mon 17.30 predictive control down at plc level rossiter

8/10/2019 Mon 17.30 Predictive Control Down at Plc Level Rossiter

1/28

1

Predictive control with PLCs

J.A. Rossiter and G. Valencia-Palomo

[email protected], [email protected]

Advances in Process Control 2011.


2/28

2

Outline

1. Introduction

2. Background on MPC

3. PLC and implementation challenges4. Efficient MPC algorithms

5. Practical implementation

6. Conclusions


3/28

3

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.


4/28

4

Predictivecontrol

PredictedError

Predictedinput

MPCstrategy

Choosepredictedinputs tominimisepredicted

errors.


5/28

5

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.


6/28

6

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


7/28

7

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.


8/28

8

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


9/28

9

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.


10/28

10

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.


11/28

11

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


12/28

12

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.


13/28

13

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!


14/28

14

Solutions 2:Laguerre functions and mpQP

In optimal MPC, replace the normal pulse functions toparameterise the input sequence with Laguerre functions:


15/28

15

Laguerre functions and mpQPLaguerre functions evolve over an infinite horizon thus

having a beneficial impact on feasibility.


16/28

16

Simulations shows that with Laguerre functions, the MCAS andnumber of regions are better than with conventional OMPC

Parametric implementations andLaguerre

LOMPC OMPC


17/28

17

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.


18/28

18

Example of shape differences 2Dcase

Stretch the polytope to the boundary of the MCAS of theOMPC problem


19/28

19

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!


20/28

20

Memory 17%

Practical implementation on aPLC linear interpolation


21/28

21

Practical implementation onlaboratory equipment


22/28

22

Practical implementation ofLaguerre based algorithm


23/28

23

Regions for speed processMemory 19%

PLC coding for Laguerre MPQP


24/28

24

Laboratorysimulations of

Laguerre MPQP


25/28

25PLC coding for suboptimalparametric algorithm

Speed process

Memory 19%


26/28

26

Simulationresults forsuboptimalalgorithm


27/28

27

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.


28/28

28

Thank you

mon 17.30 predictive control down at plc level rossiter

Documents