CN101118421A - Intelligent non-linearity PID controlling parameter tuning based on self-adapting ant colony - Google Patents
Intelligent non-linearity PID controlling parameter tuning based on self-adapting ant colony Download PDFInfo
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Abstract
The present invention provides a non-linear PID control parameter setting method based on self adaptive ant colony intelligent. The method includes the steps as follows: first, the optimum relation range of undetermined coefficient in a non-linear PID controller; second, a gridding is made in a variable region which is divided into a plurality of space regions; third, an initial parameter and a taboo table index indicating hand, every two ants are used as a partner to choose a certain node as the starting point; fourth, two ants choose the optimum relation space node according to the state transition probability and go forwards; fifth, the taboo table index indicating hand is amended, according to the route passed by the ants, the non-linear PID control undetermined coefficient corresponding to the route is calculated, and the objective function corresponding to the ants is calculated, as well as the ITAE minimal performance index in the cycle period is recorded; finally, the non-linear PID control parameter corresponding to the minimal performance index is stored in a control coefficient, at the same time, the pheromone residual coefficient adjusted in the self-adaption way, and the pheromone rail on each route is renovated. The steps are circled till an optimum result is obtained.
Description
(I) the technical field
The performance of any Proportional-derivative-Integral (PID) controller depends entirely on the optimization of its control parameters. A Non-Linear proportional-derivative-integral (NLPID) controller is a new type of controller, and its parameter optimization method and technique are constantly under development, and the optimization of NLPID parameters by using bionic intelligent method has gradually become a key technique in the PID field.
The ant colony algorithm is a new artificial intelligence algorithm, and a plurality of NP problems which are well solved by applying the ant colony algorithm are solved. Aiming at the problem of parameter optimization of a novel NLPID controller, a control parameter setting method based on self-adaptive ant colony intelligence is invented. The method is an effective technical approach for solving the NLPID parameter setting problem, and meanwhile, the method can also be applied to solving the combined optimization problem of other types of control parameters.
(II) background of the invention
The PID controller is essentially a control algorithm that estimates "past", "present", and "future" information. The PID control is already appeared in the end of the 30 th century, and is continuously updated for nearly 70 years so far, and because the PID control has the advantages of simple algorithm, convenient use, good robustness, high reliability and the like, about 90 percent of control loops in the field of control engineering still have PID structures at present.
The conventional PID control algorithm itself has certain limitations, as follows:
(1) For a conventional PID controller in an actual application occasion, due to the trouble of a parameter optimization method, the optimization is poor and the performance is poor;
(2) At present, methods such as an empirical method, a trial and error method and the like are mostly adopted in engineering for conventional PID parameter optimization, and the methods are time-consuming and labor-consuming and are often poor in optimization effect;
(3) As a linear control method, the conventional PID control is difficult to obtain a good control effect on noise interference and a complex nonlinear system.
In order to improve the performance of the PID control algorithm, a great number of international scholars research and improve the PID control algorithm, and a great number of novel PID control algorithms such as NLPID control, selective PID-PD control, I-PD control, robust PID control, intelligent PID control, adaptive PID control and the like appear.
The performance of any PID controller depends entirely on the optimization of its control parameters. For decades, the parameter optimization method and technology of the PID controller are continuously developed, and a plurality of important international journals (such as Automatica, IEEE (institute of Electrical and electronics Engineers) in the control field continuously release some new research results, wherein Hang C.C. and the like improve the classical Z-N method, and further provide an RZN method; astrom K.J. and the like propose two PID parameter optimization methods by taking the phase margin expected by the system as an index; ho w. et al propose a method for optimizing PID parameters using amplitude margin and phase margin; ott et al and Lin c.l. et al propose methods for optimizing PID parameters using an improved GA; liu Y.J. and the like and Gaing Z.L. propose a method for optimizing PID parameters by using a PSO algorithm; and so on.
The invention adopts the following characteristics of ant colony intelligence in solving the NLPID parameter setting problem:
(1) Under the reinforcing effect of continuously dispersing the bioinformatics hormones by ants, new information can be quickly added into the environment. Due to the evaporation and the update of the biological information hormone, the old information can be continuously lost, and a dynamic characteristic is embodied;
(2) Because a plurality of ants feel the distributed biological information hormones in the environment and simultaneously disperse the production information hormones, different ants have different selection strategies and have distribution;
(3) The optimal route is searched by the cooperation of a plurality of ants and becomes the route selected by most ants, and the process has synergy;
(4) The ant colony algorithm has the advantages that the ant colony algorithm can complete complex tasks due to interaction, mutual influence and mutual cooperation among individuals, groups and the environment, and the adaptability is expressed as the robustness of the ant colony algorithm;
(5) Self-organization tends to structure the behavior of ant populations because it involves a process of positive feedback. The process utilizes global information as feedback, and positive feedback enables self-enhancement of a better solution in the system evolution process to continuously change the solution of the problem to the direction of global optimization, so that the better solution can be obtained effectively.
The characteristics of parallelism, cooperativity, self-organization, dynamics, strong robustness and the like reflected in the ant colony algorithm optimizing process are in accordance with a plurality of requirements of control parameter setting. The improved self-adaptive ant colony intelligent setting NLPID control parameter can be independent of an accurate mathematical model of a controlled object, and can effectively solve a very difficult optimization problem, so that the problem processing has more flexibility, adaptability and robustness. Meanwhile, the real-time performance of NLPID parameter setting can be improved, the real-time control requirement of a complex system is met, and the method can be used for solving the problem of combination optimization of other types of control parameters.
Disclosure of the invention
The ant colony algorithm is a newly developed bionic intelligent optimization algorithm, and simulates the colony foraging behavior of natural ants. In nature, ants perform a relatively difficult task by coordinating with each other, and scientists find that ants can always find the shortest path between their nest and the food source in a relatively short time. The ant colony algorithm was first used to successfully solve the well-known traveler Problem (tracking Salesman Problem). At present, the research on the ant colony algorithm by people penetrates into a plurality of application fields from the problem field of a single traveler at first, the research on the ant colony algorithm is developed from the problem of one-dimensional static optimization to the problem of multidimensional dynamic combination optimization, the research in a discrete domain range is gradually expanded to the research in a continuous domain range, and a plurality of breakthrough progresses are made on the hardware realization of the ant colony algorithm, so that the emerging bionic optimization algorithm has the vigorous and vigorous development prospect.
The ant colony algorithm is mainly characterized in that: positive feedback, parallelism, and distributed computing. The positive feedback process enables the method to find a better solution of the problem faster; the distributed mode is easy to realize in parallel, and is combined with a heuristic algorithm, so that the method is easy to find a better solution.
According to the research of biologists, the ants are mutually communicated and influenced by a chemical substance called pheromone, pheromone is continuously secreted on a passing path when real ants go out to find food, the passing path is recorded, and the concentration of the pheromone on the path influences the traveling path of subsequent ants. For a shorter path, the number of ants passing through the path in unit time is larger, the concentration of pheromones on the path is higher, and more ants are attracted to search along the path; for a path with longer distance, because the number of ants passing through in unit time is less, the concentration of pheromones on the path is lower; the pheromone volatilizes along with time, so that the weakening of the concentration of the pheromone in a longer path is obvious, and the attenuation effect of the concentration of the pheromone in a shorter path is secondary because of more ants passing through, which is mainly reflected in that the concentration of the pheromone is enhanced by the ants passing through, thereby forming positive feedback. The positive feedback mechanism provides feasibility for the ant colony to find the optimal path. The shorter the path taken by the ant, the higher the concentration of pheromone, and the higher the concentration of pheromone, the more ants are attracted, and finally all ants are concentrated on the path with the highest concentration of pheromone, and the path is the shortest path from the nest to the food source. Fig. 1 shows the foraging process of real ants.
The ant colony algorithm is actually an intelligent multi-agent system, and the self-organization mechanism of the ant colony algorithm enables the ant colony algorithm not to have detailed knowledge of every aspect of the problem. The self-organization is essentially a dynamic process of the ant colony algorithm mechanism for increasing the entropy of the system without external action, and embodies the dynamic evolution from disorder to order, and the logical structure of the self-organization is shown in fig. 2.
The mathematical model of the ant colony algorithm is as follows: let b i (t) represents the number of ants, τ, located at element i at time t ij (t) is the information amount on the path (i, j) at the time t, n represents the TSP scale, and m is the total number of ants in the ant colony, then；Γ＝{τ ij (t)|c i ，c j V 8834C is the connection of two elements (cities) in the set C at time t ij Collection of the amount of upper residual information. At the initial time, the information amount on each path is equal, and tau is set ij (0) = const, the optimization of the basic ant colony algorithm is implemented by the directed graph g = (C, L, Γ).
The transfer direction of an ant k (k =1,2, \8230;, m) is determined according to the information amount on each path during the movement. Here, tabu is used k (k =1,2, \8230;, m) to record the city ant k currently walks, aggregated with the tab k The evolution process is dynamically adjusted. In the searching process, ants calculate the state transition probability according to the information quantity on each path and the heuristic information of the path. p is a radical of ij k (t) represents the probability of a state transition of an ant k from element (city) i to element (city) j at time t
In the formula, allowed k ＝{C-tabu k Denotes the city ant k next allowed to select. Alpha is an information heuristic factor, represents the relative importance of the track, reflects the action of information accumulated by the ants in the moving process when the ants move, and the larger the value of the value is, the more the ants tend to select the path passed by other ants, and the stronger the cooperation among the ants is; beta is an expected heuristic factor, represents the relative importance of visibility, reflects the degree of importance of heuristic information of ants in the course of movement in ant selection paths, and the larger the value is, the closer the state transition probability is to the greedy rule. Eta ij (t) is a heuristic function, expressed as follows
In the formula (d) ij Representing the distance between two adjacent cities. For ant k, d ij The smaller is, then ij The larger (t) is, p ij k The larger (t) becomes. Obviously, the heuristic represents the expected degree of transfer of ants from element (city) i to element (city) j.
In order to avoid that the residual pheromone is too much to cause the residual information to inundate the heuristic information, after each ant walks one step or completes the traversal of all n cities (namely, one cycle is finished), the residual information needs to be updated. The updating strategy simulates the characteristics of human brain memory, and when new information is continuously stored in the brain, old information stored in the brain is gradually faded or even forgotten along with the lapse of time. Thus, the amount of information on the path (i, j) at time t + n can be adjusted as follows
τ ij (t+n)＝(1-ρ)·τ ij (t)+Δτ ij (t)(3)
Where ρ represents the pheromone volatilization coefficient, 1- ρ represents the pheromone residual factor, and the range of ρ is: rho \8834; [0, 1); delta tau ij (t) indicates the pheromone increment on the path (i, j) in the present cycle, and the initial time Δ τ ij (0)＝0，Δτ ij k (t) represents the amount of information that the kth ant left on path (i, j) in this cycle.
According to different pheromone updating strategies, at present, three different basic Ant colony algorithm models are called an Ant-Cycle model, an Ant-Quantity model and an Ant-sensitivity model respectively, and the difference is delta tau ij k (t) difference in the method. Because the Ant-Quantity model and the Ant-sensitivity model are both used for locally updating the pheromone, and the Ant-Cycle modelThe method is an overall pheromone updating method, has good effect on solving the TSP problem, and uses the Ant-Cycle model as the pheromone updating method of the basic Ant colony algorithm. In the Ant-Cycle model
In the formula, Q represents pheromone intensity, which influences the convergence rate of the algorithm to a certain extent; l is a radical of an alcohol kAnd the total length of the path taken by the kth ant in the cycle is shown.
The reference input r (t) is fed to a tracking-differentiator I for extracting two signals x 11 (t) and x 12 (t)，x 11 (t) tracking r (t),
(ii) a The adjusted quantity y (t) is sent to a tracking-differentiator II to extract two signals x 21 (t) and x 22 (t)，x 21 (t) tracking y (t),
now, the following three quantities are used:
instead of three basic elements in a conventional PID controller: e (t) = r (t) -y (t), e 1 (t)，∫ 0 t e (τ) d τ. Then through e 0 、e 1 And e 2 To generate the control quantity u 1 (t) and then changing the signal into u (t) through a linear filter, and the novel NLPID controller system structure is shown in FIG. 3.
In FIG. 3, the tracking-differentiator I essentially arranges for an ideal transition x 11 (t) and gives a differential signal x for this process 12 (t), and the tracking-differentiator II recovers the adjusted quantity y (t) and gives its differentiated signal as soon as possible. Here, the basic elements of the NLPID controller are not taken directly from the input-output error, but rather are the input sumAnd carrying out nonlinear processing on the output signal to obtain a new difference and differentiation and integration thereof.
Order to
Where δ is a constant.
From this, the following specific NLPID controller can be constructed:
for the tracking-differentiator I, there are:
in the formula, R 1 Is determined according to the transient speed requirement, delta 1 Is compared with the integration step size and R 1 The parameters of interest.
Similarly, for tracking-differentiator II, there are:
in the formula, R 2 Also determined by the transient speed requirement, which is usually a ratio of R to R 1 The value of (A) is large; delta. For the preparation of a coating 2 Is with R 1 、R 2 And delta 1 The parameters that are relevant to the process are,
at the same time, defining an error integral
And e is a 0 ＝x 5 ，e 1 ＝x 1 -x 3 ，e 2 ＝x 2 -x 4 。
Let a non-linear function
When e < | δ |, there is a linear relationship between fal (e, α ', δ) and e, so that when e approaches 0, fal (e, α', δ) can achieve smooth control.
The following nonlinear combinations are thus obtained:
in the formula, beta 0 、β 1 、β 2 Representing the control coefficient, x, of the NLPID controller 6 Representing the control quantity applied to the controlled object after filtering, the filter in the formula (9) is used for improving the robust performance and stability of the system, and rho 0 Is determined by the filtering and tracking requirements, i.e. comparing u = u 1 And u = x 6 To determine that α' should be a constant between 0.5 and 1.0, and δ should also be a suitably small constant. It can be seen that the key of the new NLPID controller is its control coefficient beta 0 、β 1 And beta 2 To the optimization problem of (2).
The invention relates to a self-adaptive ant colony intelligence based nonlinear PID control parameter setting method, which comprises the following steps:
the structure of a control system for intelligently tuning NLPID control parameters based on the adaptive ant colony is shown in figure 4.
The NLPID parameter optimization problem of the control system can be classified as a typical continuous space optimization problem, and the ant colony algorithm idea for solving the continuous space optimization problem is generally as follows: firstly, the range of the optimal solution can be estimated according to the property of the problem, and the value range of the solved variable is estimatedx jlower ≤x j ≤x jupper (j =1,2,3, \8230;, n). And (3) gridding in the variable area, wherein the grid points of the space correspond to a state, ants move among the space grid points, and different information quantities are left according to the objective function values of the grid points, so that the moving direction of the next batch of ants is influenced. After a certain period of circulation, the amount of information of the grid points with small difference of the objective function (i.e., evaluation function value) between the adjacent nodes is relatively large. And according to the information amount, finding out a spatial grid point with large information amount, reducing the variable range, carrying out ant colony movement nearby the point, and repeating the process until the algorithm is stopped after the stopping condition of the algorithm.
Assuming that the parameter variables are divided into N equal parts, N variables become a decision problem of N stages, each stage has N +1 nodes, and the total of (N + 1) × N nodes are connected together from stage 1 to stage N to form a solution in the solution space, as shown in fig. 5.
As can be seen from fig. 5, the state space shows the state (3, 4, 2.., 1), which corresponds to the solution:
because the Time multiplied by the Absolute value integral of Error (ITAE) considers less large initial Error, emphasizes the overshoot and the adjustment Time, reflects the rapidity and accuracy of the control system, and is generally adopted in the control field all the Time. The concrete form is as follows:
J ITAE ＝∫t|e(t)|dt＝min (11)
discretizing the above formula, the difference equation can be obtained as:
in the formula, T represents a simulation calculation step length, and N represents the total number of points of simulation calculation.
Assuming that the total number of ants is m, when optimizing, the ants are scattered on a spatial grid point according to a random principle, and for each ant l, an objective function J with an evaluation function value of i point is defined i And an objective function J with J points adjacent to the target function J j And noting the difference value:
ΔJ ij ＝J i -J j ，i，j(13)
define the transition probability of ant l:
in the formula, allowedl represents a set of spatial grid path points allowed to be passed by ant l in the next step, and tau ij The quantity of pheromones in the neighborhood of the ant l, alpha is an information heuristic factor, and beta is an expected heuristic factor.
When optimizing, ants are scattered on the spatial grid points according to a random principle, and fairy ants with the best evaluation function values are recorded. Then, each ant is moved according to the spatial state transition probability given by equation (14). A proximity search mechanism is embedded in the search process, namely: when Δ J ij When more than 0, ants l press probability P ij Move from its neighborhood i to neighborhood j; when Δ J ij And when the number is less than or equal to 0, the ant l carries out self neighborhood search to find a better solution.
When one cycle is finished, the number of pheromones on the moving path of the ants is correspondingly adjusted according to the following formula:
where ρ is the residual coefficient of the pheromone, and Δ τ ij l The unit length of the pheromone material left on the path ij in the current cycle of the first ant can be calculated by the following formula:
wherein Q is a constant, J l And (4) representing the calculated objective function value of the first ant in the current cycle.
In addition, the larger the pheromone residual coefficient ρ is, the number of search cycles N C The larger the algorithm is, the slower the convergence speed of the algorithm becomes; if ρ is too small, although the convergence rate is accelerated, the calculation result tends to fall into a locally optimal state. Therefore, in order to improve the solving efficiency of the algorithm, the method introduces the pairThe rho value adopts a self-adaptive control strategy, namely changing rho into a threshold function:
wherein 0.9 is the set volatilization restriction coefficient rho min The lower pheromone residual coefficient bound.
In order to improve the searching speed, the optimization strategy also adopts an optimization scheme that two ants search from two limit points simultaneously, and the parallel processing strategy can effectively improve the overall convergence speed of the algorithm.
In summary, the nonlinear PID control parameter tuning method based on adaptive ant colony intelligence proposed by the present invention specifically includes the following steps:
the first step is as follows: determining parameter rho in NLPID controller according to model characteristics of actual control system 0 、 α′、δ、δ 1 、δ 2 、R 1 And R 2 And estimating the coefficient beta in the NLPID controller 0 、β 1 、β 2 The range of the optimal solution is then gridded in a variable region and divided into n small space regions; let time t =0 and number of cycles N C =0, set ant number m and maximum cycle number N Cmax Placing m ants on nodes of n small space regions to make the initialization information content tau of each edge (i, j) in the optimum solution space region ij ＝const，ρ min = const, and initial time Δ τ ij =0, wherein const denotes a constant;
the second step: number of cycles N C ←N C +1；
The third step: the taboo list index number k =1 of the ant;
the fourth step: ant number k ← k +2;
the fifth step: selecting an optimal solution space node as a starting point by taking every two ants as a party;
and a sixth step: the ant A selects an optimal solution space node j according to the probability calculated by the state transition probability formula (14) 1 And go forward, j 1 ∈{C-tabu k }; ant B also selects an optimal solution space node j according to the probability calculated by the state transition probability formula (14) 2 And go forward, j 2 ∈{C-tabu k -j 1 }；
The seventh step: if the length of the current path is larger than the shortest path of the meeting cycle of the m ants, the meeting cycle is ended;
eighth step: modifying a taboo table pointer, namely moving the ants to a new optimal solution space node after selection, and moving the optimal solution space node to the taboo table of the ant individual;
the ninth step: if the optimal solution space node in the set C is not traversed completely, namely k is less than m, jumping to Step4, otherwise continuing to the next Step10;
the tenth step: according to the path taken by the ant, the NLPID control coefficient beta corresponding to the path is calculated by using the formula (10) 0 、β 1 And beta 2 Calculating objective function value corresponding to ant by using formulas (12) and (13), recording optimal path corresponding to ITAE minimum performance index in the cycle, and storing NLPID control parameter corresponding to the optimal path into control coefficient beta 0 、β 1 And beta 2 Performing the following steps;
the eleventh step: adaptively adjusting the pheromone residual coefficient rho according to a formula (17);
the twelfth step: updating the pheromone track on each path according to the formulas (15) and (16);
and a thirteenth step of: if the number of cycles N C ≥N Cmax Or the whole ant colony converges to the same path, the circulation is ended and the optimal space node path and the NLPID control coefficient beta corresponding to the optimal space node path are output 0 、 β 1 And beta 2 Otherwise, emptying the tabu list and jumping to the second step.
The invention relates to an NLPID control parameter setting method based on self-adaptive ant colony intelligence, which has the advantages that: the flight simulation turntable system adopting the self-adaptive ant colony intelligent setting NLPID control parameter can reasonably extract a differential signal from a noisy input signal, has a strong filtering effect on noise, and has high response speed and strong robustness.
The invention is an effective technical approach for solving the NLPID parameter setting problem, and meanwhile, the method can also be applied to solving the combined optimization problem of other types of control parameters.
(IV) description of the drawings
FIG. 1 process of finding food by ant colony in reality
FIG. 2 logic structure of basic ant colony algorithm
Figure 3 novel NLPID controller system structure
Fig. 4 is an NLPID control system structure based on self-adaptive ant colony intelligence
FIG. 5 State space solution schematic
FIG. 6 flight simulation turntable tracking response under noise signal input
FIG. 7 is a graph of the evolution of the objective function with the number of iterations
The reference numbers and symbols in the figures are as follows:
r (t) -input signal
y (t) -output signal
u (t) -control signals
e (t) -error signal
Nc-number of cycles of adaptive ant colony algorithm
(V) detailed description of the preferred embodiments
The test object is a certain type of high-performance flight simulation turntable, and based on the application object, the specific implementation steps of the NLPID controller parameter setting based on the self-adaptive ant colony algorithm provided by the invention are as follows:
step 1: the interrupt sampling interval is set to 0.0008s, and the initialization parameters α =1.5, β =4.5, ρ are set min ＝0.2，τ ij ＝1，Δτ ij (0)＝0，m＝20，ρ 0 ＝0.15，R 1 ＝150，R 2 ＝100， δ 1 ＝0.002，δ 2 ＝0.0013，δ＝0.01，α′＝0.6，N Cmax =100,q =300; after a plurality of times of debugging, determining a control coefficient beta 0 、β 1 And beta 2 In the approximate range of beta 0 ⊂[0.01，0.09]， β 1 ⊂[770，790]，β 2 ⊂[0.1，0.7]；
The second step is that: number of cycles N C ←N C +1；
The third step: ant taboo list index number k =1;
the fourth step: ant number k ← k +2;
the fifth step: selecting an optimal solution space node as a starting point by taking every two ants as a party;
and a sixth step: the ant A selects an optimal solution space node j according to the probability calculated by the state transition probability formula (14) 1 And go forward, j 1 ∈{C-tabu k }; the ant B also selects an optimal solution space node j according to the probability calculated by the state transition probability formula (14) 2 And go forward, j 2 ∈{C-tabu k -j 1 }：
The seventh step: if the length of the current path is larger than the shortest path of the 20 ants meeting cycle, the meeting cycle is ended;
eighth step: modifying a tabu table pointer, namely moving the ants to a new optimal solution space node after selection is finished, and moving the optimal solution space node to the tabu table of the ant individual;
the ninth step: if the optimal solution space node in the set C is not traversed completely, namely k is less than 20, jumping to Step4, otherwise continuing to the next Step10;
the tenth step: according to the path taken by the ant, the NLPID control coefficient beta corresponding to the path is calculated by using the formula (10) 0 、β 1 And beta 2 Calculating objective function value corresponding to ant by using formulas (12) and (13), recording optimal path corresponding to ITAE minimum performance index in the cycle, and storing NLPID control parameter corresponding to the optimal path into control coefficient beta 0 、β 1 And beta 2 The method comprises the following steps:
the eleventh step: adaptively adjusting the pheromone residual coefficient ρ according to equation (17):
a twelfth step: the pheromone tracks on each path are updated according to equations (15) and (16):
and a thirteenth step of: if the number of cycles N C If the ant colony has converged to the same path or more than 100, the cycle is ended and the optimal space node path and the NLPID control coefficient beta corresponding to the optimal space node path are output 0 、 β 1 And beta 2 Otherwise, emptying the tabu list and jumping to Step2.
Continuously performing 10 times of digital simulation by using the improved adaptive ant colony algorithmIs the optimal solution mean of
. The evolution of the objective function J with the number of iterations is shown in fig. 6.
As can be seen from fig. 6, the optimal objective function J can be converged at a very fast speed, so that a satisfactory result is found, and the optimal objective function J has good convergence and stability.
Fig. 7 shows the operation condition of the flight simulation turntable system adopting the self-adaptive ant colony intelligent tuning NLPID control parameter when tracking a standard signal with noise and tracking a random signal with noise. The adopted standard sinusoidal signal with noise is r (t) =5sin (pi t) + sigma (t), and the random signal with noise is r (t) =1.5sin (2 pi t) +0.5cos (6 pi t) + sigma (t), wherein sigma (t) is 5% white noise, namely, sigma (t) | < 0.05.
FIG. 7 (a) is a graph showing the operation of tracking a noisy standard sinusoidal signal; FIGS. 7 (b) and 7 (c) are enlarged partial views, respectively, of FIG. 7 (a), designated as 1 and 2; fig. 7 (d) shows the operation when tracking a noisy random signal.
Claims (1)
1. A nonlinear PID control parameter setting method based on self-adaptive ant colony intelligence is characterized by comprising the following steps: the method comprises the following specific steps:
the first step is as follows: determining parameter rho in nonlinear PID controller according to actual control system model characteristics 0 、α′、δ、δ 1 、δ 2 、R 1 And R 2 And estimating the coefficient beta in the nonlinear PID controller 0 、β 1 、 β 2 The range of the optimal solution is then gridded in the variable region, divided into
Small spatial area(ii) a Let time t =0 and number of cycles N C =0, set number of ants m and maximum number of cycles N Cmax Placing m ants on nodes of n small space regions, and enabling the initialization information amount tau of each edge (i, j) in the optimal solution space region ij ＝const，ρ min = const, and initial time Δ τ ij =0, wherein const denotes a constant;
the second step is that: number of cycles N C ←N C +1；
The third step: the taboo list index number k =1 of the ant;
the fourth step: ant number k ← k +2;
the fifth step: selecting an optimal solution space node as a starting point by taking every two ants as a party;
and a sixth step: ant A according to the state transition probability formula
In the formula, allowed l Represents the set of spatial grid path points, τ, that ant l is allowed to walk through next ij The quantity of pheromones in the neighborhood of the ant l, alpha is an information heuristic factor, and beta is an expected heuristic factor;
the optimal solution space node j is selected according to the probability calculated by the formula 1 And go forward, j 1 ∈{C-tabu k ) (ii) a The ant B also selects an optimal solution space node j according to the probability calculated by the state transition probability formula 2 And go forward, j 2 ∈{C-tabu k -j 1 }；
The seventh step: if the length of the current path is larger than the shortest path of the meeting cycle of the m ants, the meeting cycle is ended;
the eighth step: modifying a tabu table pointer, namely moving the ants to a new optimal solution space node after selection is finished, and moving the optimal solution space node to the tabu table of the ant individual;
the ninth step: if the optimal solution space node in the set C is not traversed, namely k is less than m, jumping to the fourth step, otherwise, continuing to the next tenth step;
the tenth step: according to the path taken by ant, the following formula is used
Calculating the nonlinear PID control coefficient beta corresponding to the path 0 、β 1 And beta 2 Using the formula
In the formula, T represents the step length of simulation calculation, and N represents the total number of points of simulation calculation;
assuming that the total number of ants is m, when optimizing, the ants are scattered on a spatial grid point according to a random principle, and for each ant l, an objective function J with an evaluation function value of i point is defined i And an objective function J with J points adjacent to the target function J j And noting the difference value:
ΔJ ij ＝J i -J j ，i，j
calculating objective function value corresponding to ant by using the above formula, recording optimal path corresponding to ITAE minimum performance index in the cycle, and storing NLPID control parameter corresponding to the optimal path into control coefficient beta 0 、β 1 And beta 2 Performing the following steps;
the eleventh step: according to the formula
Adaptively adjusting a pheromone residual coefficient rho;
the twelfth step: according to the following formula
Where ρ is the residual coefficient of pheromone and Δ τ ij l The unit length of the pheromone material left on the path ij in the current cycle of the first ant can be calculated by the following formula:
wherein Q is a constant, J l Representing the objective function calculation value of the first ant in the current cycle;
updating the pheromone track on each path according to the formula;
the thirteenth step: if the number of cycles N C ≥N Cmax Or the whole ant colony converges to the same path, the cycle is ended and the optimal space node path and the corresponding nonlinear PID control coefficient beta thereof are output 0 、β 1 And beta 2 Otherwise, emptying the tabu table and jumping to the second step.
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