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, SpainPisa, October 2008.
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.
Outline
Approaches to increase the range of use of Model predictive control Motive
Control explicit using Multiparametric Programming
Approaches for using NMPC in Hybrid Systems
Mixed continuous-batch processes
Hybrid system
Reduced Order Model
Conclusions
My presentation is formed by a motive, I going to present three approaches, the first one is one explicit control using Multiparametric programming. The second approach consist in study the use of NMPC for hybrid systems. And last one is find reduced order model.
Motive
Approaches to increase the range of use of Model predictive control 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.
The model predictive control MPC is used to controlling a wide range of process industrials. The reason for such popularity is the ability of MPC designs to yield high performance control systems capable of operating without expert intervention for long periods of time. The MPC require of a time of calculation to find the optimal control signal by minimizing an objective function that depends of process model. For Hybrid or nonlinear systems this time of calculation is increased doing impossible to apply this type of controller, the optimization time is higher that the response time. The main objective of my research is find techniques that decrease the optimization time and retain all benefits of MPC. The first case studied is the control to process with fast dynamic; in this case the DC-DC converters have been studied. An explicit control has been found, which is based in find a set of solutions that depend of the process states. In this approach we using multiparametric programming, it divide the states spaces in a set of affine regions and in each region is finding the explicit solution to the MPC problem. The advantage of this technique is that the set of solutions can be implementing as a table into a commercial m-controller and apply this control online. In this work the DC-DC converters, buck-boost and buck type, have been found, also the feasibility of implementing this control in a m-controller has been studied.
Motive
Approaches to increase the range of use of Model predictive control 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
The model predictive control MPC is used to controlling a wide range of process industrials. The reason for such popularity is the ability of MPC designs to yield high performance control systems capable of operating without expert intervention for long periods of time. The MPC require of a time of calculation to find the optimal control signal by minimizing an objective function that depends of process model. For Hybrid or nonlinear systems this time of calculation is increased doing impossible to apply this type of controller, the optimization time is higher that the response time. The main objective of my research is find techniques that decrease the optimization time and retain all benefits of MPC. The first case studied is the control to process with fast dynamic; in this case the DC-DC converters have been studied. An explicit control has been found, which is based in find a set of solutions that depend of the process states. In this approach we using multiparametric programming, it divide the states spaces in a set of affine regions and in each region is finding the explicit solution to the MPC problem. The advantage of this technique is that the set of solutions can be implementing as a table into a commercial m-controller and apply this control online. In this work the DC-DC converters, buck-boost and buck type, have been found, also the feasibility of implementing this control in a m-controller has been studied.
Control explicit using Multiparametric Programming
Approaches to increase the range of use of Model predictive control Linear MPC without constraints
Using the steady states model and making predictions to the horizon prediction
Control explicit using Multiparametric Programming
Approaches to increase the range of use of Model predictive control Linear MPC without constraints
Then
Explicit Solution:
where
Control explicit using Multiparametric Programming
Approaches to increase the range of use of Model predictive control 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.
Control explicit using Multiparametric Programming
Approaches to increase the range of use of Model predictive control Linear MPC without constraints
finally, we have an explicit solution for each region CRi
Control explicit using Multiparametric Programming
Approaches to increase the range of use of Model predictive control Control mp - QP EcoSimPro Set point V0 , IL d, R MatLab States estimator States d Disturbance model DC-DC Converter (Buck-Boost type)
Average Model (continuous conduction mode)
Search method: binary search tree (Tondel, Johansen and Bemporad, 2002)
Control explicit using Multiparametric Programming
Approaches to increase the range of use of Model predictive control DC-DC Converter (Buck-Boost type)
Controller partition with 51 regions
Control explicit using Multiparametric Programming
Approaches to increase the range of use of Model predictive control Load (Ohms) Ref (Volts) V0 (Volts) DC-DC Converter
Comparison between Slide Model Control and mp-MPC.
Control explicit using Multiparametric Programming
Approaches to increase the range of use of Model predictive control Feasibility of implementing the controller.
Ts=0.1 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 for NMPC to Hybrid Systems.
Approaches to increase the range of use of Model predictive control Mixed continuous-batch processes
Parallel Production Line
Hybrid system
Solar Air conditioning plant
Parallel Production Line
Approaches to increase the range of use of Model predictive control The benchmark is a chemical process proposed by UCL, Belgium
It combines continuous and batch dynamics and involves also continuous and discrete variables
Hybrid Process
Simulation of the PVC process
The model of the PVC Process is based on detailed first principles of the process and it is available
The model was implemented in the simulation language EcosimPro that generates C++ code
Low-level control (regulatory and sequential control) are implemented as part of model
Two parallel batch reactors: Autoclave AC1 and Autoclave AC2. Deliver the same final species B produced by a 2º exothermic reaction:
An automaton takes charge doing the sequential control of the process, the stages of each autoclave are: Stand by Fill, Filling, Stand by Heat, Heating, Temperature regulation, cooling, Stand by discharge, Discharging.
PID´s controls take charge of the regulation of temperatures in regulation stage.
The resourses (reactance, hot steam and cool water) are common and limited. So, both autoclaves can’t be, at same time, in stages of Filling, Heating and discharging.
The Storage Tank (ST) receives the output product B from each autoclave, The product B is then discharged continuously from the tank to the next process.
Parallel Production Line
Approaches to increase the range of use of Model predictive control 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)
Parallel Production Line
Tcontraints=Toverlap fill+Toverlap Heat Approaches to increase the range of use of Model predictive control Tconstraints
Parallel Production Line (Simulation Results. Overview)
Approaches to increase the range of use of Model predictive control
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, Np=3 and Ncb1=Ncb2=2.
4 changes for classical continuous variables FoutST 100 1 1 1 0.1 Weight (ai) Tconstraints FoutST VSTmin VSTmax VSTref 10 40 25 VSTmin VSTmax VSTref
Parallel Production Line (Simulation Results. Overview)
Approaches to increase the range of use of Model predictive control Manipulated variable Controlled variable Batch sequences
Solar Air conditioning plant (Description)
Approaches to increase the range of use of Model predictive control Problem MINLP very complex 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)
The aims of the control system are maintaining the chilled water temperature close to its set point and the input temperature of the generator within its operating range in spite of possible disturbances.
As decision variables, one have the values of the two continuous manipulated ones: the speed of the pump vB1 and the opening of the three way valve vm3, as well as the choices on what energy sources to use at every time instant, that is, the mode of operation, which can be implemented by means of a set of on/off valves
The purpose is to accomplish the control aims using as less gas as possible in the gas heater and leaving the accumulation tanks at the end of the day with a temperature as high as possible in order to facilitate the operation of the following day. In addition, some other constraints have to be fulfilled, like the security ones on the maximum temperature allowed in the solar panels, 100 ºC. In the current conditions of operation, both temperature targets, chilled water and input to the generator, are equivalent and we will consider as the only target keeping the input temperature of the generator of the absorption machine Tgi within a operation range [76 – 95] ºC and as close as possible to a set point, with minimum consumption of gas. This led to the minimization of the cost function:
Formulated in this way, the hybrid MPC controller, while considering explicitly the structural changes associated to the uses of different sources of energy, must solve onl...
Solar Air conditioning plant (Embedded Logic Control)
Approaches to increase the range of use of Model predictive control Embedded logic control rules of Operation 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
In order to reformulate the problem in a sound way, avoiding the MINLP optimization and facilitating a real time solution, an “Embedded Logic” approach was developed incorporating physical insight into the decision procedure and developing an internal model that combines pre-defined operating policies and process dynamics with a parameterization that avoids the use of integer variables in the optimization stage of the MPC. It consists of the following elements:
The use of a fictitious variable u to represent the energy supply to the plant
The definition of a set of rules that choose the most adequate mode of operation according to the state of the plant and the energy demands
The integration of the rules and the fictitious variable into the dynamical model of the process to form the internal model of the MPC controller.
The solution of the associated optimization problem every sampling period in terms of the continuous variable u, which can be performed as a NLP problem
Comments