CN106773654B - A kind of Fractional Order PID Controller parameter optimization setting method - Google Patents
A kind of Fractional Order PID Controller parameter optimization setting method Download PDFInfo
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Abstract
The present invention provides a kind of Fractional Order PID Controller parameter optimization setting method, utilize the global optimization function of state branching algorithm, search can make the proportionality coefficient of the performance index function value global minima of Fractional Order PID control system, integral coefficient, differential coefficient, the Optimal tunning parameter of differential order and integral order as Fractional Order PID Controller.Emulation experiment is carried out to workbench closed-loop control system based on the Fractional Order PID Controller parameter optimization setting method of state branching algorithm using proposed by the present invention, the experimental results showed that adjusting resulting Fractional Order PID control system using the method for the present invention there is adjustment speed to wait fastly significantly a little compared with the Fractional Order PID control system that other control methods obtain, is a kind of Fractional Order PID Controller parameter tuning method with promotional value.
Description
Technical field
The present invention relates to automatic control technology fields, whole more particularly, to a kind of Fractional Order PID Controller parameter optimization
Determine method.
Background technique
Currently, Traditional PID (ratio (proportion), integral (integral), derivative (derivative)) control is
The most mature control method of most widely used in control system, technology, and the level of PID controller is directly related to process industrial
The level of control.Fractional order theory and PID controller adjusting theory are combined, differential, integral order μ and λ is introduced, is in recent years
Carry out the research direction of an awfully hot door.
Fractional order PIλDμThe transmission function of controller are as follows:Wherein, KPFor proportional gain, KI
For integral constant, KDFor derivative constant, λ is integral order, and μ is differential order.Due to introducing differential, integral order μ and λ,
More two adjustable parameters of entire controller, so the setting range of controller parameter becomes larger, controller can be controlled for greater flexibility
The dynamic property of controll plant processed and adjustment system, it may be desirable that obtain better control effect.It can be said that fractional order PIλDμControl
The appearance of device processed is the theoretical historical milestone of fractional order control, has established base for the development of fractional order control theory
Plinth.The meaning of fractional order control is exactly the generalization for classic integer rank control, it can establish more accurate model, obtains
To better control result.
State branching algorithm (State Transition Algorithm, STA) be proposed in recent years one kind it is novel
Randomness global optimization method.In state branching algorithm, a solution of optimization problem regards a state, the update of solution as
Process regards state migration procedure as.Using state-space expression, it can will generate one unification of process of candidate solution
Frame describe, the operator for generating candidate solution is described with state-transition matrix.The algorithm has of overall importance, optimality, fastly
The features such as speed, convergence and controllability.Therefore, state branching algorithm is applied into fractional order PIλDμController parameter optimization
Adjusting, has been a urgent problem to be solved.
Summary of the invention
The present invention in order to overcome the problems referred above or at least is partially solved the above problem, provides a kind of Fractional Order PID control
Device parameter optimization adjusts technology, obtains the optimal whole of Fractional Order PID Controller using the ability of searching optimum of state branching algorithm
Determine parameter.
According to an aspect of the present invention, a kind of Fractional Order PID Controller parameter optimization setting method is provided, comprising:
Step 1, complexity based on control system obtains the search dynamics SE of state branching algorithm optimizing and maximum allowable
The number of iterations Maxiter；It obtains Fractional Order PID Controller and waits for setting parameter range；It is generated at random in n-dimensional space described to whole
Determine the individual collection Best in parameter areak, wherein n is the number to optimizing parameter；
Step 2, for the BestkIn individual successively carry out stretching operation, rotation transformation operation and seat respectively
Transform operation is marked, optimal sample is respectively obtained, until the individual number for carrying out operation is equal to Maxiter；
Step 3, all optimal samples and corresponding performance index function value are exported.
The application proposes a kind of Fractional Order PID Controller parameter optimization setting method, utilizes the overall situation of state branching algorithm
Optimize function, search can make the proportionality coefficient of the performance index function value global minima of Fractional Order PID control system, integration system
Number, differential coefficient, the Optimal tunning parameter of differential order and integral order as Fractional Order PID Controller.It is mentioned using the present invention
Out based on the Fractional Order PID Controller parameter optimization setting method of state branching algorithm to workbench closed-loop control system carry out
Emulation experiment, the experimental results showed that adjusting resulting Fractional Order PID control system and other control methods using the method for the present invention
Obtained Fractional Order PID control system is compared, and there is adjustment speed to wait fastly significantly a little, be a kind of score with promotional value
Rank PID controller parameter setting method.
Detailed description of the invention
Fig. 1 is showing according to a kind of Fractional Order PID Controller parameter optimization setting method overall flow of the embodiment of the present invention
It is intended to；
Fig. 2 is according in a kind of workbench x-axis of Fractional Order PID Controller parameter optimization setting method of the embodiment of the present invention
Closed loop moving control system block schematic illustration；
Fig. 3 is to be shown according to a kind of response of the system of Fractional Order PID Controller parameter optimization setting method of the embodiment of the present invention
It is intended to；
Fig. 4 is with existing according to a kind of Fractional Order PID Controller parameter optimization setting method of the embodiment of the present invention based on something lost
The contrast schematic diagram of propagation algorithm and the setting method system response based on particle swarm algorithm.
Specific embodiment
With reference to the accompanying drawings and examples, specific embodiments of the present invention will be described in further detail.Implement below
Example is not intended to limit the scope of the invention for illustrating the present invention.
Such as Fig. 1, in a specific embodiment of the invention, a kind of Fractional Order PID Controller parameter optimization setting method is shown
Overall flow figure.Generally, comprising: step 1, the complexity based on control system obtains the search force of state branching algorithm optimizing
Spend SE and maximum allowable the number of iterations Maxiter；It obtains Fractional Order PID Controller and waits for setting parameter range；In n-dimensional space with
Machine generates the individual collection Best within the scope of setting parameterk, wherein n is the number to optimizing parameter；Step 2, for institute
State BestkIn individual successively respectively carry out stretching operation, rotation transformation operation and coordinate transform operation, respectively obtain most
Excellent sample, until the individual number for carrying out operation is equal to Maxiter；Step 3, all optimal samples and corresponding property are exported
It can target function value.
In another specific embodiment of the invention, a kind of Fractional Order PID Controller parameter optimization setting method, the step
1 mid-score rank PID controller waits for that setting parameter includes: Proportional coefficient KP, integral coefficient KI, differential coefficient KD, integral order λ and
Differential order μ.
In another specific embodiment of the invention, a kind of Fractional Order PID Controller parameter optimization setting method, the step
For the Best in 2kIn individual successively respectively carry out stretching operation, rotation transformation operation and coordinate transform operation,
Respectively obtain optimal sample further include: for the BestkIn individual be successively utilized respectively stretching operator, rotation transformation
Operator and coordinate transform operator operation obtain each sample of SE, and update current best individual using policy update is updated.
In another specific embodiment of the invention, a kind of Fractional Order PID Controller parameter optimization setting method, the step
For the BestkIn individual successively respectively carry out stretching operation, rotation transformation operation and coordinate transform operation, respectively
After obtaining optimal sample further include: if current optimal sample has variation, more using translation transformation operation and with same mechanism
New current preferably individual.
In another specific embodiment of the invention, a kind of Fractional Order PID Controller parameter optimization setting method, the step
Stretching operator in 1 further include:
xk+1=xk+γRexk,
Wherein, γ is contraction-expansion factor, is normal number；Re∈Rn×nFor the random diagonal matrix of unitary element Gaussian distributed.
In another specific embodiment of the invention, a kind of Fractional Order PID Controller parameter optimization setting method, the step
Rotation transformation operator in 1 further include:
Wherein, wherein α is twiddle factor, is normal number；Rr ∈ Rn × n is a random matrix, and the value of element exists
In [- 1,1] range；∥·∥2For 2 norm of vector.
In another specific embodiment of the invention, a kind of Fractional Order PID Controller parameter optimization setting method is described
Coordinate transform operator in step 1 further include:
xk+1=xk+δRaxk,
Wherein δ is the coordinate factor, is normal number；Ra ∈ Rn × n is unitary element Gaussian distributed and only one random
Position is the random diagonal matrix of nonzero value.
In another specific embodiment of the invention, a kind of Fractional Order PID Controller parameter optimization setting method, the step
Translation transformation operational form in 1 are as follows:
Wherein, β is shift factor, is normal number；Rt∈ R is a stochastic variable, and value is in [0,1] range.
In another specific embodiment of the invention, a kind of Fractional Order PID Controller parameter optimization setting method, described and institute
State the corresponding performance index function value J of optimal sample further include:
Wherein, e (k) is control system output error, and N is sample time.
In another specific embodiment of the invention, a kind of Fractional Order PID Controller parameter optimization setting method progress is specific
Using to verify its superiority.
In manufacturing industry, workstation control system is an important positioning system, and working table movement can be made to specified
Position.Workbench is driven by motor and lead screw on each axle, wherein kinetic control system block diagram such as Fig. 2 in x-axis
It is shown.Controller uses fractional order PIλDμController, research is when Spline smoothing occurs for position given value, workbench lead screw
Output position tracks the case where given value variation.
It is carried out in Fractional Order PID control parameter searching process using state branching algorithm, state branching algorithm parameter is pressed
Following principle is chosen:
Search dynamics SE, SE is bigger, and the probability for obtaining optimal solution is bigger, also can be elongated therewith but calculate the time, comprehensive
Consider, takes SE=20 herein.
Maximum number of iterations Maxiter, the number of iterations is bigger, and optimal solution is more accurate, but calculating the time simultaneously also can be longer,
According to the complexity of optimization problem, Maxiter=100 is taken here.
The value of flexible, rotation, coordinate and shift factor is respectively as follows: αmax=1, αmin=1e-4, β=1, γ=1, δ
=1.
During being directed to the parameter tuning of working table movement Fractional Order PID control system, it is assumed that Proportional coefficient KP, integral
COEFFICIENT KIWith differential coefficient KDRange be [0,100], integral order λ and differential order μ range be [0,2].
In above-mentioned setup parameter condition, the Fractional Order PID parameter optimization based on state branching algorithm adjusts result are as follows: ratio
COEFFICIENT KP=99.5701, integral coefficient KI=99.9046, differential coefficient KD=99.8779, differential order μ=0.0348, integral
Order λ=0.0287, control system performance indicator J=0.6538 corresponding to this group of optimized parameter.
Resulting Fractional Order PID parameter will be adjusted according to the present invention to put into operation, can obtain working table movement closed-loop control system
For system under setting value unit step situation of change, the output of system is as shown in Fig. 3.
For the superiority of the mentioned setting method of the verifying present invention, also the working table movement closed-loop control system is used and is based on
The setting method of genetic algorithm (GA) and particle swarm algorithm (PSO) carries out parameter tuning, and compares the effect of three kinds of setting methods,
The output of system is as shown in Fig. 4, and as can be seen from the figure setting method proposed by the invention obviously makes system adjust speed
Degree is fast, and overshoot is small, and Control platform is excellent.
Simulation result shows that the Fractional Order PID Controller parameter optimization proposed by the present invention based on state branching algorithm is whole
Determine method, efficient global search can be carried out in solution space under conditions of not needing any controlled device initial information,
The optimal Fractional Order PID that system can quickly and easily be obtained with stronger global convergence ability and faster speed of searching optimization is whole
Determine parameter.It is adjusted using the Fractional Order PID control system of the mentioned method adjusting of the invention with other two kinds common intelligent algorithms
Fractional Order PID control system compare, the regulating time of control system of the method for the present invention adjusting is obviously shortened, and overshoot is obvious
Reduce, Control platform is more excellent.And the mentioned method of the present invention, there is no any restrictions to controlled device, thus have and be generally applicable in
Property, there is great promotional value.
Finally, the present processes are only preferable embodiment, it is not intended to limit the scope of the present invention.It is all
Within the spirit and principles in the present invention, any modification, equivalent replacement, improvement and so on should be included in protection of the invention
Within the scope of.
Claims (4)
1. a kind of Fractional Order PID Controller parameter optimization setting method, which comprises the following steps:
Step 1, the complexity based on workstation control system obtains the search dynamics SE of state branching algorithm optimizing and maximum permits
Perhaps the number of iterations Maxiter；It obtains Fractional Order PID Controller and waits for setting parameter range；Generated at random in n-dimensional space it is described to
Individual collection Best within the scope of setting parameterk, wherein n is the number to optimizing parameter；
Wherein, the workbench is driven by motor and lead screw on each axle, so that when rank occurs for position given value R (s)
When transition, workbench screw output position Y (s) tracking given value changes, wherein the Fractional Order PID Controller
Equation beWherein, KPFor proportional gain, KIFor integral constant, KDFor derivative constant, λ is
Order is integrated, μ is differential order, and acts on motor via power amplifier, and the transmission function of the power amplifier isThe transmission function of motor is
Step 2, for the BestkIn individual successively respectively carry out stretching operation, rotation transformation operation and coordinate transform
Operation respectively obtains optimal sample, until the individual number for carrying out operation is equal to Maxiter；For described in the step 2
BestkIn individual successively respectively carry out stretching operation, rotation transformation operation and coordinate transform operation, respectively obtain optimal
Sample further include: for the BestkIn individual be successively utilized respectively stretching operator, rotation transformation operator and coordinate become
It changes operator operation and obtains each sample of SE, and update current best individual using policy update is updated；
The step is for the BestkIn individual successively carry out stretching operation respectively, rotation transformation operation and coordinate become
Operation is changed, after respectively obtaining optimal sample further include: if current optimal sample has variation, operate using translation transformation and with same
The current preferably individual of the new mechanism of sample；
Stretching operator in the step 1 further include:
xk+1=xk+γRexk,
Wherein, γ is contraction-expansion factor, is normal number；Re∈Rn×nFor the random diagonal matrix of unitary element Gaussian distributed；
Rotation transformation operator in the step 1 further include:
Wherein, wherein α is twiddle factor, is normal number；Rr ∈ Rn × n is a random matrix, and the value of element [- 1,
1] in range；∥·∥2For 2 norm of vector；
Coordinate transform operator in the step 1 further include:
xk+1=xk+δRaxk,
Wherein δ is the coordinate factor, is normal number；Ra ∈ Rn × n is unitary element Gaussian distributed and an only random site
For the random diagonal matrix of nonzero value；
Step 3, all optimal samples and corresponding performance index function value are exported.
2. the method as described in claim 1, which is characterized in that the step 1 mid-score rank PID controller waits for setting parameter packet
It includes: Proportional coefficient KP, integral coefficient KI, differential coefficient KD, integral order λ and differential order μ.
3. the method as described in claim 1, which is characterized in that the translation transformation operational form in the step 1 are as follows:
Wherein, β is shift factor, is normal number；Rt∈ R is a stochastic variable, and value is in [0,1] range.
4. the method as described in claim 1, which is characterized in that the corresponding performance index function value of described and described optimal sample
J further include:
Wherein, e (k) is control system output error, and N is sample time.
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| CN107832914A (en) * | 2017-10-11 | 2018-03-23 | 中南大学 | Go out the dispatching method and system of tankage task in a kind of potroom |
| CN107844458B (en) * | 2017-11-16 | 2020-11-24 | 西安西热控制技术有限公司 | Adaptive identification method for first-order inertia delay model in industrial process |
| CN109188898B (en) * | 2018-07-12 | 2021-06-18 | 哈尔滨工程大学 | Optimal parameter decision method under ship longitudinal motion multi-target strategy |
| CN108803311A (en) * | 2018-08-03 | 2018-11-13 | 佛山科学技术学院 | A kind of PID controller design method |
| CN109240362B (en) * | 2018-11-26 | 2019-11-29 | 中南大学 | A kind of method for adjusting pH value of waste water based on Fractional Order PID Controller |
| CN110090728B (en) * | 2019-01-24 | 2020-11-06 | 济南大学 | Method, device and equipment for controlling feeding amount in cement raw material vertical mill |
| CN111564978A (en) * | 2020-06-04 | 2020-08-21 | 上海应用技术大学 | Based on fractional order PIλDμControlled full-bridge LLC converter and system |
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