Main

Dynamic Estimation Tuning

Main.EstimatorTuning History

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%width=400px%Attach:mhe_tuning_widget.png
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%width=550px%Attach:mhe_tuning_widget.png
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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 adjustable parameter (FV) or manipulated variable (MV) with STATUS. Another important tuning consideration is the time horizon length. Including more points in the time horizon allows the estimator to reconcile the model to more data but also increases computational time. Below are common application, FV, MV, and CV tuning constants that are adjusted to achieve desired model predictive control performance.
to:
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 adjustable parameter (FV) or manipulated variable (MV) with STATUS. Another important tuning consideration is the time horizon length. Including more points in the time horizon allows the estimator to reconcile the model to more data but also increases computational time.

Attach:download.png [[Attach:mhe_tuning_widget.zip|MHE Tuning IPython Widget]]

%width=400px%Attach:mhe_tuning_widget.png

Below are common application, FV, MV, and CV tuning constants that are adjusted to achieve desired model predictive control performance.
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Application constants are modified by indicating that the constant belongs to the group ''nlc''. IMODE is adjusted to either solve the MHE problem with a simultaneous (5) or sequential (8) method. In the case below, the application IMODE is changed to sequential mode.

 apm_option(server,app,'nlc.IMODE',8)
to:
Application constants are modified by indicating that the constant belongs to the group ''apm''. IMODE is adjusted to either solve the MHE problem with a simultaneous (5) or sequential (8) method. In the case below, the application IMODE is changed to simultaneous mode.

 apm_option(server,app,'apm.IMODE',5)
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'''Objective:''' Design an estimator to predict an unknown parameters so that a simple model is able to predict the response of a more complex process. Tune the estimator to achieve either tracking or predictive performance. ''Estimated time: 2 hours.''
to:
'''Objective:''' Design an estimator to predict an unknown parameters so that a simple model is able to predict the response of a more complex process. Tune the estimator to achieve either tracking or predictive performance. ''Estimated time: 1 hour.''
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* Manipulated Variable (MV) tuning
to:
* Fixed Value (FV) - single parameter value over time horizon
** DMAX = maximum that FV can move each cycle
** LOWER = lower FV bound
** FSTATUS = feedback status with 1=measured, 0=off
** STATUS = turn on (1) or off (0) FV
** UPPER = upper FV bound

* Manipulated Variable (MV) - parameter can change over time horizon
January 28, 2018, at 06:21 AM by 174.148.61.237 -
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(:toggle hide gekko button show="Show GEKKO (Python) Code":)
(:div id=gekko:)
(:source lang=python:)
#%%Import packages
import numpy as np
from random import random
from gekko import GEKKO
import matplotlib.pyplot as plt

# Solve local or remote
rmt = True

#%% Process
p = GEKKO()

p.time = [0,.5]

n = 1 #process model order

#Parameters
p.u = p.MV()
p.K = p.Param(value=1) #gain
p.tau = p.Param(value=5) #time constant

#Intermediate
p.x = [p.Intermediate(p.u)]

#Variables
p.x.extend([p.Var() for _ in range(n)])  #state variables
p.y = p.SV() #measurement

#Equations
p.Equations([p.tau/n * p.x[i+1].dt() == -p.x[i+1] + p.x[i] for i in range(n)])
p.Equation(p.y == p.K * p.x[n])

#options
p.options.IMODE = 4

#p.u.FSTATUS = 1
#p.u.STATUS = 0


#%% Model
m = GEKKO()

m.time = np.linspace(0,20,41) #0-20 by 0.5 -- discretization must match simulation

#Parameters
m.u = m.MV() #input
m.K = m.FV(value=1, lb=1, ub=3) #gain
m.tau = m.FV(value=5, lb=1, ub=10) #time constant

#Variables
m.x = m.SV() #state variable
m.y = m.CV() #measurement

#Equations
m.Equations([m.tau * m.x.dt() == -m.x + m.u,
            m.y == m.K * m.x])


#Options
m.options.IMODE = 5 #MHE
m.options.EV_TYPE = 1

# STATUS = 0, optimizer doesn't adjust value
# STATUS = 1, optimizer can adjust
m.u.STATUS = 0
m.K.STATUS = 1
m.tau.STATUS = 1
m.y.STATUS = 1

# FSTATUS = 0, no measurement
# FSTATUS = 1, measurement used to update model
m.u.FSTATUS = 1
m.K.FSTATUS = 0
m.tau.FSTATUS = 0
m.y.FSTATUS = 1

# DMAX = maximum movement each cycle
m.K.DMAX = 1
m.tau.DMAX = .1

# MEAS_GAP = dead-band for measurement / model mismatch
m.y.MEAS_GAP = 0.25

m.y.TR_INIT = 1

#%% problem configuration
# number of cycles
cycles = 50
# noise level
noise = 0.25

# values of u change randomly over time every 10th step
u_meas = np.zeros(cycles)
step_u = 0
for i in range(0,cycles):
    if (i % 10) == 0:
        # random step (-5 to 5)
        step_u = step_u + (random()-0.5)*10
    u_meas[i] = step_u

#%% run process and estimator for cycles
y_meas = np.empty(cycles)
y_est = np.empty(cycles)
k_est = np.empty(cycles)
tau_est = np.empty(cycles)
for i in range(cycles):
    # process simulator
    p.u.MEAS = u_meas[i]
    p.solve(remote=rmt)
    y_meas[i] = p.y.MODEL + (random()-0.5)*noise
   
    # estimator
    m.u.MEAS = u_meas[i]
    m.y.MEAS = y_meas[i]
    m.solve(remote=rmt)
    y_est[i] = m.y.MODEL
    k_est[i] = m.K.NEWVAL
    tau_est[i] = m.tau.NEWVAL
   

#%% Plot results
plt.figure()
plt.subplot(4,1,1)
plt.plot(y_meas)
plt.plot(y_est)
plt.legend(('meas','pred'))
plt.subplot(4,1,2)
plt.plot(np.ones(cycles)*p.K.value[0])
plt.plot(k_est)
plt.legend(('actual','pred'))
plt.subplot(4,1,3)
plt.plot(np.ones(cycles)*p.tau.value[0])
plt.plot(tau_est)
plt.legend(('actual','pred'))
plt.subplot(4,1,4)
plt.plot(u_meas)
plt.legend('u')
plt.show()
(:sourceend:)
(:divend:)
April 05, 2017, at 08:46 PM by 10.5.113.121 -
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** SOLVER
*** 0=Try all available solvers
*** 1=APOPT (MINLP, Active Set SQP)
*** 2=BPOPT (NLP, Interior Point, SQP)
*** 3=IPOPT (NLP, Interior Point, SQP)

May 14, 2015, at 08:15 PM by 45.56.3.184 -
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 apm_option(server,app,'y.MEAS_GAS',1.0)
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 apm_option(server,app,'y.MEAS_GAP',1.0)
May 12, 2015, at 06:05 AM by 174.148.30.57 -
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<iframe width="560" height="315" src="https://www.youtube.com/embed/yQWgSByYjd8?rel=0" frameborder="0" allowfullscreen></iframe>
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<iframe width="560" height="315" src="https://www.youtube.com/embed/yw_a9ektOqc?rel=0" frameborder="0" allowfullscreen></iframe>
May 12, 2015, at 05:16 AM by 45.56.3.184 -
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Attach:download.png [[Attach:estimator_tuning_MATLAB_solution.zip|Estimator Tuning in MATLAB]]
Attach:download.png [[Attach:estimator_tuning_Python_solution.zip|Estimator Tuning in Python]]
May 11, 2015, at 10:54 PM by 10.5.113.160 -
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** CV_TYPE = CV type with 1=l_1-norm, 2=squared error
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** SP = set point with CV_TYPE = 2
** SPLO = lower set point with CV_TYPE = 1
** SPHI = upper set point 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 trajectory compared to end
to:
** MEAS_GAP = measurement gap for estimator dead-band
May 11, 2015, at 05:35 PM by 45.56.3.184 -
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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 adjustable parameter (FV) or manipulated variable (MV) with STATUS. Below are common application, FV, MV, and CV tuning constants that are adjusted to achieve desired model predictive control performance.
to:
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 adjustable parameter (FV) or manipulated variable (MV) with STATUS. Another important tuning consideration is the time horizon length. Including more points in the time horizon allows the estimator to reconcile the model to more data but also increases computational time. Below are common application, FV, MV, and CV tuning constants that are adjusted to achieve desired model predictive control performance.
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** IMODE = 5 or 8 for moving horizon estimation
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** IMODE = 5 or 8 for moving horizon estimation
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 apm_option(server,app,'nlc.IMODE',8)
to:
 apm_option(server,app,'nlc.IMODE',8)

!!!! Exercise

'''Objective:''' Design an estimator to predict an unknown parameters so that a simple model is able to predict the response of a more complex process. Tune the estimator to achieve either tracking or predictive performance. ''Estimated time: 2 hours.''

Attach:download.png [[Attach:estimator_tuning_source.zip|Estimator Tuning Source Files]]

Design an estimator to predict ''K'' and ''tau'' of a 1st order model to predict the dynamic response of a 1st order, 2nd order, and 10th order process. For the 2nd and 10th order systems, there is process/model mismatch. This means that the structure of the model can never exactly match the actual process because the equations are inherently incorrect. The parameter values are adjusted to best approximate the process even though the model is deficient. The process order is adjusted in the file ''process.apm'' file in the ''Constants'' section.

 Constants
  ! process model order
  n = 1  ! change to 1, 2, and 10

In each case, tune the estimator to favor either acceptable tracking or predictive performance. Tracking performance is the ability of the estimator to synchronize with measurements and is demonstrated with overall agreement between the model predictions and the measurements. Predictive performance sacrifices tracking performance to achieve more consistent values that are valid over a longer predictive horizon for model predictive control.

!!!! Solution

Attach:download.png [[Attach:estimator_tuning_MATLAB_solution.zip|Estimator Tuning in MATLAB]]
Attach:download.png [[Attach:estimator_tuning_Python_solution.zip|Estimator Tuning in Python]]

(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/yQWgSByYjd8?rel=0" frameborder="0" allowfullscreen></iframe>
(:htmlend:)
May 11, 2015, at 02:33 PM by 45.56.3.184 -
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The dynamic estimation tuning is the process of adjusting certain objective function terms to give more desirable solutions. As an example, dynamic estimation application may either track noisy data too closely or the updates may be too slow to catch unmeasured disturbances of interest.
to:
Dynamic estimation tuning is the process of adjusting certain objective function terms to give more desirable solutions. As an example, a dynamic estimation application such as moving horizon estimation (MHE) may either track noisy data too closely or the updates may be too slow to catch unmeasured disturbances of interest. Tuning is the process of achieving acceptable estimator performance based on unique aspects of the application.
May 11, 2015, at 02:11 PM by 45.56.3.184 -
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!!!! Common Tuning Parameters for MHE

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 adjustable parameter (FV) or manipulated variable (MV) with STATUS. Below are common application, FV, MV, and CV tuning constants that are adjusted to achieve desired model predictive control performance.

* Application tuning
** IMODE = 5 or 8 for moving horizon estimation
** DIAGLEVEL = diagnostic level (0-10) for solution information
** EV_TYPE = 1 for l'_1_'-norm and 2 for squared error objective
** 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 = set point with CV_TYPE = 2
** SPLO = lower set point with CV_TYPE = 1
** SPHI = upper set point 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 trajectory 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 FV named ''p''.

 apm_option(server,app,'p.LOWER',0)

The upper and lower measurement deadband for a CV named ''y'' are set to values around the measurement. In this case, an acceptable range for the model prediction is to intersect the measurement of 10.0 between 9.5 and 10.5 with a MEAS_GAP of 1.0 (or +/-0.5).

 apm_option(server,app,'y.MEAS_GAS',1.0)
 
Application constants are modified by indicating that the constant belongs to the group ''nlc''. IMODE is adjusted to either solve the MHE problem with a simultaneous (5) or sequential (8) method. In the case below, the application IMODE is changed to sequential mode.

 apm_option(server,app,'nlc.IMODE',8)
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(:title Dynamic Estimation Tuning:)
(:keywords tuning, Python, MATLAB, Simulink, moving horizon, time window, dynamic data, validation, estimation, differential, algebraic, tutorial:)
(:description Tuning of an estimator for improved rejection of corrupted data with outliers, drift, and noise:)

The dynamic estimation tuning is the process of adjusting certain objective function terms to give more desirable solutions. As an example, dynamic estimation application may either track noisy data too closely or the updates may be too slow to catch unmeasured disturbances of interest.