CN113625564B - Sliding mode control method based on system model for structural thermal test - Google Patents
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Abstract
The application discloses a sliding mode control method based on a system model for a structural heat test, which comprises the steps of establishing a hypersonic aircraft aerodynamic heat ground structural heat test system mathematical model according to an energy conservation law; constructing a nonlinear fractional order sliding mode surface equation by using tracking errors, nonlinear functions, fractional order differentiation and fractional order integration; constructing a controller of a silicon controlled rectifier conduction angle alpha (t) based on the structural heat test system mathematical model, the nonlinear fractional order sliding mode surface, the supercoiled approach rate and the time delay observer; establishing Lyapunov function V(s), satisfying V(s) positive determination,half negative definite to obtainThe convergence is verified to converge to an equilibrium state. The application improves the control effect of the whole arrival stage, and the time delay observer observes the input disturbance, so that the whole system forms a closed loop control, and the combination of the parts ensures the stability and convergence speed of the control and reduces the steady state error and overshoot of the system.
Description
Technical Field
The application relates to the technical field of aerospace automation, in particular to a sliding mode control method based on a system model for a structural thermal test.
Background
The structural heat test system is used for simulating the heat environment of the hypersonic flight process of the aircraft in the aspect of aerospace to test whether the material of the hypersonic flight can bear the heat generated in the flight process, wherein a quartz lamp is often used as a heating element due to the characteristics of high temperature speed, high power, small volume and high controllability. Although quartz filament autogenous can reach the highest temperature of the wall surface of the hypersonic aircraft in the flight process, the traditional control method, such as a PID control method, cannot accurately and truly simulate the heat energy generated by the friction of airflow in the flight process of the hypersonic aircraft due to the self parameter limitation.
The structural thermal test system is a typical complex nonlinear system with thermal inertia and time lag. The sliding mode control system is not applicable to the traditional control system any more, and in some modern control systems of today, the sliding mode control system has the capabilities of insensitivity to parameter change, external disturbance resistance and quick dynamic response, and can eliminate errors in a limited time, so that the sliding mode control system is widely applied to various control objects. However, the traditional sliding mode control can generate buffeting phenomenon in the arrival and sliding stages, and the convergence speed is poor when the sliding mode control is far away from the switching surface, so that the accurate simulation of the structural thermal test system to the real environment is difficult to meet.
Disclosure of Invention
This section is intended to outline some aspects of embodiments of the application and to briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section as well as in the description of the application and in the title of the application, which may not be used to limit the scope of the application.
The present application has been made in view of the above-described problems occurring in the prior art.
Therefore, the sliding mode control method based on the system model for the structural heat test can accurately and truly simulate and control the thermal environment of the hypersonic aircraft in the flight process based on the structural heat system.
In order to solve the technical problems, the application provides the following technical scheme: according to the law of conservation of energy, a mathematical model of a hypersonic aircraft aerodynamic heat ground structure heat test system is established; constructing a nonlinear fractional order sliding mode surface equation by using tracking errors, nonlinear functions, fractional order differentiation and fractional order integration; constructing a controller of a silicon controlled rectifier conduction angle alpha (t) based on the structural heat test system mathematical model, the nonlinear fractional order sliding mode surface, the supercoiled approach rate and the time delay observer; establishing Lyapunov function V(s), satisfying V(s) positive determination,semi-negative settingObtain->The convergence is verified to converge to an equilibrium state.
As a preferable scheme of the sliding mode control method based on the system model for the structural thermal test, the application comprises the following steps: establishing an input-output energy conservation equation according to the energy conservation law to obtain the current temperature T 1 And the conduction angle alpha of the bidirectional thyristor, i.e. the mathematical model, comprises,
Q＝w
wherein w is the electric energy provided by a power supply, Q is the electric heating energy absorbed by the structural heat test heating element, and the left side of the equation is the internal energy consumed by the structural heat test heating element, the heat energy lost in the convection heat exchange process, the heat energy lost in the heat conduction process and the heat energy output by the heat radiation effect, c, m and T respectively 1 、T 0 The specific heat capacity, the mass, the current temperature, the initial temperature, the surface area, the blackness coefficient and the working time of the structural heat test heating element are respectively shown as A, epsilon and delta t, and the beta, lambda, sigma and F are respectively shown as the convective heat transfer coefficient, the heat conduction coefficient, the Stefan-Boltzmann constant and the angular coefficient, and the right U of the equation I For the input voltage, namely the voltage at two ends of a power supply, R is the sum of resistances of the heating elements in the structural thermal test, and alpha is the conduction angle of the bidirectional thyristor.
As a preferable scheme of the sliding mode control method based on the system model for the structural thermal test, the application comprises the following steps: also included is a method of manufacturing a semiconductor device,
wherein,is T 1 For time of dayIs a derivative of (a).
As a preferable scheme of the sliding mode control method based on the system model for the structural thermal test, the application comprises the following steps: establishing the nonlinear fractional order sliding mode surface equation, including,
defining a tracking error expression as:
e(t)＝T 1 * -T 1
wherein T is 1 * Is T 1 E (t) is the tracking error;
the nonlinear function fal (e, γ, η) includes,
wherein, gamma and eta are used for nonlinear function parameter adjustment, 0< gamma <1, eta >0;
wherein,and->For slip form surface adjustment parameters,/-, for> And->The differential of the fractional order and the integral of the fractional order, respectively.
As a preferable scheme of the sliding mode control method based on the system model for the structural thermal test, the application comprises the following steps: the time delay observer comprises a time delay module,
wherein,for the input disturbance of a structural thermal test system, +.>And v is the delay time, which is the observed value of G (t).
As a preferable scheme of the sliding mode control method based on the system model for the structural thermal test, the application comprises the following steps: the supercoiled approach rate comprises,
wherein lambda is 3 And lambda (lambda) 4 Is the parameter adjusting coefficient lambda of the super-spiral approach rate 3 >0,λ 4 >0， Is the observed error and has an upper bound, error upper bound +.>Satisfies the condition
As a preferable scheme of the sliding mode control method based on the system model for the structural thermal test, the application comprises the following steps: the controller of the thyristor conduction angle alpha comprises,
wherein,to the desired output temperature T 1 * Is a derivative of (a).
As a preferable scheme of the sliding mode control method based on the system model for the structural thermal test, the application comprises the following steps: the Lyapunov function, including,
wherein V(s) is a Lyapunov function.
As a preferable scheme of the sliding mode control method based on the system model for the structural thermal test, the application comprises the following steps: the verification of the convergence includes the steps of,
V(s)>0
wherein,is the derivative of V(s);
δ T ＝[|s(t)| 1/2 sign(s(t)) -λ 4 ∫sign(s(t))dt]，
when (when)When the condition is satisfied, the condition is satisfied>I.e. there is->Make->s can converge to a steady state s 0 。
The application has the beneficial effects that: the nonlinear function, the differential of fractional order and the integral of fractional order are added on the sliding mode surface, so that the control precision in the sliding stage is increased, the convergence speed is accelerated, the high-frequency buffeting phenomenon is weakened, the super-spiral approach rate is introduced, the speed from the reaching stage to the sliding stage is accelerated, the buffeting phenomenon in the process is weakened, the control effect of the whole reaching stage is improved, the input disturbance is observed by the time delay observer, the whole system forms a closed loop control, and the combination of all parts ensures the stability and the convergence speed of the control and simultaneously reduces the steady-state error and the overshoot of the system.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art. Wherein:
FIG. 1 is a schematic view of a three-dimensional structure of a hypersonic aircraft wing portion of a sliding mode control method based on a system model for structural thermal testing according to an embodiment of the present application;
FIG. 2 is a schematic illustration of a simulation of a hypersonic aircraft wing section in finite elements of a system model based sliding mode control method for structural thermal testing in accordance with one embodiment of the present application;
FIG. 3 is a schematic diagram of sampling average temperature of a wall surface of a wing portion of a hypersonic aircraft according to a sliding mode control method for a structural thermal test based on a system model according to an embodiment of the present application;
FIG. 4 is a schematic diagram of a schematic control framework of a sliding mode control method for a structural thermal test based on a system model according to an embodiment of the present application;
FIG. 5 is a graph of hypersonic aircraft structural thermal test system fit versus a comparison of a supercoiled nonlinear fractional order sliding mode control method based on a time delay observer and a conventional PID control method for structural thermal test system model-based sliding mode control according to an embodiment of the present application;
FIG. 6 is a graph of hypersonic aircraft structural thermal test system fit versus output temperature trace versus supercoiled nonlinear fractional order sliding mode control method based on time delay observer and traditional PID control method for structural thermal test system model-based sliding mode control method according to one embodiment of the present application;
FIG. 7 is a graph of error tracking curves comparing a super-spiral nonlinear fractional order sliding mode control method based on a time delay observer of a hypersonic aircraft structural thermal test system with a conventional PID control method under a tracking fit target according to a sliding mode control method based on a system model for structural thermal test of an embodiment of the application;
fig. 8 is a partial enlarged view of an error tracking curve compared with a traditional PID control method and a supercoiled nonlinear fractional order sliding mode control method based on a time delay observer of a structural thermal test system of a hypersonic aircraft under a tracking fit target according to a sliding mode control method based on a system model of a structural thermal test of an embodiment of the present application.
Detailed Description
So that the manner in which the above recited objects, features and advantages of the present application can be understood in detail, a more particular description of the application, briefly summarized above, may be had by reference to the embodiments, some of which are illustrated in the appended drawings. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments of the present application without making any inventive effort, shall fall within the scope of the present application.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application, but the present application may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present application is not limited to the specific embodiments disclosed below.
Further, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic can be included in at least one implementation of the application. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
While the embodiments of the present application have been illustrated and described in detail in the drawings, the cross-sectional view of the device structure is not to scale in the general sense for ease of illustration, and the drawings are merely exemplary and should not be construed as limiting the scope of the application. In addition, the three-dimensional dimensions of length, width and depth should be included in actual fabrication.
Also in the description of the present application, it should be noted that the orientation or positional relationship indicated by the terms "upper, lower, inner and outer", etc. are based on the orientation or positional relationship shown in the drawings, are merely for convenience of describing the present application and simplifying the description, and do not indicate or imply that the apparatus or elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present application. Furthermore, the terms "first, second, or third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The terms "mounted, connected, and coupled" should be construed broadly in this disclosure unless otherwise specifically indicated and defined, such as: can be fixed connection, detachable connection or integral connection; it may also be a mechanical connection, an electrical connection, or a direct connection, or may be indirectly connected through an intermediate medium, or may be a communication between two elements. The specific meaning of the above terms in the present application will be understood in specific cases by those of ordinary skill in the art.
Example 1
Referring to fig. 1 to fig. 4, for a first embodiment of the present application, a sliding mode control method based on a system model for a structural thermal test is provided, where the method is based on a nonlinear fractional order sliding mode surface, and combines a time delay observer and a supercoiled approach rate, and designs a controller α (t) to achieve target tracking; referring to fig. 4, a control block diagram of a supercoiled nonlinear fractional order sliding mode control method of a hypersonic aircraft structure thermal test system based on a time delay observer according to the application specifically comprises:
s1: and establishing a hypersonic aircraft aerodynamic heat ground structure heat test system mathematical model according to the law of conservation of energy. It should be noted that, according to the law of conservation of energy, an input-output energy conservation equation is established to obtain the current temperature T 1 And the conduction angle alpha of the bidirectional thyristor, namely a mathematical model, comprising:
Q＝w
wherein w is the electric energy provided by a power supply, Q is the electric heating energy absorbed by the structural heat test heating element, and the left side of the equation is the internal energy consumed by the structural heat test heating element, the heat energy lost in the convection heat exchange process, the heat energy lost in the heat conduction process and the heat energy output by the heat radiation effect, c, m and T respectively 1 、T 0 The components A, epsilon and delta t are respectively structural heat test heating elementsSpecific heat capacity, mass, current temperature, initial temperature, surface area, blackness coefficient, working time of the piece, beta, lambda, sigma, F are respectively convection heat transfer coefficient, heat conduction coefficient, stefan-Boltzmann constant, angle coefficient, U on right side of equation I R is the sum of resistances of heating elements in a structural thermal test, and alpha is the conduction angle of the bidirectional thyristor;
wherein,is T 1 Derivative with respect to time.
S2: and constructing a nonlinear fractional order sliding mode surface equation by using the tracking error, the nonlinear function, the fractional order differential and the fractional order integral. The step needs to be described, the establishment of a nonlinear fractional order sliding mode surface equation comprises the following steps:
defining a tracking error expression as:
e(t)＝T 1 * -T 1
wherein T is 1 * Is T 1 E (t) is the tracking error;
the nonlinear function fal (e, γ, η) includes,
wherein, gamma and eta are used for nonlinear function parameter adjustment, 0< gamma <1, eta >0;
wherein,and->For slip form surface adjustment parameters,/-, for> And->The differential of the fractional order and the integral of the fractional order, respectively.
S3: and constructing a controller of the conduction angle alpha (t) of the silicon controlled rectifier based on a mathematical model of the structural thermal test system, a nonlinear fractional order sliding mode surface, a supercoiled approach rate and a time delay observer. It should be further noted that the time delay observer includes:
wherein,for the input disturbance of a structural thermal test system, +.>And v is the delay time, which is the observed value of G (t).
Further, the supercoiled approach rate includes:
wherein lambda is 3 And lambda (lambda) 4 Is the parameter adjusting coefficient lambda of the super-spiral approach rate 3 >0,λ 4 >0， Is the observed error and has an upper bound, error upper bound +.>Satisfy condition->
Still further, the controller of the conduction angle alpha of the silicon controlled rectifier comprises,
wherein,to the desired output temperature T 1 * Is a derivative of (a).
S4: establishing Lyapunov function V(s), satisfying V(s) positive determination,half-negative determination, get->The convergence is verified to converge to an equilibrium state. Lyapunov function, comprising:
wherein V(s) is a Lyapunov function.
The verification of the convergence includes the steps of,
V(s)>0
wherein,is the derivative of V(s);
δ T ＝[|s(t)| 1/2 sign(s(t)) -λ 4 ∫sign(s(t))dt]，
when (when)When the condition is satisfied, the condition is satisfied>I.e. there is->Make->s can converge to a steady state s 0 。
Specifically, the above V(s) is transformed into a quadratic form, as follows,
V(s)＝δ T Jδ
δ T ＝[|s(t)| 1/2 sign(s(t)) -λ 4 ∫sign(s(t))dt]，
deriving V(s), comprising:
according to the definition of positive definite matrix, whenWhen L is a positive definite matrix;
wherein ζ min { L } is the minimum eigenvalue of L,
wherein,
according to the condition V (0) >0, the differential equation is solved,
for a limited time and not more thane can converge to 0 and the stability of the control system is demonstrated.
Referring to fig. 1, a structural schematic diagram of a hypersonic aircraft wing in a finite element, the specific parameters of the wing are: the wing root 3550mm, the wing span 1250mm, the front edge sweepback angle 70 degrees, the rear edge sweepforward angle 15 degrees, the plate thickness 160mm, the front edge radius 40mm, the material is nickel-based superalloy GH1015, the flying environment is 20km, the speed is Mach number 5.5, and the attack angle is 10 degrees.
Referring to fig. 4, which is a control block diagram of a nonlinear fractional order sliding mode control of a hypersonic aircraft structural thermal test system based on time delay, is a further explanation of the structural thermal test control system, and according to the schematic diagram of fig. 4, the controller α (t) is composed of 3 parts: the nonlinear fractional order sliding mode surface provides a supercoiled approach rate; first order differentiation of the desired target; observing value of unknown disturbance G of system by utilizing time delay
Preferably, the embodiment also needs to explain that, compared with the prior art, the embodiment discloses a sliding mode control method based on a system model for a structural thermal test, which aims to track the expected temperature in a limited time by adopting a nonlinear fractional order sliding mode control method based on time delay observation, weaken the buffeting phenomenon in the control process, accelerate the convergence speed and ensure the robust performance of the whole control process; observing an uncertain item and external disturbance of the system by adopting a time delay observer; the nonlinear fractional order sliding mode surface and the supercoiled approach rate are adopted, so that the jitter in the approach stage can be effectively restrained, and the convergence rate is increased.
Example 2
Referring to fig. 3 and fig. 5 to fig. 8, a second embodiment of the present application, which is different from the first embodiment, provides a test comparison verification of a sliding mode control method based on a system model for a structural thermal test, and specifically includes:
in the embodiment, the output temperature and tracking error of the hypersonic aircraft structural thermal test system are measured and compared in real time by adopting the hypersonic aircraft structural thermal test system under the nonlinear fractional order sliding mode control method based on time delay and the traditional PID method.
Test environment: referring to fig. 3, a hypersonic aircraft structure thermal test system is operated on a simulation platform to simulate and track a desired target curve, and the hypersonic aircraft structure thermal test system is respectively utilized to test under a nonlinear fractional order sliding mode control method and a traditional PID method based on time delay, so as to obtain test result data; in both methods, the automatic test equipment is started, MATLB software programming is used for realizing simulation test of a comparison method, simulation data are obtained according to test results, 4 groups of data are tested in each method, each group of data is sampled for 20 seconds, each group of data input temperature and tracking error are obtained through calculation, and the calculation error is compared with the expected target temperature of simulation input.
Referring to fig. 3, a simulation diagram of finite element simulation of a wing, a wall average temperature sampling diagram and an average temperature curve fitting diagram are shown as follows:
T * ＝7.224×10 -6 ×t 6 -0.001041×t 5 +0.05614×t 4 -1.353××t 3 +11.86×t 2 +43.25t+279.2
referring to fig. 5, 6, 7 and 8, the output temperature curve graph and the partial enlarged graph, the error tracking curve contrast graph and the partial enlarged graph of the hypersonic aircraft structural thermal test system under the nonlinear fractional order sliding mode control method based on time delay and the traditional PID method are shown.
The following table shows the parameter settings of the specific embodiments:
table 1: structural thermal test system parameter table.
Table 2: the method parameter table of the application.
Table 3: conventional PID parameter tables.
Referring to fig. 5, it can be intuitively seen that 2 methods can effectively track the target curve, and in fig. 6, when the time is 0-2 s, the conventional PID method has a large overshoot.
Referring to FIG. 7, it can be intuitively seen that the conventional PID method begins to converge after 5s, and buffeting is more obvious; the hypersonic aircraft structural thermal test system has 4 ℃ of jitter at the beginning 0.01s and rapidly converges after 0.03s based on a nonlinear fractional order sliding mode control method of time delay.
Referring to fig. 8, it can be intuitively seen that the jitter phenomenon of the conventional PID method is severe within 5-10 s, and the hypersonic aircraft structural thermal test system is always kept in a stable state in the nonlinear fractional order sliding mode control method based on time delay.
Referring to fig. 5 to 8, it can be analyzed that the control method of the present application is superior to the conventional PID control method in terms of steady state error, convergence speed, overshoot, and control accuracy, and the sliding mode control method based on the system model of the present application, which benefits from the structural thermal test, weakens the buffeting phenomenon in the control process, accelerates the convergence speed, improves the control accuracy, and ensures the robust performance of the whole control process.
It should be noted that the above embodiments are only for illustrating the technical solution of the present application and not for limiting the same, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present application may be modified or substituted without departing from the spirit and scope of the technical solution of the present application, which is intended to be covered in the scope of the claims of the present application.
Claims (2)
1. A sliding mode control method based on a system model for a structural thermal test is characterized by comprising the following steps of: comprising the steps of (a) a step of,
according to the law of conservation of energy, a mathematical model of a hypersonic aircraft aerodynamic heat ground structure heat test system is established;
constructing a nonlinear fractional order sliding mode surface equation by using tracking errors, nonlinear functions, fractional order differentiation and fractional order integration;
constructing a controller of a silicon controlled rectifier conduction angle alpha (t) based on the structural heat test system mathematical model, the nonlinear fractional order sliding mode surface, the supercoiled approach rate and the time delay observer;
establishing Lyapunov function V(s), satisfying V(s) positive determination,half-negative determination, get->Verifying convergence to an equilibrium state;
establishing an input-output energy conservation equation according to the energy conservation law to obtain the current temperature T 1 And the conduction angle alpha (t) of the bidirectional thyristor, i.e. the mathematical model comprises,
Q＝w
wherein w is the electric energy provided by a power supply, Q is the electric heating energy absorbed by the structural heat test heating element, and the left side of the equation is the internal energy consumed by the structural heat test heating element, the heat energy lost in the convection heat exchange process, the heat energy lost in the heat conduction process and the heat energy output by the heat radiation effect, c, m and T respectively 1 、T 0 The specific heat capacity, the mass, the current temperature, the initial temperature, the surface area, the blackness coefficient and the working time of the structural heat test heating element are respectively shown as A, epsilon and delta t, and the beta, lambda, sigma and F are respectively shown as the convective heat transfer coefficient, the heat conduction coefficient, the Stefan-Boltzmann constant and the angular coefficient, and the right U of the equation I R is the sum of resistances of the heating elements in the structural thermal test, and is the input voltage, namely the voltage of two ends of a power supply;
also included is a method of manufacturing a semiconductor device,
wherein,is T 1 Derivative with respect to time;
establishing the nonlinear fractional order sliding mode surface equation s (t), including,
defining a tracking error expression as:
e(t)＝T 1 * -T 1
wherein T is 1 * Is T 1 E (t) is the tracking error;
the nonlinear function fal (e, γ, η) includes,
wherein, gamma and eta are used for nonlinear function parameter adjustment, 0< gamma <1, eta >0;
wherein,and->For slip form surface adjustment parameters,/-, for> And->The differential of fractional order and the integral of fractional order respectively;
the time delay observer comprises a time delay module,
wherein,for the input disturbance of a structural thermal test system, +.>An observation value of G (t), v being a delay time;
the supercoiled approach rate comprises,
wherein lambda is 3 And lambda (lambda) 4 Is the parameter adjusting coefficient of the super-spiral approach rate, is the observed error and has an upper bound, error upper bound +.>Satisfy condition->
The controller of the thyristor conduction alpha (t) comprises,
wherein,to the desired output temperature T 1 * Is a derivative of (2);
the Lyapunov function, including,
wherein V(s) is a Lyapunov function.
2. The sliding mode control method based on the system model for the structural thermal test according to claim 1, wherein: the verification of the convergence includes the steps of,
V(s)>0
wherein,is the derivative of V(s);
when (when)When the condition is satisfied, the condition is satisfied>Representing disturbance gain, ++>I.e. there is->So thats can converge to a steady state s 0 。
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