=Paper=
{{Paper
|id=Vol-3732/paper06
|storemode=property
|title=Modernizing complexes of scale and semi-scale simulation of disturbed flight
|pdfUrl=https://ceur-ws.org/Vol-3732/paper06.pdf
|volume=Vol-3732
|authors=Yurii Bezkorovainyi,Olha Sushchenko,Olha Yermolaieva,Svitlana Pavlova,Oleksander Zhdanov
|dblpUrl=https://dblp.org/rec/conf/cmse/BezkorovainyiSY24
}}
==Modernizing complexes of scale and semi-scale simulation of disturbed flight==
https://ceur-ws.org/Vol-3732/paper06.pdf
Modernizing complexes of scale and semi-scale simulation
of disturbed flight
Yurii Bezkorovainyi1,†, Olha Sushchenko1,*,†, Olha Yermolaieva1,†, Svitlana Pavlova2,†
and Oleksander Zhdanov1,†
1 National Aviation University, Liubomyra Huzara Ave., 1, Kyiv, 03058, Ukraine
2 Shanxi Agricultural University, Longcheng St., 81, Xiaodian Taiyuan, Shanxi, 030031, China
Abstract
This paper deals with solving the problem of modernization of complex scale and semi-scale
simulation of disturbed flight. The main goal of the research is to ensure the maximal proximity
of imitation of real flights. Methods of ensuring the adequacy of dynamic models of the simulator
and simulated model for scale simulation of flights are proposed. The structural diagram of the
“flying model” with the corrected dynamics is represented. New technologies to ensure the
adequacy of dynamics models of the simulator and simulated object are represented. Structural
diagrams of automated complexes of semi-scale simulation of flight have been analyzed. The
structural scheme of the modernized complex of semi-scale simulation is developed.
Keywords
disturbed flight, natural and semi-natural modeling, adequacy of models, multi-dimensional
stand1
1. Introduction
Among the many problems, for example [1, 2, 3], the creation of full-scale and semi-realistic
flight simulation complexes, as well as the related problems of creating mobile aviation
simulators, we will discuss one of the problems that arose at the current stage of the
development of these fields of science and technology such as the problem of optimal
modernization of stochastic turbulent flight simulation complexes. This problem arises
during the creation, operation, and modernization of existing mobile complexes of full-scale
and semi-full-scale flight simulation of objects for various purposes. One of the main tasks
in this case is to ensure the maximum closeness of the simulated and real flights [4, 5, 6].
The scientific and technical difficulties of solving this problem are primarily related to
the nature of the dynamics of the control process, simulating the moving object, and the
nature of the dynamics of the multidimensional simulator used in modeling as the basic part
CMSE’2024: International Workshop on Computational Methods in Systems Engineering, June 17, 2024, Kyiv,
Ukraine
∗ Corresponding author.
† These authors contributed equally.
yurii.bezkor@gmail.com (Y. Bezkorovainyi); sushoa@ukr.net (O. Sushchenko); olgermol@ukr.net
(O. Yermolaieva); pavlova_2020@ukr.net (S. Pavlova); azhdanov@gmail.com (O. Zhdanov)
0000-0001-5970-5150 (Y. Bezkorovainyi); 0000-0002-8837-1521 (O. Sushchenko); 009-0007-8623-1123
(O. Yermolaieva) ; 0000-0003-4012-9821 (S. Pavlova); 0000-0001-5273-571X (A. Zhdanov)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
of all mobile flight simulation complexes. In automatic complexes, the main aspect of the
quality of imitation is accuracy, and the choice of control of the imitation complex should be
made with the condition of achieving the highest quality of imitation. A significant
complication of the problems of improving the accuracy of simulation complexes control in
comparison with the same problems of flight control is associated with the introduction of
an additional unit into the control loop – "the flying model" of the simulator stand, which
has complex dynamics.
In mobile aviation simulators, which are mainly intended for pilot training and skills in
solving special flight tasks by operators, additional problems arise related to the reliability
of the occurrence of acceleration sensations similar to those occurring in real situations in
pilots who are learning to control flight in ground conditions.
The formulated problem is considered only for automatic modeling complexes, but
according to the results of robots related to the activities of pilots and operators in
stochastic conditions close to flight conditions, it could be extended to semi-automatic
modeling complexes [7, 8, 9].
We will assume that the statement of the problem of maximizing the accuracy of
simulation in automatic flight dynamics modeling complexes is determined by two main
circumstances. Firstly, there are significant differences between the dynamics of the "flying
model" during full-scale simulation and the dynamics of the flight simulation system on the
"computer-dynamic stand" during semi-realistic simulation from the dynamic
characteristics of the simulated moving object. This circumstance in some cases can lead to
the impossibility of flight simulation in stochastic ground conditions. Secondly, in situations
where the "adequacy" of the dynamics of the object and its imitator is achieved in the
specified manner, the maximization of the accuracy of the imitation is associated with the
choice of the optimal motion control system of the adjusted "flying model" or imitator in
full-scale and semi-full-scale simulation complexes, taking into account stochastic flight
factors. It is believed [10, 11] that the formulated accuracy problem of flight simulation can
be solved in different ways, which are described below.
2. Development of methods for ensuring the adequacy of dynamic
models of simulator and simulated object during full-scale flight
imitation
Currently, full-scale simulation of the flight of an object that is just being developed or
modernized is performed directly during the flight of some aircraft, the systems of which
allow some restructuring of parameters or structure. The structure of such a simulated
flight control does not differ from the usual one. When the adjustment limits of the flight
control system of the "flying model", which simultaneously performs the functions of flight
control and correction of the dynamics of the "flying model", are not enough to achieve the
goals of simulation, then an electronic model of the dynamics of the object being developed
can be put on board. In this model, if possible, influences, controlling, and perturbing, which
take place in flight, are taken into consideration. The result of comparing the state vectors
of the "flying" and "electronic" models must be used in a certain way to correct the dynamics
of the "flying model". Such approaches have some points that certainly reduce the quality of
modeling [12, 13, 14].
There is another way to solve the problems of full-scale simulation, which is based on
well-known [15] algorithms of synthesis, identification, observation, and analysis of
stochastic stabilization systems and consists of some research phases. In the first phase, the
structural identification [16, 17] of the "flying model" is carried out in the specified flight
modes. Then the dynamic certification [2] of on-board meters is performed, and models of
disturbance dynamics in the studied operating modes are determined. The collected
information of the second phase to carry out the dynamic design [18] of the system for
correcting the dynamics of the "flying model" to the dynamics of the object under study.
This phase is performed based on algorithms for the synthesis of closed stochastic
stabilization systems. The "flying model" in conjunction with the received dynamics
correction system creates the internal circuit of the flight control system of the "flying
model" and will be the closest model of the object under study (Figure 1). The external
control loops of the adjusted "flying model" can also be synthesized in the process of
dynamic design and implemented before the start of full-scale modeling. Even with
significant differences between the a priori accepted models of links and signals from real
flight ones, the synthesized correction and control systems will be minimax. As input
models for dynamic design will improve, their results will approach the best ones [19, 20].
If it is necessary to adaptively adjust the parameters of the selected "flying model"
correction system in real flight with the help of a synthesized observation system. It is
possible to estimate the state of the model in each specific flight mode, compare it with the
one programmed in this mode and embedded in the memory of the computer on the "flying
model" and, based on the results of the comparison, generate control signals for the contour
of the adaptive setting of parameters.
Figure 1: Structural diagram of the optimal control system.
Figure 1 shows the structural diagram of the optimal control system of the "flying model"
with adjusted dynamics. The "flying model" dynamics correction system consists of parts of
this system CS1, CS2, and CS3, which use estimates of the state vectors of the model x and
perturbations in conjunction with an a priori estimate of the control signal U y , which is
transformed in the CS2, creating a signal of the internal control loop system CS2 – drive D –
“aircraft flying model”. External stabilizing circuits relative to the created model create an
optimal autopilot (part of the controller) (ОC1) and an optimal correction system in the
disturbance circuit (ОC3, ОC3). The outer (navigational) circuit includes the optimal
structure (ОC2) that makes up the trajectory control system as constituent parts. OO1, OO2,
and OO3 are parts of the optimal observer; ОC1, ОC2, and ОC3 are parts of the optimal
regulator; KU is the block of kinematic units; 1, 2, 3 are vectors of measurement
disturbances; r0 is a vector of the deterministic flight program signal; r is the vector of the
completed flight program signal; and x 0 and x vectors of the desired and implemented
state signals of the aircraft; is the vector of error signals in the estimation of aircraft (A)
states.
Based on the results of comparing the vectors x and x0 , a vector is chosen, which can
be used to generate adaptation control signals U A in the personal computer (PC) software
and the adaptation loop (AL), which will be able to change the set parameters in the CS1 and
CS2 blocks. In some cases, it is possible to exclude contours of correction by disturbance.
When drawing up the structural diagram (Figure 1), it was considered that the main task
of the specified version of the full-scale simulation is, for example, ensuring and evaluating
the effectiveness of the optimal flight control system (ОC1, ОC2, ОC3). Scale simulation can
have other goals and objectives.
3. Development of technologies to ensure the "adequacy" of simulator
and object dynamics models during semi-scale flight simulation
In automatic systems of full-scale simulation, as well as in moving aviation simulators, we
consider the main goal of simulator dynamics correction to be the most complete
elimination of the influence of the dynamics of the stand that simulate movement, as a
dynamic unit that does not exist in real-time flight control loops [21, 22, 23].
We will briefly describe the widespread options for creating such complexes and
simulators. For certainty, we believe that the main task of the simulation complex (flight
simulator) in the first version of the design (Figure 2) is to assess the accuracy of the
functioning of a certain functional complex in conditions close to a specific flight (to
simulate the acceleration of the pilot's sensations, close to natural ones). In Figure 2, the
following designations are adopted: FS is a closed static (computer-based) flight simulator
that operates on program signals r , disturbances , and measurement noise provides
an assessment of the state of the object x for a specific operating mode; SF is a system of
filters designed to improve the dynamics of the simulation path or to smooth out the
difference in the accelerations of the pilot's sensations during their ground and field studies;
MS is a closed mobility system that has internal disturbances and is designed to convert
signals x into mechanical signals x M with dynamic characteristics closest to the state
vector x ; RO is a researched object exposed to the action of internal disturbances , the
assessment of its state y and accuracy of functioning are the goals of the research.
Figure 2: Structural diagrams of an open automatic complex of semi-realistic flight
simulation.
The positive feature of such a structure of the complex is the comparative simplicity of
the design and configuration. The essential disadvantages are the same as the impossibility
of generating signals x M close to the signals x due to inertia, the limited bandwidth of
passing the frequencies of the reference signals through the mobility system, and, as a
consequence, the insufficient correspondence of the achievable state y to the actual value.
As a result, it is impossible to obtain reliable accuracy estimates for research object, which
has high accuracy requirements [24, 25].
The variant of the modeling complex, the structural diagram of which is given in Figure
3, is usually used to estimate the quality of the real flight control system. Here, a closed
mobility system (spatial motion generator) is placed in feedback to the object (the model of
the aircraft), which is subjected to external disturbances and has a state of x . This
system includes real airborne measuring instruments (AMI) that generate signals for the
aircraft control system (ACS). The mobility system consists of a multidimensional dynamic
stand (DS) subjected to internal disturbances and covered by feedback CS (control
system) of stand motion with measurement disturbances . The state vector of the mobility
system x M should be as close as possible to the state model x . In the system of measuring
instruments, there are measuring noise , in control systems - external disturbances .
The simulation complex reproduces the program movement r0 and the vector of control
signals denoted as u .
Here, the elimination of the negative influence on the dynamics of the mobility system is
carried out by the possible expansion of frequency bandwidth. Such an approach is
associated with carrying out expensive procedures, which, however, does not lead to an
effective solution to the problem [26, 27].
A significant drawback of this modeling option is the weak consideration of external and
internal stochastic factors influencing the control results, which requires setting up and
solving other additional problems. Degradation in the quality of modeling is also associated
with imperfect knowledge of the dynamics of multidimensional mobility systems, failure to
perform complex algorithms for dynamic attestation of on-board meters, and so on.
Figure 3: Structural diagrams of a close automatic complex of semi-realistic flight
simulation.
4. Problematic issues in the modernization of highly effective complexes
of semi-scale simulation for dynamic attestation of measuring
instruments
To create or modernize moving objects that are highly efficient under stochastic conditions
of operation, we also consider it expedient to carry out work related to the maximum
mitigation of the harmful influence of mobility dynamics in modeling complexes. The
successful solution to such a problem is based on the following circumstances. First, it is
necessary to deviate from the traditional principle of building a complex, when the
dynamics of a moving object (aircraft) are completely created by its model on a computer,
and the mobility system plays the role of only a mechanical converter of the assessment
vector of the aircraft model x into a state vector of the mobility system, and such a
transformation is not suitable for current modeling requirements. Secondly, as a basic
dynamic object, it is expedient to adopt the multidimensional stand-simulator of spatial
movements itself, to adjust the dynamics of the stand to the dynamics of the simulated
aircraft using a special synthesizable optimal correction, which is implemented based on
the results of optimal synthesis on a computer. The structural diagram of the semi-scale
simulation complex modernized in the specified way is represented in Figure 4.
In Figure 4, the following designations are used: AMI is an airborne measuring
instrument; DS is dynamic stand; DS is drive system; CS1 and CS2 are optimal control
systems for determining the dynamics models of airborne measuring instruments and
measuring noise; G1, G2 generators for the appropriate identification modes; MS is
measuring system of the stand; FF is forming filter; OOS is the optimal observer of the state
of the stand; CC is coordinate converter; SEQSM is a system for assessment the quality of
imitation of stand movements; y is dynamic stand state vector; ŷ is a vector of the observed
state of the stand; x is a vector of the true state of the on-board meter; z is a vector of the
registered state of the on-board meter; ẑ s estimation of the state vector of the measuring
instruments; r is a vector of program signals; f – is stand disturbance vector; c is a vector
of the noise of stand measuring instruments; is noise vector of the airborne measuring
instruments; ̂ is the assessment of the state vector of airborne measuring instruments; ε
is an error of imitation of stand movements.
Figure 4: Structural diagram of the modernized semi-scale simulation complex.
5. Dynamic attestation of measuring instruments
The accuracy of on-board meters depends on the design quality and features, but also on
the nature of the flight mode, the features of the operating disturbances, and noises that
arise under specific operating conditions. As a rule, on-board meters are complex dynamic
systems and operate under conditions of stochastic disturbances. The main disturbing
factors include rotation of the aircraft relative to the center of mass, linear overloads of the
center of mass of the aircraft during its movement along the flight path, vibration and shock
overloads, moments of frictional forces in the axes of the suspensions of platforms and
devices [28, 29]. The success of ground tests of onboard meters depends significantly on the
presence of:
1. Test equipment capable of simulating real dynamic flight conditions;
2. Methods of certification of complex on-board measuring systems;
3. Information about real disturbing factors of flight.
Until now, in many cases, on-board meters for flight tests are certified in static conditions
or with the help of special dynamic stands, when reproducing the movement of which the
characteristics of the disturbed movement of the aircraft are not taken into account. But to
evaluate the characteristics of an onboard meter taking into account external influences, it
is necessary to know the dynamic characteristics of both the meter itself and its noises. Such
opportunities are provided by the dynamic certification procedure.
The dynamic certification of an on-board meter is understood as the process of
determining its transmission functions using a test bench that simulates the movement of
an aircraft in a given flight mode [30, 31, 32]. The efficiency of the certification is caused by
the following factors. Based on the principle of operation of most electro-mechanical units,
such as gyroscopes, the noise of the meters is correlated with the movement of the base.
Determining the transfer functions of a one-dimensional meter does not cause
complications and can be implemented by the technique of logarithmic magnitude-
frequency responses using a test stand that simulates harmonic movements. Defining the
dynamic model of a multidimensional gauge is a more complex process. For this procedure,
you must have:
1. Multi-stage test stand capable of simulating a specified spatially disturbed
movement of an aircraft;
2. Algorithms and methods of testing multidimensional onboard meters.
The problem of determining models of on-board meter noise, which are necessary for
optimizing the accuracy of aircraft control, is particularly difficult [33, 34, 35]. This difficulty
is caused by the following factors. The motion of the bench must reproduce a multi-
dimensional stochastic process with given characteristics. To ensure the possibility of
reproducing such a movement, it is necessary to create a complex dynamic certification,
which should include a stand generator of specified movements and a stand control system.
The creation of a stand management system is based on optimal synthesis algorithms [32,
33]. Such a system should provide:
1. Optimal assessment of the state of the tested meter.
2. Optimal assessment of the condition of the test bench.
3. Transformation of the measured state parameters of the tested bench into some
reference frame related to the tested measuring instrument.
4. Comparative assessment of the state of the stand and the state of the tested meter
and developing models of measuring noise.
The finite definition of measuring noise models of on-board meters is carried out with
the help of statistical processing of test results and approximation of the obtained
experimental dependencies with analytical formulas.
It will be noticed that the same tested stand can be used to determine the dynamics
models of the on-board meters themselves and the noises to their measurements. At the
same time, the stand management system must be renewed in correspondence with the
solved problem.
The block diagram of the system for dynamic certification of airborne measuring
instruments is shown in Figure 5.
Here, the stand of motion simulation (SMS) with internal disturbances and the optimal
dynamics correction system jointly make up the model of simulating aircraft, and the
correction system (CS) has two parts CS1 and CS2. Information about the state of the model
x is provided by the optimal observer OO (the noise of state measurements). The system
of airborne measuring instruments (AMI) with the noise vector supplies information to
the real control system of the aircraft (RCSA), which generates the control vector of the
model u . The RCSA block, which has its disturbance , must receive a vector of program
signals r0 .
Figure 5: Structural diagram of the spatial movements stand for dynamic attestation of on-
board meters.
The necessity of optimal observation of the state of on-board meters and the dynamic
bench takes place in all the modes of real or simulated movements. Modern optimal
observers are often built based on Kalman optimal filtering. At the same time, it is assumed
that the measuring noise is uncorrelated with the signals of the object's state vector. In
practice, this condition is often not fulfilled. To estimate the steady state of the object, it is
possible to apply the spectral method of optimal estimation, which is convenient for
practical implementation [7].
The block diagram of the formulation of the problem of optimal evaluation is shown in
Figure 6.
Figure 6: Block diagram of the optimal estimation.
In Figure 6, O is the estimation object, MS is the measuring system, OO is the optimal
observer, x is the output signal of the estimated object, y is the measured signal, x is the
estimate of the object’s output signal of the optimal observer, ε is the estimation error.
The unit of angular velocity sensors under study consists of three sensors. The
measuring axes of these sensors are arranged in three directions, which are perpendicular
to each other. To carry out the dynamic certification, the tested measuring instrument is
located at the centre of the stand’s platform in the following way. The axes of sensitivity of
the sensors are directed along the axes of the cardan suspension, along which the platform
is rotated by heading, pitch, and roll. The vector of input signals vector for the angular rate
measuring instrument is calculated in the control system of the tested bench. We believe
that an instrument for measuring angular velocity is mounted at some point. This point and
the origin of the reference frame related to the platform’s angular motion are coincided.
Then the angular velocity vector can be given in the form:
𝜔p𝑥 𝛾̇ + 𝜓̇sin𝜗
𝜔p = [𝜔p𝑦 ] = [𝜓̇cos𝜗cos𝛾 + 𝜗̇sin𝛾] , (1)
𝜔p𝑧
𝜗̇cos𝛾 − 𝜓̇cos𝜗sin𝛾
where 𝜓, 𝜗, 𝛾 are small successive angles of platform rotation.
Since the angles of rotation of the platform are assumed to be small, expression (1) can
be presented in the form:
𝜔p ≈ [𝛾̇ 𝜓̇ 𝜗̇]′ . (2)
Expression (2) is a vector of the estimated angular velocity of the platform, that is, a
vector of input signals of the angular velocity sensor block.
The imitation of linear accelerations of the stand’s rotating platform at the point of
attachment of the block of linear acceleration sensors is carried out by a displacement of
the tested measuring instrument about the place of platform suspension. Then, both linear
and angular motions influence the instrument for measuring acceleration at the same time.
To determine linear accelerations directly, we can use calculating methods. Angle velocities
of the platform and coordinates of the point of some displacement of the instrument for
measuring linear accelerations about a point of the platform’s suspension can be used as
initial data for these calculations. It is known [29] that the absolute acceleration of the
attachment point of the instrument for measuring linear acceleration is defined by the
equation
𝑑𝑣 𝑑𝜔 𝑑𝜌
= × 𝜌 + 𝜔 × = 𝑢 × 𝜌 + 𝜔 × 𝜔 × 𝜌, (3)
𝑑𝑡 𝑑𝑡 𝑑𝑡
where 𝑣 is the vector of the absolute linear speed of movement of the attachment point of
the instrument for measurement of linear accelerations; 𝜔 is the platform angular velocity
vector; 𝜌(𝑥, 𝑦, 𝑧) is the radius-vector of the attachment point of the linear acceleration of the
measuring instrument about the platform gimbals point with the appropriate coordinates
𝑥, 𝑦, 𝑧; 𝑢 is the vector of the platform’s angular accelerations.
Expanding the vector products of expression (3) and taking into account the previously
introduced notations, we obtain:
−(𝜓̇ 2 + 𝜗̇ 2 )𝑥 − (𝜗̈ + 𝛾̇ 𝜓̇)𝑦 + (𝜓̈ + 𝛾̇ 𝜗̇)𝑧
𝑤P = [ (𝜗̈ + 𝛾̇ 𝜓̇)𝑥 − (𝜗̇ 2 + 𝛾̇ 2 )𝑦 − (𝛾̈ + 𝜓̇𝜗̇)𝑧 ]. (4)
−(𝜓̈ + 𝛾̇ 𝜗̇)𝑥 + (𝛾̈ + 𝜓̇𝜗̇)𝑦 − (𝛾̇ + 𝜓̇ )𝑧
2 2
Expression (4) is a vector of calculated accelerations of the attachment point of the linear
acceleration sensor block without taking into account gravitational components.
Compensation for the component accelerations of gravitational forces can be carried out by
hardware or computational means.
Identification of dynamic models of blocks of sensitive elements and their noise is carried
out based on the spectral algorithm of structural identification. It represents the definition
of dynamic models of blocks of sensitive elements and their measuring noise based on input
and output signals measured during the experiment.
The unit of angular velocity sensors and the unit of linear acceleration sensors under
study are mounted directly on the dynamic stand platform. The platform installed in the
cardan suspension makes angular movements relative to three mutually perpendicular
directions. The movements of the platform are ensured by three reversible motors installed
behind each of the axes. The output signal of the platform is a vector of rotation angles
𝜃 = [𝜓 𝜗 𝛾]′ .
Angle motions of the platform are transformed into electrical signals and enter the
control system of the stand. Software stand control signals are formed by noise generators
and shaping filters, which are implemented by software. The communication unit converts
digital signals coming from the computer to analog ones. Stand control signals are sent to
the reversing motors through power amplifiers. A generator of standard signals is used to
ensure the possibility of checking the stand.
During tests, the angular motions of the platform are registered, while the appropriate
signals are taken from the feedback sensors. Hence, angular rates could be calculated by
developing software that realizes the differentiation algorithm with high accuracy.
Based on the obtained data on input and output signals and the above-described
algorithm, the dynamics models are determined. They represent the matrices of the transfer
functions of the investigated blocks of sensitive elements of the strap-down inertial system,
as well as the matrices of the spectral densities of noise at the output of the blocks under
conditions close to operational ones.
6. Conclusions
The scientific and technical problems of modernization of full-scale and semi-full-scale
simulation complexes were presented and briefly discussed, as well as the basic ways of
successfully solving the mentioned problems were considered. The necessary science-
intensive technologies for the proposed modernization can be obtained from the cited
literary sources.
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