Control performance assessment

in the presence of valve stiction

Wei Yu, David Wilson & Brent YoungIndustrial Information & Control CentreNew Zealand

diwilson@aut.ac.nz

Question for the day? What do you do if your control loop looks like this …?

Re-tune the loop, Service the valve, or just ignore it

Controller plant

-0.5

0

0.5

1

1.5

outp

ut

0 100 200 300 400 500 600 7000

0.2

0.4

0.6

0.8

time

Con

trolle

r Inp

ut

uuv

Characteristic triangular wave

Context & rationale Many control loops are badly tuned

We are lazy Conditions change Valves get sticky

Should I retune or service the valve ? Retuning is easier, service requires a shutdown What is my expected economic return? Calculate a CPA

What is valve stiction ? Vague term meaning valve problems Stiction: sticky/friction Typically valve sticks & jumps

Various levels of stiction

Plant under considerationLinear plant with known delay

With disturbance model

+

plant

disturbance

We want to control this system as best we can

• NL plants in CPI are smooth & benign

• Key NL are in actuators

Control Performance Assessment (CPA) Use a minimum variance controller

as a performance benchmark Estimate from closed-loop data

Must know plant delay

Harris Index

Zero is bad, 1 is probably “too good”, 0.7 is optimal Calculate from disturbance model

Estimate from ARIMA identification

Direct from data

But we need to know the deadtime, b

How do I estimate s2mv with stiction ?

Why bother? Gives an indication on how good the loop would be if the valve

was maintained Is it worth shutting down & servicing the valve?

How to remove the nonlinearities? Existance of the control invariant for NL systems (Harris & Yu) Run a smoothing spline through the data Identify periods when valve is stuck fast

+

Controller

System under consideration(With stiction)

+

plant

Valve stictionNonlinear phenomena

disturbance

measurements

Un-observable

Our scheme

Fit a non-parametric spline curve to yOK for non-differential nonlinearities

Remove nonlinearity with splineAdjust smoothing to “just remove” NLUse linearity check

Compute s2MV from d sequence

Removing the nonlinearity Fit a smooth curve to approximate z Reconstruct d from y-z

Unobservable, but smoothish

Establishing linearity & Gaussianity The power spectrum A(f) and bispectrum B(f1,f2) of this

series are

The squared bicoherence is

+

Controller

+

plantValve stiction

disturbance

measurements

Example: A plant with a sticky valve

Testing the method

Increasing level of smoothness

100 150 200 250 300 350 4000.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Time

Out

put

y=0.1=0.05=0.01

Statistical tests

Monte-Carlo Simulation results

True value

Estimation gets worse

Waiting for steady-state Select periods at steady-state Use only this data for the identification

Areas of long periods

“Islands” of long periods

Increasing noise

We are interested in the long periods when we might reach steady state

Uninteresting areaPeriod < 10

Period = 10 contour

Optimum noise level

Valve too “jumpy”

Too much noise, so valve is

continually “dancing”

Does it work?

True value

Uncertainty bounds

Good estimation due to longer sequences

Bad estimation due to excessive nonlinearities

Conclusions

Estimate the CPA even with stiction nonlinearities Do we need to shut down?

Heuristic curve smoothing is OK Extracting steady-state is better provided:

Sequences are long enough System is stable and relatively short time constants

Need to know: Approximate process deadtime Approximate dominant time constants

Now we know if it is worthwhile to service the valve.