CN101364475B - Closed-loop control apparatus enhancing dynamic performance of optical fiber current mutual inductor - Google Patents
Closed-loop control apparatus enhancing dynamic performance of optical fiber current mutual inductor Download PDFInfo
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- CN101364475B CN101364475B CN2008101151323A CN200810115132A CN101364475B CN 101364475 B CN101364475 B CN 101364475B CN 2008101151323 A CN2008101151323 A CN 2008101151323A CN 200810115132 A CN200810115132 A CN 200810115132A CN 101364475 B CN101364475 B CN 101364475B
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Abstract
The embodiment of the invention provides a closed-loop control method for improving dynamic properties of an optical fiber current transformer system and a device thereof. The method comprises the following steps: firstly, obtaining a second order feedback control gain array of the system based on optimum control theory according to the performance index requirements of the optical fiber current transformer system; secondly, calculating the feedback control variables of the system from the second order feedback control gain array; and thirdly, processing the input signal of the optical fiber current transformer system by using a second order controller obtained from the feedback control variables. The second order controller can improve the response speed of the optical fiber current transformer system on an inputted step-function signal, reduce rise time, track a speed signal astatically, and improve the dynamic properties of the system.
Description
Technical field
The present invention relates to the optical fiber current mutual inductor field, relate in particular to a kind of closed-loop control device that improves dynamic performance of optical fiber current mutual inductor.
Background technology
Development along with the current transformer technology, optical fiber current mutual inductor has obtained increasing application, because it adopts the media of optical fiber as induction of signal and transmission, not only have good insulation preformance, be subjected to the little advantage of electromagnetic interference effect, and simple in structure in addition, volume is little, light weight, unique advantages such as low cost of manufacture.Be subjected to domestic and international researcher's attention in recent ten years.
Yet along with power system development, requirement to dynamic properties such as the dynamic range of current transformer and frequency response ranges also is more and more higher, therefore improve the closed loop control algorithm of optical fiber current mutual inductor, the dynamic property that reduces system phase delay, raising system becomes the present problem that needs solution, be illustrated in figure 1 as the optical fiber current mutual inductor systematic square frame schematic diagram of equivalence in the prior art, among the figure:
R is a system input signal; U is the feedback controling variable of system; Y is the output signal of system; E is the error signal of system; k
1And k
2System parameters for the optical fiber current mutual inductor of equivalence; And D (z) is the integral element of equivalence, just the controller part.When this D (z) is single order integral element, promptly
The time, the dynamic adjustments ability of finding system from practical application is relatively poor, and analyze from Theory of Automatic Control, the output of the stable state of closed-loop optical fiber current transformer systems in this case can not astatic tracking velocity signal, that is to say that the dynamic performance index of system is relatively poor.This shows that according to existing design of Controller scheme, the dynamic adjustments ability of system is relatively poor.
Summary of the invention
Embodiment of the present invention technical problem to be solved is to provide a kind of closed loop control method and device that improves dynamic performance of optical fiber current mutual inductor, can improve response speed, the minimizing rise time of optical fiber current mutual inductor system to the input step signal, system can also astatic tracking velocity signal, has improved the dynamic property of system.
Embodiment of the present invention provides a kind of closed loop control method that improves dynamic performance of optical fiber current mutual inductor, comprising:
According to the performance index requirement of optical fiber current mutual inductor system, and obtain the second order feedback control gain battle array of system according to optimal control theory;
Try to achieve the system feedback control variables by described second order feedback control gain battle array then;
The second order controller that utilizes described feedback controling variable to obtain is handled the input signal of optical fiber current mutual inductor system.
The performance index of described optical fiber current mutual inductor system require specifically: according to the user demand of optical fiber current mutual inductor system and predefined index.
Describedly obtain the second order feedback control gain battle array of system, specifically comprise according to optimal control theory:
Draw the matrix Riccati algebraic equation according to optimal control theory, find the solution the second order feedback control gain battle array that described Riccati equation draws system.
The second order feedback control gain battle array of described system is specially:
L＝(R+B
TKB)
-1B
TKA
Wherein, A is the state matrix of system, and B is the input matrix of system, and K carries matrix for multitude's card, and R is the constant matrices of descriptive system performance index, and L is a second order feedback control gain battle array.
Embodiment of the present invention also provides a kind of closed-loop control device that improves dynamic performance of optical fiber current mutual inductor, comprising:
Feedback controling variable obtains the unit, be arranged on the controller of optical fiber current mutual inductor system, be used for performance index requirement according to the optical fiber current mutual inductor system, and obtain the second order feedback control gain battle array of system according to optimal control theory, try to achieve the system feedback control variables by described second order feedback control gain battle array then;
The second order feedback control unit is arranged on the controller of optical fiber current mutual inductor system, is used to utilize the feedback controling variable that is obtained that the input signal of optical fiber current mutual inductor system is handled.
Described feedback controling variable obtains the unit and specifically comprises:
Feedback controling variable is found the solution module, be used for drawing the matrix Riccati algebraic equation according to the performance index and the optimal control theory of system, find the solution the second order feedback control gain battle array that described Riccati equation draws system, and try to achieve the system feedback control variables by described second order feedback control gain battle array.
By the above-mentioned technical scheme that provides as can be seen, at first according to the performance index requirement of optical fiber current mutual inductor system, and obtain the second order feedback control gain battle array of system according to optimal control theory; Try to achieve the system feedback control variables by described second order feedback control gain battle array then, and then the second order controller that obtains system comes the input signal of optical fiber current mutual inductor system is handled.Like this by this second order controller just can improve the optical fiber current mutual inductor system to the response speed of input step signal, reduce the rise time, can also astatic tracking velocity signal during systematic steady state, improved the dynamic property of system.
Description of drawings
Fig. 1 is the frame structure schematic diagram of optical fiber current mutual inductor system in the prior art;
Fig. 2 is the schematic flow sheet of method that embodiment of the present invention provides;
Fig. 3 is the step input emulation schematic diagram of first-order system in the prior art;
Fig. 4 is the speed input emulation schematic diagram of first-order system in the prior art;
Fig. 5 is the step input emulation schematic diagram of the described second order controller of embodiment of the present invention;
Fig. 6 is the speed input emulation schematic diagram of the described second order controller of embodiment of the present invention;
Fig. 7 is the structural representation of embodiment of the present invention institute generator.
Embodiment
Embodiment of the present invention provides a kind of closed loop control method and device that improves dynamic performance of optical fiber current mutual inductor.When the closed loop control algorithm of optical fiber current mutual inductor system is single order integral element, find that from practical application the system dynamics regulating power is good inadequately; And at present the stable state output of closed-loop optical fiber current transformer systems can not astatic tracking velocity signal, therefore in order to make systematic steady state output astatic tracking step signal of energy and rate signal, according to optimal control theory, designed the second order controller, improve the dynamic property of system.
For better describing embodiment of the present invention, now in conjunction with the accompanying drawings the specific embodiment of the present invention is described, be illustrated in figure 2 as the schematic flow sheet of method that embodiment of the present invention provides, described method comprises:
Step 21:, and obtain the second order feedback control gain battle array of system according to optimal control theory according to the performance index requirement of optical fiber current mutual inductor system.
It can be according to the user demand of optical fiber current mutual inductor system and predefined index generally is given performance index parameter that the performance index of optical fiber current mutual inductor described here system require; And said optimal control theory is the Riccati equation of utilizing in the optimal control theory, the feedback controling variable of solving system, and the Optimal Regulator of optical fiber current mutual inductor system performance index is satisfied in design, is the second order controller in embodiment of the present invention.
Be exactly specifically, give the performance index parameter of fixed system earlier, calculate the second order feedback control gain battle array of system then according to the Riccati equation of optimal control theory, try to achieve the system feedback control variables by described second order feedback control gain battle array then; Utilizing the resulting Optimal Regulator of this feedback controling variable is exactly the second order controller.Concrete computational process to feedback controling variable is illustrated below:
At first, provide the state equation and the output equation of optical fiber current mutual inductor system, as follows:
x
1(k+1)＝x
2(k)
x
2(k+1)＝k
1k
2(-x
1(k)-x
2(k)+u(k)) x(0)＝0(5)
y＝x
1
Wherein, k
1, k
2Be the system parameters of optical fiber current mutual inductor, according to the Mathematical Modeling of optical fiber current mutual inductor k as can be known
1=0.1, k
2=1; X (k) ∈ R
nState variable for system; Parameters u (k) is the feedback controling variable of the present invention by the optimal control theory design.
According to formula (5) as can be known the state matrix of system be expressed as:
Wherein, A is a state matrix, and B is an input matrix.
Then, preestablish the performance index of optical fiber current mutual inductor system again according to the user demand of reality, represent with following formula:
Wherein, the Q in the following formula, R are the constant matrixs of symmetric positive definite.Analyze in the formula (6) each as can be known: X
T(k) QX (k) is the error sum of squares integration, can represent dynamic performance; U
T(k) RU (k) has represented catabiotic punishment.
Then according to the performance index requirement of optical fiber current mutual inductor system, and, can get the Q=I unit matrix, R=1 according to the repeatedly checking of simulation result under the different values of Q, R.Because of system is controlled, so the optimal control u (k) of J minimum is existed and unique.
According to optimal control theory, can draw the matrix Riccati algebraic equation again, as follows:
-K+Q+A
TKA-A
TKB(R+B
TKB)
-1B
TKA＝0(7)
Wherein, K carries matrix for multitude's card; Find the solution (7) formula by computer program, solve the numerical solution of K.Can solve second order feedback control gain battle array L:
L＝(R+B
TKB)
-1B
TKA (8)
Final so just can be in the hope of the feedback controling variable u (k) of system:
u(k)＝-LX(k) (9)
And optimum feedback control system state equation is expressed as:
x(k+1)＝[A-BL]x(k) (10)
Utilize above-mentioned feedback controling variable of trying to achieve just can proceed following step.
Step 22: utilize feedback controling variable to come the input signal of optical fiber current mutual inductor system is handled.
Be exactly, to obtain optimum second order controller specifically according to the feedback controling variable of being tried to achieve in the above-mentioned steps 21; Then this second order controller is brought in the optical fiber current mutual inductor system, the input signal of system is further processed.
Being the technique effect of further instruction embodiment of the present invention, relatively is that example describes with former first-order system and the resulting simulation figure of second-order system of the present invention below:
Fig. 3 and Fig. 4 are respectively at having carried out simulation calculation when system input signal is step and rate signal, wherein Fig. 3 is the step input emulation schematic diagram of first-order system, and Fig. 4 is the speed input emulation schematic diagram of first-order system.Curve among the figure is respectively input r (t), the output y (t) of system and the difference e (t) of input and output; Because the input signal of optical fiber current mutual inductor system is an electric current, so ordinate unit is an ampere (A) among the figure, abscissa unit is chronomere's millisecond (ms).
Fig. 5 and Fig. 6 are the second-order system of Optimal Control Design, and Fig. 5 is the step input emulation schematic diagram of second order controller, and Fig. 6 is the emulation schematic diagram of second order controller speed input, and the implication of each parameter as mentioned above among the figure.
Contrast from above-mentioned figure as can be seen because second-order system can astatic tracking step and rate signal, so curve of output has covered input curve; When system was in stable state, input was almost nil with the difference of output; Simultaneously, the second order controller with the optimal control theory design has significantly improved the response speed of closed-loop optical fiber current transformer systems to step signal; And former first-order system can not astatic tracking velocity signal, and as shown in Figure 4, Fig. 6 has proved that then the second-order system after the redesign can improve the dynamic property of system.
Embodiment of the present invention also provides a kind of closed-loop control device that improves dynamic performance of optical fiber current mutual inductor, be illustrated in figure 7 as the structural representation of the described device of embodiment of the present invention, described device comprises that feedback controling variable obtains unit and second order feedback control unit, wherein:
Feedback controling variable obtains the unit and is arranged on the controller of optical fiber current mutual inductor system, be used for performance index requirement according to the optical fiber current mutual inductor system, and obtain the second order feedback control gain battle array of system according to optimal control theory, try to achieve the system feedback control variables by described second order feedback control gain battle array then, as above the method execution mode is described for the concrete process that obtains.
The second order feedback control unit is arranged on the controller of optical fiber current mutual inductor system, is used to utilize the feedback controling variable that is obtained that the input signal of optical fiber current mutual inductor system is handled.
In addition, the above feedback controling variable acquisition unit is specifically as follows feedback controling variable and finds the solution module, described feedback controling variable is found the solution module and is used for drawing the matrix Riccati algebraic equation according to the performance index and the optimal control theory of system, find the solution the second order feedback control gain battle array that described Riccati equation draws system, and try to achieve the system feedback control variables by described second order feedback control gain battle array.
Above-described device can integratedly be arranged in the controller, also can be arranged to independent functional entity, maintains the connection with controller.
In sum, embodiment of the present invention can improve the optical fiber current mutual inductor system to the response speed of input step signal, reduce the rise time, can also astatic tracking velocity signal during systematic steady state, improved the dynamic property of system.
The above; only be the preferable embodiment of the present invention; but protection scope of the present invention is not limited thereto; anyly be familiar with those skilled in the art in the technical scope that the embodiment of the invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection range of claim.
Claims (2)
1. a closed-loop control device that improves dynamic performance of optical fiber current mutual inductor is characterized in that, comprising:
Feedback controling variable obtains the unit, be arranged on the controller of optical fiber current mutual inductor system, be used for performance index requirement according to the optical fiber current mutual inductor system, and obtain the second order feedback control gain battle array of system according to optimal control theory, try to achieve the system feedback control variables by described second order feedback control gain battle array then;
The second order feedback control unit is arranged on the controller of optical fiber current mutual inductor system, is used to utilize the feedback controling variable that is obtained that the input signal of optical fiber current mutual inductor system is handled.
2. the closed-loop control device of raising dynamic performance of optical fiber current mutual inductor as claimed in claim 1 is characterized in that, described feedback controling variable obtains the unit and specifically comprises:
Feedback controling variable is found the solution module, be used for drawing Riccati equation according to the performance index and the optimal control theory of system, find the solution the second order feedback control gain battle array that described Riccati equation draws system, and try to achieve the system feedback control variables by described second order feedback control gain battle array.
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| CN1687795A (en) * | 2005-06-13 | 2005-10-26 | 北京航空航天大学 | Optical fibre current transformer and its loop detector of transformer |
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