Background: Control
law development for aircraft has relied predominantly on one-loop-at-the time
frequency response and root locus design techniques. This approach to control
law design is essentially the same as that outlined by Bollay (1951). The methods
have been used successfully for both single loop and multi loop control problems.
The success and continued acceptance of this approach is evident by the fact that
for most new aircraft today, the control laws for autopilot and primary flight
control functions were or are being developed relying to a great extent on these
techniques. In spite of
the availability of efficient computational algorithms and software (Matlab and
other packages), the practicing control engineers in industry have been reluctant
to adopt the more direct and formal multi loop design techniques. These techniques
have their roots in the theories of optimal control developed by Pontryagin (Pontryagin
et al. 1962)
and Bellman (Bellman 1957). Since then there has been a proliferation
of extensions and variations developed within the academic community mostly in
terms of theory, and to a lesser extent in terms of real applications. The
first significant practical application of multivariable control techniques by
the authors dates back to 1978. The material to be presented captures the cumulative
experiences from many practical applications since then, some of which are summarized
in “Practical control law design for aircraft using multivariable techniques”,
Advances in Aircraft Control (Taylor & Francis 1996), but will include subsequent
updates and lessons learned. The tutorial will draw on material taught one-on-one
and as a formal course within industry, and will focus those concepts and techniques
the authors have found most useful in practical applications. Tutorial
content: Summary A
practical control law development process and practical design examples will be
presented. The
process - combines key
elements of multivariable control techniques with classical frequency-domain interpretation
of control loop performance and robustness,
-
decomposes the solution into two steps a) the solution of a control problem and
b) the solution of an information problem,
-
comprises guidelines for transforming practical design requirements into the mathematical
formulation of solutions,
-
solves problems with strong nonlinearities using essentially linear methods to
develop appropriate nonlinear control laws, and
-
addresses some key issues associated with implementation of the control laws into
redundant flight control computers.
Although
these design techniques have been developed based on applications to aircraft
control problems, the approach is general enough to apply other industrial applications. Outline
of topics
-
Design process flow overview – Dagfinn Gangsaas
Define operating
points for control law design and analysis, generate airplane linear models over
the operating range, incorporate system models (sensors, actuators, data buses,
computers etc.), conduct analyses of open loop
characteristics, define control
law gain scheduling parameters, define parameter variations to be addressed a)
via robustness and b) via gain scheduling, map design requirements into the control
gain synthesis and determine achievable performance, define sensors (information)
required to meet objectives for control performance and robustness, design and
incorporate filters and state observers as required, analyze linear stability
and stability margins over the operating map, build gain schedules, repeat linear
stability and stability margins analyses with gain schedules, and conduct full
nonlinear simulations. -
Review of key elements of relevant control theory and concepts
– James D. Blight & Fabricio Reis Caldeira
Although
most of the attendees will be very familiar with this material the authors will
summarize those aspects found most useful in their work. The focus will be on
the practical applications of the theory and concepts. Examples: Nyquist
stability
criterion and the concept of gain and phase margins, where to measure stability
margins, connection to multi loop stability margin analyses, classical root locus
design, the importance of control loop zeros, gain design using linear
quadratic
synthesis and associated LQ asymptotic properties including the role and importance
of transmission zeros, linear tracker design and problem formulations, design
of state observers (steady-state Kalman filters as part of an
LQG solution),
use of complementary filters, design of lead/lag, lag/lead and notch filters and
when and where to use these, and the concepts of the control loop crossover frequency
and control performance crossover frequency. -
Solving the control problem – Dagfinn Gangsaas
Based on
control requirements construct frequency domain functions to be used in the LQ
gain design solution. Adjust quadratic penalties to satisfy control loop crossover
frequency limitations, and desired cross over frequencies in the
performance
loops without any a priori assumptions of sensor information required. This is
a formal process a) allowing a systematic trade off between performance and robustness
within the constraints of a real system, and b) generation of gains easily scheduled
over the operating range. -
Solving the information problem – James D. Blight
The gain
design defines the information required. For those signals not directly available
or contaminated by undesirable noise signals are reconstructed via the design
of complementary filters or state observers. -
Dealing with strong nonlinearities –
Dagfinn Gangsaas
An implementation method that removes the undesirable
effects of highly nonlinear state dependent gain schedules will be presented.
This approach allows design of highly nonlinear control laws using linear methods. -
Implementing the control laws into redundant parallel control paths
– Dagfinn Gangsaas
For safety reasons flight control systems contain
redundant and independent parallel control paths. For control laws with integral
control there will be integrator drift unless the computations in the parallel
paths are bit by bit identical
and time congruent. That latter is rarely the
case in real systems. Methods for synchronizing parallel and redundant integrators
will be discussed.
Applications
(each has been selected to capture some unique aspect of aircraft control) Three
applications papers will be presented (electronic copies will be available) - “The
Design of an Angle of Attack Limiting Function” –
Dagfinn Gangsaas
This represents one of the more challenging tasks in
flight control design due to the highly nonlinear aerodynamic characteristics
and the stringent safety requirements. The focus is on how performance and robustness
are ensured in the presence of strong nonlinear behavior as the aircraft enters
the stall region. These nonlinear characteristics vary greatly within the flight
envelope as functions of angle of attack, dynamic pressure, Mach number and aircraft
configuration (flap setting). Good
control performance and robustness are achieved via a) nonlinear gain scheduling
based on a priori model predictions of nonlinear characteristics, b) a special
technique that allows nonlinear gain scheduling with rapidly changing outputs
(angle of attack), c) high gain integral control to minimize tracking errors and
thus ensure performance, and d) a feedback control structure insensitive to parameter
variations such as those due to uncertainties in aerodynamic force and moment
characteristics, variations with weight and center of gravity, presence of ice
on wings and control surfaces, and un-modeled dynamics. This approach was used
in the design of an angle of attack limit function that is certified and in service.
Comparisons between predicted performance and flight test results will be presented. “The
Design of a Coupled Yaw Axis and Roll Axis Control Law”
– James D. Blight
The roll and yaw dynamics of an aircraft are
highly coupled. However, traditionally the control law designs for these axes
have been treated as two independent single input/output design problems followed
by ad hoc integration and adjustments. In this paper a formal direct multi loop
design approach will be presented. The feedforward and feedback control laws for
both control loops are designed directly using the Linear Quadratic synthesis
technique. The combined yaw and roll design requirements such as for mode frequency
and damping, command responses, gust disturbance rejection, passenger ride qualities,
control surface activity etc. are captured in frequency domain functions that
allow a systematic trade off between performance and control actuation demands.
The design of a) nonlinear gain schedules that extends the design to the full
flight envelope, and b) filters to remove unwanted gust inputs and eliminate coupling
with high frequency structural modes are described. - “The
Design of a Landing-Flare Control Law for Automatic Landings”
– Fabricio Reis Caldeira
This is the most demanding control task
performed by an aircraft autopilot. The maneuver starts at about 50 feet above
ground and must be performed safely in the presence of wind shears, gusts and
system failures. The maneuver which takes 5 to 10 seconds is dynamic in that the
aircraft does not reach a steady state. The control law is required to bring the
aircraft from a wide range of initial states (sink rate, position etc.) at start
of the flare to a successful landing with stringent requirements for maximum vertical
sink rate and position on the runway at touchdown. For certification, compliance
with the requirements is demonstrated via extensive flight test and Monte Carlo
simulations. Traditionally
flare control laws like other autopilot control laws have been designed via a
two step process a) inner loop design – for flare a pitch inner loop design,
and b) outer loop design – for flare a flare path outer loop design. The
rationale being that inner loop designs which are highly airplane dependent can
be common to the outer loop control laws used for other flight phases, and because
the latter are less airplane dependent, outer loop control laws can be reused
from other applications. This approach should in theory reduce the amount of control
law design work and
embedded flight control software development. During a
recent design and certification of an automatic landing system the authors found
that this assumption was not true. The pitch inner loop design found acceptable
for other flight phases
required redesign to meet the more stringent performance
requirements for the landing flare. In the end excellent landing performance was
achieved as demonstrated during flight test and by Monte Carlo simulations. However,
the expected economic savings from less design effort were not realized. Drawing
upon this recent experience, in particular the good understanding of landing flare
performance requirements, the authors will present a different approach. The new
design is based on the solution of a simplified two point boundary value problem
using linear quadratic optimization theory where the backward integration is performed
over a sliding time window. With this approach the complete design is direct and
more formal thus avoiding the somewhat time consuming and more ad hoc inner/outer
loop design iterations. Data will be presented showing significant performance
improvements over the existing design based on the same Monte Carlo simulation
analysis used in the certification of the original design.
References
Bollay,
W., 1951, The Fourteenth Wright Brothers Lecture – “Aerodynamic stability
and automatic control” Journal of Aeronautical Science.
Pontryagin,
L.S., Boltyanskii, R.V., Gamkrelidze, R.V., Mischenko, E.F., 1962, “The Mathematical
Theory of Optimal Processes”, (New York: Wiley). Bellman,
R., 1957, “Dynamic Programming”, (Princeton, NJ: Princeton University
Press). Blight,
J.D., Dailey, R.L., Gangsaas, D. “Practical control law design for aircraft
using multivariable techniques”, Advances in Aircraft Control (Taylor &
Francis 1996)
|
