Controller System to Aid Diagnostics

John A. Bernard Nuclear Reactor Laboratory

Massachusetts Institute of Technology

Note: Several figures in these notes have been removed for copyright reasons.

Readers are referred to the following U.S. Patents by Dr. J. A. Bernard for more information:

1) Apparatus and Method for Closed-Loop Control of Reactor Power: Standard Dynamic Period Equation (No. 4,637,911)

2) Apparatus and Method for Closed-Loop Control of Reactor Power: Alternate Dynamic Period Equation (No. 4,710,341)

3) Apparatus and Method for Closed-Loop Control of Reactor Power in Minimum Time (No. 4,781,881)

Backeroun d

• Project began in late 1970s. Principal areas of research include:

Modeling of system components.

Signal validation with analytic redundancy.

Fault-tolerant operation.

Reactivity constraint approach.

Closed-loop digital conkol experiments.

Rule-based conkol. Period-generator control. Use of predictive displays. Expert systems.

Real-time PWR model ( space-time ) .

Steam generator level control.

Multi-modular control. Spacecraft reactor conkol.

— Develop leoretical basis for generic melodologies for the closed-loop digital control of nuclear reactors:

a ) Neu8onic power

b ) CoretemperaNre

c ) Steam generator level

— Demonstrate these methodologies under conditions of closed-loop digital control on several research/test reactors:

a ) 5 MWt MIT Research Reactor

b ) SNL's Annular Core Research Reactor

— Conool techniques are to be based on rigorous models of reactor dynamics.

a ) For research and test reactors, this has meant deriving non-linear space-independent models, the dynamic period equations.

b ) For large PWR cores, this has meant developing numerical codes that describe spatial and temporal behavior both accurately and in real time.

Anticipate d Benefits

— Larg e PW R Cores :

— Improved reliability.

— Maintain competitiveness with non-U.S. vendors.

— Alter man-machine interface so that reactor operation is monitored by both man and digital surveillance system.

— Reduce incidence of challenges to safety system.

— Researc h an d Tes t Reactors

— Generate experimental evidence of the validity of the

con7ol concepts.

— Provide a generic melod for the closed-loop, digital control of these reactors.

— Soac e Reactors

— Provide the enabling technology for space nuclear propulsion.

— Multi-Modula r Reactors

— Allow operation with unbalanced loads so as to avoid

need for simultaneous refueling of all modules

— Contain costs by limiting number of operating crews.

Maio r Accomnlishments

1970s Real-time model of reactor components. 1981 Signal validation and instrument fault

detection.

1983 Reactivity constraint approach.

1985 Rule-based control.

Rigorous derivation of dynamic period equation.

NRC license approval of reactivity consaaint approach.

1986 MIT-SNL minimum time laws.

On-line reconfiguration of control laws.

1987 Achievement of time-optimal control of neutronic power.

Demonstration of MIT theories on SNL's Annular Core Research Reactor.

1988 Development of near real-time codes for the determination of neuoonic and thermal- hydraulic behavior in cores characterized by spatial dynamics.

Maior Accom lishments

Cont.

1988 Derivation of conditions for global stability and stability against oscillations about a specified trajectory.

The incorporation and extensive ev%uation of proportional-integral-derivative feedback in the MIT-SNL period-generated minimum time control laws.

1989 Preliminary efforts for the control of system temperature.

Design of a controller for power and temperature in cores characterized by spatial dynamics.

Incorporation of a fixed source term in the nodal code QUANDRY to permit the study of source effects on reactor power increases from subcritical.

1990 A comparative assessment of the merits of spatial versus point kinetics as a means of properly describing a reactor's dynamics during startup.

1992 Experimental sNdies to illustrate need for conkoller self-diagnostics.

Renorts

Dieita l Contro l o f Nuclea r Powe r Reactors, ( Jan.

Fault-Tolerant S stems A roach Toward Closed-Loo

1988/NSF )

• Reactivity Constraint Approach

2. Formulatio n an d Experimenta l Evaluatio n o f Closed-Form Contro l Law s fo r th e Rapi d Maneuverin g o f Reactor Neuooni c Power, ( June 1989/SNL-DOE ) .

• Development of MIT-SNL Control Laws

Startu

Inde enden t Kinetics, ( April 1990/SNL-DOE ) .

and Control of Reactors Characterized b ace-

• Applications of MIT-SNL Control Laws

Reactors Characterized b

Closed-Loo

Dieital Control of Power and Tern erature in

atia l Kinetics, ( Sept.

1990DOE )

• Extension of MIT Control Concepts to PWR Cores

5. Studie s o n th e Closed-Loo o D i ita l Contro l o f Multi- Modula r Reactors, ( Nov. 1992OOE-ORNL ) .

• Control of Multi-Modular Reactor and Steam Generator Level

6. Bernard, J.A. and T. Washio, E ert S ste s ADDlication s Withi n th e Nuclea r Industry, American Nuclear Society, La Grange Park, IL ( Oct. 1989 ) .

Visio n fo r Controlle r Structure

1. Features

• Separation of safety and control systems.

• Multi-tiered structure.

Supervisory loop.

Control law loop.

• Signal validation.

• Use of reconfiguration logic to select con4ol law.

• Automated reasoning to identify reactor state and evaluate controller performance.

2. StaNs

• All components developed and demonstrated experimentally except for the automated reasoning.

Superviso r Contro l of Neutroni c Power

• Reactivit Constr nt A roach Developed in 1983.

Demonstrated on-line under closed-loop control for MIT Research Reactor in 1983.

Demonstrated on-line under closed-loop control for SNL's Annular Core Research Reactor in 1988.

Under patent ( U.S. /Canada ) to MIT.

Figures remove d for copyright reasons.

Effec t o f Reacto r Dynamic s o n Reacto r Control

— Changes in reactor power are determined by the behavior of the prompt and delayed neutron populations.

( a ) Promp t Neutrons :

— Produced directly from fission.

— Generation time is typically 100 microseconds.

— Directly proportional to the fission

rate.

— Subject to immediate control by altering the fission rate.

Effec t o f Reacto r Dynamic s o n Reacto r Control

( continued )

( b ) Delaye d Neutrons :

Produced from daughter nuclides that result from the beta decay of certain fission products.

— Generation time average s 12.2 seconds.

— Not propoaional to the fission rate but rather a function of the power history.

— Not subject to immediate control.

— If power overshoots are to be averted, it is essential to limit the delayed neutron contribution so that, upon attainment of the desired power, the insertion of the control mechanism will make the rate of change of the prompt neutrons sufficiently negative so as to offset the continued increase in the delayed neutrons.

Graph removed for copyright reasons.

Non-Linear Model of Reactor Dvnamics

— Dynamic Period Equation:

• Gives the instantaneous reactor period as a function of the rate of change of reactivity, the reactivity, and the rate of redis7ibution of the delayed neutron precursors.

• Obtained by differentiating ie neutron kinetics equation and then substituting to eliminate terms containing precursor concentrations.

• The in-hour relation is a specialized form of this equation.

— Advantages to its use:

• Rigorous within limits .of space-independent kinetics.

• Describes all reactor behaviors from subcritical to prompt

critical.

• Explicitly .shows each physical process that can affect ie

reactor period.

Dynami c Perio d Equation

1. It is useful to relate reactivity to period. Most text books do this by use of the Inhour Equation which is valid only a long time after reactivity changes. A more general relation, one that is valid under all conditions, is the dynamic period equation. ( This relation was developed at MIT in the mid-1980s and is the basis of MIT's very successful program on digital control of reactors. ) A simplified version is:

j? — p ( t )

;i ( t ) + Y N ( t ) p ( t )

Dvnamic Period E uation

( cont. )

O uantity

d ( t )

Meaning

Rate of change of reactivity. This is proportional to the prompt neuoon population. Changes in the velocity of a conool device therefore have an immediate effect on the period.

Z S ( t ) p ( t )

This term is proportional to the dela y¿ _ ed

neukon

population. Reactivity can not be changed on demand. Rather, a control device's position has to be altered or the Bumable poison concentration has to be adjusted. This takes time.

Dvnamic Period E uation

( cont. )

2. It is important to note that the reactor period depends on both the rate of change of reactivity ( [i ) and the total reactivity ( p ) . The former corresponds to prompt neutron effects; the latter to delayed ones. Hence:

( i ) The speed at which one changes reactivity alters the period. This is the basis of power cutbacks that involve high speed rod insertions.

( ii ) The reactor period is a function of the power history because the decay term rejects the power level that existed when the delayed neutron precursors were created. This is one reason why it is important to approach a final power level slowly.

( iii ) The relation between period and reactivity is not readily solved. Hence, operators may find predictive displays to be of use.

namic Period E uation

( cont. )

*• ( t )

N

(

* ( t )

( p—p ( t ) ) + ñz ( t )

+ m ( t ) + I

( t ) — e ( t )

( ) + ‘e ( ) ( t ) + e 1s ( • —p ( t ) )

where the standard, effective, multi-group decay parameter is defined as:

‘e ( t ) ‘i i’ H i ( t ) for i = 1, N

and where symbols not previously defined are:

tñ ( t ) is the rate of change of the inverse of the dynamic reactor period, m ( t ) is the inverse of the dynamic reactor period,

¥ e ( t ) is the rate of change of the standard, effective, multi-group decay parameter,

C i ( t ) is the concentration of the iJJ; precursor group normalized to the initial power,

and

N is the number of groups of delayed neutrons, including photo-neu4ons.

Superviso r Control

— Traditional function of a control algorithm is to specify plant trajectory and, if the actual state differs from the desired one, generate a feedback signal to reduce the error.

— For safety-constrained systems, the control algorithm should also both define the envelope of conditions under which it will be possible to halt the transient and preclude operation beyond that envelope.

— Supervisory control is especially important for non-linear or time-delayed systems.

Feasibilit v o f ConPol

• A system is conrollable if it is possible to transfer "any initial state to any final state in a finite time by some conEol sequence”. This propeHy places no restricti o ns on the aajectory taken between the initial and final states.

• A reactor is 'feasible to control' is it can be transferred from some initial power level and rate of change of power ( i.e., period ) to a desired steady-state power level without overshoot. This concept limits the allowable trajectories.

— Excludes oajectories involving acNal overshoots.

— Excludes states from which overshoots could not be averted by mani.pulation of the specified control mechanism.

• 'Conaollability-' concerns only the capability to change from one state to another. 'Feasibility of control' is more restrictive because it also concerns the capability to remain in the final state. That is, can the Sansient be halted?

Graphs removed for copyright reasons.

Constrain t Approach

- Implementation of supervisory control is achieved by utilizing constraints that take the form of inequalities:

• The time required to establish conditions under which the force driving the transient can be negated must be less than the time remaining to attain the limiting condition.

No use is made of predictive models.

The intent is to allow a real-time decision to be made as to the need to alter the present control signal in order to avoid a future challenge to a limiting condition.

Controlle r Des£gn

If power is to'be leveled smoothly, must limit the delayed neutron contribution so that, upon attainment of the desired power, the insertion of the control mechanism will make the rate of change of the prompt neutrons sufficiently negative so as to offset the continued rise in the delayed neutrons.

[ h ) s ( t ) + e

where

1s the maximum available rate of

reactivity change.

Note that J c J 1s always a pos i tive number

regardless of whe ther or not the contro 1

mechanl sm 1s aovlng.

Conraint A roach

lied to Nuclear Reactors

Constraints have been developed for reactors subject to limitations on:

• Neuronic power

• Energy production

• Temperature

If power is to be leveled smoothly, must limit the delayed neutron contribution so that, upon attainment of the desired power, the insertion of Ie consol mechanism will make the rate of change of the prompt neurons sufficiently negative so as to offset the continued rise in the delayed neutrons.

IP ( ) - Pc / e ( ) I / Pc ñ < I ) ( F A ( t ) )

where J p e l is the maximum available rate of reactivity

change.

Model-Base d Contro l Laws

1. Investigated a number of techniques for the control of reactor power.

• Proportional control ( no model ) .

• Feed forward control.

• State-space methods ( linear ) .

• Time-optimal.

2. Method of choice is "period-generated" control which is analogous to the "computed-torque" method in robotics.

Backeroun d

1. Period-generated control was developed for purpose of adjusting nuclear reactor power in a very rapid yet safe manner.

2. Intended application is control of spacecraft reactors that will be used for manned expeditions to Mars.

3. Principal result of research is the MIT-SNL Period- Generated Minimum Time Control Laws which have been shown through experiment to be capable of safely raising reactor power by five-seven orders of magnitude in a few seconds.

P e zi›i d-Generate d Conaol

— Method for tracking trajectories that are defined in terms of a demanded rate.

— Control signal is computed by first using feedback to generate a demanded inverse period ( a velocity ) and then substiNting that inverse period into a system model.

— Use of feedback compensates for penurbations and modeling errors.

- Use of model compensates for non-linear dynamics.

— Characteristic feaNre is rapid change of conkol signal upon oansient initiation and termination.

- Advantages are that ie technique is:

— Readfiy implemented.

— Applicable to non-linear systems.

— Capable of near time-optimal response.

Figures remove d for copyright reasons.

Basi s o f Period-Generate d Conkol

— Define error signal by comparison of demanded and observed oajectories.

Compute demanded inverse period in terms of the error signal.

— Process the error signd through an inverse model of the system dynamics to obtain conool signal.

— Apply conool signal to actud system.

e ( t ) = ln[nq ( t < jAt ) / ( n ( t ) ]

m d ( t ) = te ( t ) + ( UT I ) J e ( t ) dt + Tdé ( t ) ]/jAt

ñ, ( t ) = R ( t ) m d ( t ) — ? ( t ) + [m d ( t ) — m ( t ) ]/kAt

• ( t ) = ( R ( t ) ) 'ia. ( t ) +r ( t ) -ñ ( t ) l

MIT-S W Period-Generate d Mlnlmu m Tim e Contro l Law s

S t andard :

e

‹/• ( t ) + y° ( ( ( t ) ) 2 + ip ( t ) o ( t ) - ( ip ( t ) / i p ( t ) ) w ( t ) )

Alternate :

S ” u • i ( t ) + S *

( ( * ( t ) ) 2

z i .- x e (

+ ¥ ' ( t ) o ( t ) )

e

Graph removed for copyright reasons.

Real-Time Calculation Of Dela ed Neuaon Precurso r Concenaations

— Calculation of precursor concentrations requires simultaneous solution of the neuaon and precursor kinetics equations. This is difficult because of the exoeme stiffness of the frst of lese equations.

— Solution is to decouple the neutron and precursor kinetics equations by assuming a particular shape for the neutronic response during each sampling interval. Precursor equations, which aren't in themselves stiff, are then solved using time steps on ie order of the sampling interval ( 0.05 s - 1.0 s ) .

— Studies were made of the method's accuracy using linear, polynomial, and exponential shapes. Linear was chosen because it is simplest to program and quite accurate.

— Technique is refered to as 'Time Integration Method wit An Assumed Power Prof3e.'

Accurate Trackin of Non -Line n S stems

— The feedback signd is computed from a comparison of the demanded and observed values of'the system ouQut. This signal is then input to an inverse dynamics model of the process that is being conoolled. The solution is a form of feedforward control in the sense that the ouQut of the inverse dynamics calculadon is Ie actuator signal which, upon application to the actual process, will cause the system ouQut to oack the demanded oajectory.

e ( t ) = ln[n d ( t + jAt ) / ( n ( t ) ]

m d ( t ) - [e ( t ) + ( 1/T I ) J e ( t ) dt + T d é ( t ) ]/jAt

;i, ( t ) = R ( t ) m d ( t ) — é ( tj + [m d ( t ) — m ( t ) ]/kAt

m ( t ) = ( ;; ( t ) ) * f1i« ( t ) + r ( t ) 'i› ( t ) ]

— The combination of Ie inverse dynamics calculation and the feedforward action results in a canceling of Ie system dynamics:

m ( t ) = <d ( ) + ( R ( t ) ) ' Imd ( t ) m ( t ) ]/kAt — ñ ( t ) J

= m d ( t ) once acceleration effecu die out.

Ne u T ime - O o tima l Behavior

— Most techniques for achieving time-optimal control are computation-intensive. Even with modern computers, a time-optimal trajectory must often be computed off-line and applied in an open-loop manner. No use of feedback is possible.

— Period-generated conool combines feedback with a system model to generate the control signal that couesponds to movement along a given path. If a system is limited by a certain rate, len selection of the path that corresponds to that rate will result in a response that is very close to time- optimal.

— Period-generated conool therefore offers near time-optimal peNormance wit Ie couective action of feedback.

Rule-Base d Control

1. Study of rule-based control is useful in order to appreciate human capability to do diagnostics.

2. Study was done at MIT in 1984-1985 to answer certain questions.

• Should rule-based systems be used for process

conool?

• Can rule-based and analytic approaches be merged?

• Can diagnostic expert systems be developed for

conoollers?

Human A

roach to Process Control

1. P1an 2 _ gnin

• Goal formulation.

• Evaluate options.

• Determine desired response.

2. Prediction

• Form expectation of plant response based on mental models, knowledge of trends, equipment staNs.

3. Implementation

• Initiation of the conool action ( often automated ) .

4. Assessment

• Characterized by two feedback loops. Was the control signal implemented?

Was the control signal properly formulated?

• The operator must decide if his or her mental model is valid.

• Must compare current observation with pre ious1y- made predictions. Was the model in error or has the plnt changed?

Figure removed for copyright reasons.

Desig n o f Rule-Base d Controlle r

1. Identified the rules that operators use by use of questionnaires and observation.

2. Translated these rules into mathematical statements via fuzzy logic.

3. Assembled a set of 21 rules and used that set as a closed- loop controller on the MIT Research Reactor in 1985.

"Fuzzy " Loeic

1. Humans express themselves in linguistic terms. For example, the reactor period is "too short."

2. Fuzzy logic is a means of describing and combining these linguistic terms in a manner suitable to a digital system.

Example:

• An observed reactor period might be described with the labels "too short," "short," or "negative." Transitions between labels are not abrupt and a given reading might belong to several groups. Thus, a positive period of 90 seconds might be "too short" to degree 0.2, "short" to degree 1.0 and "negative" to degree 0.0.

• The parameter being classified ( the period ) is a "universe of discourse."

• Individual labels ( "too short" ) are "subsets" of that universe.

• The degree to which a measured value belongs to a subset is its "grade of membership."

Figures remove d for copyright reasons.

Assessmen t o f Rule-Base d Controllers

1. Rule-based controller achieved control over a wide range

of initial conditions, including non-equilibrium ones.

2. Rule-based and analytic approaches were of comparable accuracy, with analytic one slightly better.

3. Response time of analytic system superior.

4. Rule-based system insensitive to high frequency noise.

5. Rule-based system very difficult to maintain.

6. Rule-based system more tolerant of sensor failures.

Possibl e Rol e o f Rule-Base d S v stems

1. Rule-based systems are robust. Use to return plants to a safe condition on failure of analytic controls.

2. Provide "reasoning" behind decisions of analytic controllers to human operators.

3. Further research is necessary to develop efficient methods for the calibration of rule-based systems. In particular, uniform methods for defining the functions that describe the linguistic variables are needed.

Proeres s Toward s Automate d Diaenostics

1. Method being explored emulates the human approach to diagnostics.

• Did system respond as expected? This requires availability of predictive model.

• If not, what are the symptoms of the problem?

• Once a symptom is identified, what are the possible causative agents?

2. One of the last publications from the MIT-SNL Program reprinted a series of experiments that illustrated the need for automated diagnostics:

• Bernard, J.A. and F. J. Wyant, "Experiments Illustrating the Importance of Automated Reasoning," IEEE Control System Magazine, Vol. 12, No. 2, April 1992, pp 84-92.

Surve'

1 92

erimen

1. Norma l Response: Power increase 3.0 kW - 12 MW on a demanded period of 0.60 s. Spectacular Result.

2. Effec t oJ_3nitia l ro d bagk . he i h t a n abilit Yv o co_; g let e a. transient: If the available rate of reactivity change is insufficient, the conooller fails. ( Too slow and achieved wrong

.power level ) .

Effect o f incor rect reactiv it estimat results.

3. Degraded peJormance

4. Effec t ofLaile d sensor : Conooller functions adequately because of signal validation.

Figures remove d for copyright reasons.

Automate d Diagnostics

1. Each of the three experiments shown couesponds to a problem with a different parameter.

• Rate of change of reactivity

• Reactivity

• Power Level

2. This suggests an approach to automated diagnostics. .Express the system in state-space and try to identify each aberrant behavior as initiating from a particular state v axiable.

• Assumes all state variables are measurable.

• Assumes each is identifiable. This may not be achievable given signal noise.

• Requires linearized system.

Diaenostics

1. The diagnostic analysis would be done using a multi-layere d approach.

• Evaluation of system response.

• Symptom identification.

• Fault identification.

2. System response is judged by means of comparing desired and actual response.

3. System identification may perhaps be done using the state-space representation.

4. Fault identification may be done using expert system approach subject to assumption that all causes for a symptom deviation are pre-identified and instrumented so as to be detectable.

Inpac t o f Automate d Diaenostics

1. Two experiments are shown:

• For first one, an error in a safety command caused a premature halt of the control device, and the run failed.

• For the second, the run was completed successfully despite a dropped rod.

2. This raises another major unresolved issue. To what extent should an automated diagnostic system be allowed to implement corrective action when safety is involved?

Figures remove d for copyright reasons.