Approaches to increase the range of use of Model predictive control

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Approaches to increase the range of use of Model
predictive control

• Miguel Rodriguez
• Advisor Cesar De Prada
• Systems Engineering and Automatic Control
  Department
• University of Valladolid, Spain

Pisa, October 2008.
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Outline

• Motive
• Control explicit using Multiparametric
  Programming
• Approaches for using NMPC in Hybrid Systems
• Mixed continuous-batch processes
• Hybrid system
• Reduced Order Model
• Conclusions

Approaches to increase the range of use of Model
predictive control
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Motive

• MPC is used to controlling a wide range of
  process industrials.
• MPC is capable of operating without expert
  intervention for long periods time.
• Centralized control, Multi-level, complex plants.
• Constraint handling, Input saturation, states
  constraints, etc.
• But
• MPC to require a time of calculation to find the
  optimal control signal.
• The time of calculation is increased when the
  systems are Hybrid or Nonlinear.
• If optimization time is higher that the response
  time, MPC is impossible to apply.

Approaches to increase the range of use of Model
predictive control
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Motive

• The main objective is find techniques that
  decreased the optimization time and retain all
  benefits of MPC approach.
• Three approach are presented in this work
• Control explicit using Multiparametric
  Programming
• Approaches for NMPC to Hybrid Systems
• Mixed continuous-batch processes
• Hybrid system
• Reduced Order Model

Approaches to increase the range of use of Model
predictive control
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Control explicit using Multiparametric
Programming

• Linear MPC without constraints
• Using the steady states model and making
  predictions to the horizon prediction

Approaches to increase the range of use of Model
predictive control
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Control explicit using Multiparametric
Programming

• Linear MPC without constraints
• Then
• Explicit Solution
• where

Approaches to increase the range of use of Model
predictive control
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Control explicit using Multiparametric
Programming

• Linear MPC with constraints
• Using multiparametric programming, z is
  dependent variable of the current states x and
  the system constraints.
• with the KKT conditions, we can found, of way
  iterative, the explicit solution into the region
  where it solution is valid.

Approaches to increase the range of use of Model
predictive control
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Control explicit using Multiparametric
Programming

• Linear MPC without constraints
• finally, we have an explicit solution for each
  region CRi

Approaches to increase the range of use of Model
predictive control
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Control explicit using Multiparametric
Programming

• DC-DC Converter (Buck-Boost type)
• Average Model (continuous conduction mode)
• Search method binary search tree (Tondel,
  Johansen and Bemporad, 2002)

Approaches to increase the range of use of Model
predictive control
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Control explicit using Multiparametric
Programming

• DC-DC Converter (Buck-Boost type)
• Controller partition with 51 regions

Approaches to increase the range of use of Model
predictive control
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Control explicit using Multiparametric
Programming

• DC-DC Converter
• Comparison between Slide Model Control
  and mp-MPC.

Load (Ohms)
Ref (Volts)
V0 (Volts)
Approaches to increase the range of use of Model
predictive control
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Control explicit using Multiparametric
Programming

• Feasibility of implementing the controller.
• Ts0.1 ms
• State Estimator ( 16 multiplications 32
  assignations ) 50 cycles
• Signal capture ( 2 input, Voltage and Current)
  4 cycles
• Search of region (51 regions X 5 operations )
  205 cycles
• Calculation control signal (3 multiplications 3
  assignations) 6 cycles
• Output PWM (3 assignations) 6 cycles
• Total of cycles 270 cycles
• mController frequency
• Standard floating point DSP controller (Texas,
  Microchip, etc)

Approaches to increase the range of use of Model
predictive control
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Approaches for NMPC to Hybrid Systems.

• Mixed continuous-batch processes
• Parallel Production Line
• Hybrid system
• Solar Air conditioning plant

Approaches to increase the range of use of Model
predictive control
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Parallel Production Line

• The benchmark is a chemical process proposed by
  UCL, Belgium

Approaches to increase the range of use of Model
predictive control
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Parallel Production Line

• Aims of control
• Maximize the productivity in the presence of
  uncertainties and disturbances.
• Maximize the output flow of storage tank and hold
  transfer continuously to downstream processing
  stage.
• To avoid the total discharge in the storage tank.
  
• Decision variables
• Standby times for filling, heating and
  discharging of both autoclaves.
• Outflow of B product from storage tank (FoutST)
• Non-measured disturbances
• Change in the temperature of hot steam (Th)

Approaches to increase the range of use of Model
predictive control
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Parallel Production Line

• Tconstraints

Approaches to increase the range of use of Model
predictive control
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Parallel Production Line (Simulation Results.
Overview)

• Values of the parameters of Objective Function
• Values of the weights
• Almost, for each batch unit, 3 batches are
  predicted, 2 of them are controlled. So, Np3 and
  Ncb1Ncb22.
• 4 changes for classical continuous variables
  FoutST

Approaches to increase the range of use of Model
predictive control
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Parallel Production Line (Simulation Results.
Overview)
Manipulated variable
Controlled variable
Batch sequences
Approaches to increase the range of use of Model
predictive control
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Solar Air conditioning plant (Description)

• The absorption machine
• Energy supply systems
• solar collector
• gas heater
• Accumulation tank
• Aims of control
• Maintaining the chilled water temperature
  (75º-95º)
• Minimize the gas used
• Decision variables
• Continuous
• vB1, vm3
• Discrete
• mode of operation (set of on/off valves)

Problem MINLP very complex
Approaches to increase the range of use of Model
predictive control
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Solar Air conditioning plant (Embedded Logic
Control)

• Fictitious variable u to represent the energy
  supply to the plant
• Definition of a set of rules
• Integration of the rules and the fictitious
  variable
• Solution of the associated optimization problem
  every sampling period
• Objective function

Embedded logic control rules of Operation
Approaches to increase the range of use of Model
predictive control
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Solar Air conditioning plant (Sensibility
problems)
For u(t) we are solving
For u(tTs) we are solving
Sub-optimal solution, but no problem with the
sensibility
Approaches to increase the range of use of Model
predictive control
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Solar Air conditioning plant (Controller
implementation)
Sequential approach to dynamic optimization
Approaches to increase the range of use of Model
predictive control
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Solar Air conditioning plant (Results)

• Simulation results

Controlled variable
Manipulated variables
Approaches to increase the range of use of Model
predictive control
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Solar Air conditioning plant (Results)

• Test real plant

Controlled variable
Manipulated variables
Approaches to increase the range of use of Model
predictive control
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Reduced Order Model (The open plate reactor)
Controlled variables ? conversion Ti
temperature along the reactor Manipulated
variables uB1, uB2, feed flows rates of B
TfeedA, temperature of reactant A, Tcool the
cooling temperature.
It combines heat exchanger and micro-reactor
more efficient but more difficult to control
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The open plate reactor (Dynamics and Aims)
Start-up of the plate reactor avoiding hot spots
Highly non-linear distributed process
Aim Finding a reduced dynamic model that
facilitates the use of NMPC
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The open plate reactor (Proper Orthogonal
Decomposition POD)
DFM
A field x can be represented as a complete series
of orthonormal globally defined functions ?i
POD
A projection is made on a subspace retaining
of the energy of the signals, allowing to obtain
a model with a smaller number of ODEs
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The open plate reactor (NMPC)
NMPC based on continuous time formulation with
the POD model and a sequential approach for the
NLP problem
Results of the reactor start-up
Inputs
Outputs
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Conclusions

• Approaches to apply NMPC in Fast-System and
  hybrid system have been presented.
• Transformation of problem discrete variables to
  Continuous variables.
• To use NLP approach to solver Mixed integer no
  linear problem.
• A study of feasibility to implementing mp-MPC in
  mcontrollers has been presented.

Approaches to increase the range of use of Model
predictive control
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Reference

• M. Rodríguez, D. Sarabia, and C. de Prada Hybrid
  Predictive Control of a Simulated Chemical Plant.
  Taming Heterogeneity and Complexity of Embedded
  Control Systems, International Scientific
  Technical Encyclopedia (ISTE), London, Editors
  F. Lamnabhi-Lagarrigue, S. Laghrouche, A. Loria
  and E. Panteley, pp. 617-634, 2007
• M. Rodríguez, C. De Prada, F. Capraro, S.
  Cristea, and R. M. C. De Keyser Hybrid
  Predictive Control of a Solar Air Conditioning
  Plant. 17th IFAC World Congress, Seoul, Korea,
  2008.
• D. Sarabia, C. de Prada, and S. Cristea A Mixed
  Continuous-Batch Process Implementation of
  Hybrid Predictive Controllers. Proc. 7th IFAC
  Symp. on Advances in Control Education, 2006,
  Paper-ID 148.
• M. Rodríguez, C. de Prada, A. A. Alonso, C.
  Vilas and M. García A nonlinear model predictive
  controller for the start-up of a open plate
  reactor, International Workshop on Assessment and
  Future Directions Of Nonlinear Model Predictive
  Control, Pavia, Italy, 2008.

Approaches to increase the range of use of Model
predictive control
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Questions?

• Thank you.

Approaches to increase the range of use of Model
predictive control