Model Predictive Control - PowerPoint PPT Presentation

Loading...

PPT – Model Predictive Control PowerPoint presentation | free to download - id: 16bc62-ZDc1Z



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Model Predictive Control

Description:

Several types of industrial MPC but DMC is the most widely used form. ... If available, run steady-state process simulator. Read the plant operating manuals ... – PowerPoint PPT presentation

Number of Views:333
Avg rating:3.0/5.0
Slides: 191
Provided by: jbri9
Learn more at: http://www.che.ttu.edu
Category:
Tags: control | dmc | model | predictive | run

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Model Predictive Control


1
Chapter 16
  • Model Predictive Control

2
Single Loop Controllers
3
MPC Controller
4
Model Predictive Control
  • Most popular form of multivariable control.
  • Effectively handles complex sets of constraints.
  • Has an LP on top of it so that it controls
    against the most profitable set of constraints.
  • Several types of industrial MPC but DMC is the
    most widely used form.

5
DMC is based on Step Response Models
  • Allow the development of empirical input/output
    process models.
  • The coefficients correspond to the step response
    behavior of the process

6
Example of a SRM
  • t i Du y(t) ai
  • 0 0 1 0 0
  • 1 1 0 0 0
  • 2 2 0 0.63 0.63
  • 3 3 0 0.87 0.87
  • 4 4 0 0.95 0.95
  • 5 5 0 0.98 0.98
  • 6 6 0 0.99 0.99
  • 7 7 0 1.00 1.00
  • 8 8 0 1.00 1.00

7
Open-Loop Step Test for Thermal Mixer
8
SRM for the Thermal Mixer (Du0.05)
i ti yi ai
0 5 50.00 0.0 0.0
1 10 49.77 -0.23 -4.68
2 15 49.35 -0.65 -13.0
3 20 49.08 -0.92 -18.4
4 25 48.94 -1.06 -21.2
5 30 48.87 -1.13 -22.6
6 35 48.84 -1.16 -23.2
7 40 48.83 -1.17 -23.5
8 45 48.82 -1.18 -23.7
9 50 48.82 -1.18 -23.7
9
Example of SRM Applied to a Process with Complex
Dynamics
  • SRM 0 0 -0.3 -0.1 0.05 0.1 0.2 0.3 . . .

10
Complex Dynamics
  • An integrating process (e.g., a level) is modeled
    the same except that the Tss is based on
    attaining a constant slope (i.e., a constant ramp
    rate).
  • An integrating variable is referred to as a ramp
    variable.

11
SRM for Ramp Function
12
Using SRM to Calculate y(t)
  • Given SRM 0 0.4 0.8 0.9 1.0
  • y05 Du5 DTs20 sec
  • Solve for y(t)
  • y y0 Du SRM
  • y15 50 5 y2 5 50.4 7
  • y3 5 50.8 9 y4 5 5.9 9.5
  • y5 5 51 10 or in vector form
  • y 5 7 9 9.5 10 10 10
  • y(20 s)5 y(40 s)7 y(60 s)9 y(80 s)9.5
  • y(100 s)10 y(120 s)10 y(140 s)10 ...

13
Class Exercise
  • Given SRM 0 0.4 0.8 0.9 1.0
  • y05 Du-2 DTs20 sec
  • Solve for y(t)

14
Solution to Class Exercise
  • Given SRM 0 0.4 0.8 0.9 1.0
  • y05 Du-2 DTs20 sec
  • Solve for y(t)
  • y y0 Du SRM
  • y15 -20 5 y2 5 -20.4
    4.2
  • y3 5 -20.8 3.4 y4 5 -2.9
    3.2
  • y5 5 -21 3 or in vector
    form
  • y 5 4.2 3.4 3.2 3 3 3

15
Calculating SRM from Step Response Data
  • Remember previous equation
  • y y0 Du SRM
  • Solving for SRM yields
  • SRM (y-y0)/Du

16
Example of the Calculation of SRM from Step
Response Data
17
Class Exercise for the Calculation of the SRM
from Step Response Data
18
Class Exercise for the Calculation of the SRM
from Step Response Data
19
Simulation Demonstration
  • A thermal mixing process mixes two streams with
    different temperatures (25ºC and 75ºC) to produce
    a product (about 50ºC).
  • Consider a 10 increase (0.05 kg/s) increase in
    the flow rate of colder stream.
  • Develop SRM from step response.

20
Step Test Result and SRM
21
Comparison for the Same Du (10)
22
Comparison for the Same Du (-10)
23
Demonstration Conclusions
  • MPC model agrees closely for the same step input
    change, but shows significant mismatch for a
    different size of input change due to process
    nonlinearity.

24
Nonlinear Effects
  • This SRM will not accurately represent negative
    changes in the MV or different magnitude MV
    changes due to process nonlinearity.
  • Therefore, a better way to develop a SRM is to
    make a number of MV changes with different
    magnitude and directions and average the results
    to get the SRM.

25
SRMs for Different Size Dus
26
Another Approach
  • Use the average ais

27
Using Average ais for Du10
28
Using Average ais for Du-10
29
Using Average ais for Du5
30
Relation to MPC Model Identification
  • Developing SRMs that represent an average
    response is the basis of good MPC models.

31
Class Exercise
  • Using the composition mixer simulator (CMIXER),
    use a 5 step input change (0.025 kg/min) to
    generate a SRM for this process
  • First, implement the step input change
  • Next, determine the model interval
  • Then, calculate the SRM coefficients
  • Finally, compare simulator result to MPC model
    prediction for Du (10 to -10)

32
SRM Summary
  • SRMs represent the dynamic behavior of a
    dependent variable (output variable) for a
    process for a unit step change in an input.
  • SRMs are empirical models that are flexible
    enough to model complex dynamics
  • SRMs are linear approximations of process
    behavior and can be estimated using step
    responses for the process.

33
SISO MPC Controller
  • Application of SRM for a Series of Input Changes

34
A Series of Input Changes
  • Definition of the SRM is based on a single step
    input change.
  • But feedback control requires a large number of
    changes to the input variables.
  • To use a SRM to predict the output behavior for a
    series of input changes, linear superposition is
    assumed, i.e., the process response is equal to
    the sum of the individual step responses.

35
Superposition of Two Step Input Changes
36
Superposition of Two Step Input Changes
37
Equation Form for Two Sequential Input Changes
  • Consider the the response of a process to two
    step input changes separately

38
Combined Response for Two Input Changes
39
Combined Response for a Series of 4 Input Changes
40
Matrix Form for Combined Response for a Series of
4 Input Changes
41
The Dynamic Matrix
  • The Dynamic Matrix determines the dynamic
    response of the process to a series of input
    changes, nc, for a prediction horizon of np steps
    into the future.
  • The dynamic Matrix is constructed from the
    coefficients of the SRM
  • A is npnc SRM is m (this case has 4 inputs and
    7 output predictions)

42
Zeros in Dynamic Matrix
  • Where do they come from?
  • Consider the first row y1 is cannot be affected
    by Du1, Du2, and Du3 because y1 is measured
    before Du1, Du2, and Du3 are applied.
  • Likewise, y2 is cannot be affected by Du2 and Du3

43
The Matrix Form of the Generalized Model Equation
44
Dynamic Matrix Example
45
Class Exercise
46
Solution to Class Exercise
47
SISO MPC Controller
  • Prediction Vector

48
Previous Inputs Affect Future Response of the
Process
49
Previous Inputs Affect Future Response of the
Process
50
Prediction Vector
  • The prediction vector, yP, contains the combined
    effect of the previous input changes on the
    future values of the output variable.
  • The prediction vector is calculated from the
    product of the previous input changes and the
    prediction matrix, which is constructed using the
    coefficients of the SRM.

51
Process Model
  • The future values of the output variable are
    equal to the sum of the contribution from
    previous inputs (prediction vector) and the
    contribution from future change in the input
    variable

52
Process Model
  • In order to correct for the mismatch between the
    predicted value of y at the current time and the
    measured value, a correction vector, e, is added
    to the process model equation.

53
Correction for Mismatch in Ramp Variable
  • The error between the predicted value of y(t0)
    and the measured value is applied as before e
    y(t0) - yP(t0)
  • An unmeasured disturbance can affect the slope of
    the modeled SRM
  • Therefore, an additional tuning factor for ramp
    variables is the rotation factor (RF), which is
    the fraction of the mismatch e that is used to
    change the slope of the SRM of the ramp variable.
    SlopenewSlopeoldRFe

54
SISO MPC Controller
  • DMC Controller

55
Development of DMC Control Law
56
DMC Control Law
57
Analysis of DMC Controller
  • (ATA)-1AT is a constant matrix that is
    determined explicitly from the coefficients of
    the SRM.
  • If you double the number of coefficients in the
    SRM, you will increase the number of terms in the
    dynamic matrix by a factor of 4
  • E takes into account changes in the setpoint, the
    influence of previous inputs, and the correction
    for model mismatch.
  • A full set of future moves are determine by this
    control law at each control interval.

58
Moving Horizon Controller
59
Moving Horizon Controller
  • Even though the DMC controller calculates a
    series of future moves, only the first of the
    calculated moves is actually implemented.
  • The next time the controller is called (DTs
    later), a new series of moves is calculated, but
    only the first is applied.
  • If the SRM were perfect, the subsequent set of
    first moves would be equal to the first series of
    moves calculated by the DMC controller.

60
SISO MPC Controller
  • Implementation Details

61
Implementation Details
  • Choose DTs based on when new information is
    available on the CV. E.g., analyzer update. For
    temperature sensor, use DTs10-15 s.
  • Model horizon m Tss / DTs (normally set
    m60-90 coefficients. Always set mgt30.
  • Control horizon nc½m
  • Prediction horizon npmnc

62
Controller Implementation Example
  • Consider a SISO DMC temperature control loop that
    has an open loop time to steady-state equal to 20
    minutes.
  • Applying the previous equations

63
Class Example
  • Consider a SISO DMC controller applied to the
    overhead product of a C3 splitter. The overhead
    composition analyzer update every 10 min and the
    time to steady-state for the overhead composition
    for a reflux flow rate change is 7 hours.
    Determine m, np and nc for this controller.

64
Solution
65
SISO MPC Controller
  • Tuning

66
DMC Controller Tuning
  • Previous DMC control law results in aggressive
    control because it is based on minimizing the
    error from setpoint without regard to changes in
    the MV.
  • (ATA)-1 is usually ill-conditioned due to normal
    levels of process/model mismatch.
  • These problems can be overcome by adding a
    diagonal matrix, Q, to the Dynamic Matrix, A.

67
DMC Controller with Move Suppression
68
The Dynamic Matrix with the Move Suppression
Factor Added
69
Move Suppression
70
DMC Control Law
71
Effect of Move Suppression Factor
  • The larger q, the greater the penalty for DMV
    moves. The smaller q, the greater the penalty
    for errors from setpoint.

72
Tmixer DMC Tuning Example Q300
73
Tmixer DMC Tuning Example Q100
74
Tmixer DMC Tuning Example Q60
75
Tmixer DMC Tuning Example Q30
76
Tmixer DMC Tuning Example Q20
77
Tmixer DMC Tuning Example Q10
78
Controller Tuning
  • Reliability versus performance.
  • Meeting the overall process objectives.

79
Checking the Controller Tuning for a Setpoint
Changes in the Opposite Direction Q30
80
Class Exercise SISO DMC Tuning
  • Tune the DMC controller for the CMixer

81
SISO MPC Controller
  • Testing

82
Controller Testing
  • Use disturbance upsets to test controller
    performance

83
Controller Disturbance Rejection Q60
84
Controller Disturbance Rejection Q30
85
Controller Disturbance Rejection Q10
86
Class Exercise Testing the Controller Tuning
  • Using disturbance upset tests, test the
    performance of your tuned DMC controller.

87
Model Identification The Least Squares Solution
88
Controller Disturbance Rejection DTs7, Q30
89
What if the SRM become worse? DTs11 Q30
90
What if the SRM become worse? DTs15 Q30
91
SRM Model Mismatch
  • The controller still works in this case, but the
    performance is penalized.

92
MIMO DMC Control
93
MIMO DMC Control
  • Extension of SISO to MIMO
  • Constraint control
  • Economic LP
  • Large-scale applications

94
MIMO DMC Control
  • Extension of DMC to MIMO processes

95
Dynamic Matrix for a MIMO Process
96
Recall The SISO Dynamic Matrix
97
Example of a Partitioned Dynamic Matrix
98
Dynamic Matrix for a MIMO Process
99
A Partitioned Control Vector
100
An Example of a Partitioned Control Vector
101
Control Law for MIMO DMC Controller
102
Relative Weighting Factor
  • The relative weighting factor, wi , allows the
    application control engineer to quantitatively
    rank the importance of each CV and constraint.
  • For each of the constraints and CVs, the control
    engineer must determine how large a violation of
    the constraint or deviation from setpoint
    requires drastic action to maintain reliable
    operation (Equal Concern Errors).

103
Equal Concern Errors
  • ECEs are based on process experience.
  • Consider a distillation column
  • 0.5 psi above the differential pressure limit of
    2 psi will cause drastic action to prevent
    flooding.
  • 1 impurity levels above the specified impurity
    levels in the products will require rerunning the
    product.
  • Reboiler temperatures greater than 10ºF above the
    reboiler temperature constraint will result in
    excessive fouling of the reboiler.

104
Feedforward Variables
  • Measured disturbances should be modeled as inputs
    for the MPC controller to reduce the effect of
    those disturbances on the CV.
  • FF variables are treated as inputs that are not
    manipulated.

105
MIMO DMC Control
  • Constraint Control

106
Constraint Control
  • With DMC, constraints are treated as CVs.
  • As different combinations of constraints become
    active, different weighting factors, wi, are used
    which are based on the equal concern errors.
    Therefore, as different combinations of active
    constraints are encountered, the wis
    automatically determine the relative importance
    of each.
  • The DMC controller determines the optimal control
    action based on considering that the wis change
    along the entire path to the setpoints.
    Therefore, the entire control law must be solved
    at each control interval.

107
MIMO DMC Control Law
108
MIMO DMC Control
  • MPC Model Identification

109
MPC Model ID
110
MIMO Model Identification
  • For DMC, impulse models are used for
    identification so that bad data can be sliced
    out of the training data.
  • Sources of bad data analyzer failure, data not
    recorded, process not operated in normal fashion
    (by-pass opened, atypical feed to the process,
    saturated regulatory controls, etc.), and large
    unmeasured disturbance to the process.

111
Model Identification
  • SRMs have the flexibility to model a full range
    of process dynamics (e.g., recycle systems).
  • MPC controllers that use preset functional forms
    for models (e.g., state-space models or a set of
    preset transfer function models) can be inferior
    to SRM based models in certain cases.

112
MIMO DMC Control
  • Economic LP

113
Economic LP
  • The LP combines process optimization with the DMC
    controller.
  • The LP is based on economic parameters (e.g.,
    product values, energy costs, etc.) and the
    steady-state gains of the process.
  • The last term in each SRM is used to provide the
    necessary gain information therefore, the LP is
    consistent with the MPC controller.

114
Example of an LP
115
Economic LP and PID Control Performance
116
Economic LP and MPC Control Performance
117
MPC Control Performance (i.e., size of control
circle)
  • Depends on accuracy of models (e.g., process
    nonlinearity, type and size of unmeasured
    disturbances, changes in the process and
    operating conditions).
  • Depends on the performance of regulatory controls
    and sensors.
  • Can also depend on the control MPC technology
    used.

118
Economic LP
  • Consider the case with 5 MVs and 10 control
    objectives (i.e., upper and lower limits on CVs,
    upper and lower limits on MVs, and upper rate of
    change limit on MVs) because there are 5
    degrees-of-freedom (i.e., one for each MV) the LP
    will determine which 5 constraints to
    simultaneously operate against.
  • The 5 constraints, in this case, become the
    setpoints for the MPC controller.
  • The LP is applied each control interval along
    with the MPC controller.

119
The LP and the MPC Controller
  • Both use the steady-state gains from the SRM.
  • The LP determines the setpoints for the
    controller from the economic parameters and the
    process gains.
  • The controller drives the process to the most
    profitable set of constraints, i.e., keeps the
    process making the most profit even though the
    most profitable set of process constraints
    changes with time parameters.
  • Balanced ramp variables are constraints for the
    LP.

120
MIMO DMC Control
  • Large-Scale Applications

121
Size of a Typical Large MPC Application
  • MVs 40
  • CVs 60
  • Constraints 75-100
  • There are some companies that have even larger
    applications.

122
MPC Project Organization
123
MPC Project Organization
  • Understand the process
  • Set the scope of the MPC controller
  • Choose the control configuration
  • Design the Plant Test
  • Conduct the Pretest
  • Conduct the Plant Test and collect the data
  • Analyze data and determine MPC model
  • Tune the controller
  • Commission the controller
  • Post audit

124
MPC Project Organization
  • Understand the process

125
Understand the Process
  • Process understanding is the single most
    important issue for a successful MPC application.
  • Stated another way, if you do not fully
    understand the process and its preferred
    operation, it is highly unlikely that you will be
    able to develop a successful MPC application.

126
How to Develop Process Understanding
  • Study PFDs
  • Study PIDs
  • Talk to the operators (how it really works!)
  • Talk to plant engineers (how they want it to
    work)
  • Interview plant economic planners (how much its
    worth).
  • If available, run steady-state process simulator
  • Read the plant operating manuals
  • Spend time at the process on graveyards.

127
Be able to answer the following questions
  • What is the purpose of the plant?
  • Where does the feed come from?
  • Where do the product go?
  • How much flexibility is there for feed supply and
    product demand?
  • How do the seasons affect the operation? Also,
    feed supply and product demand?

128
Be able to answer the following questions
  • What are the 3 or 4 most important constraints
    that operators worry about?
  • Where is energy used and how expensive is it?
  • What are the product specifications?
  • Are there environmental or tax issues that affect
    plant operations?

129
MPC Project Organization
  • Set the scope of the MPC controller

130
Set the Scope of the Project (Very Important Step)
  • What part of the plant should be included in the
    controller? That is, how much of the plant
    should be included in the MPC controller to meet
    the project objectives?
  • To answer this question, you must discuss the
    objectives of the project with the operations
    personnel, the technical staff for that portion
    of the plant, and the scheduling people. Only
    then can you be sure that you are solving the
    correct problem.

131
MPC Project Organization
  • Select the control configuration

132
MPC Configuration Selection
  • Which PID loops do you open (i.e., turn over to
    MPC controller) and which do you leave closed.
    That is, if you leave a PID loop closed, the MPC
    controller sets the PID loop setpoint (e.g., flow
    controller).
  • What are the MVs for the distillation columns in
    the process? Should the MPC controller be
    responsible for accumulator or reboiler level
    control?

133
MPC Configuration Selection
  • From an overall point of view, what are the MVs
    and the CVs for the MPC controller?
  • A challenging problem that requires process
    knowledge and control experience while keeping
    focused on the overall process objectives.

134
Reasons for Leaving a PID Loop Closed
  • The PID loop may be more effective in eliminating
    certain disturbance due to the higher frequency
    of application. For example, flow control loops.
    In addition, certain pressure, level, and
    temperature PID loops should be left closed.

135
Situations for which a PID loop should be opened
  • Loops with very long dynamic and/or large
    deadtime
  • Process lines with two control valves in series.
  • Certain levels for which allowing the MPC
    controller control the level adds important
    flexibility to better meet the primary objectives
    of the process. For example, it can provide more
    effective decoupling.

136
Use Good Control Engineering
  • Ensure that the MVs have a direct and immediate
    affect on the CVs.
  • Use computed MVs to reject certain disturbances,
    e.g., use internal reflux control to reduce the
    effect of rain storms or computed heat input for
    a pumparound.
  • Use inferential measurements to reduce the effect
    of deadtime (e.g., inferential temp control)
  • Use CV transformations that linearize the overall
    response of the process.

137
Variable Transformations
  • For a control valve, DPKFlow2
  • For high purity distillation columns, use log
    transformed compositions xlog(x)
  • Use different linear models depending on the
    operating range.

138
MPC Project Organization
  • Design the Plant Test

139
Plant Test Guidelines
  • Make from 5 to 15 step tests for each MV
  • The MV changes should be as random as possible to
    prevent correlated data.
  • MV moves should be as large as possible but not
    so large that it upsets the process (e.g.,
    1-10).
  • For each MV, make a change after 1tp, 2tp, 3tp,
    4tp, and 5tp, where tp is Tss/4.
  • Above all, remember the product specs and the
    process constraints

140
Develop the Testing Plan
  • Identify all the MVs you plan to move. Tabulate
    the following data for each MV
  • Tag number of the MV and physical description
  • Nominal value
  • Range of move sizes
  • Make a proposed testing sequence and indicate
    when each MV is moved and by how much.
  • Discuss the MV move sizes with operations.
    Remember the spec and constraints.

141
Choose Sampling Period
  • Small sample period high time resolution but
    increased size of data set. In general, sample
    as new information become available.
  • For fast responding processes, sample every few
    seconds.
  • For slow processes, sample every 5 min
  • Look at the smallest expected Tss.
  • Estimate sample period as Tss/50
  • Compare with sensor dynamics

142
Make MV Changes one MV at a Time to Generate
Uncorrelated Results
143
Develop a Roughed-out Gain Matrix
  • Using your process knowledge, determine whether
    the steady-state process gain is positive,
    negative, or zero for each input (MV DV)/
    output (CV) pair.
  • Using for positive, - for negative, or 0 for
    zero, construct the roughed-out gain matrix.
    Inputs are listed vertically while outputs are
    listed horizontally.

144
Roughed-out Gain Matrix Ex.
145
Ex. Roughed-out Gain Matrix
146
MPC Project Organization
  • Conduct the Pretest

147
Pretest
  • Check all the sensors, control valves and
    regulatory control loops for proper operation.
  • Ensure that the process equipment is in proper
    repair. Check material and energy balances on
    the unit. Make sure that all the major pieces of
    equipment are in operation. Check the feed to
    the unit.
  • Then, apply step input changes for each MV and
    compare to your roughed out gain matrix.
  • Reconcile any deviations from what you expected
    (e.g., roughed out gain matrix, dynamic response,
    etc.). This will enhance your process
    understanding.

148
MPC Project Organization
  • Conduct the Plant Test and collect the data

149
Testing in Optimal Operating Mode
  • Because you will want your plant to operate
    effectively at its optimum operating conditions,
    you should, if possible, test you plant near the
    optimum operating conditions to reduce the
    effects of process/model mismatch.
  • Therefore, you will need to determine the optimum
    operating conditions for your plant, e.g.,
    discuss with an experienced plant engineer or use
    a nonlinear process optimizer.

150
Plant Test Overview
  • The plant test is the most important step in an
    MPC project because if the MPC models do not
    agree with the process, controller reliability
    and performance will be poor.
  • If the process changes (e.g., different equipment
    configuration, different feed, different
    regulatory controller tuning, etc.), mismatch
    between the MPC model and the process will
    result, affecting controller performance.

151
Plant Test Check List
  • Meet (5-10 min) with the operators at the start
    of each shift and explain what you are doing.
  • Make sure that each MV move is made on time, in
    the proper direction, and by the correct amount.
  • Make sure that a technical person is observing
    entire testing period (24-7).

152
Plant Test Check List
  • Make real-time plots of the data and explain all
    the behavior that you see.
  • Identify abnormal periods and make notes
    significant unmeasured disturbances, instrument
    failures, utility outages. The MPC model should
    not be trained using data collected during these
    periods.
  • Talk to the operators about the process.
  • Buy pizza, donuts, ice cream and barbeque for the
    operators

153
Using Roughed-out Gain Matrix
  • During the testing phase, make sure that the
    plant results agree with your roughed-out gain
    matrix.
  • If not, you will need to explain the difference.
    That is, your process knowledge needs to be
    improved a bit or something is not working
    properly (e.g., an analyzer is off-line)

154
Unmeasured Disturbances
  • Training an MPC controller on data collected
    during periods with unmeasured disturbances will
    reduce the accuracy of your model and reduce the
    effectiveness of the overall project.
  • Some unmeasured disturbances are inevitable, but
    you must strive to keep them to an absolute
    minimum.

155
Examples of Unmeasured Disturbances to be Avoided
  • Back flushing a condensor
  • Changes in by-pass streams
  • Product grade changes
  • Changes in the controller settings for the
    regulatory controllers.
  • Any change in the process operating conditions
    not modeled in the controller or process
    equipment changes

156
Identified Periods with Unmeasured Disturbances
  • Slice out the data from those periods so that
    this data is not used to train the MPC model
    therefore, the identified model will not be
    corrupted.

157
MPC Project Organization
  • Analyze the data and develop the MPC model

158
Obtain the MPC Process Models
  • Use the accepted plant test data with the MPC
    model identification software to develop each of
    the input/output SRM models.

159
Evaluate Process Models
  • For each input/output pair, plot the SRM on a
    small graph.
  • Arrange the SRM models into a matrix similar to
    the roughed-out gain matrix.
  • Review the results to ensure that you have models
    that make sense.
  • Use the statistical tools from the MPC model ID
    software to evaluate each SRM

160
Evaluate Process Models
  • Examine the difference between the plant test
    data and your models (residual).
  • Plot the residual for positive and negative MV
    changes. This will help identify the degree of
    process nonlinearity. Also, it will help
    evaluate CV transformations that behave more
    linearly.

161
Plant Economics
  • The LP will require incremental costs (feed
    costs, utility costs) and incremental revenues
    (product values)
  • For previous distillation example, you will need
    the incremental cost of steam (/lb), the
    incremental cost of feed (/lb), and the
    incremental value of both products (/lb).

162
MPC Project Organization
  • Tune the controller

163
General Approach to Tuning
  • Use the SRMs of the process (MPC model) off-line
    as the process to develop the preliminary
    settings for the controller.
  • Three areas that you need to get right
  • Economics
  • Constraints
  • Dynamics

164
Testing Economics
  • Run plant/controller simulations (off-line) with
    different combinations of constraints to ensure
    that the controller pushes the plant in the
    correct direction.
  • Run test cases to see which LP constraints are
    operative.

165
Constraints
  • Check the equal concern errors for each
    constraint to ensure that the proper relative
    weighting factors for each combination of active
    constraints is used. That is, when constraint 1
    and 5 are active, what is the relative importance
    of the CVs and constraints.
  • Also, use the plant/controller simulation
    (off-line) to test the relative weighting.

166
Dynamics
  • Select the move suppression factors for each MV
    using off-line simulations of the plant. Run the
    simulations a number of times for setpoint
    changes and unmeasured disturbances to get the
    MSFs right. Operators are a good source for
    letting you know how much the MVs should move in
    certain situations and how fast the process
    should move to CVs, but remember that they are
    most familiar with how the plant used to operate.

167
Operator Training
  • In some states, it is a legal requirement.
  • Typically operators receive one to two hours of
    training with MPC.
  • Nevertheless, better operator training increases
    your chance for success.

168
Watchdog Timer
  • The controller should run every minute 24-7
  • Otherwise, a DCS alarm should sound.
  • The most common approach is to use a watchdog
    timer (a small program running on the DCS) to
    communicate with the MPC controller. If the
    watchdog fails to receive a healthy response from
    the controller after an appropriate period of
    time, the watchdog forces each MV into a fallback
    (shed) position and writes an alarm to the
    operator.

169
MPC Project Organization
  • Commission the controller

170
General Approach
  • Now it is time to install the controller in the
    closed loop in the process.
  • Since the controller will directly affect the
    plant operation, it is essential to proceed
    methodically and with caution.
  • Use a checklist and be observant

171
Commissioning Checklist
  • Make sure that the operators have been trained
  • Install control software, database, and other
    real-time components.
  • Check controller database
  • Control CVs, DVs, and MVs match raw DCS inputs
    exactly
  • Controller models, tuning parameters, etc. match
    off-line versions exactly

172
Commissioning Checklist (cont.)
  • Turning controller on the prediction mode
  • Each MV configured correctly in the DCS?
  • Correct shed mode for each MV?
  • MVs out of cascade (controller cannot change)?
  • Controller turned on the prediction mode?
  • The size of the calculated DMV moves make sense?
  • The CV predictions make sense?

173
Commissioning Checklist (cont.)
  • First-time MV check
  • Use conservative controller settings
  • Reduce difference between upper and lower limits
    on MV (or rate limits)
  • Make sure controller is running
  • Put MVs into cascade one at a time.
  • Ensure that the calculated MV change is applied
    to DCS setpoint.

174
Commissioning Checklist (cont.)
  • Close the loop
  • Ensure that the controller is running
  • Turn ON the controller master switch
  • With MVs clamped, put one or two MVs into
    cascade
  • Relax the MV limits somewhat and check for good
    controller behavior
  • Add more MVs gradually, ensuring good control
    performance.

175
Final Checks
  • Ensure that the standard deviations of the CVs
    decrease and that the MVs are not moving around
    too much.
  • Ensure that the LP is driving the process in the
    correct direction.

176
MPC Project Organization
  • Post audit

177
Post audit
  • Collect post commissioning data for the key CVs
    and compare to pre-project data.
  • Ensure that the standard deviations of the key
    CVs have decreased.
  • Evaluate whether the upper and lower limits on
    the MVs are still set correctly.
  • Ensure that the controller is running the process
    at the economically best set of constraints most
    of the time.

178
Advantages of MPC
  • Combines multivariable constraint control with
    process optimization.
  • A generic approach that can be applied to a wide
    range of processes.
  • Allows for more systematic controller
    maintenance.
  • Depends on the particular process

179
MPC Offers the Most Significant Advantages
  • For high volume processes, such as refineries and
    high volume chemical intermediate plants.
  • For processes with unusual process dynamics.
  • For processes with significant economic benefit
    to operated closer to optimal constraints.
  • For processes that have different active
    constraints depending on product grade, changes
    in product values, summer/winter operation, or
    day/night operation.
  • For processes that it is important to have smooth
    transitions to new operating targets.

180
Application Example
  • C3 splitter in an ethylene plant (reboiler duty
    is free therefore, run at maximum reboiler duty
    and apply single-ended control.)
  • DCS 70 of cost 35 of inc. benefit
  • AdPID 10 of cost 60 of inc. benefit
  • MPC 10 of cost 3 of inc. benefit
  • RTO 10 of cost 2 of inc. benefit

181
Application Example
  • Reformer. Control is easy since it only involve
    inlet temperature controllers.
  • DCS 70 of cost 35 of inc. benefit
  • AdPID 10 of cost 30 of inc. benefit
  • MPC 10 of cost 5 of inc. benefit
  • RTO 10 of cost 30 of inc. benefit

182
Application Examples
  • FCC Unit. Optimal constraints change with
    economics, operating conditions, etc. Finding the
    optimal riser temperature requires RTO (yield
    model and nonlinear problem).
  • DCS 70 of cost 35 of inc. benefit
  • AdPID 10 of cost 10 of inc. benefit
  • MPC 10 of cost 35 of inc. benefit
  • RTO 10 of cost 30 of inc. benefit

183
Limitations of MPC
  • It is a linear method therefore, it is not
    recommended for highly nonlinear processes (e.g.,
    pH control).
  • It does not adapt to process changes. If the
    process changes significantly, the MPC model must
    be re-identified.
  • For certain cases, the economic LP may not be
    accurate enough. For these cases, it may be
    necessary to add nonlinear optimization on top of
    the LP.

184
Different Forms of MPC
185
Primary Commercial MPC Software
  • ABB
  • Aspentech DMCplus
  • Fisher-Rosemount
  • Foxboro
  • Honeywell RMPCT
  • Yokogawa

186
  • MPC software based on models with specified
    dynamic characteristics can be inferior to SRM
    based approaches.

187
Conclusions
188
Conclusions
  • The challenges of this course
  • A very difficult area with considerable
    mathematics and industrial practice.
  • Only two days
  • Wide variety of backgrounds of the students.

189
Conclusions
  • You should now be familiar with MPC terminology
    and technology and the major issues associated
    with the commercial application of MPC.
  • Are you an MPC expert? Not yet! But with more
    study and a lot more experience, you can become
    one.

190
Conclusions
  • This is not the end.
  • It is not even the beginning of the end.
  • But it is, perhaps, the end of the beginning
  • (Sir Winston Churchill, Nov. 10, 1942)
About PowerShow.com