Dynamic Control Tuning

March 04, 2022, at 12:50 AM by 10.35.117.248 -

Deleted lines 97-98:

~~Attach:controller_tuning.mp4~~

March 04, 2022, at 12:50 AM by 10.35.117.248 -

Added lines 99-100:

Attach:controller_tuning.mp4

Added lines 103-110:

(:html:)
<video width="550" controls autoplay loop>
<source src="/do/uploads/Main/controller_tuning.mp4" type="video/mp4">
Your browser does not support the video tag.
</video>
(:htmlend:)

March 04, 2022, at 12:47 AM by 10.35.117.248 -

Changed lines 107-112 from:

~~m = GEKKO~~()

to:

from IPython import get_ipython

# detect if IPython is running
ipython = get_ipython() is not None

m = GEKKO(remote=False)

Changed lines 182-183 from:

~~display.clear_output(wait=True)~~
~~plt~~.~~clf~~()

to:

if ipython:
display.clear_output(wait=True)
else:
plt.clf()

Deleted line 205:

~~plt.pause(0.01)~~

Added line 209:

plt.pause(0.01)

March 04, 2022, at 12:37 AM by 10.35.117.248 -

Added lines 147-156:

# Make an MP4 animation?
make_mp4 = True
if make_mp4:
import imageio # required to make animation
import os
try:
os.mkdir('./figures')
except:
pass

Changed lines 181-182 from:

plt.plot(tm,u.value,'k-',~~linewidth~~=2)
plt.~~legend~~(~~'u'~~)

to:

plt.plot(tm,u.value,'k-',lw=2,label='u')
plt.ylim([-1,11])
plt.legend(loc=1)

Changed lines 188-191 from:

plt.plot(tm,z['x.tr_hi'],'b--',label='x traj')
plt.plot(tm,z['x.tr_lo'],'b--')
plt.legend()

to:

plt.plot(tm,z['x.tr_hi'],'k--',label='x traj')
plt.plot(tm,z['x.tr_lo'],'k--')
plt.legend(loc=1)

Changed lines 194-196 from:

plt.plot(tm,z['y.tr_hi'],'r--',label='y traj')
plt.plot(tm,z['y.tr_lo'],'r--')
plt.legend()

to:

plt.plot(tm,z['y.tr_hi'],'k--',label='y traj')
plt.plot(tm,z['y.tr_lo'],'k--')
plt.legend(loc=1)
plt.draw()

Added lines 199-212:

if make_mp4:
filename='./figures/plot_'+str(i+10000)+'.png'
plt.savefig(filename)

# generate mp4 from png figures
if make_mp4:
images = []
for i in range(40):
filename='./figures/plot_'+str(i+10000)+'.png'
images.append(imageio.imread(filename))
try:
imageio.mimsave('results.mp4', images)
except:
print('Error: Install mp4 generator with "pip install imageio-ffmpeg"')

March 04, 2022, at 12:17 AM by 10.35.117.248 -

Changed line 132 from:

x.TR_INIT = 2

to:

x.TR_INIT = 1

March 04, 2022, at 12:15 AM by 10.35.117.248 -

Changed lines 99-190 from:

~~Attach:download.png [[Attach:mpc_tuning_solution.zip|MPC Tuning Solution]]~~

to:

(:toggle hide gekko button show="Gekko Solution":)
(:div id=gekko:)
(:source lang=python:)
import numpy as np
from gekko import GEKKO
import matplotlib.pyplot as plt
import json
from IPython import display
m = GEKKO()
t = np.linspace(0,15,31)
m.time = t # 0.5 cycle time
u = m.MV(1,name='u')
x = m.CV(name='x')
y = m.CV(name='y')
m.Equations([5*x.dt() ==-x+1.5*u,\
15*y.dt()==-y+3.0*u])
m.options.IMODE = 6
m.options.NODES = 3

# MV tuning
u.DCOST = 0.1
u.DMAX = 1.5
u.STATUS = 1
u.FSTATUS = 0
u.UPPER = 10
u.LOWER = 0

# CV tuning
x.STATUS = 1
x.FSTATUS = 0
x.SPHI = 10
x.SPLO = 9
x.TAU = 2
x.TR_INIT = 2
x.TR_OPEN = 5
x.WSPHI = 100
x.WSPLO = 100

y.STATUS = 1
y.FSTATUS = 0
y.SPHI = 7
y.SPLO = 2
y.TAU = 0
y.TR_INIT = 0
y.TR_OPEN = 1
y.WSPHI = 200
y.WSPLO = 50

# plot solution
plt.figure(figsize=(8,5))
plt.ion()
plt.show()

for i in range(40):
m.solve(disp=False)

# update time
tm = m.time+i*0.5

# x is more important at t=10
if tm[0]>=10:
x.WSPLO = 500
x.WSPHI = 500

# get trajectory information
with open(m.path+'//results.json') as f:
z = json.load(f)

display.clear_output(wait=True)
plt.clf()
plt.figure(1,figsize=(8,5))
plt.subplot(3,1,1)
plt.plot(tm,u.value,'k-',linewidth=2)
plt.legend('u')
plt.ylabel('MV')

plt.subplot(3,1,2)
plt.plot(tm,x.value,'b-',lw=2,label='x')
plt.plot(tm,z['x.tr_hi'],'b--',label='x traj')
plt.plot(tm,z['x.tr_lo'],'b--')
plt.legend()

plt.subplot(3,1,3)
plt.plot(tm,y.value,'r-',lw=2,label='y')
plt.plot(tm,z['y.tr_hi'],'r--',label='y traj')
plt.plot(tm,z['y.tr_lo'],'r--')
plt.legend()
plt.pause(0.01)
(:sourceend:)
(:divend:)

Attach:download.png [[Attach:mpc_tuning_solution.zip|MPC Tuning Solution (APM MATLAB and APM Python]]

March 03, 2022, at 11:51 PM by 10.35.117.248 -

Changed lines 67-68 from:

Use the following system of linear differential equations for this exercise by placing the model definition in the file ''myModel.apm''.

to:

Use the following system of linear differential equations for this exercise by placing the model definition in the file ''myModel.apm'' (APMonitor) or in a Python script (Gekko).

'''APMonitor Model'''

Changed lines 79-94 from:

to:

'''Gekko Model'''

(:source lang=python:)
import numpy as np
from gekko import GEKKO
m = GEKKO()
t = np.linspace(0,15,76)
m.time = t # 0.2 cycle time
u = m.MV(1,name='u')
x = m.CV(name='x')
y = m.CV(name='y')
m.Equations([5*x.dt() ==-x+1.5*u,\
15*y.dt()==-y+3.0*u])
(:sourceend:)

May 25, 2018, at 07:48 PM by 10.5.113.123 -

Added lines 7-8:

Attach:download.png [[Attach:mpc_tuning_widget.zip|MPC Tuning IPython Widget]]

Deleted lines 9-12:

Attach:download.png [[Attach:mpc_tuning_widget.zip|MPC Tuning IPython Widget]]

%width=300px%Attach:mpc_tuning_widget.png

May 25, 2018, at 07:48 PM by 10.5.113.123 -

Changed line 17 from:

* Application ~~tuning~~

to:

* [[https://apmonitor.com/wiki/index.php/Main/DbsGlobal|Application tuning]]

Changed line 30 from:

* Manipulated Variable (MV) ~~tuning~~

to:

* [[https://apmonitor.com/wiki/index.php/Main/DbsVariable|Manipulated Variable (MV) tuning]]

Changed line 40 from:

* Controlled Variable (CV) ~~tuning~~

to:

* [[https://apmonitor.com/wiki/index.php/Main/DbsVariable|Controlled Variable (CV) tuning]]

May 25, 2018, at 07:44 PM by 10.5.113.123 -

Changed line 11 from:

%width=~~400px~~%Attach:mpc_tuning_widget.png

to:

%width=300px%Attach:mpc_tuning_widget.png

May 25, 2018, at 07:43 PM by 10.5.113.123 -

Added lines 6-7:

Attach:mpc_tuning.gif

August 16, 2017, at 04:14 PM by 173.117.178.94 -

Added lines 8-9:

%width=400px%Attach:mpc_tuning_widget.png

August 10, 2017, at 05:56 AM by 10.5.113.229 -

Changed line 7 from:

download.png [[Attach:mpc_tuning_widget.zip|MPC Tuning IPython Widget]]

to:

Attach:download.png [[Attach:mpc_tuning_widget.zip|MPC Tuning IPython Widget]]

August 10, 2017, at 05:56 AM by 10.5.113.229 -

Added lines 6-7:

download.png [[Attach:mpc_tuning_widget.zip|MPC Tuning IPython Widget]]

April 05, 2017, at 08:45 PM by 10.5.113.121 -

Added lines 18-22:

** SOLVER
*** 0=Try all available solvers
*** 1=APOPT (MINLP, Active Set SQP)
*** 2=BPOPT (NLP, Interior Point, SQP)
*** 3=IPOPT (NLP, Interior Point, SQP)

July 16, 2016, at 11:34 AM by 66.87.137.245 -

Changed line 30 from:

** COST = (+) minimize MV, (-) maximize MV

to:

** COST = (+) minimize CV, (-) maximize CV

Changed line 35 from:

** STATUS = turn on (1) or off (0) MV

to:

** STATUS = turn on (1) or off (0) CV

May 29, 2015, at 02:04 PM by 45.56.3.184 -

Changed line 76 from:

to:

May 29, 2015, at 01:21 PM by 45.56.3.184 -

Changed line 69 from:

In this case, the parameter ''u'' is the manipulated variable and ''x'' and ''y'' are the controlled variables. It is desired to maximize ''x'' and maintain values between 9 and 10. It is desired to maintain values of ''y'' between 2 and 5. For the first 10 minutes, the priority is to maintain the range for ''y'' and following this time period, it is desired to track the range for ''x''. Tune the controller to meet these objectives while minimizing MV movement.

to:

In this case, the parameter ''u'' is the manipulated variable and ''x'' and ''y'' are the controlled variables. It is desired to maximize ''x'' and maintain values between 9 and 10. It is desired to maintain values of ''y'' between 2 and 7. For the first 10 minutes, the priority is to maintain the range for ''y'' and following this time period, it is desired to track the range for ''x''. Tune the controller to meet these objectives while minimizing MV movement.

May 29, 2015, at 01:20 PM by 45.56.3.184 -

Added lines 72-73:

Attach:download.png [[Attach:mpc_tuning_solution.zip|MPC Tuning Solution]]

May 29, 2015, at 01:18 PM by 45.56.3.184 -

Added line 13:

** CV_TYPE = CV type with 1=l_1-norm, 2=squared error

Deleted line 20:

** CV_TYPE = 1 for l'_1_'-norm and 2 for squared error

Deleted line 30:

** CV_TYPE = CV type with 1=l_1-norm, 2=squared error

May 29, 2015, at 01:07 PM by 45.56.3.184 -

Added lines 54-76:

!!!! Exercise

'''Objective:''' Design a model predictive controller with one manipulated variable and two controlled variables with competing objectives that cannot be simultaneously satisfied. Tune the controller to achieve best performance. ''Estimated time: 2 hours.''

Use the following system of linear differential equations for this exercise by placing the model definition in the file ''myModel.apm''.

Parameters
u
Variables
x
y
Equations
5 * $x = -x + 1.5 * u
15 * $y = -y + 3.0 * u

In this case, the parameter ''u'' is the manipulated variable and ''x'' and ''y'' are the controlled variables. It is desired to maximize ''x'' and maintain values between 9 and 10. It is desired to maintain values of ''y'' between 2 and 5. For the first 10 minutes, the priority is to maintain the range for ''y'' and following this time period, it is desired to track the range for ''x''. Tune the controller to meet these objectives while minimizing MV movement.

!!!! Solution

(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/yw_a9ektOqc?rel=0" frameborder="0" allowfullscreen></iframe>
(:htmlend:)

May 11, 2015, at 02:07 PM by 45.56.3.184 -

Added line 20:

** CV_TYPE = 1 for l'_1_'-norm and 2 for squared error

May 11, 2015, at 02:03 PM by 45.56.3.184 -

Changed lines 32-34 from:

** SP = ~~setpoint~~ with CV_TYPE = 2
** SPLO = lower ~~setpoint~~ with CV_TYPE = 1
** SPHI = upper ~~setpoint~~ with CV_TYPE = 1

to:

** SP = set point with CV_TYPE = 2
** SPLO = lower set point with CV_TYPE = 1
** SPHI = upper set point with CV_TYPE = 1

Changed line 38 from:

** TR_OPEN = opening at initial point of ~~traj~~ compared to end

to:

** TR_OPEN = opening at initial point of trajectory compared to end

May 11, 2015, at 02:01 PM by 45.56.3.184 -

Added lines 6-52:

!!!! Common Tuning Parameters for MPC

Tuning typically involves adjustment of objective function terms or constraints that limit the rate of change (DMAX), penalize the rate of change (DCOST), or set absolute bounds (LOWER and UPPER). Measurement availability is indicated by the parameter (FSTATUS). The optimizer can also include (1=on) or exclude (0=off) a certain manipulated variable (MV) or controlled variable with STATUS. Below are common application, MV, and CV tuning constants that are adjusted to achieve desired model predictive control performance.

* Application tuning
** IMODE = 6 or 9 for model predictive control
** DIAGLEVEL = diagnostic level (0-10) for solution information
** MAX_ITER = maximum iterations
** MAX_TIME = maximum time before stopping
** MV_TYPE = Set default MV type with 0=zero-order hold, 1=linear interpolation

* Manipulated Variable (MV) tuning
** COST = (+) minimize MV, (-) maximize MV
** DCOST = penalty for MV movement
** DMAX = maximum that MV can move each cycle
** FSTATUS = feedback status with 1=measured, 0=off
** LOWER = lower MV bound
** MV_TYPE = MV type with 0=zero-order hold, 1=linear interpolation
** STATUS = turn on (1) or off (0) MV
** UPPER = upper MV bound

* Controlled Variable (CV) tuning
** COST = (+) minimize MV, (-) maximize MV
** CV_TYPE = CV type with 1=l_1-norm, 2=squared error
** FSTATUS = feedback status with 1=measured, 0=off
** SP = setpoint with CV_TYPE = 2
** SPLO = lower setpoint with CV_TYPE = 1
** SPHI = upper setpoint with CV_TYPE = 1
** STATUS = turn on (1) or off (0) MV
** TAU = reference trajectory time-constant
** TR_INIT = trajectory type, 0=dead-band, 1,2=trajectory
** TR_OPEN = opening at initial point of traj compared to end

There are several ways to change the tuning values. Tuning values can either be specified before an application is initialized or while an application is running. To change a tuning value before the application is loaded, use the ''apm_option()'' function such as the following example to change the lower bound in MATLAB or Python for the MV named ''u''.

apm_option(server,app,'u.LOWER',0)

The upper and lower deadband targets for a CV named ''y'' are set to values around a desired set point of 10.0. In this case, an acceptable range for this CV is between 9.5 and 10.5.

sp = 10.0
apm_option(server,app,'y.SPHI',sp+0.5)
apm_option(server,app,'y.SPHI',sp-0.5)

Application constants are modified by indicating that the constant belongs to the group ''nlc''. IMODE is adjusted to either solve the MPC problem with a simultaneous (6) or sequential (9) method. In the case below, the application IMODE is changed to simultaneous mode.

apm_option(server,app,'nlc.IMODE',6)

March 26, 2015, at 05:19 PM by 127.0.0.1 -

Added lines 1-5:

(:title Dynamic Control Tuning:)
(:keywords tuning, Python, MATLAB, Simulink, nonlinear control, model predictive control, tutorial:)
(:description Tuning of an optimizing controller for improved following of a desired trajectory or to reach an optimal state:)

Dynamic controller tuning is the process of adjusting certain objective function terms to give more desirable solutions. As an example, a dynamic control application may either exhibit too aggressive manipulated variable movement or be too sluggish during set-point changes. Tuning is the iterative process of finding acceptable values that work over a wide range of operating conditions.

Dynamic Optimization

Dynamic Control Tuning

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