The concept of Life Extending Control (LEC) is introduced. Possible extensions to the cyclic damage prediction approach are presented based on the identification of a model from elementary forms. Several candidate elementary forms are presented. These extensions will result in a continuous or differential form of the damage prediction model. Two possible approaches to the LEC based on the existing cyclic damage prediction method, the measured variables LEC and the estimated variables LEC, are defined. Here, damage estimates or measurements would be used directly in the LEC. A simple hydraulic actuator driven position control system example is used to illustrate the main ideas behind LEC. Results from a simple hydraulic actuator example demonstrate that overall system performance (dynamic plus life) can be maximized by accounting for component damage in the control design

Lorenzo, Carl F.

Merrill, Walter C.

English

NASA Technical Reports Server

N93-31581
LIFE EXTENDING CONTROL-
AN INTERDISCIPLINARY ENGINEERING THRUST
Carl F. Lorenzo and Walter C. Merrill
NASA Lewis Research Center
Cleveland, Ohio 44135 /"
Systems with high performance requirements often have a small number of critical
components that operate close to mechanical design margins and that define the
effective lifetime of the system. The concept of life extending controll_LEC)
proposes an active approach to simultaneously managing the damage accumulation
of these components while maintaining dynamic performance %o increue system
effectiveness.
The concept depends on the prediction of fatigue life of the critical compo-
nents. Currently, fatigue life prediction is based on local cyclic strain
behavior such as:
a, = )t Dj) ÷e, (,)
Where Vi is the damage due %o cycle i, and o_, E, b, e, and c are material
constants and #=v is an average tensile strength. Using the Palmgren-Minor
approach the tota_ damage is estimated as
The life usage predicted by this equation is directly related to strain magni-
tude (figure 1). Other more accurate and complex approaches are also possible.
With these approaches, damage can only be estimated upon the completion of a
stress-strain cycle. With current cyclic forms of damage modelling only
indirect or implicit forms of LEC are possible.
IHPLICI2 LEC
The implicit approach to Life Extending Control recognizes that current frac-
ture/fatigue science can not predict the differential damage on less than a full
cycle of strain. The implicit approach (see fiL_tre 2) selects a sequence of
typical command transients (and disturbances) that are representative of those
the system would experience in service. Two performance measures are defined:
Jp, an objective function that maximizes dynamic performance (possibly by
mznimizing quadratic state and control excursions) and Jn a damage measure.which
uses the best (current) fatigue/fracture theory available to calculate the
damage accumulated over the sequence of command transients. An overall perfor-
mance measure is defined where a represents the relative importance between
J = Jp + aJa (S)
performance and life extension. The implicit approach then selects a 'best'
control algorithm which is applied for the full sequence of command transients.
229
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The dynamic perfonBnce and damage accumul_ion over the sequence axe optimised
(relative to the selected measures) s_ainst the control algorithm parameters.
The expectation is to find an algorithm such that the loss in dynamic perfor-
mance is. small. (i.e. J_v s min - Jp,o,m_ in figure S), for a significant
reduction in accumulate_ _amage over _ne sequence of transients (i.e.,
JV,o,mSn - JD,m,mi- iS large and llfe is extended). Rere the subscript o refers
to optimizing _or _ynamic performance only. An actual operating gain set (point
q in figure 3) is then chosen which satisfies the desired weighting between
performance and damage (i.e. J). During the design process, two types of
feedback variables are considered: 1) the performance variables normally used
to manage dynamic performance and 2) nonlinear functions of the performance
variable representative of the damage variables (stresses, strains, temperature
and various rates). Various control algorithsm are then examined within this
feedback structure. That is, the sequence of selected performance and distur-
bance transients are applied to a simulated system with a trial control and
performance J (or J, and JD separately) is calculated. Superior LEC algorithms
can then be identified as those that minimise J (or Jp and JD separately).
Algorithms for Implicit LEC may be formulated intuitively, i.e., minimising the
mean tensile stress, mean strain, and temperature levels and minimising the-.
cyclic amplitude of stress, strain, and temperature should minimise damage.
Also, minimising the number of cycles of stress and strain should contribute to
extending critical component life.
LIFE _C,F,_F,I_ LEO
A second indirect approach is called Life Management LEC and is shown in
figure 4. Here the LEC would have a hierarchical structure similar to that
found in other proposed intelligent control systems (ICS). At the coordination
level, the task planner uses performance requirements and balances these against
life usage and appropriate control commands or strategies are selected. This is
accomplished by simulation of the system for a few pre-selected trajectories.
From the results of this simulation and for a given performance definition, a
commanded trajectory is selected that optimises system performance and minimises
component damage over a sub-interval of the task. Within the task planner,
information from a cyclic damage prediction model ranks various candidate
trajectories of the successive interval in the planning and selection process.
Outside of the task planner another cyclic prediction model assesses the actual
damage accumulated during a sub-interval. The execution level implements the
selected strategy in the interval by translating the commanded trajectory into
control co,ands and applylng these co,ands to the system.
CONTIIV_OUS LIFE PI_F,DICTION APPROACH
The Implicit LEC approaches taken above do not directly control the damage rates
of critical components. Direct control will require continuous forms of the
damage laws instead of the current cyclic forms.
To achieve a continuous formulation of the life prediction process, an interdis-
ciplinary approach is required. Here the knowledge of material properties and
life prediction of fracture and fatigue scientists must be combined with the
control engineers' knowledge of dynamics and modeling to develop these continu-
ous forms. The objective is to functionally relate measurable performance
information with a differential form of the damage laws. This would allow the
direct use of the differential estimate of damage in the life extending control
230
law and, when integrated over complete cycles, would give equivalent or superior
damage predictions to those associated with the cyclic theory. Two approaches
are possible here: 1) derive such forms from basic theory (the current research
thrust of the field) or 2) empirically select likely fores with a significant
number of unspecified parameters and use optimisation theory to best nfitw the
parameters using available data sets. Adopting the second approach, several
elementary forms, given in T&ble I, are proposed. These forms are determined
either by intuition or by observing the important relationships embodied in the
current theory of life prediction. Various weighted, linear and nonlinear
combinations of these elementary forms would be linearly regressed against the
available fatigue life data to obtain a continuous formulation.
JtE,,LSUPkEDXg4GE VABZABL_ LEC
In this approach (figure 5) both the plant performance and the damage related
variables (measured stresses, strains, temperatures, forces, etc.) associated
with critical components are measured and used as feedback information for the
control. Here the control attempts to directly regulate life as a resource. It
is presumed that a Wreal-timeW predictive damage model (described above) exists
that would allow the prediction of the incremental damage as a continuous
function of selected incremental control action. That is, the influence of
changes in the performance variables (presumed to be controllable) on the
behavior of the critical .life variable is known. This is in the form of the
local damage rates DV1, DVs... in figure 5. Thus, in filure 6, at a time A, the
damage associated with damage variable DV1 can be predicted for any incremental
u are considered and result in damages D1,control action (here actions Ul, us, # . . ._
Ds, Ds respectively). (Note damage while shown as a continuous function of time
will likely be modelled as a continuous function of local stresses, strains,
etc.). The control problem then is to minimise damage of the critical life
components while maximising (dynamic) performance of the plant. The performance
objective approach of equation (2) can be used to achieve this optimisation.
One implementation of a measured damage variables LEC would achieve control
performance by adaptively modifying the control feedback structure to permit
damage to accumulate at a "setpointn rate, a linear rate over time for example.
The measured damage variables could be used directly in a feedback law or to
modify the gains or even the structure of the existing control. The emphasis
here is on obtaining desired system operation by an active, feedback control
approach.
ESTIE4TED D,IE4GE VARI4BLES LEC
Unlike the Measured Damage Variables LEC approach, this concept, shown in
figure 7 uses a real time model to estimate the damage rates (and damage accumu-
lation) of critical components. The models can be driven by performance
variables or performance variables augmented by available damage measures.
Conceptually the models can vary from simple, precomputed, linear, influence
coefficients to detailed, non-linear, real time structural models which may
require considerable computation. These models would be a direct consequence of
the continuous life model described above and would result in a damage estimator
that estimates real time damage rates. The controller design would follow in
much the same manner as for the measured damage variables approach.
231
_JJ_l,g SYST_I
The example system of fiKure 8 is used to i11umtrate LBC. In filpn'e 9 pulse
sequence trajectory number 1 w_s applied to the system. Also shown in figure g
are the system position and scaled force trajectory resulting from pulse
trajectory 1. The performance endpoints were selected na XI=-Y_=I. In this
cnse, N=ll and T--4.g sec. and D--0.0213 units of damage bued upon a total
component life of 1 unit were predicted.
A modified conuanded pulse sequence trajectory, called trajectory number 2, was
applied to the same system. The commanded trajectory, the system position, and
the scaled force for case 2 is shown in figure 10. In case 2, N=g and T=4.6
sec. and D--O.OI21. Because the connanded pulse trajectory hu been slowed
slightly, the resultant force trajectory hsJ smaller peak mngnitudes. Conse-
quently, the stress-strain cycles have smaller magnitudes and the damage will be
less. The example results are summarised in Tmble TT.
CONCLUSIONS
The concept of Life Extending Control was introduced. Possible extensions to
the cyclic damage prediction approach were presented based on the identification
of s model from elementary forms. Several candidate elementary forns were
presented. These extensions would result in a continuous or differential gore
of the damage prediction model.
Two possible approaches to Life Extending Control based on the existing cyclic
damage prediction method, called implicit LEC and life management LEC approach
were proposed. Two possible approaches to Life Extending Control based on the
proposed continuous damage prediction method, called measured variables LEC and
estimated variables LEC approach were defined. Here damage measurements or
estimates would be used directly in the LEC. A simple hydraulic actuator
driven, position control system example is used to illustrate the main ideas
behind Life Extending Control. Results from a simple hydraulic actuator example
demonstrate that overall system performance, that is, dynamic plus life, can be
maximized by accounting for critical component damage in the control design.
. Carl F. Lorenzo and Walter C. Merrill: Life Extending Control - A Concept
Paper, to be published American Control Conference, June 26-28, 1991,
Boston, i_.
232
Sir(fin Mc_gnitude
0.05
0.03
0.02
O.Ot
0.005
0.003
0.002
0.001
1L - 07
I M1S MTS MTS I
O 501001/.
................... .,,/
/,'.,"
i1_/ "
I I Ill 'Hi ........ l , , , ,,,,,t ..... I,*l ........ I ........
IL-Ob 1L-05 0.0001 OiY-.) 1 U.01 0.1
Life Usage
F_ure 1. Life usage versus component strain
parBeterized by mean tensile stress.
TYPICAL
COMMAND _ I
TRANSIENT --_']
SEQUENCE_
DAMAGE
RELATED
VARLABLE (,
_ TYPICAL DISTURBANCE SEQUENCE
CONTROL U Ii
PLANT
PERFORMANCE VARL_BLES
Y
I NONLINEAR CALC
OF STRESS, STRAIN,
TEMPERATURES, ETC.
DAMAGE THEORY OFFLINE CALC
BASED OFFLINE
OF JpCALC OF JD
L-IO OUL T'I
J - Jp + oJ D
Figure 2. Implicit life extending control approach
233
Jp JD OPTIMIZING Jp ONLY
i
ALGORITHM
_=q'IMIZING Jp ONLY Y Z
Z
....ALGORITHMGAIN SPACE
FiKure 3. Effect of various life extending
control algorit_s on performance (Jp) Lnd
d_age (JD)"
COMMANDED
TRAJECTORY
t TRIAL TASK
t TRIAL TRAJECTORY
t SIMULATEDOUTPUT
REQUIRED TASK
PERFORMANCE
REQUIREMENTS
PERFORMANCE
v ;
Ilii_
ACCUMULATED "" '-_
DAMAGE
_,.,r,,,._ I OAMACE I I CALCULATIONI
1 CALCULAT'ONi L J _ _1
..........................................................
Figure 4. Life management life extending control approach.
234
LOCAL
Ir_TIS$ ,
Ovl,Ov2,..Ovn
fmES$,
IqERFOm_NCEV_IRi
Figure 5 Measured damage variables life
extending control approach.
DA_(_(o)FOR
DAMAGE VARIABLE I(DrI)
4; ul
! /i
U3
'n_[
FiEure 6. Incremental damage
relationship
_DI
D2
D3
PERF (3RI_J,NC E VARIABLES
S_TqE55E$ DYNAMIC
1 EST Ikt*'TOR .5,T.., N S MODEL ,_
TEMPE;
[ra/,Ti
Figure ? Estimated Damage Variables Life
Extending Control Approach. 235
FORCE
I I i 'I
X I 0 X2 I
IX
N=# of Limes X=XI or X2
1=lime to ochieve N I
Domage(Nod) = t(I-ORCE) = f(N,T) !
I
Figure 8 A hydraulic _ctuator
position system.
-lt
1
|nllllo I It t P I IlClllenC CIIIll nd J.
• ...,.,.,,UIIOT ....
Cllll Ill I_1 Forcl I
_--_,t.......:-i---_ .......,.-_--_-..... {-_--"_........!_.-"_ .......:..................
:. I _ t ', _ r i 0 I : ' I _ :
XI "1!1'I:(1' I XI"IXI' 1I . t t , t ,": ; " I ; I :,: _. I, ,.. ,..
! !. .'l, ! i "_,
_: I: tt : l:
I I I I i
-2 0 1 2 3 4 5 8
Time, sec.
Figure 9 Example results for Case 1
tra ectory command.
EltapO II_t PI lICMMmt Cmlmi_nll
2L _..I ,..., L. " I "-'-':"'
L',
_._ ..........i_..._ .........._., ...........i-_,-_ .........._....................
0 _- .... ,i...... _-i ...... _:, .,_ .--...... _.t........................|
._ ""..I:',It I _, I;"
: :1 I : :t I _ :_ I : :_ ,
.......i-.-.-v-'...........i#-.w-.....
!:j _ /
Min_" cycle c 1
-1
-2
..LL.._. ........... _-...I_. ......................
I I I I
0 1 2 3 4 5
Time. sec.
Figure I0 Example results for Case 2
trajectory command. 236
I.ea_ stress L..v.11 - I_f:oCt)dCl
I_olio s_o,-I- f:,o' - '_fo'ott'de3')d_
I o rl; I'rl; Io,TI,
etc.
Table I. Elementary damage prediction _orms
Table II EXAMPLE LIFE EXTENDING CONTROL RESULTS
CASE N T, sec N/T FMAX CYCLES D T r
l II 4.9 2.2448 1.6 5 MAJOR 0.0213 230
2 9 4.6 1.9565 1.4 4 MAJOR 0.0121 380
8 MINOR
N_
516
743
PERFORMANCE
8O2
1106
237



Life extending control: An interdisciplinary engineering thrust

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