AU2020400213A1 - Modeling method for simplified model of servo mechanism, storage medium and server - Google Patents
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Abstract
A modeling method for a simplified model of a servo mechanism, a storage medium and a server. The modeling method comprising the steps of: determining expected values of the amplitude, phase and frequency characteristics of a simplified model of a servo mechanism; analyzing and determining a model structure; and using an optimized control algorithm to solve feature parameters of the model, and verifying the amplitude, phase and frequency characteristics of the model. The described method improves the structure of the simplified model of the servo mechanism that is commonly used at present, and introduces the link between amplitude and phase correction to ensure that the simplified model has high modeling accuracy in a plurality of frequency bands. At the same time, the problem of simulating the feature parameters of the simplified model of the servo structure is transformed into an optimal control problem, which avoids the trial and error process of feature parameters, and significantly improves the efficiency of the solution.
Description
Technical Field
The present disclosure relates to the field of aerospace, in particular to a technology for
controlling and simulating launch vehicle, especially to a modeling method for simplified
model of a launch vehicle servo mechanism, a storage medium and a server.
Background Art
In the attitude control system of a large launch vehicle represented by a launch rocket,
the servo mechanism is an actuating device that controls the actuator. It accepts the command
signal given by the attitude control law and drives the swing engine to swing, thereby correcting
the deviation of the flight trajectory and attitude. The electric servo mechanism is a high-order
system with nonlinear characteristics such as dead zone, gap and saturation. When the small
deviation stability analysis of the rocket control system is carried out, considering the
convenience of modeling work, the electric servo mechanism is usually simplified as a
second-order oscillatory link.
For a large launch rocket using liquid fuel as propellant, when analysing its attitude
stability, it is necessary to consider the influence of propellant sloshing and elastic vibration on
the stability of the rocket attitude system. Therefore, the stability analysis model of a large
launch rocket is a high-order system composed of a rigid body-elasticity-sloshing coupled
rocket body, control law, and dynamic characteristics of servo mechanisms. The attitude control
system of large liquid rockets usually needs to take into account the amplitude and phase
stability margin indicators in the low-frequency rigid body segment. The first-order liquid
sloshing frequency and the first-order elastic frequency are relatively low, and it is difficult to
achieve amplitude stabilization, so phase stabilization is usually adopted. For elastic
frequencies above the second-order, the amplitude stabilization method is usually adopted.
The correctness of the simplified model of servo mechanism directly affects the
correctness of the stability analysis results of the attitude control system. Therefore, in order to
ensure the correctness of the stability analysis results, it is necessary to pay attention to the key
frequency characteristics such as the amplitude-frequency and phase-frequency characteristics
of the servo mechanism model in the low-frequency rigid body segment, the phase-frequency
characteristics near the first-order sloshing and the first-order elastic oscillation frequency, and
amplitude-frequency characteristics of high frequency bands (second-order elastic oscillation
frequency and above). However, the traditional simplified model of servo mechanism described
by only one second-order oscillation link is difficult to meet the high-precision servo
mechanism modeling requirements of multiple key frequency points, such as above rigid body,
sloshing and elastic oscillation, at the same time.
Summary of the Invention
Aiming at the problem of the simplified model that using the second-order oscillation
link as the servo mechanism is difficult to meet the requirements of the amplitude-frequency
and phase-frequency characteristics of the servo mechanism at multiple frequency points at the
same time, the purpose of the present disclosure is to provide a more perfect modeling method
for simplified model of servo mechanism. The modeling method includes the determination of
the structure of the model and a method that can quickly solve the characteristic parameters of
the model.
One aspect of the present disclosure provides a modeling method for simplified model
of servo mechanism, comprising:
determining amplitude-phase-frequency characteristics that the simplified model of
servo mechanism needs to meet, including expected values of amplitude and phase at a series of
key frequency points;
adopting a traditional second-order oscillation link to perform preliminary simplified
modeling of the servo mechanism, and analysing an error of the model between the amplitude-phase-frequency characteristics at the key frequency point and an expected value, if an amplitude error and a phase error are both smaller than a set threshold value, it is determined that the simplified model of servo mechanism is the second-order oscillation link, otherwise a system formed by the second-order oscillation link and an amplitude-phase correction link in series is used as the simplified model of servo mechanism; for a simplified model of the series structure composed of the second-order oscillation link and the amplitude-phase correction link, determining characteristic parameters of the model by an optimal control algorithm, wherein an item in the amplitude-phase-frequency characteristics that needs to be corrected is used as an optimization target, and the other item is used as an optimization constraint; and verifying whether the error of the simplified model of servo mechanism between the amplitude-phase-frequency characteristics at the key frequency point and the expected value meets a requirement.
Further, the threshold value of the amplitude error is taken as l dB.
Further, the threshold value of the phase error is taken as 2 degrees.
Further, the amplitude-phase correction link comprises but is not limited to a lag-lead
link and a time delay link, wherein the lag-lead link is used to correct the amplitude error or the
phase error, and the time delay link is used to increase a delay of the phase.
Further, the number of the lag-lead link or the time-delay link connected in series in
the simplified model of servo mechanism is not limited to one.
Further, on the basis of the second-order oscillation link, two lag links are connected in
series to correct phase characteristics of the second-order oscillation link, and such a series
system is used as the simplified model of servo mechanism.
Further, specific steps of determining characteristic parameters of the model by an
optimal control algorithm are:
determining a transfer function of the simplified model of servo mechanism, according
to a structure of the simplified model of servo mechanism; converting the problem of solving characteristic parameters into an optimization problem, taking minimization of an error of the item in the amplitude-phase-frequency characteristics that needs to be corrected relative to the expected value as the optimization target, and taking the other item satisfying the expected value as the optimization constraint; solving the optimization problem with an optimal control method for nonlinear constraint optimization problem; and substituting an obtained optimal solution into the transfer function to obtain the characteristic parameters of the simplified model of servo mechanism.
Further, the transfer function of the simplified model of servo mechanism composed of
the second-order oscillation link in series with two lag links is:
co -rs+1 ar s+1 G,(s) = 2 R 9 112 s + 2' c ;rn s+1 _r2s+1
where, o, 4., a, TI, and T21 are the characteristic parameters of the simplified model of
servo mechanism to be solved.
Further, when the item needs to be corrected is a phase-frequency characteristics, the
optimization target is taken as: min J
J =$wj|P(co,)-P,(CO )| where,
wherein, n is the number of key frequency points involved in the phase-frequency
characteristics that needs to be corrected; (0 is the key frequency point involved in the
phase-frequency characteristics that needs to be corrected; P(CO) is a phase value of the
simplified model of servo mechanism at the key frequency point involved; P,(I) isan
expected phase value at the key frequency point involved; and wi is a weighted value.
Further, the key frequency points include key frequency points corresponding to a
first-order rigid body segment, a first-order liquid sloshing frequency and a first-order elastic oscillation frequency, and the optimization target is to minimize the phase error at the key frequency points relative to the expected value, the optimization constraint is an amplitude requirement of frequency point corresponding to second-order and above oscillation frequencies, and the characteristic parameters of the simplified model of servo mechanism are obtained by solving the optimization target.
Further, the optimal control algorithm adopts a SQP algorithm.
Another aspect of the present disclosure provides a storage medium, an executable
program is stored therein, the executable program, when being called, executes the
above-mentioned modeling method for simplified model of servo mechanism.
Yet another aspect of the present disclosure provides a server comprising a memory
and a processor, the memory stores an executable program, and the processor is configured to
call the executable program to execute the above-mentioned modeling method for simplified
model of servo mechanism.
It can be seen that the modeling method for simplified model of servo mechanism
provided by the present disclosure improves the structure of the simplified model of servo
mechanism commonly used at present, and introduces an amplitude-phase correction link to
ensure that the simplified model has high modeling accuracy in multiple frequency bands;
meanwhile, the characteristic parameter fitting problem of the simplified model of servo
mechanism is transformed into an optimal control problem, which avoids the trial-and-error
procedure of characteristic parameters and significantly improves the solving efficiency.
It is to be understood that the foregoing general description and the following detailed
embodiments are exemplary and explanatory only, and are not intended to limit the scope of the
invention as claimed.
Brief Description of the Drawings
The accompanying drawings, which are part of the specification of the disclosure,
illustrate exemplary embodiments of the disclosure and, together with the description of the
specification, serve to explain the principles of the disclosure.
FIG. 1 is a flowchart of a modeling method for simplified model of servo mechanism
according to an exemplary embodiment;
FIG. 2 is a bode diagram of the simplified model of servo mechanism obtained by the
modeling method for simplified model of servo mechanism according to the exemplary
embodiment.
Detailed Description of Embodiments
Exemplary embodiments of the present disclosure will be described in detail below
with reference to the accompanying drawings. The various embodiments should not be
construed as limitations of the present disclosure, but should be understood as more detailed
descriptions of certain aspects, characteristics and implementations of the present disclosure.
Various modifications and changes can be made to the specific embodiments of the present
disclosure by those skilled in the art without departing from the scope or spirit of the present
disclosure.
FIG. 1 shows a flowchart of a modeling method for simplified model of servo
mechanism according to an exemplary embodiment. As shown in FIG. 1, the method comprises
the following steps:
(1) Determining amplitude-phase-frequency characteristics that the simplified model of
servo mechanism needs to meet, including expected values of amplitude and phase at a series of
key frequency points.
The amplitude-frequency and phase-frequency characteristics that the simplified model
of servo mechanism needs to meet is comprehensively determined based on the measured value
or index value of the amplitude-frequency and phase-frequency characteristics of the servo mechanism, combined with the rigid body cutoff frequency of the launch vehicle, the first-order liquid sloshing frequency, and the lateral first-order, second-order and third-order elastic oscillation frequencies, etc.
Taking a large liquid launch rocket as an example. The first-order liquid sloshing
frequency and the first-order elastic frequency of this vehicle are relatively low, and a phase
stabilization method needs to be adopted, while it needs to be considered both the amplitude
stability margin and the phase stability margin for the low-frequency rigid body segment. Such
frequency relationship usually satisfies: rigid body cutoff frequency < first-order liquid sloshing
frequency < first-order elastic mode frequency. Therefore, for the frequency points in the
measured value or index value of the amplitude and phase characteristics of the servo
mechanism that are lower than the first-order elastic oscillation frequency of the rocket, the
simplified servo mechanism model is required to have high amplitude accuracy and phase
accuracy at the same time; the second-order elastic oscillation and the third-order elastic
oscillation need to adopt a method with stable amplitude. Therefore, in the frequency range of
the second-order elastic oscillation and third-order elastic oscillation, the simplified servo
mechanism model is required to have high amplitude accuracy; while the frequency points in
the measured value or index value of the servo mechanism that are higher than the third-order
elastic oscillation frequency require a simplified servo model having appropriate amplitude
accuracy.
(2) Adopting a traditional second-order oscillation link to perform preliminary
simplified modeling of the servo mechanism, and analysing an error of the model between the
amplitude-phase-frequency characteristics at the key frequency point and an expected value, if
an amplitude error and a phase error are both smaller than a set threshold value, it is determined
that the simplified model of servo mechanism is the second-order oscillation link, otherwise a
system formed by the second-order oscillation link and an amplitude-phase correction link in
series is used as the simplified model of servo mechanism.
Here, the amplitude-phase correction link is used to adjust the amplitude-phase
characteristics of the simplified model of servo mechanism composed of only the traditional
second-order oscillation link that have a large error to the expected value, so that it is close to
the amplitude-phase characteristics that need to be satisfied.
As a preferred solution, the amplitude-phase correction link may adopt a lag-lead link
or a time delay link, wherein the lag-lead link is used to correct the amplitude error or the phase
error, and the time delay link is used to increase a delay of the phase. Of course, those skilled in
the art may also adopt all other existing links capable of adjusting the amplitude-frequency or
phase-frequency characteristics of the system according to specific requirements.
As a preferred example, the threshold value of the amplitude error is 1 dB, and the
threshold value of the phase error is 2 degrees.
In addition, the number of the lag-lead link or the time-delay link connected in series in
the simplified model of servo mechanism is not limited to one. A preferred example is:
On the basis of the second-order oscillation link, two lag links are connected in series
to correct the phase characteristics of the second-order oscillation link, and such a series system
is used as the simplified model of servo mechanism.
(3) For a simplified model of the series structure composed of the second-order
oscillation link and the amplitude-phase correction link, characteristic parameters of the model
are determined by an optimal control algorithm, wherein an item in the
amplitude-phase-frequency characteristics that needs to be corrected is used as an optimization
target, and the other item is used as an optimization constraint.
For the simplified model of servo mechanism consisting only of an oscillation link, the
estimation of the characteristic parameters of the model is a mature technology, which may
usually be estimated based on empirical values.
For the simplified model of the series structure composed of the second-order
oscillation link and the amplitude-phase correction link, in the present disclosure, the
characteristic parameter fitting problem of this type of model is transformed into an optimization problem, and the optimization index and optimization constraint are determined according to the expected values of amplitude and phase of the simplified model of servo mechanism obtained in step 1 at key frequency points.
As a preferred solution, the specific steps of determining characteristic parameters of
the model by an optimal control algorithm are:
(i) Determining a transfer function of the simplified model of servo mechanism,
according to a structure of the simplified model of servo mechanism;
(ii) Converting the problem of solving characteristic parameters into an optimization
problem, taking minimization of an error of the item in the amplitude-phase-frequency
characteristics that needs to be corrected relative to the expected value as the optimization
target, and taking the other item satisfying the expected value as the optimization constraint;
(iii) Solving the optimization problem with an optimal control method for nonlinear
constraint optimization problem; and
(iv) Substituting an obtained optimal solution into the transfer function to obtain the
characteristic parameters of the simplified model of servo mechanism.
Taking the aforementioned simplified model of servo mechanism composed of a
second-order oscillation link in series with two lag links as an example, the transfer function of
the model is:
2 -rs+1 ar s+1 G,(s) = 2 R 9 112 s + 2rco,,s o is+1 1 _r2 1s+1
In the formula, 0o, 4n, a, T1 1 , and T2 1 are the characteristic parameters of the
simplified model of servo mechanism to be solved.
When determining the item that needs to be corrected in the
amplitude-phase-frequency characteristics, since the requirements of the amplitude-frequency
characteristics can be easily satisfied by reasonably selecting the characteristic parameters of
the second-order oscillation link, the phase is generally used as the optimization index, and the
amplitude is used as the optimization constraint.
As a preferred solution, when the item needs to be corrected is a phase-frequency
characteristics, the optimization target is taken as: min J
n J =$ |~-P(6))-P,(Co)| Where,
In the formula, n is the number of key frequency points involved in the
phase-frequency characteristics that needs to be corrected; (0 is the key frequency point
involved in the phase-frequency characteristics that needs to be corrected; P(oi) is a phase value
of the simplified model of servo mechanism at the key frequency point involved; Pre() is an
expected phase value at the key frequency point involved; and wi is a weighted value.
Further, the key frequency points include key frequency points corresponding to a
first-order rigid body segment, a first-order liquid sloshing frequency and a first-order elastic
oscillation frequency, and the optimization target is to minimize the phase error at the key
frequency points relative to the expected value, the optimization constraint is an amplitude
requirement of frequency point corresponding to second-order and above oscillation
frequencies, and the characteristic parameters of the simplified model of servo mechanism are
obtained by solving the optimization target.
As a preferred solution, the optimal control algorithm adopts a sequential quadratic
programming method, that is, the SQP algorithm. It can be realized by using the fmincon
function of matlab.
(4) Verifying whether the error of the simplified model of servo mechanism between
the amplitude-phase-frequency characteristics at the key frequency point and the expected value
meets a requirement. If the requirement is not met, the previous model structure is adjusted to
further correct the amplitude-phase characteristics.
Application Examples
According to the analysis results of the elastic characteristics and sloshing
characteristics of a launch rocket, the first-order liquid sloshing frequency is in the range of
0.2Hz ~1Hz, the first-order elastic oscillation frequency is in the range of 1.8Hz ~ 3.1Hz, the
second-order elastic oscillation frequency is in the range of 5.4Hz ~ 9.0Hz, and the third-order
elastic oscillation frequency is in the range of 8.4Hz ~ 12.1Hz.
The index requirements of the servo mechanism are shown in Table 1.
Table 1: Frequency characteristic requirements of servo mechanism
Frequency (Hz) Amplitude (dB) Phase(°) 0.16 <0.3 >-6 1 < 0.3 > -12 2 <0.3 >-19 3 < 0.3 > -28 5 < 0.3 > -42 8 <0.3 >-56 10 < 0.3 > -66 12 < 0.3 > -75 15 < -2.0 > -90
The modeling process of the simplified model of servo mechanism includes the
following steps:
(1) Determining expected values of amplitude-phase-frequency characteristics
By analysing the sloshing and elastic frequency of the liquid rocket and the index
requirements of the servo mechanism, and considering that the theoretical analysis results of the
stability margin should have a certain margin compared with the actual situation, the obtained
expected values of the amplitude-frequency and phase-frequency characteristics of the
simplified model of servo mechanism at the key frequency points are: in the range of 0.16Hz ~
12Hz, the amplitude is about OdB; at 15Hz, the amplitude is about -2dB; at 0.16Hz, 1Hz, 2Hz
and 3Hz, the phases are about -6°, - 12°, -19° and -28°, respectively.
(2) Analysing and determining the structure of the simplified model of servo
mechanism
The second-order oscillation link has the characteristics of amplitude attenuation of
3dB and phase lag of 90 at its bandwidth. According to the amplitude index in Table 1, the
servo mechanism is simplified as:
2
G,(s)= , 2 n" +C 2 s" + 2j,<cos t)o;
In the formula, 4,=0.707, (0=17Hz.
Table 2: Frequency characteristics of the second-order oscillation link
Frequency (Hz) Amplitude (dB) Phase(0) 0.16 0 -0.8 1 0 -4.7 2 0 -9.5 3 0 -14.3 5 0 -24.3 8 -0.2 -40.2 10 -0.4 -51.5 12 -0.9 -63.0 15 -2.0 -79.8
It can be seen that if the model of servo mechanism is approximated as a second-order
oscillation link, its amplitude can meet the index requirements of the servo mechanism, but the
phase lag is significantly smaller than the index requirements. If the second-order oscillation
link is used as the simplified model of servo mechanism for system stability analysis, the phase
margin obtained for the low-frequency rigid body segment and the first-order liquid sloshing
may be larger than actual situation, making the stability analysis results inaccurate.
In order to solve this problem, two lag links are connected in series on the basis of the
second-order oscillation link to improve the phase characteristics of the simplified model, and
such a series system is used as the simplified model of servo mechanism. The transfer function
of the simplified model of servo mechanism is:
__ 0___-_______ S+1__ T21S+
s o222-so ; jrs+1 ra2 s+1 (1)
In the formula, (on, n, a, Tu and T2 1 are the characteristic parameters of the servo
mechanism to be confirmed.
(3) Characteristic parameters solving
On the basis of the simplified model of servo mechanism determined in step 2, the
characteristic parameter fitting problem of the simplified model of servo mechanism is
transformed into an optimization problem. Since the amplitude-frequency characteristic
requirements are easily satisfied by reasonably selecting the characteristic parameters of the
second-order oscillation link, the lag-lead link is mainly used to improve the phase-frequency
characteristics of the simplified model of servo mechanism, making it closer to the index
requirements of the servo mechanism. Therefore, according to the expected value of the
phase-frequency characteristics of the simplified model of servo mechanism obtained in step 1,
the optimization index is taken as:
J w |P(mi P mi }
In the formula, n=4; (0 1 =0.16Hz, (0 2 =lHz, (0 3=2Hz, (0 4=3Hz; P(co) is the phase value
of the simplified servo mechanism model at each key frequency point; Pref(i) is the expected
phase value of the servo mechanism at each key frequency point. According to the analysis in
step 1, Pre#(i)=-6°, Pret(02)=-12°, Pref(W3)=-19°, Pret(o4)=- 2 8 0; and wi is a weighted value.
The above optimization indicators ensure the phase accuracy of the simplified model
of servo mechanism at the frequency points such as the low-frequency rigid body segment, the
first-order liquid sloshing frequency and the first-order elastic oscillation frequency. For the
amplitude requirements of frequency points, such as 5Hz - 15Hz, in the frequency
characteristic index, they are used as the optimization constraints. The characteristic parameter determination problem of the simplified model of servo mechanism is transformed into the following optimization problem: min J
M(co) 0.3dB M(co )0.3dB s.t. M(co7 ) 0.3dB M(co,) 0.3dB M (cog) -2dB
In the formula, (0 5 =5Hz, 0 6=8Hz, 0 7 =1OHz, 0 8=12Hz, and 0 9=15Hz.
Use the fmincon function of matlab to solve the above optimal problem, and substitute
the optimal solution 05 =12.5, 4=0.5, T 1=1.02, T 1=0.0064 and a =0.899 into the formula (1)
to obtain the simplified model of servo mechanism.
(4) Model validating
Check whether the error between the amplitude-frequency and phase-frequency
characteristics of the above-mentioned simplified model of servo mechanism at the key
frequency points and the index value meets the requirements.
A bode diagram of the simplified model of servo mechanism is drawn, as shown in
Figure 2. The frequency characteristics of the key frequency points given in step 1 of the
simplified model are shown in Table 3.
Table 3: Key frequency characteristics of the simplified model of servo mechanism
Simplified model Index value Frequency(Hz) Amplitude (dB) Phase(°) Amplitude (dB) Phase(°) 0.16 -0.4 -4.5 < 0.3 > -6 1 -0.9 -10.2 < 0.3 > -12 2 -0.8 -19.0 < 0.3 > -19 3 -0.7 -28.3 < 0.3 > -28 5 -0.3 - < 0.3 > -42 8 0.3 - < 0.3 > -56 10 0.2 - < 0.3 > -66 12 -0.6 - < 0.3 > -75 15 -3.0 - < -2.0 > -90
It can be seen that the amplitude-frequency characteristics of the simplified model of
servo mechanism meets the requirements of the index, and the error between the phase
characteristics at the key frequency point and the index value is less than 2 degrees. Compared
with the traditional second-order simplified model, the simplified model of servo mechanism
has higher phase accuracy at the key frequency points concerned by the stability analysis of the
control system, and the obtained simplified model of servo mechanism is reasonable.
The above-described embodiments of the present application may be implemented in
various hardware, software coding, or a combination of both. For example, the embodiments of
the present application may also represent program codes for executing the above method in a
digital signal processor (Digital Signal Processor, DSP). The application may also relate to
various functions performed by computer processors, digital signal processors,
microprocessors, or Field Programmable Gate Arrays (FPGAs). The above-described
processors may be configured in accordance with the present application to perform specific
tasks by executing machine-readable software code or firmware code that defines the specific
methods disclosed herein. The software code or firmware code may be developed to represent
different programming languages and different formats or forms. It can also represent different
target platform compiling software codes. However, different code styles, types and languages
of software codes for performing tasks in accordance with this disclosure and other types of
configuration codes do not depart from the spirit and scope of this disclosure.
The above description is only an exemplary embodiment of the present disclosure,
without departing from the concept and principle of the present disclosure, any equivalent
changes and modifications made by those skilled in the art shall fall within the protection scope
of the present disclosure.
Claims (13)
1. A modeling method for simplified model of servo mechanism, characterized by
comprising:
determining amplitude-phase-frequency characteristics that the simplified model of servo
mechanism needs to meet, including expected values of amplitude and phase at a series of key
frequency points;
adopting a second-order oscillation link to perform preliminary simplified modeling of the
servo mechanism, and analysing an error of the model between the amplitude-phase-frequency
characteristics at the key frequency point and an expected value, if an amplitude error and a
phase error are both smaller than a set threshold value, it is determined that the simplified
model of servo mechanism is the second-order oscillation link, otherwise a system formed by
the second-order oscillation link and an amplitude-phase correction link in series is used as the
simplified model of servo mechanism;
for a simplified model of the series structure composed of the second-order oscillation link
and the amplitude-phase correction link, determining characteristic parameters of the model by
an optimal control algorithm, wherein an item in the amplitude-phase-frequency characteristics
that needs to be corrected is used as an optimization target, and the other item is used as an
optimization constraint; and
verifying whether the error of the simplified model of servo mechanism between the
amplitude-phase-frequency characteristics at the key frequency point and the expected value
meets a requirement.
2. The modeling method for simplified model of servo mechanism according to claim 1,
wherein, the threshold value of the amplitude error is taken as ldB.
3. The modeling method for simplified model of servo mechanism according to claim 1,
wherein, the threshold value of the phase error is taken as 2 degrees.
4. The modeling method for simplified model of servo mechanism according to claim 1, wherein, the amplitude-phase correction link comprises but is not limited to a lag-lead link and a time delay link, wherein the lag-lead link is used to correct the amplitude error or the phase error, and the time delay link is used to increase a delay of the phase.
5. The modeling method for simplified model of servo mechanism according to claim 4,
wherein, the number of the lag-lead link or the time-delay link connected in series in the
simplified model of servo mechanism is not limited to one.
6. The modeling method for simplified model of servo mechanism according to claim 5,
wherein, on the basis of the second-order oscillation link, two lag links are connected in series
to correct phase characteristics of the second-order oscillation link, and such a series system is
used as the simplified model of servo mechanism.
7. The modeling method for simplified model of servo mechanism according to claim 1,
wherein, specific steps of determining characteristic parameters of the model by an optimal
control algorithm are:
determining a transfer function of the simplified model of servo mechanism, according to a
structure of the simplified model of servo mechanism;
converting the problem of solving characteristic parameters into an optimization problem,
taking minimization of an error of the item in the amplitude-phase-frequency characteristics
that needs to be corrected relative to the expected value as the optimization target, and taking
the other item satisfying the expected value as the optimization constraint;
solving the optimization problem with an optimal control method for nonlinear constraint
optimization problem; and
substituting an obtained optimal solution into the transfer function to obtain the
characteristic parameters of the simplified model of servo mechanism.
8. The modeling method for simplified model of servo mechanism according to claim 7,
wherein, the transfer function of the simplified model of servo mechanism composed of the second-order oscillation link in series with two lag links is:
)2 -rs+1 ar s+1 G,(s) = 2 R 9 112 s + 2 ,mss s+1 _rIs+1
where, o, 4., a, TI, and T2 1 are the characteristic parameters of the simplified model of
servo mechanism to be solved.
9. The modeling method for simplified model of servo mechanism according to claim 1 or
7, wherein, when the item needs to be corrected is a phase-frequency characteristics, the
optimization target is taken as: min J
I =wi | P(Coi )P, (wi )
where,
wherein, n is the number of key frequency points involved in the phase-frequency
characteristics that needs to be corrected; (0 is the key frequency point involved in the
phase-frequency characteristics that needs to be corrected; P(oi) is a phase value of the
simplified model of servo mechanism at the key frequency point involved; Pret(Oi) is an
expected phase value at the key frequency point involved; and wi is a weighted value.
10. The modeling method for simplified model of servo mechanism according to claim 9,
wherein, the key frequency points include key frequency points corresponding to a first-order
rigid body segment, a first-order liquid sloshing frequency and a first-order elastic oscillation
frequency, and the optimization target is to minimize the phase error at the key frequency points
relative to the expected value, the optimization constraint is an amplitude requirement of
frequency point corresponding to second-order and above oscillation frequencies, and the
characteristic parameters of the simplified model of servo mechanism are obtained by solving
the optimization target.
11. The modeling method for simplified model of servo mechanism according to claim 1 or 7, wherein, the optimal control algorithm adopts a SQP algorithm.
12. A storage medium, characterized in that an executable program is stored therein, the
executable program, when being called, executes the modeling method for simplified model of
servo mechanism according to any one of claims 1-11.
13. A server, characterized by comprising a memory and a processor, the memory stores an
executable program, and the processor is configured to call the executable program to execute
the modeling method for simplified model of servo mechanism according to any one of claims
1-11.
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