,omega)
CS = lambda omega : alg.compute_complementarysensitivity(ss,KY,B,D,omega)
sv = lambda X : np.linalg.svd(X, compute_uv = False)
fig, ax = plt.subplots(1,3, sharey=True, figsize=cm2in(plot_width,plot_height))
# Loop over the methods for controller design
for methods in range(0,3):
if methods == 0:
cur_method = "RGA"
# Make a decentralized controller
KY,B,D = alg.Control_Decentral(K,T,L)
ax[methods].set_ylabel('\overline{\sigma}')
elif methods == 1:
cur_method = "Astroem"
# Make a decoupled controller with Astrom
KY,B,D = alg.Control_Astrom(K,T,L,hmax*np.eye(2,2))
else:
cur_method = "R2D2"
# Make a decoupled controller with modified Astrom
KY,B,D = alg.Control_Decoupled(K,T,L,hmax*np.eye(2,2))
# Loop over Frequency
w = np.logspace(-3,1, 1e4)
SV = np.empty((2,len(w)))
TV = np.empty((2,len(w)))
for i in range(0,len(w)):
freq = w[i]
SV[:,i] = sv(S(freq))
TV[:,i] = sv(CS(freq))
# Find the maximum Singular Value
max_sv = np.argmax(SV[0,:])
w_max = w[max_sv]
max_sv = SV[0,max_sv]
# Find Robustness Area, Last Element less than one
rob_sv = np.argmax(SV[0,:]>.99)
w_rob = w[rob_sv]
rob_sv= SV[0,rob_sv]
# Make a Plot
ax[methods].set_title(cur_method)
ax[methods].axvspan(np.min(w),w_rob, color ='green', alpha =0.2)
ax[methods].axvspan(w_rob,np.max(w), color ='red', alpha =0.2)
ax[methods].loglog(w,TV[0,:], color=TUBScolorscale[6], label="$\ma{T}$", linewidth=1)
ax[methods].loglog(w,TV[1,:], color=TUBScolorscale[6], linewidth=1)
ax[methods].loglog(w,SV[0,:], color=TUBScolorscale[1], label="$\ma{S}$", linewidth=1)
ax[methods].loglog(w,SV[1,:], color=TUBScolorscale[1], linewidth=1)
ax[methods].loglog(w_max, max_sv,marker="o", color='w', label="\overline{\sigma} "+ "(%.2f, %.2f)" %(w_max ,max_sv))
ax[methods].set_xlabel('\omega')
ax[methods].grid(True)
# Set the xticks and labels
ax[methods].set_xticks([1e-2,1e0])
ax[methods].set_xticklabels([r'$10^{-2}$', r'$10^0$'])
plt.savefig(export_folder+model_name+"_SV.svg")
plt.show()
In [5]:
# Get the step_info and the Disturbance Info
# Define Method Name
cur_methods = ['RGA', 'Astroem', 'R2D2']
cur_ouput = ['$y_1$','$y_2$']
steptime = 100
# Make structure for storage
File = open(export_folder+model_name+"_StepInfo.tex","w")
# Add the header
File.write('\\begin{tabular}{l|c| c|c|c|| c|c|c|} \n ')
File.write('\\multicolumn{2}{l}{\multirow{3}{*}} & \\multicolumn{3}{c}{Tracking Performance} & \\multicolumn{3}{l}{Rejection Performance} \\\ \\cline{3-8} \n')
File.write('\\multicolumn{2}{l|}{} & $T_{Rise}$ & $m_P$ & $T_{Settle}$ & $T_{p}$ & $m_{\Delta}$ & $T_{Settle}$ \\\ \\cline{3-8} \n')
File.write('\multicolumn{2}{l|}{} & s & \% & s & s & \% & s \\\ \\hline \\hline \n')
for methods in range(0,3):
for outputs in range(0,2):
# Get the current Output
y1 = y[methods][outputs]
t1 = time[methods][outputs]
y2 = y[methods][1-outputs]
t2 = time[methods][1-outputs]
# Write to File
if outputs == 0:
# Get the StepInfo
tr, mp, ts, ys = alg.Step_Info(y1[np.where(t1<steptime)],t1[np.where(t1<steptime)])
trd, mpd, tsd, ysd = alg.Disturbance_Info(y2[np.where(t1<steptime)],t2[np.where(t1<steptime)])
File.write(' & '+cur_ouput[outputs]+'& %.2f & %.2f & %.2f & %.2f & %.2f & %.2f\\\ \\cline{2-8} \n'%(tr,mp,ts, trd, mpd, tsd))
else:
# Get the StepInfo
tr, mp, ts, ys = alg.Step_Info(y1[np.where(t1>steptime)],t1[np.where(t1>steptime)])
trd, mpd, tsd, ysd = alg.Disturbance_Info(y2[np.where(t1>steptime)],t2[np.where(t1>steptime)])
alg.Disturbance_Info(y1[np.where(t1<steptime)],t1[np.where(t1<steptime)])
File.write('\\multirow{-2}{*}{'+cur_methods[methods]+'} & '+cur_ouput[outputs]+'& %.2f & %.2f & %.2f & %.2f& %.2f& %.2f\\\ \\hline \\hline\n'%(tr,mp,ts, trd, mpd, tsd))
File.write('\\end{tabular}')
File.close()
In [6]:
y1[-1]
Out[6]:
p = bk.figure(title = cur_method,
width = plot_height, height = plot_height,
x_axis_type ="log", y_axis_type = "log",
x_axis_label = "Frequency [rad/s]", y_axis_label = "Gain")
# Robustness Area
p.add_layout(BoxAnnotation(right = w_rob, fill_alpha=0.1, fill_color='green'))
p.add_layout(BoxAnnotation(left = w_rob, fill_alpha=0.1, fill_color='red'))
# Sensitivity
p.line(w,SV[0,:], color = TUBScolorscale[0], legend="$\ma{S}$")
p.line(w,SV[1,:], color = TUBScolorscale[0])
# Complementary Sensitivity
p.line(w,TV[0,:], color = TUBScolorscale[6], legend= "$\ma{T}$")
p.line(w,TV[1,:], color = TUBScolorscale[6])
# Maximum Sensitivity
p.scatter(w_max, max_sv,size = 10, line_color = TUBScolorscale[0], fill_color = "white", legend="$\overline{\sigma}$ "+"(%.2f, %.2f)" %(w_max ,max_sv))
# Format
p.xaxis.formatter = LogTickFormatter()
p.xaxis.axis_label_text_font_size = "10pt"
p.yaxis.axis_label_text_font_size = "10pt"
p.toolbar.logo = None
p.toolbar_location = None
p.legend.visible = False
p.legend.location = "bottom_left"
bk.show(p)
p.output_backend = "svg"
export_svgs(p, export_folder+model_name+cur_method+"_SV.svg")
bk.reset_outputfrom bokeh.layouts import gridplot,layout
p1 = bk.figure(height= plot_height, width = plot_width, y_range = (-0.5,2.0), y_axis_label = "$y_1$") l1 = p1.line(res["time"],res["fmu.y[1]"], color = "grey", line_width = 1, line_dash = "dashed") l2 = p1.line(time[0][0],y[0][0], color = TUBScolorscale[6], line_width = 2) l3 = p1.line(time[1][0],y[1][0], color = TUBScolorscale[0], line_width = 2) l4 = p1.line(time[2][0],y[2][0], color = TUBScolorscale[2], line_width = 2)
p2 = bk.figure( height= plot_height, width = plot_width, y_range = (-0.2, 1.2), x_axis_label = "Time [s]", y_axis_label = "$y_2$") l5 = p2.line(res["time"],res["fmu.y[2]"], color = "grey", line_width = 1, line_dash = "dashed", legend="Reference") l6 = p2.line(time[0][1],y[0][1], color = TUBScolorscale[6], line_width = 2, legend="RGA") l7 = p2.line(time[1][1],y[1][1], color = TUBScolorscale[0], line_width = 2, legend="Astroem") l8 = p2.line(time[2][1],y[2][1], color = TUBScolorscale[2], line_width = 2, legend="R2D2")
p2.legend.location = "bottom_right"
p1.output_backend = "svg" export_svgs(p1, export_folder+model_name+"_y1.svg") p2.output_backend = "svg" export_svgs(p2, export_folder+model_name+"_y2.svg")
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