CN113495486A - Model prediction control method based on extended state observer for structural thermal test - Google Patents
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Abstract
The invention discloses a model prediction control method based on an extended state observer for a structural thermal test, which comprises the steps of constructing a mathematical model of the relation between the output temperature of a structural thermal test system and the conduction angle of a silicon controlled rectifier based on the law of energy conservation; dispersing a differential equation of the output temperature at the current moment k into a prediction model at the moment k +1 by a forward Euler formula; constructing a discrete linear extended state observer, and observing the uncertainty item and the external disturbance of the structural thermal test system; selecting the state quantity and the control quantity, and establishing a state equation of a prediction model of the structural thermal test system; expressing the state quantity and the output quantity at the future moment through the control quantity and the state value at the current moment; and constructing a cost function related to the predicted output error and the controlled variable to obtain the controlled variable. The rolling optimization of the invention replaces global optimization with local optimization, does not need parameter setting, fully invokes control action, improves control precision, reduces steady-state error and accelerates convergence speed.
Description
Technical Field
The invention relates to the technical field of aerospace automation, in particular to a model prediction control method based on an extended state observer for a structural thermal test.
Background
One of the most difficult problems of the high-ultrasonic aircraft in the design stage is the problem of thermal barrier in the flight process. Exacerbating the "thermal barrier" problem can seriously undermine the structural load-bearing capacity and material strength limitations of the aircraft, and even more can threaten the stability of the internally delicate electronic equipment. Simulation of the thermal environment in flight would be critical in determining the materials of the aircraft and in developing the aircraft. The structural thermal test system is a set of thermal strength test device for detecting hypersonic aircraft materials and structures by simulating real thermal environment in a flight state through controlling a quartz lamp heater. Considering that the temperature field of the surface of the aircraft during the real flight is highly nonlinear and transient, the design of a control method with high control precision, high convergence rate, high ascending rate and small overshoot is required.
Tests with quartz lamps as radiant heat elements are mostly based on empirical formulas, lack of mathematical models and systematic analysis. The effect of empirically based control methods is often an inefficient trade-off between control accuracy and decision selection. For example, the conventional PID control method brings the contradiction from rapidity to overshoot by the simple linear superposition of tracking errors. With the development of control theory, Model Predictive Control (MPC), which is an important branch of modern control theory, is emerging and widely applied to various control systems. MPC is a control algorithm for predicting the state quantity and output quantity at the future time by the state quantity at the current time, control input and a prediction model and then performing rolling optimization according to a cost function. Compared with other modern control methods, the MPC has low requirement on the precision of a mathematical model, does not need parameter setting, replaces global optimization with local optimization, and can utilize actual measurement information to feed back and increase the robust performance of a control system.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The present invention has been made in view of the above-mentioned conventional problems.
Therefore, the invention provides a model prediction control method based on an extended state observer for a structural thermal test, which accurately simulates the flight thermal environment of a hypersonic aircraft from local optimal to global optimal through model prediction.
In order to solve the technical problems, the invention provides the following technical scheme: constructing a mathematical model of the relationship between the output temperature of the structural thermal test system and the conduction angle of the silicon controlled rectifier based on the law of conservation of energy; dispersing a differential equation of the output temperature at the current moment k into a prediction model at the moment k +1 by a forward Euler formula; constructing a discrete linear extended state observer, and observing the uncertainty item and the external disturbance of the structural thermal test system; selecting the state quantity and the control quantity, and establishing a state equation of a prediction model of the structural thermal test system; expressing the state quantity and the output quantity at the future moment through the control quantity and the state value at the current moment; and constructing a cost function related to the predicted output error and the controlled variable to obtain the controlled variable.
As a preferred scheme of the model predictive control method based on the extended state observer in the structural thermal test, the method comprises the following steps: establishing an input and output energy conservation equation according to the energy conservation law to obtain the current temperature T1And the conduction angle a of the triac, i.e. the mathematical model, comprises,
Q＝w
wherein, w is the electric energy provided by the power supply, Q is the electric heat energy absorbed by the heating element in the structural thermal test, the left side of the equation is respectively the internal energy consumed by the heating element in the structural thermal test, 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, and c, m and T1、T0A, epsilon and delta t are respectively the specific heat of the heating element of the structural thermal testCapacity, mass, current temperature, initial temperature, surface area, blackness coefficient and working time, wherein beta, lambda, sigma and F are respectively a convective heat transfer coefficient, a thermal conductivity coefficient, a Stefan-Boltzmann constant and an angle coefficient, and the right side U of the equationIThe input voltage is the voltage at two ends of the power supply, R is the sum of the resistances of the heating elements in the structural thermal test, and alpha is the conduction angle of the bidirectional thyristor.
As a preferred scheme of the model predictive control method based on the extended state observer in the structural thermal test, the method comprises the following steps: also comprises the following steps of (1) preparing,
wherein the content of the first and second substances,
is T1Derivative with respect to time.
As a preferred scheme of the model predictive control method based on the extended state observer in the structural thermal test, the method comprises the following steps: discretizing a differential equation of the output temperature of the current sampling period k into a prediction model of k +1 sampling periods by the forward euler formula, including,
the prediction model of the output temperature of the (k +1) th sampling period is expressed by the current sampling period k as:
wherein, T1(k +1) is the predicted temperature, T, for the (k +1) th sampling period1(k) Is the output temperature of the current sampling period k, T is the time interval of each sampling period, alpha (k) is the control input quantity of the current sampling period k, delta (alpha (k)) is the system disturbance term,
as a preferred scheme of the model predictive control method based on the extended state observer in the structural thermal test, the method comprises the following steps: the discrete linear extended state observer, comprising,
wherein e is1To output the observed error of temperature, z1To output an observed value of temperature, z2Is an observed value of δ (α).
As a preferred scheme of the model predictive control method based on the extended state observer in the structural thermal test, the method comprises the following steps: also comprises the following steps of (1) preparing,
wherein e is1(k) Is the observed error of the output temperature of the current sampling period k, z1(k) Is T1(k) An observed value of z1(k +1) output temperature observation, β, for the (k +1) th sampling period1And beta2Is a positive gain coefficient of a linearly extended state observer, z2(k +1) is an observed value of δ (α (k +1)), and χ is a compensation factor of the estimator.
As a preferred scheme of the model predictive control method based on the extended state observer in the structural thermal test, the method comprises the following steps: also comprises the following steps of (1) preparing,
the state variables of the system are defined,
changing the predictive model to a form of a state equation, including,
wherein the state variable x (k) ═ x1(k),x2(k)]TOutput variable y (k) x1(k)，ymin≤y(k)≤ymaxControl input variable u (k) ═ α (k), umin≤u(k)≤umaxMoment of system
Input matrix
Output matrix C ═ 10]Compensation matrix
As a preferred scheme of the model predictive control method based on the extended state observer in the structural thermal test, the method comprises the following steps: the state quantity at the future time includes the control quantity and the state value at the current time,
x(k+1)＝Ax(k)+Bu(k)+D
x(k+2)＝Ax(k+1)+Bu(k+1)+D
＝A(Ax(k)+Bu(k)+D)+Bu(k+1)+D
＝A2x(k)+ABu(k)+Bu(k+1)+AD+D
x(k+n)＝Anx(k)+An-1Bu(k)+An-2Bu(k+1)+…+An-qBu(k+q-1)+An-1D+…+D
wherein n is a prediction time domain;
the output quantity at the future time is included with the control quantity and the state value at the present time,
y(k+1)＝Cx(k+1)＝CAx(k)+CBu(k)+CD
y(k+2)＝Cx(k+2)＝CA2x(k)+CABu(k)+CBu(k+1)+CAD+CDy(k+n)＝Cx(k+n)
＝CAnx(k)+CAn-1Bu(k)+CAn-2Bu(k+1)+…+CAn-qBu(k+m-1)+CAn-1D+…+CD
wherein q is a control time domain, and q is less than or equal to n;
writing output variables at future time into matrix form
As a preferred scheme of the model predictive control method based on the extended state observer in the structural thermal test, the method comprises the following steps: the cost function may include, for example,
J＝(Y*-Y)TQ(Y*-Y)+uTRu
wherein the desired output matrix
Control input matrix
Q is an error weight matrix and R is a control input weight matrix.
As a preferred scheme of the model predictive control method based on the extended state observer in the structural thermal test, the method comprises the following steps: the control quantity may include, for example,
order to
The control quantity u is as follows,
the invention has the beneficial effects that: the model prediction control method based on the extended state observer for the structural thermal test is applied to a hypersonic missile structural thermal test system, a mathematical model of the structural thermal test system is established according to the law of conservation of energy, the mathematical model is further discretized into a prediction model, a discrete linear extended state observer observes disturbance and system uncertainty, a value function is constructed according to prediction output errors and control input, and a controller u is designed under the calculation of rolling optimization, so that on one hand, the model prediction does not need a too accurate mathematical model; on the other hand, the rolling optimization replaces the global optimization with the local optimization, the parameter setting is not needed, the control action is fully invoked, the control precision of the control is improved, the steady-state error is reduced, the convergence speed is accelerated, and the robustness of the control system is improved by the feedback of the actually measured information in the rolling optimization process.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
FIG. 1 is a schematic three-dimensional structure diagram of a hypersonic velocity missile based on a model predictive control method of an extended state observer in a structural thermal test according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a finite element simulation of a hypersonic velocity missile according to an embodiment of the invention, wherein the structural thermal test is based on a model prediction control method of an extended state observer;
FIG. 3 is a schematic diagram of a schematic control framework of a model prediction control method based on an extended state observer for a structural thermal test according to an embodiment of the present invention;
FIG. 4 is a tracking curve diagram of the highest point temperature of a hypersonic velocity missile based on a model predictive control method of an extended state observer in a structural thermal test in comparison with a traditional PID control method (2) in a model predictive control method (1) based on a discrete linear extended state observer according to an embodiment of the invention;
fig. 5 is a partial enlarged view of a tracking curve of a hypersonic velocity missile based on a model predictive control method of an extended state observer in a maximum temperature comparison between a model predictive control method (1) based on a discrete linear extended state observer and a conventional PID control method (2) in a structural thermal test according to an embodiment of the present invention;
FIG. 6 is a graph of error tracking curves of peak temperatures of a hypersonic velocity missile based on a model predictive control method of an extended state observer in a structural thermal test according to an embodiment of the present invention compared with a traditional PID control method (2) in a model predictive control method (1) based on a discrete linear extended state observer;
fig. 7 is a partial enlarged view of an error tracking curve of the hypersonic velocity missile based on the model predictive control method of the extended state observer in the maximum temperature comparison between the model predictive control method (1) based on the discrete linear extended state observer and the conventional PID control method (2) in the structural thermal test according to an embodiment of the present invention;
FIG. 8 is a graph of a wall mean temperature fitting target curve (1) of a structural thermal test hypersonic missile structural thermal test system based on a model predictive control method of an extended state observer under finite element simulation and an output temperature tracking curve compared between a model predictive control method (2) based on a discrete linear extended state observer and a traditional PID control method (3) according to an embodiment of the invention;
fig. 9 is a partial enlarged view of a wall surface average temperature fitting target curve (1) of a hypersonic velocity missile structure thermal test system of a structural thermal test based on an extended state observer model predictive control method under finite element simulation and an output temperature tracking curve compared with a traditional PID control method (3) based on a discrete linear extended state observer model predictive control method (2), according to an embodiment of the present invention;
FIG. 10 is an error tracking curve diagram comparing a discrete linear extended state observer-based model predictive control method (1) and a conventional PID control method (2) of a hypersonic missile structure thermal test system under a tracking fit target according to an extended state observer-based model predictive control method of a structure thermal test according to an embodiment of the invention;
fig. 11 is a partial enlarged view of an error tracking curve of a structural thermal test based on an extended state observer, in which a discrete linear extended state observer based model predictive control method (1) of a hypersonic velocity missile structural thermal test system is compared with a conventional PID control method (2) under a tracking fit target according to an embodiment of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, specific embodiments accompanied with figures are described in detail below, and it is apparent that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making creative efforts based on the embodiments of the present invention, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. 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.
The present invention will be described in detail with reference to the drawings, wherein the cross-sectional views illustrating the structure of the device are not enlarged partially in general scale for convenience of illustration, and the drawings are only exemplary and should not be construed as limiting the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.
Meanwhile, in the description of the present invention, it should be noted that the terms "upper, lower, inner and outer" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation and operate, and thus, cannot be construed as limiting the present invention. 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 connected" in the present invention are to be understood broadly, unless otherwise explicitly specified or limited, for example: can be fixedly connected, detachably connected or integrally connected; they may be mechanically, electrically, or directly connected, or indirectly connected through intervening media, or may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1
Referring to fig. 1 to 4, for a first embodiment of the present invention, a model prediction control method based on an extended state observer for a structural thermal test is provided, the method of the present invention designs a control input u based on a prediction model of the structural thermal test, in combination with a discrete extended state observer and a cost function; referring to fig. 4, a schematic diagram of a principle control framework of a model prediction control method based on an extended state observer for a hypersonic missile structure thermal test of the invention specifically includes:
s1: and constructing a mathematical model of the relationship between the output temperature of the structural thermal test system and the conduction angle of the silicon controlled rectifier based on the law of conservation of energy. It should be noted that, the input and output energy conservation equation is established according to the energy conservation law to obtain the current temperature T1And the conduction angle α of the triac, i.e. a mathematical model, comprising:
Q＝w
wherein, w is the electric energy provided by the power supply, Q is the electric heat energy absorbed by the heating element in the structural heat test, and the left side of the equation is respectively the internal energy consumed by the heating element in the structural heat test, the heat energy lost in the convection heat exchange process, the heat energy lost in the heat conduction process and the heat output by the heat radiation effectCan, c, m, T1、T0A, epsilon and delta t are respectively the specific heat capacity, mass, current temperature, initial temperature, surface area, blackness coefficient and working time of the heating element of the structural thermal test, beta, lambda, sigma and F are respectively the convective heat transfer coefficient, heat conduction coefficient, Stefin-Boltzmann constant and angle coefficient, and the right U of the equationIThe input voltage is the voltage at two ends of the power supply, R is the sum of the resistances of the heating elements in the structural thermal test, and alpha is the conduction angle of the bidirectional thyristor;
wherein the content of the first and second substances,
is T1Derivative with respect to time.
S2: and dispersing the differential equation of the output temperature at the current moment k into a prediction model at the moment k +1 by a forward Euler formula. It should be noted that, in this step, the differential equation of the output temperature of the current sampling period k is discretized into a prediction model of k +1 sampling periods by a forward euler formula, and the method includes:
the prediction model of the output temperature for the (k +1) th sampling period is expressed as:
wherein, T1(k +1) is the predicted temperature, T, for the (k +1) th sampling period1(k) Is the output temperature of the current sampling period k, T is the time interval of each sampling period, alpha (k) is the control input quantity of the current sampling period k, delta (alpha (k)) is the system disturbance term,
s3: and (3) constructing a discrete linear extended state observer, and observing the uncertainty item and external disturbance of the structural thermal test system. It is also to be noted that the discrete linear extended state observer includes:
wherein e is1To output the observed error of temperature, z1To output an observed value of temperature, z2An observed value of δ (α);
wherein e is1(k) Is the observed error of the output temperature of the current sampling period k, z1(k) Is T1(k) An observed value of z1(k +1) output temperature observation, β, for the (k +1) th sampling period1And beta2Is a positive gain coefficient of a linearly extended state observer, z2(k +1) is an observed value of δ (α (k +1)), and χ is a compensation factor of the estimator;
the state variables of the system are defined,
the predictive model is modified to the form of a state equation, including,
wherein the state variable x (k) ═ x1(k),x2(k)]TOutput variable y (k) x1(k)，ymin≤y(k)≤ymaxControl input variable u (k) ═ α (k), umin≤u(k)≤umaxSystem matrix
Input matrix
Output matrix C ═ 10]Compensation matrix
S4: and selecting the state quantity and the control quantity, and establishing a state equation of the prediction model of the structural thermal test system.
S5: the state quantity and the output quantity at the future time are expressed by the control quantity and the state value at the current time. It should be further noted that the control quantity for the state quantity at the future time and the state value at the current time include:
x(k+1)＝Ax(k)+Bu(k)+D
x(k+2)＝Ax(k+1)+Bu(k+1)+D
＝A(Ax(k)+Bu(k)+D)+Bu(k+1)+D
＝A2x(k)+ABu(k)+Bu(k+1)+AD+D
x(k+n)＝Anx(k)+An-1Bu(k)+An-2Bu(k+1)+…+An-qBu(k+q-1)+An-1D+…+D
wherein n is a prediction time domain;
the output quantity at the future time is included with the control quantity and the state value at the present time,
y(k+1)＝Cx(k+1)＝CAx(k)+CBu(k)+CD
y(k+2)＝Cx(k+2)＝CA2x(k)+CABu(k)+CBu(k+1)+CAD+CDy(k+n)＝Cx(k+n)
＝CAnx(k)+CAn-1Bu(k)+CAn-2Bu(k+1)+…+CAn-qBu(k+m-1)+CAn-1D+…+CD
wherein q is a control time domain, and q is less than or equal to n;
writing output variables at future time into matrix form
S6: and constructing a cost function related to the predicted output error and the controlled variable to obtain the controlled variable. It should be further noted that, the cost function includes:
J＝(Y*-Y)TQ(Y*-Y)+uTRu
wherein the desired output matrix
Control input matrix
Q is an error weight matrix, and R is a control input weight matrix;
further, the control amount includes:
order to
The control quantity u is as follows,
referring to fig. 2, a finite element simulation diagram of a hypersonic missile is shown, and the temperature distribution of the wall surface of the missile at a certain moment in the simulation process can be seen.
Referring to fig. 1, a schematic diagram of a three-dimensional structure of a hypersonic missile is shown, and main parameters of the missile are as follows: the total length is 7600mm, the projectile body length is 4270mm, the projectile body diameter is 1168.4mm, the included angle of the guidance part is 7 degrees, the radius of the guidance head is 30mm, the included angle is 12.84 degrees, the flying environment is 32km, the speed is 6.0 Mach number, and the attack angle is 10 degrees for cruising.
Referring to fig. 3, the schematic diagram is a schematic diagram of a principle control framework of a hypersonic missile structure thermal test system based on a model prediction control method of an extended state observer, and is a further description of the structure thermal test control system, according to the schematic diagram of fig. 4, a controller alpha (t) is solved by combining a prediction model, a cost function and an observer, the prediction model provides state quantity at a future moment, the observer observes disturbance and system uncertainty, and the cost function is subjected to rolling optimization to solve an optimal control result which is not influenced by parameter setting.
Preferably, it should be further explained that, compared with the prior art, the embodiment discloses a model predictive control method based on an extended state observer for a structural thermal test, and aims to improve the control accuracy, accelerate the convergence speed, reduce the overshoot, and increase the robust performance of the control system by adopting the model predictive control method based on the extended state observer; wherein, a discrete linear extended state observer is adopted to observe the uncertain item and the external disturbance of the system; the accuracy requirement of the mathematical model of the system is not high by adopting model predictive control, the model predictive control method replaces global optimization with local optimization in the calculation process, parameter setting is not needed, control actions are fully invoked, the control accuracy of the control is improved, steady-state errors are reduced, the convergence speed is accelerated, and the robustness of the control system is improved by feedback of actual measurement information in the rolling optimization process.
Example 2
Referring to fig. 2, 4 to 11, a second embodiment of the present invention is different from the first embodiment in that a test comparison verification of a structural thermal test based on an extended state observer model prediction control method is provided, which specifically includes:
in this embodiment, the output temperature and the tracking error of the thermal test system of the hypersonic missile structure are measured and compared in real time by adopting the thermal test system of the hypersonic missile structure under a model predictive control method (1) based on a linear extended state observer and a traditional PID method (2).
And (3) testing environment: referring to fig. 2, a hypersonic missile structure thermal test system is operated on a simulation platform, the highest temperature of the wall surface of a hypersonic missile is taken as a target value, and the test is respectively carried out under a model prediction control method (1) based on a linear extended state observer and a traditional PID method (2) to obtain test result data; taking a fitting curve of the mean temperature of the wall surface of the hypersonic missile changing along with time as a tracking expected target curve, respectively testing by using a hypersonic missile structure thermal test system under a model prediction control method (1) based on a linear extended state observer and a traditional PID method (2) and obtaining test result data; in both methods, the automatic test equipment is started, MATLB software programming is used for realizing simulation test of the 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 10s, each group of data is calculated to obtain input temperature and tracking error of each group of data, and the input temperature and the tracking error of each group of data are compared with expected target temperature input by simulation and calculation error.
An expression of a fitting curve of the mean temperature of the wall surface of the hypersonic missile along with the change of time is as follows: t is*＝-1.448×10-7×t8+1.835×10-5×t7-0.0005538×t6-0.00386×t5+0.4455×t4-7.239××t3+30.19×t2+194.6t+289.1
Referring to fig. 4 to 7, a graph of an output temperature curve of a hypersonic missile structure thermal test system with the highest temperature 1703K as a target temperature under a model predictive control method (1) based on a linear extended state observer and a traditional PID method (2), a 0 to 1s local enlarged view of the graph, an error tracking curve comparison graph and a 0 to 1s local enlarged view of the graph are shown.
Referring to fig. 8-11, a fitting curve of the mean temperature of the wall surface of a hypersonic missile structure thermal test system changing along with time is used as an output temperature curve of a target temperature under a model prediction control method (1) based on a linear extended state observer and a traditional PID method (2), and a 0-1s local enlarged view, an error tracking curve comparison graph and a 0-2 s local enlarged view of the error tracking curve comparison graph are obtained.
The specific embodiment has the following parameter settings:
the quartz filament adopts an iodine-tungsten filament electric heating tube, and the specific parameters are shown in table 1.
Table 1: and (4) a structural thermal test system parameter table.
Table 2: the method of the invention is a parameter table.
Table 3: conventional PID parameter tables.
Referring to fig. 4, both the method (1) and the method (2) can stably track the highest point temperature of the wall surface of the hypersonic missile finally, but from the simulation effect of 10s, the overshoot of the method (1) is obviously smaller than that of the method (2) and the convergence speed is faster.
From the enlarged partial view of 0-1s in fig. 5, it can be seen that 1703K can be stably tracked before almost 0.01 s in method (1), while the highest temperature can be stably tracked only after 0.8s in method (2), and overshoot is hardly seen in method (1), while overshoot of about 30% is seen in method (2).
Referring to fig. 6 to 7, the effect of the method (2) is more reflected in terms of tracking error than the effect of the method (1) in terms of rapidity, overshoot, and convergence rate.
Referring to fig. 8, it can be seen that, when the control target is a fitted curve of the wall surface average temperature changing with time, both the method (1) and the method (2) can perform tracking control on the target curve, and finally both can achieve convergence.
However, as seen from the enlarged view of the 0-1s in fig. 9, the method (1) can accurately track the target curve, and there is almost no overshoot, while the method (2) cannot converge yet in the 0-1s, and cannot track the target curve yet, and the overshoot amount is significant, and as analyzed from the tracking error curve diagrams in fig. 10-11, the method (2) converges after 2s, and the convergence rate is much lower than that of the method (1), and the control effect is not as good as that of the method (1) in all aspects.
Referring to fig. 4 to 11, it can be analyzed that the control method of the present invention is superior to the conventional PID control method in 4 aspects of convergence rate, control accuracy, steady-state error, and overshoot, and benefits from that the magic predictive control method based on the linear extended state observer of the structural thermal test of the present invention replaces global optimum with local optimum in the calculation process, and does not need parameter setting, fully mobilizes control actions, improves control accuracy, reduces steady-state error, and accelerates convergence rate, and the feedback of measured information in the rolling optimization process increases the robust performance of the control system.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.
Claims (10)
1. A model prediction control method based on an extended state observer for a structural thermal test is characterized by comprising the following steps: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
constructing a mathematical model of the relationship between the output temperature of the structural thermal test system and the conduction angle of the silicon controlled rectifier based on the law of conservation of energy;
dispersing a differential equation of the output temperature at the current moment k into a prediction model at the moment k +1 by a forward Euler formula;
constructing a discrete linear extended state observer, and observing the uncertainty item and the external disturbance of the structural thermal test system;
selecting the state quantity and the control quantity, and establishing a state equation of a prediction model of the structural thermal test system;
expressing the state quantity and the output quantity at the future moment through the control quantity and the state value at the current moment;
and constructing a cost function related to the predicted output error and the controlled variable to obtain the controlled variable.
2. The structural thermal test extended state observer-based model predictive control method of claim 1, characterized in that: establishing an input and output energy conservation equation according to the energy conservation law to obtain the current temperature T1And the conduction angle alpha of the triac, i.e. soThe mathematical models described above, including,
Q＝w
wherein, w is the electric energy provided by the power supply, Q is the electric heat energy absorbed by the heating element in the structural thermal test, the left side of the equation is respectively the internal energy consumed by the heating element in the structural thermal test, 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, and c, m and T1、T0A, epsilon and delta t are respectively the specific heat capacity, mass, current temperature, initial temperature, surface area, blackness coefficient and working time of the heating element of the structural thermal test, beta, lambda, sigma and F are respectively the convective heat transfer coefficient, heat conduction coefficient, Stefin-Boltzmann constant and angle coefficient, and the right U of the equationIThe input voltage is the voltage at two ends of the power supply, R is the sum of the resistances of the heating elements in the structural thermal test, and alpha is the conduction angle of the bidirectional thyristor.
3. The structural thermal test extended state observer-based model predictive control method of claim 2, characterized in that: also comprises the following steps of (1) preparing,
wherein the content of the first and second substances,
is T1Derivative with respect to time.
4. The structural thermal test extended state observer-based model predictive control method according to claim 2 or 3, characterized in that: discretizing a differential equation of the output temperature of the current sampling period k into a prediction model of k +1 sampling periods by the forward euler formula, including,
the prediction model of the output temperature of the (k +1) th sampling period is expressed by the current sampling period k as:
wherein, T1(k +1) is the predicted temperature, T, for the (k +1) th sampling period1(k) Is the output temperature of the current sampling period k, T is the time interval of each sampling period, alpha (k) is the control input quantity of the current sampling period k, delta (alpha (k)) is the system disturbance term,
5. the structural thermal test extended state observer-based model predictive control method of claim 4, characterized in that: the discrete linear extended state observer, comprising,
wherein e is1To output the observed error of temperature, z1To output an observed value of temperature, z2Is an observed value of δ (α).
6. The structural thermal test extended state observer-based model predictive control method of claim 5, characterized in that: also comprises the following steps of (1) preparing,
wherein e is1(k) Is the observed error of the output temperature of the current sampling period k, z1(k) Is T1(k) An observed value of z1(k +1) output temperature observation, β, for the (k +1) th sampling period1And beta2Is a positive gain coefficient of a linearly extended state observer, z2(k +1) is an observed value of δ (α (k +1)), and χ is a compensation factor of the estimator.
7. The structural thermal test extended state observer-based model predictive control method of claim 6, characterized in that: also comprises the following steps of (1) preparing,
the state variables of the system are defined,
changing the predictive model to a form of a state equation, including,
wherein the state variable x (k) ═ x1(k),x2(k)]TOutput variable y (k) x1(k)，ymin≤y(k)≤ymaxControl input variable u (k) ═ α (k), umin≤u(k)≤umaxSystem matrix
Input matrix
Output matrix C ═ 10]Compensation matrix
8. The structural thermal test extended state observer-based model predictive control method of claim 7, characterized in that: the state quantity at the future time includes the control quantity and the state value at the current time,
x(k+1)＝Ax(k)+Bu(k)+D
x(k+2)＝Ax(k+1)+Bu(k+1)+D
＝A(Ax(k)+Bu(k)+D)+Bu(k+1)+D
＝A2x(k)+ABu(k)+Bu(k+1)+AD+D
x(k+n)＝Anx(k)+An-1Bu(k)+An-2Bu(k+1)+…+An-qBu(k+q-1)+An-1D+…+D
wherein n is a prediction time domain;
the output quantity at the future time is included with the control quantity and the state value at the present time,
y(k+1)＝Cx(k+1)＝CAx(k)+CBu(k)+CD
y(k+2)＝Cx(k+2)＝CA2x(k)+CABu(k)+CBu(k+1)+CAD+CD
y(k+n)＝Cx(k+n)
＝CAnx(k)+CAn-1Bu(k)+CAn-2Bu(k+1)+…+CAn-qBu(k+m-1)+CAn-1D+…+CD
wherein q is a control time domain, and q is less than or equal to n;
writing output variables at future time into matrix form
9. The structural thermal test extended state observer-based model predictive control method of claim 8, characterized in that: the cost function may include, for example,
J＝(Y*-Y)TQ(Y*-Y)+uTRu
wherein the desired output matrix
Control input matrix
Q is an error weight matrix and R is a control input weight matrix.
10. The structural thermal test extended state observer-based model predictive control method of claim 9, characterized in that: the control quantity may include, for example,
order to
The control quantity u is as follows,
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