Described here are Boeing software tools used for the development of control laws of flexible structures. The Boeing Company has developed a software tool called Modern Control Software Package (MPAC). MPAC provides the environment necessary for linear model development, analysis, and controller design for large models of flexible structures. There are two features of MPAC which are particularly appropriate for use with large models: (1) numerical accuracy and (2) label-driven nature. With the first feature MPAC uses double precision arithmetic for all numerical operations and relies on EISPAC and LINPACK for the numerical foundation. With the second feature, all MPAC model inputs, outputs, and states are referenced by user-defined labels. This feature allows model modification while maintaining the same state, input, and output names. In addition, there is no need for the user to keep track of a model variable's matrix row and colunm locations. There is a wide range of model manipulation, analysis, and design features within the numerically robust and flexible environment provided by MPAC. Models can be built or modified using either state space or transfer function representations. Existing models can be combined via parallel, series, and feedback connections; and loops of a closed-loop model may be broken for analysis

Anissipour, Amir A.

Benson, Russell A.

Coleman, Edward E.

English

NASA Technical Reports Server

N90-10090
b .
MODELING AND CONTROL SYSTEM DESIGN AND ANALYSIS TOOLS FOR FLEXIBLE
STRUCTURES
Amlr A. Anlsslpour
Russell A. Benson
Edward E. Coleman
The Boeing Company
Seattle, Washington
ABSTRACT
Design and analysis of control-systems for flexible structures require accurate mfith---'_
models of flexible structures _md software design with the analysis tools capable of
t!andling these models while makr_talnlng numerical accuracy. Since aeroelastlc models
• 'e' of flexible structures tend to be lat=ge [e.g., 100 states), the availability of tools to handle
st_ch large models is cruciall Initial model development is based on aerodynamlc
mathematical models, ' wind tunnel data, mathematical structural models, and ground
:. _ '; shalte test .results. E_entually, flight test data are used to update and refine the rnodell ......
t --._.__ q._l_oape$describe s Boeing software tools used for the development of control laws of
flexible structures.
The Boeing Company has developed a software tool called Modem Control Software
Package (MPAC). MPAC provides the environment necessary for linear model
development, analysls, and controller design for large models of flexible structures. There
are two features of MPAC which are particularly appropriate for use with large models: (I)
numerical accuracy and (2) label-drlven nature. With the first feature MPAC uses double
precision arithmetic for all numerical operations and relies on EISPAC and LINPACK for
the numerical foundation. With the second feature, all MPAC model inputs, outputs, and
slates are referenced by user-deflned labels. This feature allows model modification while
nmlntainlng the same state, input, and output names. In addition, there Is no need for the
user to keep track of a model variable's matrix row and column locations.
There is a wide range of model manipulation, analysis, and design features within the
numerlcalIy robust and flexible environment provided by MPAC. Models can be built or
modified using either state space or transfer function representations. Existing models
can be combined via parallel, series, and feedback connections; and loops of a closed-loop
model may be broken for analysis. Analysis tools available include:
eigenvalue/eigenvector, controllability matrix, observabillty matrix, transfer function
generation, frequency response and singular value plots, covariance response to white
noise or atmospheric turbulence models, model simulation using step, sinusoidal,
random, or user-defined inputs. Control system deslgn tools include: root locus, LQG full
state feedback gain matrix computation, LQG full-order estimator design, and robust low
order controller (SANDY] design as developed by Dr. Uy-Lol Ly at Stanford.
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https://ntrs.nasa.gov/search.jsp?R=19900000774 2020-03-20T00:28:30+00:00Z
The existing Boeing Company structural analysis and design software package. ATLAS.
has been extended in order to form a state-space model for input to MPAC. The new
capability, a module named DYFORM. is an outgrowth of earlier work under a NASA
contract for Integrated Application of Active Controls. The structural and theoretical
aerodynamic mathematical model originates within ATLAS In exactly the same fashion
as for conventional flutter and dynamic loads analyses. The DYFORM module is then used
to construct the state-varlable model as required by MPAC. Its capabilities include (I)
control surfaces and/or gust vector as inputs. {2) sensors and/or loads quantities as
outputs. (3) formulation in body-Paced or inertial axes. (4) modification of the theoretical
aerodynamics using wind tunnel/flight test data from rigid or flexible-model tests, and (5)
use of S-plane rational airloads expressions to formulate the state model including
augmented states to represent unsteady aerodynamic effects.
MPAC has been used for yaw damper design [including active flexible mode suppression) of
the Boeing 767 and 747 airplanes. The flexible structural models of these planes, as large
as 100 states, have been handled by MPAC without loss of numerical accuracy.
The Boeing Company plans for the development of a system identification and parameter
estimation (SIPE] software tool. The system identification algorithms employ a multiple
stepwlse regression technique to determine the structure of the system. The parameter
estimation algorithms update the current model using maximum likelihood estimation.
The SIPE routines will be compatible with MPAC and RF_DATA (a data correction and
reformatting program also developed by Boeing). The SIPE routines will be flexible.
allowing the user to select gradient methods, integration algorithms, and Riccati solution
algorithms. The MPAC compatible model structure slated for the SIPE package will be
applicable to any dynamic system. Aerodynamic, aeroelastlc, ground effects, and sensor
noise modeling will all be possible.
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BOEING COMMERCIAL AIRPLANES
GUIDANCE AND CONTROL RESEARCH
This is an example MPAC command file. The output file generated using this
command file is given on the following pages.
*MPAC READ PLANT
LAT2.MDL
*COMPUTE EIGENVALUES OF PLANT
*DEFINE PLANT
DELETE STATE PSI
CREATE STATE BETA INT.dot:
CREATE OUTPUT PHI--CRIT:
CREATE OUTPUT BETA CRIT:
END
i. BETA
i. PHI.dot
i. BETA.dot
5.0 PHI
3.2 BETA 4. BETA INT
*DESIGN GAIN MATRIX FOR PLANT
.001
2, 2
'AIL'
'RUD'
'PHI CRIT'
'BETA CRIT'
'WLOCUS '
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FIRST CUT LATERAL GAIN LOCUS
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PHI CRIT=4. BETA CRIT=I.
*CREATE CONTROLLER FOR PLANT
'NODIRECT'
*FORM PLANT + CONTROLLER
*PRINT CLOSED-LOOP SYSTEM
*COMPUTE EIGENVALUES OF CLOSED-LOOP SYSTEM
*MPAC WRITE CLOSED-LOOP SYSTEM
CLOSED LOOP.MDL
232
BOEING COMMERCIAL AIRPLANES
GUIDANCE AND CONTROL RESEARCH
MPAC output file example. Output file generated using command file on previous
MPAC RELEASE VERSION 4.00 05 MAY 1987
COMMAND FILE example.cmd
MODEL FILE
INPUT BINARY FILE
OUTPUT BINARY FILE
MPAC OUTPUT FILE example.out
MPAC GGP PLOT FILE example.ggp
MPAC USER DATA FILE NO.I
MPAC USER DATA FILE NO.2
MPAC USER-DEFINED UBIN FILE --
TIME OF MPAC JOB EXECUTION --- Tuesday, July 5, 1988
(CONFIGURATION CONTROL I
3:50:36 pm (PST)
*** MODEL READ FROM FILE: LAT2.MDL ***
* 07/05/88 *
* 15:50:54 *
*************
ELAPSED TIME (SEC) : 0.24
233
BOEING COMMERCIAL AIRPLANES
GUIDANCE AND CONTROL RESEARCH
SAMPLING TIME : DELTA = 0.0000
******** EIGENVALUES OF PLANT ***********************
COUNT REAL PART IMAG PART DAMPING FREQ (RAD/S) FREQ (HZ)
1 0.0000 0.0000 0.0000 0.0000 0.0000
2 -1.2989E-02 0.0000 1.000 1.2989E-02 2.0673E-03
3 -0.1403 1.676 8.3426E-02 1.682 0.2677
4 -0.1403 -1.676 8.3426E-02 1.682 0.2677
5 -1.946 0.0000 1.000 1.946 0.3097
ELAPSED TIME (SEC) : 0.14
DELETED STATE PSI
CREATED STATE BETA INT.:
CREATED OUTPUT PHI _RIT:
CREATED OUTPUT BETA CRIT:
ELAPSED TIME (SEC): 0.i0
1.000
1.000
1.000
BETA
PHI.
BETA.
5.000
3.200
PHI
BETA
BOEING COMMERCIAL AIRPLANES
GUIDANCE AND CONTROL RESEARCH
DESIGN PARAMETERS:
ALPHA = 1.00000E-03
CONTROL VARIABLE CONTROL WEIGHT
AIL 1.0000
RUD 2.0000
(R)
CRITERIA VARIABLE CRITERIA WEIGHT
PHI CRIT 4.0000
BETA CRIT 1.0000
(Q)
== = = === =___===== = ======================== ....
= = STEADY STATE RICCATI SOLUTION .....
1= == == 1=: 1= == I===I= == == ==
1 2 3 4 5
1 15.95 -2.100 -6.876 -5.891 9.802
2 -2.100 1.105 4.050 0.7099 -0.3128
3 -6.876 4.050 15.73 2.397 -2.262
4 -5.891 0.7099 2.397 3.222 -3.365
5 9.802 -0.3128 -2.262 -3.365 14.39
SAMPLING TIME : DELTA = 0.0000
******** EIGENVALUES OF A + B*G
******** OPTIMAL CL EIGENVALUES
COUNT REAL PART IMAG PART DAMPING FREQ (RAD/S) FREQ (HZ)
1 -0.9492 0.0000 1.000 0.9492 0.1511
2 -1.574 1.453 0.7346 2.142 0.3409
3 -1.574 -1.453 0.7346 2.142 0.3409
4 -4.442 2.532 0.8688 5.113 0.8138
5 -4.442 -2.532 0.8688 5.113 0.8138
= FEEDBACK GAIN MATRIX
BETA P PHI R BETA INT
AIL 5.470 -2.605 -9.524 -2.000 1.093
RUD -3.065 -0.5127 -2.059 2.056 -2.722
ELAPSED TIME (SEC) : 1.17
BOEING COMMERCIAL AIRPLANES
GUIDANCE AND CONTROL RESEARCH
***** FULL STATE FEEDBACK CONTROLLER *****
***** NO MODEL FOLLOWING *****
***** DIRECT F.B. STATES TO PLANT *****
BETA P PHI R BETA INT
ELAPSED TIME (SEC) : 0.50
***** FULL STATE FEEDBACK CONTROLLER *****
***** NO MODEL FOLLOWING *****
ELAPSED TIME (SEC) : 2.16
BOEING COMMERCIAL AIRPLANES
GUIDANCE AND CONTROL RESEARCH
SAMPLING TIME : DELTA = 0.0000
BETA P PHI R BETA INT
BETA
P
PHI
R
BETA INT
-0.2401 5.9648E-02 -4.8458E-02 -0.9132
-4.579 -8.932 -25.99 2.8649E-02
0.0000 1.000 0.0000 8.7813E-02
7.526 0,4025 2.215 -3,809
1.000 0.0000 0.0000 0.0000
AIL RUD
BETA 2.5320E-03 4.0504E-02
P 2.284 2.060
PHI 0.0000 0.0000
R 0.1228 -1.645
BETA INT 0.0000 0.0000
===== C .....
BETA
-0.1075
-3.112
0.0000
4,611
0.0000
PHI CRIT 0.0000
BETA CRIT 2.960
AIL+-- 5.470
RUD+ -3.065
AIL= 5.470
RUD= -3.065
P PHI R BETA INT
1.000 5.000 8.7813E-02
5.9648E-02 -4.8458E-02 -0.9132
-2.605 -9.524 -2.000
-0.5127 -2.059 2.056
-2.605 -9.524 -2.000
-0.5127 -2.059 2.056
0.0000
3.892
1,093
-2.722
1.093
-2.722
AIL RUD
PHI CRIT 0.0000 0.0000
BETA CRIT 2.5320E-03 4.0504E-02
AIL+-- 0.0000 0.0000
RUD+ 0.0000 0.0000
AIL= 1.000 0.0000
RUD = 0.0000 1.000
ELAPSED TIME (SEC) : 0.12
BOEING COMMERCIAL AIRPLANES
GUIDANCE AND CONTROL RESEARCH
SAMPLING TIME : DELTA = 0.0000
******** EIGENVALUES OF CLOSED-LOOP SYSTEM **********
COUNT REAL PART IMAG PART DAMPING FREQ (RAD/S) FREQ (HZ)
1 -0.9492 0.0000 1.000 0.9492 0.1511
2 -1.574 1.453 0.7346 2.142 0.3409
3 -1.574 -1.453 0.7346 2.142 0.3409
4 -4.442 2.532 0.8688 5.113 0.8138
5 -4.442 -2.532 0.8688 5.113 0.8138
ELAPSED TIME (SEC) : 0.18
TOTAL JOB ELAPSED TIME (SEC) : 10.24
238
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Modeling and control system design and analysis tools for flexible structures

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