mon 17.30 predictive control down at plc level rossiter
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8/10/2019 Mon 17.30 Predictive Control Down at Plc Level Rossiter
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Predictive control with PLCs
J.A. Rossiter and G. Valencia-Palomo
j.a.rossiter@shef.ac.uk, gvalencia@ith.mx
Advances in Process Control 2011.
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Outline
1. Introduction
2. Background on MPC
3. PLC and implementation challenges4. Efficient MPC algorithms
5. Practical implementation
6. Conclusions
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Motivation
Despite numerous successful applications, MPC has stillnarrow impact for low level control loops where PI still themain option.
PFC the most varied range of industrial applications (in theMPC family).
Conclusion : There is an opportunity to propose morerigorous, intuitive and simple MPC algorithms to be equally
embedded in cheap control units.
Reasons for the success of PFCPromotion and support Training the technical staff.Controller set up Tuning and maintenance.
Hardware Industrial standard.
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Predictivecontrol
PredictedError
Predictedinput
MPCstrategy
Choosepredictedinputs tominimisepredicted
errors.
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Modelling (e.g. State space model)
Modelling and constraints
Disturbance rejection and offset free tracking
Constraints
Model isused toform
predictionsand
compare toconstraints.
These
details notcore today.
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Prediction class (embed feedback into predictions)
Optimal MPC or OMPC
Performance index (define good and bad predicted performance)
Optimal MPC (popular formulation for MPC)
Use the first element of in the control law with K.
Constraints
Performance
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Operating regions
Maximum admissible set (MAS):nominal control law does notviolate constraints.
Maximum controllable
admissible set (MCAS):prediction class can ensure
constraint satisfaction.
Usually the larger the numberof d.o.f., the larger theMCAS or operating region.
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1. Stability.
Incorporate design features that guarantee stability in a senserelevant to the control problem they aim to solve, i.e. stabilization,tracking or disturbance rejection.
2. Feasibility.
Larger values of nc result in a larger MCAS.3. Performance requirements.Tighter performance demands often lead to smaller MCAS;increasing the d.o.f. nc usually improves constrained optimality.
4. Computational complexity is affected by:Number of constraints ( n y ), number of optimisation variables ( n c ),class of optimisation problems, requirement for guarantees, .
5. Robustness.Affected by choice of J and underlying feedback K.
OMPC Design issues
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Industrial standard and by far the most accepted computersin industry.
Tailored for ease integration into on-site racks. Ease to debug, dedicated I/O, communication, etc. On-line monitoring and programming. Redundancy in computations.
PLC and challenges
Why a PLC?
Allen Bradley PLC
SCL500 processor family.
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IEC 61131-3 Programming languages (3/5 available) Ladder diagram. Function block diagram. Structured text.
Ladder diagram language. Function block diagram language.
PLC and challenges
More restrictive thancomputers normally used
to implement MPC.
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Programming challenges with constrained MPC Can allocate matrices but only one by one element
operations. Program memory. Computational time.
SolutionConstrained MPC
explicit solution
easy to code
SUMMARY: Replace on-line optimisation by either a simpleoptimisation or a look-up table.
PLC challenges and solutions
Recent work showsthis is possible
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Parametric implementations
The optimisation problem
for OMPC has a solutionof the form
That is, if the currentsystem state is in regionr, then use control lawr.Hence this is a look uptable.
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Solutions 1:Linear interpolation
Interpolate two unconstrained control laws, one with goodfeasibility and one with good performance.
where
the optimisation is just a constraint check, and the
interpolation detunes the controller if necessary.
Useful concept that is used in several algorithms.Linear interpolation is easy to code!
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Solutions 2:Laguerre functions and mpQP
In optimal MPC, replace the normal pulse functions toparameterise the input sequence with Laguerre functions:
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Laguerre functions and mpQPLaguerre functions evolve over an infinite horizon thus
having a beneficial impact on feasibility.
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Simulations shows that with Laguerre functions, the MCAS andnumber of regions are better than with conventional OMPC
Parametric implementations andLaguerre
LOMPC OMPC
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Solutions 3. A suboptimalparametric solution
Construct which is the unionof a nD cube and a nD crosspolytope.
Polytope for the 3D case.
Use regularshapes to allow
for more efficientsearch algorithms
and coding.
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Example of shape differences 2Dcase
Stretch the polytope to the boundary of the MCAS of theOMPC problem
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Suboptimal parametric algorithm
Those points at the vertices are stored with theircorresponding solution.
Due the regular definitions of the vertices of the region of the actual initial point of be easily located.
The control law is the interpolation of the solution of the
vertices enclosing that region.
Uses the single variable interpolation; trivial to code!
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Memory 17%
Practical implementation on aPLC linear interpolation
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Practical implementation onlaboratory equipment
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Practical implementation ofLaguerre based algorithm
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Regions for speed processMemory 19%
PLC coding for Laguerre MPQP
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Laboratorysimulations of
Laguerre MPQP
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Speed process
Memory 19%
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Simulationresults forsuboptimalalgorithm
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Conclusions
Simple modifications to MPC can allow much simpler codingand lower online computational loads.
These modifications allow a reduction in memoryrequirements without severe performance degradation andstill retain guaranteed stability.
These algorithms can be coded in a standard PLC withoutexcessive memory and computational requirements.
It has been demonstrated that MPC is a realistic industrialalternative to PID in loops primarily controlled with PLCunits. This final contribution opens up the potential for muchimproved control of loops where PID may be a poor choice.
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Thank you
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