A flexible aircraft or space structure with active control is typically modeled by a large-order state space system of equations in order to accurately represent the rigid and flexible body modes, unsteady aerodynamic forces, actuator dynamics and gust spectra. The control law of this multi-input/multi-output (MIMO) system is expected to satisfy multiple design requirements on the dynamic loads, responses, actuator deflection and rate limitations, as well as maintain certain stability margins, yet should be simple enough to be implemented on an onboard digital microprocessor. A software package for performing an analog or digital control law synthesis for such a system, using optimal control theory and constrained optimization techniques is described

Mukhopadhyay, V.

Noll, Thomas

Pototzky, A.

English

NASA Technical Reports Server

Ng()- 10111 '
CONTROL LAW SYNTHESIS AND OPTIMIZATION SOFTWARE
FOR IARGE ORDER AEROSERVOEIASTIC SYSTEMS
V. Mukhopadhyay, A. Pototzky, and T. Noll
NASA Langley Research Center
Hampton, Virginia
ABSTRACT
Motivation: A flexible aircraft or space structure with active control Is typically modeled
by a large-order state space system of equations in order to accurately represent the rigid
and flexible body modes, unsteady aerodynamic forces, actuator dynamics and gust
spectra. The control law of this multi-input/mulU-output [MIMO) system is expected to
satisfy multiple design requirements on the dynamic loads, responses, actuator deflection
and rate l_ltations, as well as maintain certain stabflRy margins, yet should be simple
enough to be Implemented on an onboard digital microprocessor. This paper describes a
software package for performing an analog or digital control law synthesis for such a
system, using optimal control theory and constrained optimization techniques.
Software Capabilities: The primary soRware capabtlRy is the optlmL_Uon of the system
by changing the control law design variables to Improve stability and performance. A
block diagram of the optimization scheme is shown in Fig. 1.
1) The opUmlzation module minimizes a linear quadratic Gaussian (LOG) type cost
function, while trying to satisfy a set of constraints on the conflicting design
requirements such as design loads, responses and stabflRy margins. Analytical
expressions for the gradients of the cost function and the constraints, with respect to the
control law design variables, are used for computation. This facflRates rapid convergence
of the numerical optimization process. The designer can choose the structure of the
control law and the design variables. This enables optimization of a classical control law
as well as an estimator-based full or reduced order control law. Selected design responses
are incorporated as inequality constraints instead of lumping them into the cost function.
This feature is used to modify a control law to meet individual root-mean-square {RMS}
response limitations and design requirements.
2} In order to Improve the mulUloop system stability robustness properties in the
frequency domain, the minimum singular value of the return difference matrix at the
plant Input and output are as additional inequality constraints.
3) Other supporting capabilities include: {a) singular value analysis evaluation and
plotting at the plant input and output; Co) linear quadratic optImal control law synthesis:
(c] Kalman Filter design. LOG Loop transfer recovery; {d) pole-zero computation; {e)
frequency response. Nyquist and Bode Plot; {l) root locus plot; {g) block diagonallzation; (h)
modal restdualization and truncation; {l) transient response to deterministic and white
noise input; (J) transfer of quadruple data to and from MATRIX-X and DIGIKON: (k)
parameter search to stabilize an unstable control law. and (1) both interactive and batch
mode execution using the Cyber NOS system.
https://ntrs.nasa.gov/search.jsp?R=19900000795 2020-03-20T00:27:44+00:00Z
AppllcaUmm:Thesoftwarehasbeenusedin the past for the followingapplications: (1)
flutter suppressioncontrollaw for theARW-Iwind tunnelwingmodel; (2}gust load
alleviationcontrol law for the ARW-U drone; (3) flutter suppression control law synthesis
for ARW-II drone and the DC-10 Derivative wlnd tunnel wing model: (4) robust Digltal gust
load alleviation control law synthesis for ARW-II drone; and the (5) Active Flexible wing
_AFW) flutter suppression control law synthesis which is presently being carrled out.
JSTATE SPACE MODEL + DATABASEJ
___CONTINUOUS SYSTEM CONTROL LAW DESIGN
OPTIMAL CONTROL LAW SYNTHESIS
CONTROL LAW ORDER REDUCTION
[CONTINUOUS PLAINT + CONTROL LAW J
÷
CONTINI uousiDIscr_ETIZE']_--i
I.ED_S,GN1 NO_ NO ,
I
__ METHODOF !
FEASIBLE
DIRECTION
UPDATE WlCONTROL LA
CI4ANGE AT 1
I SOLVE H SINGULARLYPUNOV EQ. VAL ES
I I
1
COST FUNCTION
CONSTRAINTS
GRADIENTS
OPTIMIZED 1
CONTROL LAWJ
FIG. 1 Optimization scheme block diagram
CONTRO LAW SYNTHESIS AND OPTIMIZATION
SOFTWARE
FOR LARGE ORDER
AEROSERVOELASTIC SYSTEMS
By
V. Mukhopadhyay, A. Pototzky and T. Noll
Aeroservoelasticity Branch
NASA Langley Research Center
Hampton, VA
Workshop on Computational Aspects in the
Control of Flexible Systems
Williamsburg, Virginia
July 12-14, 1988
Abstract
A flexible aircraft or space structure with active control is typically modeled by a large
order state space system of equations in order to accurately represent the rigid body and
flexible modes, unsteady aerodynamic forces, actuator dynan_cs and gust spectra. The
control law of this multi-input multi-output (MIMO) system is expected to satisfy multiple
design requirements on the dynamic loads, root mean square (RMS) responses, actuator
deflection and rate limitations as well as maintain certain guaranteed stability margins, yet
should be simple enough to be implementable on an onboard digital microprocessor. This
paper describes an interactive software named DESIGN for analysis and synthesis of analog
and digital control laws for such a system, using optimal control theory and constrained
optimization techniques.
large flex. sys
dig.comp
Overview
A multi-input m_alti-output aeroservoelastic system is typically represented by a large order
state-space system of equations in order to accurately represent the rigid body and flexible modes,
unsteady aerodynamic forces, actuator dynamics, gust spectra, antialiasing filters, computational
delays etc. The active control law is expected to satisfy a set of conflicting design requirements on
the performance and stability margins, yet should be simple enough to be implementable on an
onboard digital microprocessors. This objective can be achieved using the synthesis software
described in this paper. The methodology used are optimal control theory, order reduction
techniques, unconstrained and constrained optimization with constraints on the design RMS
responses and the minimum singular value of the return difference matrix at the plant input and
output. Optimization can be performed for both continuous system and discrete systems. The
methodology has been used to synthesize a) Analog and digital gust load alleviation control laws
for a remotely controlled drone b) Analog and digital flutter suppression control laws for Active
Flexible Wing (AFW) wind tunnel model. Other potential future applications include a) Rapid
maneuver load control for AFW d) Vibration suppression for large space structure and control
structure interaction study.
OVERVIEW
CONTROL LAW SYNTHESIS AND OPTIMIZATION
SOFTWARE FOR FLEXIBLE STRUCTURE
DESIGN OBJECTIVES
LOW ORDER ROBUST CONTROL LAW FOR A
HIGH ORDER AEROSERVOELASTIC SYSTEM
METHODOLOGY
OPTIMAL CONTROL THEORY
CONTROL LAW ORDER REDUCTION
NUMERICAL OPTIMIZATION
COST FUNCTION
CONSTRAINTS
SYSTEMS
CONTINUOUS
LQG TYPE
RMS RESPONSES
SINGULAR VALUES
DISCRETE
APPLICATIONS
GUST LOAD ALLEVIATION OF A DRONE
FLU'lEER SUPPRESSION OF AFW MODEL
RAPID MANEUVER LOAD CONTROL
Optimization Block Diagram
The optimization procedure minimizes a linear quadratic Gaussian (LQG) type cost function,
while trying to satisfy a set of constraints on the conflicting design requirements such as dynamic
loads, design RMS responses and singular value based stability margins at the plant input and
output. The analytical expressions for the gradients of the cost function and the constraints, with
respect to the control law design variables are used for computation. This facilitates rapid
convergence of the optimization process. The designer can choose the structure of the control law
and the design variables. This enables optimization of classical control law as well as an estimator
based full or reduced order control law. Selected design responses are incorporated as inequality
constraints instead of lumping them into the cost function. This feature is used to modify a control
law to meet individual RMS response limitations and design requirements.
DISCRETE SYSTEM
I STATE SPACE MODEL + DATABASE I
+
|CONTINUOUS SYSTEM CONTROL LAW DESIGN I
-_! OPTIMAL CONTROL LAW SYNTHESIS ICONTROL LAW ORDER REDUCTION
I CONTINUOUS PLANT + CONTROL LAW J
I CONTINUOUS/DISCRETIZE _--I
IREDESIGNI
I NO NO i cHANGE ,_TII
SOLVE t.J SINGULARi , ,u.ov o.nv,,u s
I I- ,'OOOF COST FUNCTION
I-_ FEASIBLE CONSTRAINTS
I DIRECTION GRADIENTS
OPTIMIZED
G99
Software Organization
The interactive software DESIGN is organized to interact with several well used
softwares such as 1) ISAC (Interaction of Structure, Aerodynamics and Control) for receiving
state-space quadruple data, 2) DIGIKON for discretization, interconnection, model
generation, digital design, verification and graphics and 3) MATRIX-X for matrix
manipulation, interconnection, quadruple data transfer, graphics and design
verification. DESIGN can also be run in batch mode on the CYBER/NOS system for large
order problems involving systems with more than 120 states with large number of design
variables and constraints. This batch version was previously known as PADLOCS
(Program for Analysis and Design of Linear Optimal Control Systems).
DIGIKON
ISAC
DESIGN
INTERACTIVE
PADLOCS
BATCH
700
Basic Command Summary
The quadruple data is generated and stored in a sequencial binary file called QDATA. The
design starts with the file command
GET, QDATA.
GET, DESIGN.
DESIGN.
The random access files DBASE, and sequencial file PLDATA are used to transport quadruple
data to and from DIGIKON and MATRIX-X, while random access file TAPE7 is ued to transfer
data from ISAC.using the UTILITY commands. The system parameter and quadruple data are
read by the SYSTEM INPUT commands as shown in the figure above. The primary capability of
this software is the optimization of the system by changing the control law design variables to
improve the stability robustness and performance requirements. The supporting capabilities include
a) Linear quadratic optimal control law synthesis; b) Kalman filter design, linear quadratic
Gaussian design (LQG) and loop transfer recovery (LTR); c) Singular value analysis, evaluation
and plotting at the plant input and output; d) Pole-zero computation; e) Open and closed loop
frequency response, Nyquist and Bode plot, and loop breaking test; f) Root locus plot g) Block
diagonal transformation; h) Modal residualization and truncation; i) Transient response to
deterministic and white noise input; etc.
ISAC
MATRIX-X
DESIGN
DIGIKON
Macintosh
Graphics
FILE COMMAND
GET, QDATA
GET, DBASE
GET, TAPE7
GET, DESIGN
GET, PLDATA.
DESIGN.
SYSTEM INPUT
READ TITLE
READ INPUT
$1NPUT... $
PRINT SYSTEM
PRINT INPUT
READ SYSTEM
UTILITIES
EXC
EXC
EXC
EXC
EXC
EXC
QDATA
DBGD
MATD
MXTQ
ITRC OPEN
ITRC CLOSED
701
Basic Design Commands
The basic design commands are shown in the figure above. For systems with known stable
control laws the optimization procedure can be executed directly using the command EXC OPTM
for continuous systems and EXC OPTD for discrete systems. For MIMO systems with no known
initial stabilizing control laws, In'st an Linear Quadratic Gaussian (LQG/LTR) design is performed
to obtain a full order robust control law using a set of LQG design commands. The order of the
control law is then reduced by truncation, residualization or balanced realization method using
DESIGN, DIGIKON or MATRIX-X. The singular value analysis and block diagonal
transformation procedure is very helpful in the reduction process. Since this reduced order control
law is not optimal and may not satisfy the design requirements, constrained optimization procedure
is used to update the reduced order control law. Constraints can be imposed on the design RMS
responses and minimum singular values at the plant input and output.
BASIC DESIGN COMMANDS
LQ
LQG/LTR
REDUCE
LOG DESIGN
SING. VAL
C
EXC OFSF
EXC KFGM
EXC WRES
EXC COVA
EXC RMSV
EXC OLFR
EXC ZERO
CONSTRAIN RMS SV I/O
ORDER REDUCTION
EXC DIAG
EXC EIGN
EXC PERM
TRUNCATE
RESIDUALiZE
aALANCE(MX)
EXC ITRC
EXC EIGN
EXC TIME
ANALYSE/REOPTIMIZE
OPTIMIZATION
EXC OPTM
EXC ITRC CLOSED
EXC SING
EXC OPTD
EXC ITRC OPEN
EXC FREQ
EXC EIGN
EXC SONG
EXC TiME
Gust Load Alleviation of A Flexible Drone
The synthesis procedure was applied to the gust load alleviation problem of a flexible drone.
The basic control scheme is shown in the figure. In longitudinal motion, the symmetric elevator
and outboard aileron deflections are used as the two control inputs. The accelerometer sensors at
the outboard aileron and on the fuselage near the center of gravity are used as two measurement
outputs. The output signals are filtered through first order antialiasing filters 50/(s+50) before
digitization at 100 Hz. The two input two output system was modeled by a 32nd order system
flying symmetrically through a Dryden gust.
GUST LOAD ALLEVIATION OF
FLEXIBLE DRONE
8a
._r-- :_ltb°ard
acce,orometer;//
eleva_to r
so
d/a 8e 32nd order plant a.a.fil s+50
flex. aircraft
actuator sensor
2 rbm 3 flex. mode
control law
a/d
Z w
z b
703
Gust Load Alleviation Design Requirements
The objective is to obtain a low order robust digital GLA control law which would reduce the
open loop root-mean- square values of the wing root bending moment and shear by 50% without
increasing the wing outboard bending moment and torsion The control law should maintain certain
guaranteed stability margins based on minimum singular value of 0.6 at both the plant input and
output. The control surface deflections and rates should be within the allowable limits. First a full
order LQG control law is synthesized to satisfy the design requirements. This 32nd order control
law is then reduced to a second order control law and then discretized. This control law does not
satisfy the design requirements. After unconstrained optimization most of the requirements are
satisfied except the wing outboard bending moment and the singular values. Using constraints on
the RMS wing loads and on the minimum singular values of the return difference matrix at the
plant input and output, the control law parameters are reoptimized (Ref. 1,2).
GUST LOAD ALLEVIATION
DESIGN REQUIREMENTS
Accl _ Aileron
sensors_
_--_ Elev_ator
32nd order
airplane eqns.
control law
Physical quantities Design objectives How we do it
Root bending moment 50% reduction
Root shear 50% reduction
Outboard bending mom No increase
Outboard torsion No increase
Elevator deflection Within max limit
Elevator rate Within max limit
Aileron deflection Within max limit
Within max limitAileron rate
1. LQG design
2. Control law
order reduction
3. Discretize
4. Optimization
5. Apply constraints
a) on rms loads
b) on singular val.
704-
Symmetric Flutter Suppression System
The software has been used in the past for the following applications: a) Robust flutter
suppression control law synthesis for ARW-I wind tunnel wing model; b) Flutter suppression
control law synthesis for ARW-II drone and DC-10 derivative wind tunnel wing model and c) s
plane summation of forces load model (Ref. 3). A brief survey of the research activities is
presented in Ref.4.Digital robust control law synthesis for the Active Flexible Wing (AFW) wind
tunnel model is presently being carded out in collaboration with Rockwell International. The basic
block diagram for a two input two output symmetric flutter suppression system is shown in the
figure for a sting mounted model using leading edge outboard (LEO) and trailing edge outboard
(TEO) symmetric actuators and colocated accelerometer sensors.The sampling rate is 200Hz.The
design takes into account the effects of actuator dynamics, 4th order 100Hz Butterworth filters and
one cycle computational delay at each channel. Full order and reduced order analog and discrete
robust control laws were synthesized based on an approximate 38th order system at 300 psf design
dynamic pressure. The discrete 8th order control law was able to stabilize the system over the
range 300 to 150 psf.The more detailed 80th order model was also stable at 300 and 200 psf.
Starting with these preliminary control laws detailed analysis will be carded out using the discrete
system optimization procedure EXC OPTD.
SYMMETRIC FLUTTER SUPPRESSION
SYSTEM
| OOIll _ ¥4.,.
LW gOWN 4m
C8 BO'/N _.m
• A ,,,quint
_nan*:s
gmlm
W*
AFW SYM STIFF
BAG OJ.AT
LEAST SO.
STATE SPACE
PLANT MODEL
_,I_ pll
(10rmd_._
eo,,aO start
_,200 pd
L(IG 38U10RDIER
4m ord_ CONT.
ml OAOER CONT.
ll_ ORDER O#TM.
7US'FIN
IIIm ¢elW
leo _ o . ---'
(100 HZ 1=1ozd.)
tloi_ . .dell/
bo, ddl
leo. ddl
bo. rile
leo. rim
I
CONCLUDING REMARKS
• Software Improvement
1. Direct time response constraints
2. New reduction techniques
3. H-infinity design
4. Additional derivative/sensitivity capabilities
5. User help and online documemauon
Portability improvement
1. Microvax
2. NOS VE
Future Applications
1. AFW rapid roll maneuver
2. Large space structure-control interaction
AFW RAPID ROLL CONTROL
Acllve FlexibleWlng Rapid Roll Mechanization
Wind Tunnel'Modal DigitalControl
LARGE SPACE STRUCTURE
ACTIVE CONTROL
7O6
lo
.
.
Q
References
Mukhopadhyay, V., "Digital Robust Active Control Law Synthesis for Large Order Systems
using Constrained Optimization," AIAA Paper 87-2588 CP, Guidance, Navigation and Control
Conference, Monterey, CA, 1987.
Mukhopadhyay. V., "Digital Robust Control Law Synthesis Using Constrained Optimization,"
Journal of Guidance Control and Dynamics,1988 (TBP)
Pototzsky, A. S. and Perry, III, B.,"New and Existing Techniques for Dynamic Loads
Analyses of Flexible Airplanes," Journal of Aircraft, April 1986, pp. 340-347.
Abel, I. and NoU, T.E., Research and Applications in Aeroservoelasticity at the NASA
Langley Research Center," 16th ICAS Congress, Jerusalem, Israel, August, 1988.
'7O7


Control law synthesis and optimization software for large order aeroservoelastic systems

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