CN113341696A - Intelligent setting method for attitude control parameters of carrier rocket - Google Patents

Intelligent setting method for attitude control parameters of carrier rocket Download PDF

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CN113341696A
CN113341696A CN202110651033.2A CN202110651033A CN113341696A CN 113341696 A CN113341696 A CN 113341696A CN 202110651033 A CN202110651033 A CN 202110651033A CN 113341696 A CN113341696 A CN 113341696A
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quantum
goblet
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sea squirt
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高华宇
王佩
张科
吕梅柏
邢超
周大明
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Northwestern Polytechnical University
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Abstract

The invention discloses an intelligent setting method for attitude control parameters of a carrier rocket, which comprises the following steps: acquiring a nonlinear controller parameter and an objective function of the attitude of the carrier rocket; performing setting optimization on the parameters of the nonlinear controller by solving the maximum value of the objective function by adopting a quantum goblet sea squirt algorithm to determine the optimal parameters of the nonlinear controller; the determination of quantum goblet ascidian algorithm comprises: on the basis of a standard goblet ascidian algorithm, determining the state of the quantum goblet ascidian by adopting a probability amplitude coding mode of quantum bits; and determining objective function values of two position coordinates according to sine and cosine position variables corresponding to two positions in the parameter solution space, and taking the maximum value as the objective function value of the quantum goblet sea squirt state. The invention combines quantum theory and goblet and sea squirt algorithm, each quantum goblet and sea squirt state is equivalent to occupying two positions in the optimization parameter space, each goblet and sea squirt state corresponds to two solutions of the optimization problem, thereby improving the ergodicity of the algorithm and increasing the global convergence rate of the algorithm.

Description

Intelligent setting method for attitude control parameters of carrier rocket
Technical Field
The invention relates to the field of setting of nonlinear attitude controller parameters of a carrier rocket, in particular to an intelligent setting method of attitude control parameters of the carrier rocket based on a quantum goblet sea squirt algorithm.
Background
Although the carrier rocket nonlinear attitude controller can better solve the influence of gust, parameter perturbation, unknown interference and the like on the rocket attitude control compared with the traditional carrier rocket PID control, the parameters of the nonlinear controller are greatly increased compared with the PID control, and due to the introduction of a nonlinear function, the parameter setting of the nonlinear controller presents the problems of multivariable, nonlinearity, multi-extreme value and the like, and the analysis and setting method similar to the PID controller parameters cannot be obtained. Therefore, the problem of controller parameter setting needs to be solved by converting the problem of controller parameter setting into an optimization design problem which takes control performance as a target function and controller parameters as design variables, and aiming at the problem caused by introduction of nonlinear characteristics, an intelligent clustering algorithm with multivariable global optimization capability can be adopted to carry out parameter solution, so that the setting of the controller parameters is realized.
In 2017, S.Mirjalli and the like propose a Salp Swarm Algorithm (SSA) [ SEYEDALIM, AMIRHG, SEYEDEHZM, et al, Salp Swarm Algorithm: A bio-induced optimization for Engineering design schemes [ J ]. Advances in Engineering Software,2017,114(1): 163-191 ], according to the luminous behavior of the sea squirts in nature, and an intelligent optimization Algorithm constructed by simulating the foraging behavior of the sea squirts is very suitable for solving the multivariate optimization problem, is a novel intelligent clustering Algorithm with strong global search capability, fast convergence and good self-adaptability, and is applied to solving the mathematical parameter optimization design problem in the fields of multivariate, financial and the like by virtue of the advantages of simple concept, clear steps, strong realizability and the like.
However, the standard goblet ascidian algorithm still has some defects: although the early stage can realize large-range rapid convergence, the later stage convergence efficiency is not good; the search accuracy for the global optimal result at a fixed step size is not ideal. Therefore, many scholars have developed improved studies on algorithms to address the above problems; for example, aiming at the problem of fixed step length, a self-adaptive mechanism is introduced, and the step length is dynamically adjusted to improve the later-stage optimization precision; the simulated annealing algorithm is combined with the goblet sea squirt algorithm, so that the convergence rate is further improved, and the like. The performance of the goblet sea squirt algorithm is improved to a certain extent through the research, but the problems of reduced later convergence performance, low precision of global optimization results, easy falling into local optimization and the like still exist, and from the viewpoint of improving the control parameter setting efficiency and the optimal control effect, the goblet sea squirt algorithm needs to be greatly improved to obtain a better parameter setting result.
Disclosure of Invention
Therefore, in order to solve the technical problem, it is necessary to provide an intelligent setting method for attitude control parameters of a carrier rocket.
The embodiment of the invention provides an intelligent setting method for attitude control parameters of a carrier rocket, which comprises the following steps:
acquiring a nonlinear controller parameter of the attitude of the carrier rocket, and multiplying time by an absolute value integral of an attitude control error of the nonlinear controller to be used as a target function for parameter setting of the nonlinear controller;
performing setting optimization on the parameters of the nonlinear controller by solving the maximum value of the objective function by adopting a quantum goblet sea squirt algorithm to determine the optimal parameters of the nonlinear controller;
wherein, the determination of the quantum goblet sea squirt algorithm comprises the following steps:
on the basis of a standard goblet sea squirt algorithm, determining the state of the quantum goblet sea squirt by adopting a probability amplitude coding mode of quantum bits; wherein, the quantum goblet sea squirt state occupies two positions in the parameter solution space, and respectively corresponds to the probability amplitude of quantum state |0> and |1 >;
determining objective function values of two position coordinates in the parameter solution space according to sine position variables and cosine position variables corresponding to two positions in the parameter solution space, and taking the maximum value of the objective function values of the two position coordinates in the parameter solution space as the objective function value of the quantum goblet sea squirt state;
and assigning the maximum value in the objective function values of the quantum goblet and the ascitess state and the corresponding parameter solution space position to the bulletin board.
In one embodiment, the determining of the nonlinear controller parameter and the objective function defined by the nonlinear controller parameter specifically includes:
establishing a carrier rocket attitude motion model;
according to the order of the attitude motion model of the carrier rocket, an integral chain differentiator is designed to track the attitude angle deviation measurement signal, and the expression of the integral chain differentiator is as follows:
Figure BDA0003111172030000031
Figure BDA0003111172030000032
Figure BDA0003111172030000033
wherein r is a tracking velocity factor, v is an attitude angle deviation measurement signal,
Figure BDA0003111172030000034
respectively a tracking estimation value, a speed estimation value and an acceleration estimation value of the attitude angle deviation measurement signal v;
from acceleration estimates
Figure BDA0003111172030000035
Removing the modeled part f in the attitude motion model of the carrier rocket0(x, u) estimating the internal and external uncertainty terms of the model to obtain the uncertain portion compensator
Figure BDA0003111172030000036
Figure BDA0003111172030000037
By means of a master controller ucontrolAnd indeterminate portion compensator
Figure BDA0003111172030000038
Constructing a nonlinear feedback controller:
Figure BDA0003111172030000039
Figure BDA00031111720300000310
Figure BDA00031111720300000311
in the formula (I), the compound is shown in the specification,
Figure BDA00031111720300000312
a current attitude angle deviation control instruction is obtained; b30Is a nominal system control item parameter; dtIs the set of distances between goblet and sea squirt;
forming a nonlinear controller parameter X ═ K through 5 parameters of the nonlinear feedback controller and 1 parameter of the integral chain differentiatorp Ki Kd α β r]T；
Determining a target function for nonlinear controller parameter tuning based on nonlinear controller parameters
Figure BDA00031111720300000313
In one embodiment, the quantum goblet sea squirt state comprises:
Figure BDA00031111720300000314
in the formula, theta ij2 pi × radmn, i ═ 1,2, …, m, j ═ 1,2, …, n, and radmn are random numbers between (0, 1); m is the population size; n is the optimization variable space dimension; each goblet sea squirt state occupation parameter emptyingTwo positions in between, corresponding to quantum state |0>And |1>Amplitude of probability of, i.e.
SQic＝(cos(θi1),cos(θi2),…,cos(θin))
SQis＝(sin(θi1),sin(θi2),…,sin(θin))
In the formula, SQicIs in a cosine state, SQisIs in a sinusoidal state.
In one embodiment, the determining the objective function value of the quantum goblet and ascidian state specifically includes:
let the current quantum state SQiA k-th qubit of
Figure BDA0003111172030000041
The corresponding sine and cosine position variables X in the corresponding solution spaceQijJ ═ c, s denotes:
Figure BDA0003111172030000042
Figure BDA0003111172030000043
through I0(XQi) Calculating the current quantum state SQiCorresponding spatial position coordinates X of each solutionQijJ is the objective function value of c, s, and takes the maximum value as the objective function value of the current qubit:
Figure BDA0003111172030000044
in the formula I0(. is the self brightness of the goblet sea squirt algorithm; [ Low ]k,Highk]For the optimization range of the kth design variable, HighkIs upper bound of range, LowkThe lower range.
In one embodiment, the determining of the quantum goblet ascidian algorithm further comprises:
the quantum goblet and ascidian state is updated through the updating of the quantum revolving door corner.
In one embodiment, the updating of the quantum goblet ascidian state through the updating of the quantum rotating gate corner specifically includes:
the updating of the state of the quantum goblet ascidians comprises: leader state updates and follower state updates;
the leader state update formula is:
Figure BDA0003111172030000045
in the formula: delta thetaLiA argument change of an ith dimension updated for the representation leader; c. C1,c2,c3Respectively three control parameters, c2And c3Is a random number between 0 and 1, c2Determining the size of the update amount, c3Determining the direction of the updating amount; c. C1Determining the key parameters of the updating effect, and defining the values as:
Figure BDA0003111172030000051
in the formula: step is the maximum updating Step length; e represents a natural constant; l, L represents the current and maximum number of iterations L ═ 1,2, …, L, respectively;
leading person goblet SLThe two new positions after updating are:
Figure BDA0003111172030000052
Figure BDA0003111172030000053
the quantum revolving door synchronously moves the two updated positions of the sea squirts of the leading goblet by changing the quantum amplitude angle of the sea squirts of the leading goblet;
the follower state update formula is as follows:
Figure BDA0003111172030000054
in the formula:
Figure BDA0003111172030000055
the updated quantum argument of the follower state; thetaijThe j-dimension quantum argument of the ith individual before the state update; thetai-1jRepresenting the quantum argument of j dimension of the adjacent individual in front of the ith individual;
followup goblet SQiThe two new positions after updating are:
Figure BDA0003111172030000056
Figure BDA0003111172030000057
the quantum revolving door synchronously moves the two updated positions of the followed goblet ascidians by changing the quantum amplitude angle of the followed goblet ascidians.
In one embodiment, the determining of the quantum goblet ascidian algorithm further comprises:
and (3) introducing variation operation in a single iteration flow of the standard goblet sea squirt algorithm by adopting a quantum NOT gate.
In one embodiment, the mutation operation specifically includes:
setting a probability of variation PmutJudging whether the goblet ascidian has variation or not by extracting a random number randm () from each goblet ascidian; if PmutAnd if the quantum is greater than randm (), mutation occurs, randomly selecting a mutation qubit j ═ ceil (6 × randm ()), and changing the angle of the mutation qubit by using a quantum not gate:
Figure BDA0003111172030000058
in the formula:
Figure BDA0003111172030000059
the updated quantum argument of the follower state; thetaijThe j-dimension quantum argument of the ith individual before the state update; and pi is the circumferential ratio.
Compared with the prior art, the intelligent setting method for the attitude control parameters of the carrier rocket provided by the embodiment of the invention has the following beneficial effects:
in order to overcome the problems that the parameter optimizing convergence precision of a carrier rocket nonlinear controller is poor, the later convergence speed is seriously reduced and the carrier rocket attitude controller is easy to fall into local optimization by the conventional parameter setting method, the invention provides the carrier rocket attitude controller parameter setting method based on the quantum goblet sea squirt algorithm. The control system parameter setting method based on the quantum goblet and ascidian algorithm has the advantages of higher convergence rate, better controller parameter setting efficiency and higher controller parameter global optimization capability.
Specifically, the quantum theory is combined with the goblet and sea squirt algorithm, and each quantum goblet and sea squirt state is equivalent to two positions in the optimized parameter space, so that each goblet and sea squirt state corresponds to two solutions of the optimization problem, the ergodicity of the algorithm is improved, and the global convergence speed of the algorithm is increased.
Specifically, the quantum revolving door realizes synchronous movement of two positions by changing the quantum argument of the goblet sea squirt, expands the traversability of a search space under the condition of unchanged population scale, and improves the efficiency of single state updating.
Specifically, the standard cask ascidian algorithm only accepts the optimal solution in the search process, so that the local optimal solution may be trapped and the global optimal solution cannot be achieved. The invention increases the strategy of jumping out of the local optimum by introducing the variation operation, not only accepts the optimum solution but also reconstructs the goblet sheath state with a certain probability by introducing the variation behavior, thus leading the algorithm to jump out of the local optimum controller parameter at irregular intervals, improving the probability of reaching the global optimum and expanding the capability of jumping out of the local optimum by the algorithm.
Drawings
FIG. 1 is a flow chart of a method for intelligently tuning attitude control parameters of a launch vehicle based on a Quantum goblet sea squirt algorithm, according to an embodiment;
FIG. 2 is a view of a configuration of attitude control parameter settings of a launch vehicle based on the Quantum goblet sea squirt algorithm according to an embodiment;
FIG. 3 is a flow chart of an optimized design method for a Quantum goblet sea squirt algorithm according to an embodiment;
FIG. 4 is a flow chart of a goblet ascidian location update operation provided in an embodiment;
FIG. 5 is a flow chart of the quantum goblet and ascidian variation operation provided in one embodiment;
FIG. 6 is a process diagram of the setting of attitude control parameters of a launch vehicle using the Quantum goblet sea squirt algorithm provided in one embodiment;
FIG. 7 is a diagram illustrating the effect of controlling the attitude of the launch vehicle on each generation of optimal controller parameters during the tuning process provided in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
In one embodiment, the method for intelligently setting the attitude control parameters of the carrier rocket specifically comprises the following steps:
step 1, establishing a motion model of a carrier rocket and designing a nonlinear attitude controller
Firstly, according to the order of a carrier rocket attitude dynamics model, designing an integral chain differentiator with 3 orders to track an attitude angle deviation measurement signal, wherein the expression of the integral chain differentiator is as follows:
Figure BDA0003111172030000071
Figure BDA0003111172030000072
Figure BDA0003111172030000073
wherein r is a tracking velocity factor, v is an attitude angle deviation measurement signal,
Figure BDA0003111172030000074
respectively a tracking estimation value, a speed estimation value and an acceleration estimation value of the attitude angle deviation measurement signal v.
By deviating the acceleration signal from the extracted attitude angle
Figure BDA0003111172030000075
And removing the modeled part in the carrier rocket dynamics model, and estimating internal and external uncertainty of the system.
Figure BDA0003111172030000081
In the formula (I), the compound is shown in the specification,
Figure BDA0003111172030000082
an acceleration signal f output after tracking the attitude angle deviation measurement signal by an integral chain differentiator0(x, u) is the modeled segment in the launch vehicle dynamics model.
Is connected withThe non-linear feedback controller of the meter is composed of a main controller unonlinearAnd indeterminate portion compensator
Figure BDA0003111172030000083
Two parts are formed.
Figure BDA0003111172030000084
Figure BDA0003111172030000085
Finally, obtaining the output u of the nonlinear attitude controller according to the control item parameters in the nominal system modelcontrolComprises the following steps:
Figure BDA0003111172030000086
in the formula (I), the compound is shown in the specification,
Figure BDA0003111172030000087
for the current attitude angle deviation control command,
Figure BDA0003111172030000088
an attitude angle deviation tracking signal outputted from the integral chain differentiator, b30The nominal system control item parameters.
The nonlinear controller parameters are composed of nonlinear feedback controller parameters and uncertain compensator parameters, wherein the number of the nonlinear feedback control parameters is 5, the number of the integral chain differentiator parameters is 1, and therefore the number of the whole controller parameters is 6.
Determining a parameter X ═ K to be setp Ki Kd α β r]TSelecting time multiplied by absolute value of error Integral (ITAE) index as an objective function of controller parameter setting
Figure BDA0003111172030000089
Thus, the controller parameter is setThe problem is converted into an optimization problem of the controller parameters, and the problem is expressed as follows:
Figure BDA00031111720300000810
X＝[Kp Ki Kd α β r]T
since the goblet sea squirt algorithm is to find the maximum value of the objective function, and the expected attitude control error of the attitude control of the carrier rocket is the minimum, the self-brightness calculation formula of the goblet sea squirt algorithm is I0And (X) — f (X), wherein f (X) is a value for a controller parameter setting objective function, and can be realized by adopting a controller attitude control error.
Step 2, setting algorithm parameters
Optimization Range of design variables [ Lowk,Highk]K is 1,2, …, n, n is the design variable spatial dimension, [ Low [ ]k,Highk]Optimizing Range for the kth design variable, HighkIs upper bound of range, LowkIs the lower bound of the range; maximum number of iterations is lmax,lmaxIs greater than 0; the mutation probability is Pmut,0＜PrmutLess than 1; the calculation formula of the distance between the goblet and the sea squirt is di,j＝||Xi-XjL; the current iteration number l is 1.
Step 3, initializing quantum state of goblet sea squirt
The current state of the ascidian is determined by the probability amplitude coding of the qubit,
Figure BDA0003111172030000091
in the formula, theta ij2 pi × radmn, i ═ 1,2, …, m, j ═ 1,2, …, n, and radmn are random numbers between (0, 1); m is the population size; n is the optimization variable space dimension; each goblet sea squirt state occupies two positions in the parameter space and respectively corresponds to a quantum state |0>And |1>Amplitude of probability of, i.e.
SQic＝(cos(θi1),cos(θi2),…,cos(θin))
SQis＝(sin(θi1),sin(θi2),…,sin(θin))
In the formula, SQicIs in a cosine state, SQisIs in a sinusoidal state.
Step 4, quantum search
Each probability amplitude of goblet ascidian qubit corresponds to an optimized variable scheme in the parameter solution space, and the current quantum state S of goblet ascidian is setQiA k-th qubit of
Figure BDA0003111172030000092
The corresponding sine and cosine position variables X in the corresponding solution spaceQijJ ═ c, s denotes:
Figure BDA0003111172030000093
Figure BDA0003111172030000094
then through I0(XQi) Calculating the current quantum state SQiCorresponding spatial position coordinates X of each solutionQijThe maximum value is taken as the objective function value I of the current qubit0Qi(SQi)。
Figure BDA0003111172030000095
Step 5, bulletin board updating
The objective function value according to the current state of each quantum goblet sea squirt is I0Qi(SQi) Will be the maximum value Yboard＝max(I0Q1(XQ1),I0Q2(XQ2),…,I0QN(XQN) And corresponding goblet ascidiolytic spatial location Xboard＝XQij，if I0Qi(SQij)＝Yboard，i＝12, …, m, j ═ c, s is assigned to the bulletin board.
Step 6, updating the state
The state updating of the goblet ascidians consists of leader updating and follower updating. The quantum movement is realized by the quantum revolving door, so the quantum goblet and ascidian state update can be realized by the update of the corner of the quantum revolving door:
(1) the state update formula of the leader is as follows:
Figure BDA0003111172030000101
in the formula: delta thetaLiA argument change of an ith dimension updated for the representation leader; c. C1,c2,c3Are respectively three control parameters, c2And c3Is a random number between 0 and 1, c2Determines the scale of the update amount, c3The direction of the update amount may be determined to be either an addition or subtraction on the original basis. c. C1The key parameter for determining the updating effect is defined as:
Figure BDA0003111172030000102
in the formula: step is the maximum updating Step length; e represents a natural constant; l, L represent the current and maximum number of iterations L ═ 1,2, …, L, respectively.
It can be seen that the smaller the number of iterations, c1The larger the value, the larger the update amplitude. In the first few iterations, the large update amplitude can ensure that the leader approaches the region around the global optimum more quickly, so that the optimization algorithm has good global performance. And when the number of iterations approaches the maximum number of iterations, c1The value gradually goes to 0, i.e. the update step size becomes smaller and smaller, indicating that as accurate a position as possible is obtained when approaching the optimal solution. In contrast, c2And c3The two random variables always enhance the randomness of updating, and further improve the global searching capability.
Leading person goblet SLThe two new positions after updating are:
Figure BDA0003111172030000111
Figure BDA0003111172030000112
therefore, the quantum revolving door realizes synchronous movement of two positions by changing the quantum amplitude angle of the goblet sea squirt, and expands the ergodicity of the search space under the condition of unchanged population scale.
(2) In the foraging process of goblet sea squirts, followers are sequentially connected end to present a chain type combined shape, the chain type structure enables the motion state of the followers to be strongly influenced by front and rear individuals, therefore, the position updating of the followers depends on the positions of the followers and the individuals in front of the followers adjacent to the followers, and the state updating formula of the followers is as follows:
Figure BDA0003111172030000113
in the formula:
Figure BDA0003111172030000114
the updated quantum argument of the follower state; thetaijThe j-dimension quantum argument of the ith individual before the state update; thetai-1jRepresenting the quantum argument of the j dimension of the adjacent individual in front of the i individual.
Let the ith goblet SQiThe current state is Si＝[θi1 θi2 … θin]Using dij＝||Si-SjCalculating the ith goblet sea squirt S by | | |1 ≦ j ≦ NQiDistance d between the sea squirt and the jth gobletijTo obtain the ith goblet sea squirt SQiDistance D between other sea squirt of gobleti＝(di1,di2,…,dij,…,diN)；
And judging the individuals adjacent to the ith goblet ascidian according to the shortest distance.
Followup goblet SQiThe two new positions after updating are:
Figure BDA0003111172030000115
Figure BDA0003111172030000116
therefore, the quantum revolving door realizes synchronous movement of two positions by changing the quantum amplitude angle of the goblet sea squirt, and expands the ergodicity of the search space under the condition of unchanged population scale.
Step 7, mutation treatment
The goblet sea squirt algorithm sometimes falls into a local extreme value in the solving process, the variation operation in the genetic algorithm is used for reference, the population diversity is increased, premature convergence is avoided, and the variation processing is realized by using a quantum NOT gate. Setting a probability of variation PmutAnd judging whether the goblet is mutated or not by extracting a random number randm () from each goblet. If PmutWhen mutation occurs, a mutation qubit j ═ ceil (6 × randm ()) is randomly selected, and the angle of the position is changed by using a quantum not gate, so that diversity is increased.
Figure BDA0003111172030000121
Step 8, if the current iteration times l is less than or equal to lmaxIf yes, let l be l +1, and execute step 4; otherwise step 9 is performed.
Step 9, outputting the status S of goblet sea squirt on the bulletin boardboardAnd optimum result Yboard。
Step 10, if the objective function value meets the requirement, SboardI.e. the optimal attitude controller parameters. Otherwise, returning to step 2, resetting the quantum goblet and ascidian algorithm parameters, and executing step 3E10。
Example 1
Method for verifying solving precision and convergence of quantum goblet sea squirt algorithm by using test function
In order to verify the improvement effect of the improved algorithm in the aspects of solving precision and convergence, a standard test function two-dimensional F1 function and an Ackley function are selected to compare the algorithm effects before and after improvement, and a target function Y (F), (X) g (g) is obtained for the problem of the minimum value based on two function calculation methodsh(X) h ═ G, R; the mathematical expressions and the global optimum solution for the two standard test functions are given in table 1.
Suppose there are N quantum goblet ascidians in the quantum goblet ascidian group, and F ═ XQ1,XQ2,…,XQi,…,XQN) I is more than or equal to 1 and less than or equal to N, and the state X of each quantum goblet and ascidian individualQParameter X of available test functionQ＝(θ1,θ2) To optimize design variables; [ Down ]k,Upk]Optimizing Range, Up, for the kth design variablekIs the range upper bound, DownkIs the lower bound of the range; xQi＝(θ1i,θ2i,…,θni) Representing a current location of an ith quantum bottle ascidian in the quantum bottle ascidian group; thetaki(k 1, …, N, i 1, …, N) represents the current value of the kth design variable in the ith quantum goblet position; the brightness of the current position of quantum goblet ascidian is defined as f (X)Q) Expressing, wherein Y is an objective function value and reflects the quality degree of the problem model solved at different positions; the distance between quantum goblet and ascidian is di,j＝||Xi-XjL; the maximum update Step length parameter Step has the maximum iteration number of lmax,lmaxIs greater than 0; the mutation probability is Pmut,0＜Prmut＜1。
Table 1 table of specific information of test functions in the examples
Figure BDA0003111172030000131
The quantum goblet and ascidian algorithm of the invention is different from the standard goblet and ascidian algorithm mainly in the following aspects:
(1) the current position of the goblet sea squirt is expressed by adopting a quantum coding mode,
Figure BDA0003111172030000132
so that the position of each quantum goblet ascidian will actually occupy two positions in the traversal space.
(2) The state update of the goblet ascidian leader is combined with the quantum rotation to realize the state update operation of the leader,
Figure BDA0003111172030000133
quantum coding means that one quantum position update corresponds to two positions in an actual search space, and single optimization efficiency is greatly improved.
(3) At the end of the single iteration process of the standard goblet sea squirt algorithm, variation operation is introduced to increase the jumping-out
Optimizing the capacity.
Mutation behavior is determined by increasing the mutation probability parameter PmutBy extracting random numbers, P is judgedmut> rand () is whether aperiodic trigger mutated behavior is established. If variation happens, randomly selecting variation quantum bit j ═ ceil (5 ═ rand ()), and adopting quantum NOT gate to change the angle of the quantum coding position
Figure BDA0003111172030000134
Diversity is increased, local optimum is prevented from being trapped, and global optimum search is performed.
Fig. 3 shows a flow chart of the quantum goblet and ascidian algorithm, and fig. 4 shows a flow chart of the quantum goblet and ascidian location update operation. FIG. 5 is a flow chart showing the variation behavior of quantum goblet and ascidian.
In example 1, the quantum goblet ascidian algorithm of the present invention is compared with the standard goblet ascidian algorithm, and the results are shown in table 2. Wherein the number N of goblet and ascidian algorithm is 50, the state dimension N is 2, the state variable ranges of F1 function and Ackley function are respectively [ UpGi,DownGi]＝[-20,20],[UpRi,DownRi]＝[-5.12,5.12]Maximum Step length Step of the movement of goblet sea squirt is 2 and maximumNumber of iterations lmax100. The same parameter setting in the quantum goblet and ascidian algorithm is the same as that of the standard goblet and ascidian algorithm, and the newly added algorithm parameter setting variation probability is Pmut＝0.2,0＜Prep＜1。
In example 1, each test function is repeatedly run 100 times by using each algorithm to obtain an optimized result, the convergence times and the iteration times during convergence are recorded, and the average iteration times and the convergence success rate are obtained, where the convergence success rate is the convergence success times/100, and table 2 shows a comparison of convergence results.
TABLE 2 comparison of test results for convergence of different test functions for the examples
Figure BDA0003111172030000141
As can be seen from the convergence test result of example 1, the quantum goblet ascidian algorithm in the present invention has a greatly improved convergence compared to the standard goblet ascidian algorithm. This also demonstrates the improved correctness of the present invention for the standard goblet ascidian algorithm.
In example 1, each test function is repeatedly run 100 times by using each algorithm, the optimal solution and the corresponding goblet and sea squirt position are recorded, the average optimization result is calculated, and the comparison of the optimal value optimization solution results is given in table 3.
TABLE 3 comparison table of the results of solving the optimum values of different test functions in the examples
Figure BDA0003111172030000142
Figure BDA0003111172030000151
As can be seen from the convergence test result of embodiment 1, compared with the standard goblet and ascidian algorithm, the quantum goblet and ascidian algorithm of the present invention has a substantially improved accuracy of the result of the optimal solution, an improved accuracy of approximately 1 order of magnitude at the optimal solution position, and a substantially improved optimization solution. The standard deviation of the optimization result is larger due to the influence of random factors by adopting the standard goblet ascidian algorithm, the optimization stability is general, the robustness of the quantum goblet ascidian algorithm is greatly improved, the standard deviation is greatly reduced, and the improvement amplitude is at least 1 magnitude order, which also proves the accuracy of the improvement of the standard goblet ascidian algorithm in the invention.
Example 2
Verification of feasibility of attitude control parameter setting of quantum goblet and ascidian algorithm carrier rocket
Referring to the attached drawings 1-7, the method of the invention comprises the following steps:
step 1, establishing a carrier rocket attitude motion model to obtain nominal data:
1. rigid motion modeling of carrier rocket
According to the analysis of the attitude motion of the carrier rocket, a rocket pitching channel motion model is established in view of the symmetry characteristic of the carrier rocket, and the model consists of three parts, namely rigid motion, elastic motion and attitude measurement.
The rigid body equation of motion is:
Figure BDA0003111172030000152
Figure BDA0003111172030000153
Figure BDA0003111172030000154
the elastic vibration equation is:
Figure BDA0003111172030000155
the inerter measurement equation is:
Figure BDA0003111172030000156
Figure BDA0003111172030000157
wherein Δ θ is a deviation of a ballistic inclination angle; delta alpha is the deviation of the angle of attack of the rocket body;
Figure BDA0003111172030000158
an engine pivot angle input for a pitch channel;
Figure BDA0003111172030000161
inputting engine yaw acceleration of a pitching channel; alpha is alphawIs the wind attack angle;
Figure BDA0003111172030000162
interference force suffered by the rocket;
Figure BDA0003111172030000163
the moment is the interference moment on the rocket;
Figure BDA00031111720300001612
is the deviation of the pitch angle;
Figure BDA0003111172030000164
and
Figure BDA0003111172030000165
the method is characterized in that output signals measured by an inertial measurement unit platform and a rate gyro, other parameters and a reference of 'design of an anti-interference fractional order controller of a launch vehicle' can be defined. The parameters of each part under the nominal condition of a certain second point given in the literature 'design of anti-interference fractional order controller of a carrier rocket' are used.
c1＝0.161,c2＝0.095,c3＝0.036,c30＝5.02e-5,
c11＝-4.86e-4,c21＝-1e-5,c10＝0
b1＝0.046,b2＝-0.0411,b3＝0.553,b30＝5.56e-2,
b11＝-0.268,b21＝-1.95-4,b20＝1.61e-5
ζi＝0.005,ωi＝8.65,D11＝-1.89,D21＝7.31；
D31＝16.55,D301＝0.021
Wzi(Xgz)＝0.018,Wzi(Xst)＝0.066
2. Estimating system uncertainty using differentiators
For attitude control of the carrier rocket pitching channel, a pitch angle deviation differential equation can be arranged as follows:
Figure BDA0003111172030000166
wherein, b3＝b3′0+b30，b30For a known coefficient of pivot angle, b3′0Is an uncertain part of the swing angle coefficient caused by various reasons.
Order to
Figure BDA0003111172030000167
And if the pitch angle differential equation is regarded as an unknown item, the pitch angle differential equation is further arranged as follows:
Figure BDA0003111172030000168
because the pitch angle deviation differential equation is of 2 orders, a 3-order integral chain type differentiator is adopted to track the pitch angle deviation signal, and the form of the three-order integral chain type differentiator is as follows:
Figure BDA0003111172030000169
Figure BDA00031111720300001610
Figure BDA00031111720300001611
in the formula (I), the compound is shown in the specification,
Figure BDA0003111172030000171
which is the tracking signal of the differentiator on the input signal v,
Figure BDA0003111172030000172
are respectively as
Figure BDA0003111172030000173
I.e. the estimated signals of the differentiator for the first and second derivatives of the input signal v, r is the tracking parameter of the differentiator.
The unknown term f (x) is estimated using the second derivative of the differentiator output:
Figure BDA0003111172030000174
the effect of differential tracking can be controlled by adjusting r.
3. Design of nonlinear feedback controller
Respectively calculating the current control error and the first derivative of the error by utilizing the tracking estimation value and the control instruction of the integral chain type differentiator to the attitude deviation signal, and obtaining a control output u by adopting the steepest control comprehensive functionnonlinear。
Figure BDA0003111172030000175
Figure BDA0003111172030000176
The part has 6 parameters to be set, which are respectively as follows: kp、Ki、Kd、α、β、r。
4. Estimation of system uncertainty by integrated differentiator
Figure BDA0003111172030000177
And the output u of the non-linear feedback controllernonlinearForm the total output u of the anti-interference controllercontrolThe controller structure is shown in figure 2.
Figure BDA0003111172030000178
In the formula, b30The nominal system control item parameters.
5. And selecting an error index, and setting the parameters of the controller.
Parameter setting is carried out based on the optimization idea, an ITAE evaluation index is selected, and a controller parameter is used as an optimization variable, namely X is equal to [ K ]p Ki Kd α β r]TThe objective function is
Figure BDA0003111172030000179
Thus, the problem of setting the parameters of the controller is converted into an optimization problem expressed as follows:
Figure BDA00031111720300001710
X＝[Kp Ki Kd α β r]T
the ITAE evaluation index is selected as the objective function,
Figure BDA00031111720300001711
setting the simulation step length h of the controller to be 0.01, and setting the calculation time to be [ 010 ]]Second, the initial value of the pitch angle of the carrier rocket is 0 DEG thetacmd＝1°。
Step 2, setting parameters
Setting the algorithm of goblet and ascidianThe number N of the artificial fish is 50, the state dimension N is 6, and the state variable range [ Up1,Down1]＝[1,20]、[Up2,Down2]＝[0,20]、[Up3,Down3]＝[5,20]、[Up4,Down4]＝[0,1]、 [Up5,Down5]＝[0,1]，[Up6,Down6]＝[0.1,50]The maximum Step length Step of the motion of the goblet ascidians is 1, the same parameter setting in the quantum goblet ascidian algorithm is consistent with the standard goblet ascidian algorithm, and the parameter setting variation probability of the newly added algorithm is Pmut＝0.2,0＜PrepLess than 1; let the objective function be Y ═ J (X)ITAE。
Step 3, quantum goblet sea squirt initialization
Combining the function expression of the embodiment, the state of each ascidian of the goblet group is a 6-dimensional vector, determining the number N of ascidians N equal to 50 and the design variable dimension N equal to 6, generating random numbers between N equal to 6 rows and N equal to 50 columns of 0-1 by using rand () function, and combining the design angle variable range [0,2 pi ], initializing to obtain N equal to 50 quantum ascidians.
The probability amplitude of the quantum bit is used as the current position code of the goblet sea squirt,
Figure BDA0003111172030000181
in the formula, theta ij2 pi × radmn, i ═ 1,2, …, m, j ═ 1,2, …, n, and radmn are random numbers between (0, 1); m is the population size; n is the optimization variable space dimension; each goblet sea squirt state occupies two positions in the parameter space and respectively corresponds to a quantum state |0>And |1>Amplitude of probability of, i.e.
SQic＝(cos(θi1),cos(θi2),…,cos(θin))，SQis＝(sin(θi1),sin(θi2),…,sin(θin))
In the formula, SQicIs in a cosine state, SQisIs in a sinusoidal state.
Step 4, quantum search
Each of goblet sea squirt quantum bitAn optimized variable scheme in the solution space of the parameters corresponding to the individual probability amplitude, and the current quantum state S of the sea squirtQiA k-th qubit of
Figure BDA0003111172030000182
The corresponding sine and cosine position variables X in the corresponding solution spaceQijJ ═ c, s denotes:
Figure BDA0003111172030000183
then through I0(XQi) Calculating the current quantum state SQiCorresponding spatial position coordinates X of each solutionQijThe maximum value is taken as the objective function value I of the current qubit0Qi(SQi)。
Figure BDA0003111172030000191
Step 5, bulletin board updating
The objective function value according to the current state of each quantum goblet sea squirt is I0Qi(SQi) Will be the maximum value Yboard＝max(I0Q1(XQ1),I0Q2(XQ2),…,I0QN(XQN) And corresponding goblet ascidiolytic spatial location Xboard＝XQij，if I0Qi(SQij)＝YboardI 1,2, …, m, j c, s is assigned to the bulletin board.
Step 6, updating the state
The state updating of the goblet ascidians consists of leader updating and follower updating. The quantum movement is realized by the quantum revolving door, so the quantum goblet and ascidian state update can be realized by the update of the corner of the quantum revolving door:
1. the state update formula of the leader is as follows:
Figure BDA0003111172030000192
in the formula: delta thetaLiA argument change of an ith dimension updated for the representation leader; c. C1,c2,c3Are respectively three control parameters, c2And c3Is a random number between 0 and 1, c2Determines the scale of the update amount c3The direction of the update amount may be determined to be either an addition or subtraction on the original basis. c. C1The key parameter for determining the updating effect is defined as:
Figure BDA0003111172030000193
in the formula: step is the maximum updating Step length; e represents a natural constant; l, L represent the current and maximum number of iterations L ═ 1,2, …, L, respectively.
It can be seen that the smaller the number of iterations, c1The larger the value, the larger the update amplitude. In the first few iterations, the large update amplitude can ensure that the leader approaches the region around the global optimum more quickly, so that the optimization algorithm has good global performance. And when the number of iterations approaches the maximum number of iterations, c1The value gradually goes to 0, i.e. the update step size becomes smaller and smaller, indicating that as accurate a position as possible is obtained when approaching the optimal solution. In contrast, c2And c3The two random variables always enhance the randomness of updating, and further improve the global searching capability.
Leading person goblet SLThe two new positions after updating are:
Figure BDA0003111172030000201
Figure BDA0003111172030000202
therefore, the quantum revolving door realizes synchronous movement of two positions by changing the quantum amplitude angle of the goblet sea squirt, and expands the ergodicity of the search space under the condition of unchanged population scale.
(2) In the foraging process of goblet sea squirts, followers are sequentially connected end to present a chain type combined shape, the chain type structure enables the motion state of the followers to be strongly influenced by front and rear individuals, therefore, the position updating of the followers depends on the positions of the followers and the individuals in front of the followers adjacent to the followers, and the state updating formula of the followers is as follows:
Figure BDA0003111172030000203
in the formula:
Figure BDA0003111172030000204
the updated quantum argument of the follower state; thetaijThe j-dimension quantum argument of the ith individual before the state update; thetai-1jRepresenting the quantum argument of the j dimension of the adjacent individual in front of the i individual.
Let the ith goblet SQiThe current state is Si＝[θi1 θi2 … θin]Using dij＝||Si-SjCalculating the ith goblet sea squirt S by | | |1 ≦ j ≦ NQiDistance d between the sea squirt and the jth gobletijTo obtain the ith goblet sheath XiDistance D between other sea squirt of gobleti＝(di1,di2,…,dij,…,diN)；
And judging the individuals adjacent to the ith goblet ascidian according to the shortest distance.
Followup goblet SQiThe two new positions after updating are:
Figure BDA0003111172030000205
Figure BDA0003111172030000206
therefore, the quantum revolving door realizes synchronous movement of two positions by changing the quantum amplitude angle of the goblet sea squirt, and expands the ergodicity of the search space under the condition of unchanged population scale.
Step 7, mutation treatment
The goblet sea squirt algorithm sometimes falls into a local extreme value in the solving process, the variation operation in the genetic algorithm is used for reference, the population diversity is increased, premature convergence is avoided, and the variation processing is realized by using a quantum NOT gate. Setting a probability of variation PmutAnd judging whether the goblet is mutated or not by extracting a random number randm () from each goblet. If PmutWhen mutation occurs, a mutation qubit j ═ ceil (6 × randm ()) is randomly selected, and the angle of the position is changed by using a quantum not gate, so that diversity is increased.
Figure BDA0003111172030000211
Step 8, if the current iteration times l is less than or equal to lmaxIf yes, let l be l +1, and execute step 4; otherwise step 9 is performed.
Step 9, outputting the state S of the quantum goblet sea squirt on the bulletin boardboardAnd optimum result Yboard。
Step 10, if the objective function value meets the requirement, SboardI.e. the optimal attitude controller parameters. Otherwise, returning to the step 2, resetting the quantum goblet and ascidian algorithm parameters, and executing the steps 3-10.
FIG. 1 shows a flow chart of the method for setting the controller parameters, and FIG. 2 shows a structure chart of the method for setting the attitude controller of the carrier rocket. FIGS. 3-5 are flow charts of the quantum goblet ascidian algorithm in FIG. 1. FIG. 6 shows a tuning process diagram of embodiment 2, and FIG. 7 shows a pitch attitude control curve under the action of each current optimal controller parameter in the tuning process.
Referring to fig. 6, it can be seen that the objective function value decreases with the increase of the number of iterations, and finally stabilizes at about 0.312. Fig. 7 shows a control effect diagram of each generation of current optimal controller parameters, which shows that the optimal control parameters are continuously updated and the attitude control effect is continuously improved as the number of iterations increases. The optimal controller parameters obtained after setting are as follows:
Kp＝20.358、Ki＝1.0016、Kd＝29.9356、α＝1.361、β＝1.2012、r＝29.6
the optimal ITAE indices are: 0.312, it can be seen that the carrier rocket nonlinear attitude controller parameter setting can be completed through 50 iterations. The method of the invention improves the standard goblet sea squirt algorithm by introducing variation lines by combining quantum theory on the basis of the standard goblet sea squirt algorithm, accelerates the convergence speed of parameter setting of the controller, and improves the global search capability and the solving precision of the optimal parameters.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features. In addition, the above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (8)

1. An intelligent setting method for attitude control parameters of a carrier rocket is characterized by comprising the following steps:
acquiring a nonlinear controller parameter of the attitude of the carrier rocket, and multiplying time by an absolute value integral of an attitude control error of the nonlinear controller to be used as a target function for parameter setting of the nonlinear controller;
performing setting optimization on the parameters of the nonlinear controller by solving the maximum value of the objective function by adopting a quantum goblet sea squirt algorithm to determine the optimal parameters of the nonlinear controller;
wherein, the determination of the quantum goblet sea squirt algorithm comprises the following steps:
on the basis of a standard goblet ascidian algorithm, determining the state of the quantum goblet ascidian by adopting a probability amplitude coding mode of quantum bits; wherein the quantum goblet sea squirt state occupies two positions in the parameter solution space, and respectively corresponds to the probability amplitude of the quantum state |0> and |1 >;
determining objective function values of two position coordinates in a parameter solution space according to sine position variables and cosine position variables corresponding to two positions in the parameter solution space, and taking the maximum value of the objective function values of the two position coordinates in the parameter solution space as the objective function value of the quantum goblet sea squirt state;
and assigning the maximum value in the objective function values of the quantum goblet and ascidian states and the corresponding parameter solution space position to a bulletin board.
2. The intelligent tuning method for launch vehicle attitude control parameters according to claim 1, wherein the determination of the non-linear controller parameters and the objective function of the nonlinear controller parameter tuning specifically comprises:
establishing a carrier rocket attitude motion model;
according to the order of the attitude motion model of the carrier rocket, an integral chain type differentiator is designed to track the attitude angle deviation measurement signal, and the expression of the integral chain type differentiator is as follows:
Figure FDA0003111172020000011
Figure FDA0003111172020000012
Figure FDA0003111172020000013
wherein r is a tracking velocity factor, v is an attitude angle deviation measurement signal,
Figure FDA0003111172020000014
respectively a tracking estimation value, a speed estimation value and an acceleration estimation value of the attitude angle deviation measurement signal v;
from acceleration estimates
Figure FDA0003111172020000021
Removing the modeled part f in the attitude motion model of the carrier rocket0(x, u) estimating the internal and external uncertainty terms of the model to obtain the uncertain portion compensator
Figure FDA0003111172020000022
Figure FDA0003111172020000023
By means of a master controller ucontrolAnd indeterminate portion compensator
Figure FDA0003111172020000024
Constructing a nonlinear feedback controller:
Figure FDA0003111172020000025
Figure FDA0003111172020000026
Figure FDA0003111172020000027
in the formula (I), the compound is shown in the specification,
Figure FDA0003111172020000028
a current attitude angle deviation control instruction is obtained; b30Is a nominal system control item parameter; dtIs the set of distances between goblet and sea squirt;
forming a nonlinear controller parameter X ═ K through 5 parameters of the nonlinear feedback controller and 1 parameter of the integral chain differentiatorp Ki Kd α β r]T；
Determining a target function for nonlinear controller parameter tuning based on nonlinear controller parameters
Figure FDA0003111172020000029
3. The intelligent tuning method for attitude control parameters of a launch vehicle according to claim 1, wherein the quantum goblet sea squirt state comprises:
Figure FDA00031111720200000210
in the formula, thetaij2 pi × radmn, i ═ 1,2, …, m, j ═ 1,2, …, n, and radmn are random numbers between (0, 1); m is the population size; n is the optimization variable space dimension; each goblet sea squirt state occupies two positions in the parameter solution space and respectively corresponds to a quantum state |0>And |1>Amplitude of probability of, i.e.
SQic＝(cos(θi1),cos(θi2),…,cos(θin))
SQis＝(sin(θi1),sin(θi2),…,sin(θin))
In the formula, SQicIs in a cosine state, SQisIs in a sinusoidal state.
4. The intelligent setting method for attitude control parameters of a launch vehicle according to claim 3, wherein the determination of the objective function value of the quantum goblet sea squirt state specifically comprises:
let the current quantum state SQiA k-th qubit of
Figure FDA00031111720200000211
The corresponding sine and cosine position variables X in the corresponding solution spaceQijJ ═ c, s denotes:
Figure FDA0003111172020000031
Figure FDA0003111172020000032
through I0(XQi) Calculating the current quantum state SQiCorresponding spatial position coordinates X of each solutionQijJ is the objective function value of c, s, and takes the maximum value as the objective function value of the current qubit:
Figure FDA0003111172020000033
in the formula I0(. is the self brightness of the goblet sea squirt algorithm; [ Low ]k,Highk]Optimizing Range for the kth design variable, HighkIs upper bound of range, LowkThe lower range.
5. The intelligent tuning method for attitude control parameters of a launch vehicle of claim 1, wherein the determination of the quantum goblet ascidian algorithm further comprises:
the quantum goblet and ascidian state is updated through the updating of the quantum revolving door corner.
6. The intelligent setting method for attitude control parameters of a launch vehicle according to claim 5, wherein the updating of the quantum goblet sea squirt state is realized by updating the rotation angle of the quantum revolving door, and specifically comprises:
the updating of the state of the quantum goblet ascidians comprises: leader state updates and follower state updates;
the leader state update formula is:
Figure FDA0003111172020000034
in the formula: delta thetaLiA argument change of an ith dimension updated for the representation leader; c. C1,c2,c3Respectively three control parameters, c2And c3Is a random number between 0 and 1, c2Determining the size of the update amount, c3Determining a direction of an update amount; c. C1Determining the key parameters of the updating effect, and defining the values as:
Figure FDA0003111172020000035
in the formula: step is the maximum updating Step length; e represents a natural constant; l, L represents the current and maximum number of iterations L ═ 1,2, …, L, respectively;
leading person goblet SLThe two new positions after updating are:
Figure FDA0003111172020000041
Figure FDA0003111172020000042
the quantum revolving door synchronously moves the two updated positions of the sea squirts of the leading goblet by changing the quantum amplitude angle of the sea squirts of the leading goblet;
the follower state update formula is as follows:
Figure FDA0003111172020000043
in the formula:
Figure FDA0003111172020000044
the updated quantum argument of the follower state; thetaijThe j-dimension quantum argument of the ith individual before the state update; thetai-1jRepresenting the quantum argument of j dimension of the adjacent individual in front of the ith individual;
followup goblet SQiThe two new positions after updating are:
Figure FDA0003111172020000045
Figure FDA0003111172020000046
the quantum revolving door synchronously moves the two updated positions of the followed goblet ascidians by changing the quantum amplitude angle of the followed goblet ascidians.
7. The intelligent tuning method for attitude control parameters of a launch vehicle of claim 1, wherein the determination of the quantum goblet ascidian algorithm further comprises:
and (3) introducing variation operation in a single iteration flow of the standard goblet sea squirt algorithm by adopting a quantum NOT gate.
8. The intelligent tuning method for attitude control parameters of a launch vehicle of claim 7, wherein the mutation operation specifically comprises:
setting a probability of variation PmutJudging whether the goblet ascidian has variation or not by extracting a random number randm () from each goblet ascidian; if PmutAnd if the quantum is greater than randm (), mutation occurs, randomly selecting a mutation qubit j ═ ceil (6 × randm ()), and changing the angle of the mutation qubit by using a quantum not gate:
Figure FDA0003111172020000047
in the formula:
Figure FDA0003111172020000048
the updated quantum argument of the follower state; thetaijThe j-dimension quantum argument of the ith individual before the state update; and pi is the circumferential ratio.
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