Model Predictive Model Predictive Controller Controller Emad Ali Emad Ali Chemical Engineering Chemical Engineering Department Department King Saud University King Saud University
Dec 21, 2015
Model Predictive Model Predictive ControllerController
Emad AliEmad Ali
Chemical Engineering Chemical Engineering DepartmentDepartment
King Saud UniversityKing Saud University
ReviewReview
Major Control Elements:Major Control Elements:
InstrumentationInstrumentationControl algorithmControl algorithmProcess modelProcess model
ReviewReview
Control AlgorithmsControl Algorithms:: Classical:Classical:
PID, cascade, override, ratio, split range, inferentialPID, cascade, override, ratio, split range, inferential
Advanced:Advanced:Adaptive controlAdaptive controlFuzzy logic controlFuzzy logic control Internal model controlInternal model controlOptimal controlOptimal controlNeural network controlNeural network controlGlobally linearizing controlGlobally linearizing controlModel predictive controlModel predictive control
Benefits of MPCBenefits of MPC
1. Optimization: consistent product quality, reduced off-specs products, minimizing the operating cost.
2. Multivariable: Superior for processes with large
number of manipulated and controlled variables with strong coupling.
3. Constraints: Allows constraints to be imposed on
both MV and CV. 4. Prediction: good for time delays, inverse response,
inherent nonlinearities, changing control objectives and sensor failure.
Industrial MPC TechnologyIndustrial MPC Technology IDCOM (Identification and Command)IDCOM (Identification and Command)
Model type: Impulse response Model type: Impulse response Optimization is solved by QP approachOptimization is solved by QP approach
DMC (Dynamic Matrix Control)DMC (Dynamic Matrix Control) Model type: Step responseModel type: Step response Optimization is solved by LP approach Optimization is solved by LP approach
OPC (Optimum Predictive Control)OPC (Optimum Predictive Control) Use step response, solves LP problemUse step response, solves LP problem Model building, controller design and simulation Model building, controller design and simulation tasks are carried out on PCstasks are carried out on PCs
PCT (Predictive Control Technology)PCT (Predictive Control Technology) Combines the aspects of IDCOM and DMCCombines the aspects of IDCOM and DMC
HMPC (Horizon Multivariable Predictive Control)HMPC (Horizon Multivariable Predictive Control) For proprietary reasons, information is unavailable For proprietary reasons, information is unavailable
Multivariable vs. Multi-loopsMultivariable vs. Multi-loops
Process
Controller
Process
Controller
Controller
Outputs
Outputs
Inputs
Inputs
Mulit-loops Scheme
Mulit-variables Scheme
Receding Horizon ConceptReceding Horizon Concept(Prediction)(Prediction)
k k+1 k +M -1 k + P
FuturePast
Reference, r (k+1)
Predicted output, y (k+1/k)
Control action, u (k/k)
Control horizon
Prediction horizon
Process ModelProcess Model
Model:
Y(k/k) = [y(k/k) y(k+1/k) … y(k+n-1/k)]
Y(k-1/k) = [y(k-1/k) y(k/k) … y(k+n-2/k)]
Prediction:
Y(k+1/k) = [y(k/k) y(k+1/k) … y(k+P-1/k)]
U(k/k) = [u(k/k) u(k+1/k) … u(k+M-1/k)]
Y(k/k) = M Y(k-1/k) + S u(k-1/k)
Y(k+1/k) = MP Y(k/k) + SP U(k/k)
Process Model CorrectionProcess Model Correction
Output Feedback:Output Feedback:
Y(k+1/k) = Y(k+1/k) + N yp(k)-ym(k)]
Methods of SolutionMethods of Solution
1. Algebraic Equation:
2. Linear Programming (LP)
R(k+1)=Y(k+1) = MP Y(k) + SP U(k)
|R(k+1)-Y(k+1)| =
|R(k+1)-[MP Y(k) + SP U(k)]| = 0
3. Quadratic Programming
Methods of solutionMethods of solution
4. Constrained QP
min [R(k+1)-Y(k+1)]T [R(k+1)-Y(k+1)] + UT(k) U(k)U(k)
min [R(k+1)-Y(k+1)]T [R(k+1)-Y(k+1)] + UT(k) U(k)U(k)
Ul ≤ U ≤ Uu
Ul ≤ U ≤ Uu
Methods of solutionMethods of solution
AlgebraicLPQPConstrained QP
difficultySmallmediumLargeLarger
optimizationNoYesbetterbetter
constraintsNoNoNoYes
Tuning ParametersTuning Parameters
Output weights:
3
2
1
0 0
0 0
0 0
Input weights:
3
2
1
0 0
0 0
0 0
Prediction horizon: Y(k+1/k) = [y(k+1/k) y(k+2/k) … y(k+P/k)]
Control horizon: U(k/k) = [u(k/k) u(k+1/k) … u(k+M-1/k)]
Tuning GuidelinesTuning Guidelines
Tuning Tuning parameteparameterr
functionfunction
Gives more weight to a Gives more weight to a specific outputspecific output
Slower response, stabilizing Slower response, stabilizing effecteffect
PPMore stable and robust More stable and robust responseresponse
MMFaster (even unstable) Faster (even unstable) responseresponse
Generating Step Response Generating Step Response ModelModel
1 .Step testing
DynamicProcess
Input 1 Output 1
s1,1
s2,1
s3,1
sn,1
Unit Step Response
Output nyInput nu
Input 2
Unit Step Change
Constant
Constants1,ny
s2,ny
s3,nysn,ny
h1,1
h2,1
h3,1
h1,ny
h2,ny
h3,ny
Generating Step Response Generating Step Response ModelModel
2 .PBRS Testing
DynamicProcess
Input 1 Output 1
Unit Step Response
Output nyInput nu
Input 2
PBRS
PBRS
PBRS
Step Vs. PBRSStep Vs. PBRS
Step Step Simple and Simple and straightforwardstraightforward
Requires long Requires long testing timetesting time
PBRSPBRSRequires Requires knowledge knowledge about about identification identification theory theory
Requires less Requires less testing timetesting time
Implementation requirementImplementation requirement
DCS systemDCS systemPersonal ComputerPersonal ComputerStep response modelStep response modelTuningTuning
Special Features of MPCSpecial Features of MPC
Feed-forward capabilityFeed-forward capability
Inferential controlInferential control
Output ConstraintsOutput Constraints
Y(k+1/k) = M Y(k/k) + S U(k/k) + W d(k/k)
Y(k+1/k) = M Y(k/k) + S U(k/k)
Z(k+1/k) = CY(k+1/k)
Yl (k+1) ≤ Y (k+1) ≤ Yu(k+1)
Special Features of MPCSpecial Features of MPC
Variable set point Variable set point
or constraintsor constraints
Simulation ExampleSimulation Example
Pump-1
F200T200
F5
F4
L2
F2C2T2
F1C1T1
F3
P2
P100F100T100
Steam
Separator
Coolingwater
ProductFeed
0.14
0.16
0.18
0.20
C2
set po in t
P = 2
P = 50
0 35 70
T im e (m in)
3 2
3 2 . 4
3 2 . 8
3 3 . 2
3 3 . 6
P2
(kP
a)
0.14
0.16
0.18
0.20
C2
set po in t
P = 2 , G = 1 /1 , L = 0 /0
P = 2, G = 1 /1, L = 0 .001/0.001
P = 2, G = 10/1 , L = 0 .001/0 .001
0 35 70
T im e (m in)
32.0
32.4
32.8
33.2
33.6
P2
(kP
a)