CN116243600A - Buck circuit self-adaptive dynamic surface control method based on energy storage system - Google Patents
Buck circuit self-adaptive dynamic surface control method based on energy storage system Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2310/00—The network for supplying or distributing electric power characterised by its spatial reach or by the load
- H02J2310/50—The network for supplying or distributing electric power characterised by its spatial reach or by the load for selectively controlling the operation of the loads
- H02J2310/56—The network for supplying or distributing electric power characterised by its spatial reach or by the load for selectively controlling the operation of the loads characterised by the condition upon which the selective controlling is based
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2310/00—The network for supplying or distributing electric power characterised by its spatial reach or by the load
- H02J2310/50—The network for supplying or distributing electric power characterised by its spatial reach or by the load for selectively controlling the operation of the loads
- H02J2310/56—The network for supplying or distributing electric power characterised by its spatial reach or by the load for selectively controlling the operation of the loads characterised by the condition upon which the selective controlling is based
- H02J2310/58—The condition being electrical
- H02J2310/60—Limiting power consumption in the network or in one section of the network, e.g. load shedding or peak shaving
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Abstract
The invention relates to a Buck circuit self-adaptive dynamic surface control method based on an energy storage system, which realizes given performance indexes by introducing a performance function and an error conversion function, combines a neural network system with limited coverage theory, and compensates time delay generated in the measuring process of a sensor; by adjusting the parameters of the controller, the tracking error can be converged into any small residue, so that the output voltage of the Buck circuit is stabilized. The invention has the advantages that: compared with the existing Buck circuit controller designed by using a back-stepping method, the dynamic surface control method introduces a first-order low-pass filter to calculate the derivative of the virtual control law, so that differential explosion phenomenon is avoided; introducing a performance function and an error conversion function to realize a given performance index; the neural network system is combined with the finite coverage primer, so that not only can an unknown smooth function be approximated, but also the time delay generated by the system can be compensated, and the tracking error is reduced.
Description
Technical Field
The invention relates to the field of power load control, in particular to a Buck circuit self-adaptive dynamic surface control method based on an energy storage system.
Background
With the rapid development of power electronics technology, electronic devices have penetrated into various aspects of life of people, and have important roles in more fields such as medical appliances, military equipment, agricultural production and the like. Among them, power electronic converters, in particular DC/DC converters, have been widely used in different industrial fields. Maintaining the stability of the DC/DC converter output voltage in the event of an uncertainty in the converter input voltage and load has a variety of uses, such as in communication devices, in adapters for computers and industrial control electronics, etc. Therefore, DC/DC converters aimed at providing a stable DC output voltage have been rapidly developed.
The Buck circuit is a core component of a DC/DC converter in a power electronic system, the working state of the Buck circuit has strong nonlinear characteristics, the high-frequency switching of a switch of the Buck circuit further enables the working state to have timeliness, under certain circuit parameter conditions and initial states, the Buck circuit has a plurality of nonlinear phenomena, the conditions can lead the DC/DC converter to malfunction so that the equipment cannot normally operate, and if no remedial measures are taken, any malfunction of the components can lead to serious damage, thereby disabling the whole system. The traditional voltage regulation control method can not meet the requirements of technical application in various fields, and how to utilize a high-efficiency control strategy to improve the control performance of a DC/DC converter, so that the capability of stabilizing the output voltage when the input voltage or the load of a non-minimum phase system is changed is improved, and the method becomes a core problem for researching the Buck circuit control strategy.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide the self-adaptive dynamic surface control method of the Buck circuit based on the energy storage system, which adopts the self-adaptive dynamic surface control method of the Buck circuit by combining a performance function, an error conversion function and a neural network system with a finite coverage primer, can effectively compensate time delay generated in the measuring process of a sensor, ensures that all signals in a closed loop system are semi-globally consistent and finally bounded, and can converge tracking errors into any small residue by adjusting parameters of a controller, thereby realizing the purpose of stabilizing the output voltage of the Buck circuit.
In order to achieve the above purpose, the present invention is realized by the following technical scheme:
a Buck circuit self-adaptive dynamic surface control method based on an energy storage system realizes given performance indexes by introducing a performance function and an error conversion function, combines a neural network system with limited coverage primer, and compensates time delay generated in the measuring process of a sensor; by adjusting the parameters of the controller, the tracking error can be converged into any small residue, so that the output voltage of the Buck circuit is stabilized;
the dynamic surface control method is realized based on the following steps:
s1, adopting mathematical transformation to transform a state space equation of a Buck DC/DC converter into a mathematical model in a general form, and using the mathematical model as a controlled object of a dynamic surface control method;
s2, adopting a performance function and an error conversion function to ensure a given tracking performance index;
s3, approximating an unknown function with time delay in a mathematical model of the controlled object by adopting a mode of combining a neural network and a finite coverage primer;
s4, designing a dynamic surface controller, enabling the virtual control law to pass through a first-order low-pass filter, enabling the input of a neural network to be known, adopting the neural network to compensate time delay by combining a technology of limited coverage quotients, combining a performance function and an error conversion function in the step S2 to ensure a given tracking performance index, and designing the self-adaptive dynamic surface controller of the Buck circuit with time delay compensation.
The state space equation of the Buck DC/DC converter in the step S1 is shown in the formula (1):
in the formula (1), u H A unit V representing a battery side voltage; i.e L Representing inductor current, unit a; u (U) de The direct current busbar voltage of the direct current micro-grid is represented by a unit V; l is battery energy storage inductance, unit mH; c (C) H The unit mF is a battery side filter capacitor; r is the internal resistance of the battery, and is the unit omega; buck circuit considering external disturbance without loss of generalityThe state space equation of (2) can be rewritten into a mathematical model shown in the formula (2) in a mathematical transformation mode, and is used as a controlled object of the dynamic surface control method:
in the formula (2), the amino acid sequence of the compound,
it is emphasized that the value is unknown during the controller design process; τ i ，/>
And d i I=1, 2, respectively represent an unknown time delay constant generated during the sensor measurement, a time delay and a battery side voltage u H The related unknown nonlinear function is smooth and the external disturbance of the system;
in the formula (2), u is the duty ratio of the MOS tube, namely the control input signal of the system;
representing an output of the system;
for a mathematical model of a controlled object of a dynamic surface control method, the following assumptions are specified:
suppose 1: g i Not equal to 0, i=1, 2, is an unknown normal number, and satisfies g i ≥g imin ：
Suppose 2: desired tracking y r Is a smooth and bounded function;
belonging to a tight set:
suppose 3: τ i I=1, 2 is an unknown normal number and satisfies 0.ltoreq.τ i ≤τ M Wherein τ M Denoted τ i Is the maximum value of (2):
suppose 4: unknown external disturbance d i I=1, 2, satisfy
To introduce step S2, a performance function and an error transfer function are used, and a tracking error e is defined as shown in equation (3):
e＝x 1 -y r (3)
for any moment when t is greater than or equal to 0, the performance function p (t) is a smooth and decreasing positive function, and the specific form is as shown in the formula (4):
in the formula (4), 0 < sigma < 1 and lim t→∞ ＝p ∞ ＞0，p ∞ Is the maximum value of the tracking error allowed when the system is stable; to convert equation (4) to an equivalent function, an error transfer function of the form is introduced as shown in equation (5):
e(t):＝p(t)Φ(S 1 ), (5)
in the formula (5), S 1 Is a conversion error converted by an error conversion function, Φ (S 1 ) Is a smooth and strictly monotonically increasing function whose inverse has the following properties:
and is also provided with
As can be seen from formula (7), if
Then equation (6) holds; taking further consideration of p (t) > 0 and formula (5), it is possible to obtain- σp (t) < p (t) Φ (S 1 ) =p (t) < 1 (when e (0) > 0) or-p (t) < Φ (S) 1 ) =p (t) < σp (t) (when e (0) < 0), i.e., formula (4) holds; because ofFrom the above analysis, it is clear that only +.>
The preparation method is finished; from phi (S) 1 ) The strictly monotonically increasing nature of (2) can give a conversion error S 1 The method comprises the following steps:
adopting the step S3 neural network to approach the unknown smooth function f in the mathematical model of the controlled object on line i :
Wherein (1)>
Representing a tight set, q being the dimension of the input vector; the neural network approximates the expression of the unknown function as shown in equation (9):
f i (ζ i )＝W i *T ψ i (ζ i )+ε i , (9)
in the formula (9), the amino acid sequence of the compound,
is an input vector to the neural network; />
Is an optimal weight vector, and N is the number of nodes of the neuron, as shown in formula (10):
in the formula (10), the amino acid sequence of the compound,
is a weight vector function; kappa (kappa) j (ζi i ) Is a radial basis function, e.g.Formula (11):
κ j (ζ i )＝exp[-||ζ i -ξ j ||/2μ j 2 ],j＝1,...,N (11)
in the formula (11): zeta type toy j Is the center of the j-th basis function, mu j Is the width of the basis function; epsilon i Is the estimated error of the neural network;
suppose 5: epsilon i |≤υ i ，
Wherein v i An upper bound value representing an estimation error;
annotation 1: it should be emphasized that when the unknown smoothing function has an unknown time delay constant τ i When, for example, f i (ζ i ,ζ i (t-τ i ) A direct approximation cannot be made using a neural network; however, due to the tight set
Can be used to determine the unknown function using a neural network combined with a finite coverage primer>
Performing approximation;
lemma 1: assume an input vector ζ i ＝(ζ i ,ζ i (t-τ i ) In line with time t, where τ i ∈[0,τ M ]Is an unknown time delay constant; then, for any given error
There is a finite interval [0, τ ] independent of time t M ]In the form shown in the formula (12):
0＜t 1 ＜…＜t m ＜τ M (12)
from one time point in formula (12), the following is satisfied:
the method can obtain:
combining lemma 1 and hypothesis 3, there are multiple time points τ 1/1 ,…,τ n/n ∈{t 1 ,...,t m -representing the unknown smooth function with time delay as shown in equation (15):
in formula (15):
the estimation error representing the finite coverage theory, combined with the expression of the neural network approximation unknown function, equation (15) can be approximated as the one shown in equation (16):
in delta i The sum of the upper bound value representing the neural network estimation error and the estimation error of the finite coverage primer;
and input vector
Θ i ＝(x 1 ,...,x i ,...,x 1 (t-t 1 ),...,x k (t-τ k/k ),...,x i (t-t m )) (17)
Step S4, designing an adaptive dynamic surface controller, which comprises the following steps:
s41, combining a mathematical model of the controlled object, and converting the error S 1 The first derivative with respect to time t is shown in equation (18):
in formula (18):
x 2d is a virtual control law;
from the formula (18), as shown in the formula (19):
in the formula (19), the amino acid sequence of the compound,
combining formula (16), the unknown term in formula (19)
Can be written as shown in formula (20):
and input vector theta 1 ＝(x 1 ,x 1 (t-t 1 ),...,x 1 (t-τ k/k ),...,x 1 (t-t m ),Ψ)；
With the help of the young's inequality, the following holds:
constructing a first candidate lyapunov function as shown in formula (23):
in the formula (23), the amino acid sequence of the compound,
and->
Is a positive parameter of the design, estimation error +.>
And->
Wherein (1)>
And
respectively express theta 1 And v 1 * Is a function of the estimated value of (2);
deriving a first candidate lyapunov function by combining the correlation calculation obtained in the formulas (19) - (22) to obtain:
the virtual control quantity and the self-adaptive law are designed as follows:
wherein k is 1 ，
And->
Are all positive parameters of the design;
substituting the designed virtual control quantity and the adaptive law into the derivative of the first candidate lyapunov function can be obtained as shown in formula (28):
a first order low pass filter as shown in equation (29) is introduced to calculate the derivative of the virtual control quantity:
in formula (29), τ and z 1 The time constant and the output of the filter, respectively;
will filter the error y 1 Is defined as shown in formula (30):
y 1 ＝z 1 -x 2d (30)
dynamic face error S 2 Is defined as shown in formula (31):
S 2 ＝x 2 -z 1 (31)
by filtering error y 1 And dynamic surface error S 2 The expression (32) can be obtained as follows:
x 2 -x 2d ＝S 2 +z 1 -x 2d ＝S 2 +y 1 (32)
consider the following inequality:
in combination with formula (32), it can be demonstrated that as shown in formula (38):
s42, according to the mathematical model of the controlled object, the dynamic surface error S 2 As shown in formula (39):
in formula (39): ,
obtainable by formula (39), as shown in formula (40):
in the formula (40), the amino acid sequence of the compound,
constructing a second candidate lyapunov function as shown in formula (41):
in the formula (41),
and->
Is a positive parameter of the design, estimation error +.>
And->
Wherein->
And
respectively is theta 2 And v 2 * Is a function of the estimated value of (2);
combining equation (40), deriving a second candidate lyapunov function is available as shown in equation (42):
combining formula (16), the unknown term in formula (42)
Can be written as shown in formula (43): :
and input vector theta 2 The same as defined in formula (17);
in the same way as step S41, the derivative of the second candidate lyapunov function can be rewritten as shown in the formula (44) using the inequality of the formulas (21) - (22):
the design control law and the update law are as follows:
wherein k is 2 ，
And->
Is a positive parameter of the design;
the designed control law and update law are brought into the derivative of the second candidate lyapunov function as shown in equation (48):
in the same way as in step S41, according to the young' S inequality, the formula (48) can be written as:
compared with the prior art, the invention has the beneficial effects that:
1. compared with the existing Buck circuit controller designed by using a back-stepping method, the dynamic surface control method introduces a first-order low-pass filter to calculate the derivative of the virtual control law, so that differential explosion phenomenon is avoided; introducing a performance function and an error conversion function to realize a given performance index;
2. the neural network system is combined with the finite coverage primer, so that not only can an unknown smooth function be approximated, but also the time delay generated by the system can be compensated, and the tracking error is reduced;
3. the control law u (t) designed by the dynamic surface control method can avoid differential explosion phenomenon generated by a back-stepping method, and stability analysis shows that the designed self-adaptive controller can ensure that all update laws, design parameters and the like in a control system are semi-globally consistent and finally bounded, and tracking errors of the system can be converged to an adjustable tight set by means of an initialization skill.
Drawings
Fig. 1 is a block circuit topology diagram.
Fig. 2 is a structural diagram of an experimental system.
Fig. 3 is a trace performance graph.
Fig. 4 is a tracking error map.
Detailed Description
The present invention will be described in detail below with reference to the drawings of the specification, but it should be noted that the practice of the present invention is not limited to the following embodiments.
Referring to fig. 1-4, the self-adaptive dynamic surface control method of the Buck circuit based on the energy storage system is realized based on the following steps:
s101, adopting mathematical transformation to transform a state space equation of a Buck DC/DC converter into a mathematical model in a general form, and using the mathematical model as a controlled object of a dynamic surface control method;
s102, designing a dynamic surface controller, enabling a virtual control law to pass through a first-order low-pass filter, enabling the input of a neural network to be known, adopting the neural network to compensate time delay by combining a technology of limited coverage quotation, combining a performance function and an error conversion function to ensure a given tracking performance index, and designing an adaptive dynamic surface controller of a Buck circuit with time delay compensation;
s103, controlling stability analysis and semi-physical simulation by using a Buck circuit of the self-adaptive dynamic surface control method.
The state space equation of the Buck class DC/DC converter in the step S101 is shown in the formula (50):
in the formula (50), u H A unit V representing a battery side voltage; i.e L Representing inductor current, unit a; u (U) de The direct current busbar voltage of the direct current micro-grid is represented by a unit V; l is battery energy storage inductance, unit mH; c (C) H The unit mF is a battery side filter capacitor; r is the internal resistance of the battery, and is in units of omega. The topology structure of the Buck circuit is shown in figure 1, wherein V 1 ，V 2 Representing a diode. Without loss of generality, considering external disturbance, the state space equation of the Buck circuit can be rewritten into a mathematical model in the following form by adopting a mathematical transformation mode, and the mathematical model is used as a controlled object of the dynamic surface controller:
in the middle of
It is emphasized that the value is unknown during the controller design process; τ i ，/>
And d i I=1, 2, respectively represent the unknown time delay constant generated during the sensor measurement, the unknown smoothness and time delay related battery side voltage u H Is a function of (c) and external disturbances; u is the duty ratio of the MOS tube, namely the control input signal of the system; />
Representing the output of the system.
For a mathematical model of a controlled object of a dynamic surface controller, the following assumptions are specified:
suppose 1: g i Not equal to 0, i=1, 2, is an unknown normal number, and satisfies g i ≥g imin 。
Suppose 2: desired tracking y r Is a smooth and bounded function;
belonging to a tight set.
Suppose 3: τ i I=1, 2 is an unknown normal number and satisfies 0.ltoreq.τ i ≤τ M Wherein τ M Denoted τ i Is a maximum value of (a).
Suppose 4: unknown external disturbance d i I=1, 2, satisfy
The control objective of the dynamic surface control method is to stabilize the energy storage system side voltage in the Buck circuit near the expected voltage value by adopting the self-adaptive dynamic surface control algorithm under the condition of considering the unknown time delay and external interference generated in the measuring process of the sensor, all signals in the closed loop system are consistent and finally bounded, and the tracking error can be converged into one residual set.
Step S102, designing a dynamic surface controller, which comprises the following steps:
s1021: combining the mathematical model of the controlled object, converting the error S 1 The first derivative with respect to time t is:
in the formula (52), the amino acid sequence of the compound,
x 2d is a virtual control law.
From formula (52):
in the formula (53), the amino acid sequence of the compound,
combining formula (16), unknown term in formula (53)
Can be written in the following form:
and input vector theta 1 ＝(x 1 ,x 1 (t-t 1 ),...,x 1 (t-τ k/k ),...,x 1 (t-t m ),Ψ)。
With the help of the young's inequality, the following holds:
the first candidate lyapunov function is constructed as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
and->
Is a positive parameter of the design, estimation error +.>
And->
Wherein (1)>
And->
Respectively express theta 1 And v 1 * Is used for the estimation of the estimated value of (a).
Combining equations (53) - (56), deriving the first candidate lyapunov function yields:
the virtual control quantity and the self-adaptive law are designed as follows:
wherein k is 1 ，
And->
Are all positive parameters of the design.
Substituting the designed virtual control quantity and the adaptive law into the derivative of the first candidate Lyapunov function to obtain:
now, a first order low pass filter of the form below is introduced to calculate the derivative of the virtual control quantity:
wherein τ and z 1 The time constant and the output of the filter, respectively.
Will filter the error y 1 The definition is as follows: y is 1 ＝z 1 -x 2d (64)
Dynamic face error S 2 The definition is as follows:
S 2 ＝x 2 -z 1 (65)
by filtering error y 1 And dynamic surface error S 2 The method can obtain:
x 2 -x 2d ＝S 2 +z 1 -x 2d ＝S 2 +y 1 (66)
consider the following inequality:
in combination with formula (62), it can be demonstrated that:
s1022: according to the mathematical model of the controlled object, the dynamic surface error S 2 The derivative of (2) is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
from the above formula:
wherein, the liquid crystal display device comprises a liquid crystal display device,
constructing a second candidate lyapunov function as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
and->
Is a positive parameter of the design, estimation error +.>
And->
Wherein->
And->
Respectively is theta 2 And v 2 * Is used for the estimation of the estimated value of (a).
Combining equation (74), deriving a second candidate lyapunov function yields:
combining formula (16), the unknown term in formula (76)
Can be written in the following form:
and input vector theta 2 As defined in equation (17).
In step S1021, the derivative of the second candidate Lyapunov function can be rewritten as follows using the inequality of the formulae (55) - (56):
the design control law and the update law are as follows:
wherein k is 2 ，
And->
Is a positive parameter of the design.
Bringing the designed control law and update law to the derivative of the second candidate lyapunov function yields:
in step S1021, according to the Young' S inequality, equation (82) may be written as:
step S103 uses a Buck circuit control stability analysis and semi-physical simulation of the self-adaptive dynamic surface control method, and comprises the following steps:
first, the stability of the proposed adaptive dynamic surface control scheme will be discussed analytically.
Theorem 1: given the assumption of 1-5, the update laws of equations (80) and (81) of the present invention, the control law in equation (79), and for any given normal number q, if V (0) satisfies V (0). Ltoreq.q, all signals in the closed loop system are consistently bounded. By selecting a suitable design parameter k i ，
And->
The tracking error may converge into a residue.
And (3) proving: for filtering error y 1 The derivation can be obtained:
wherein B is a continuous function.
Consider the following third candidate lyapunov function:
the derivation of three candidate lyapunov functions is available:
order the
And in combination with equations (72), (83) and (86), the derivatives of which are: />
According to hypothesis 2, set:
is that
Last one tight set and B 0 > 0. Furthermore, the set:
is that
A tight set of the above. Due to the aggregate xi 1 ×Ξ 2 Also->
A tight set of the above. Thus, B is in the tight set of Xis 1 ×Ξ 2 There is a maximum value M.
The following inequality is combined:
and order
And
order the
I.e. v=q,
thus, for any time t.gtoreq.0, if V (0). Ltoreq.q, V (t). Ltoreq.q.
Solving the differential inequality (91) yields:
simultaneously means:
thus, all signals in a closed loop system, e.g. e, S i ，
And y 1 The uniformity is finally bounded. Furthermore, by selecting an appropriate design parameter k i ，/>
And->
Equation (94) can be arbitrarily small. Thus, all signals e, S in V (t) i ，/>
And y 1 Can be arbitrarily small. It should be noted here that, for any instant t.gtoreq.0, the switching error S 1 The constraint of (c) ensures that the tracking error e will remain in the performance function p (t) defined by equation (8) at all times. The syndrome is known.
The validity of the proposed algorithm was verified using a semi-physical simulation platform, the structure of which is shown in fig. 2. In the establishment of the power electronic real-time simulation experiment platform, a Buck circuit second-order state space model in a formula (50) is considered to be used as a controlled object, a controlled object model and a controller model which are built and programmed by Simulink in Matlab are respectively used for generating codes through a real-time simulator and a rapid control prototype and are downloaded into experiment equipment, a closed loop is formed between the real-time simulator and real-time hardware, and real-time simulation and online verification experiments are carried out.
In the simulation experiment, parameters of the Buck circuit are set as follows: u (U) de ＝1000V，L＝10mH，C H =1mf and r=0.1Ω. Will beInitializing design parameter setting of a controller: k (k) 1 ＝130，k 2 ＝150，
a 1 ＝a 2 =3. The time constant of the first order low pass filter is τ=0.01. Select reference signal y r =450. Error transfer function->
Wherein, input vector in neural network system
And
wherein t is 1 ＝0.2，t 2 ＝0.4，t 3 =0.8. For the basis function psi 1 (Θ 1 ) 243 nodes are selected, centered at center ζ j J=1,..243, distributed one by one over the interval [ -3,3]×[-3,3]×[-3,3]×[-3,3]×[-3,3]And its width mu j =1; for the base function ψ 2 (Θ 2 ) 81 nodes are selected, the center of which is xi j J=1, &..81, distributed one by one over the interval [ -3,3]×[-3,3]×[-3,3]×[-3,3]On the width mu j ＝1。
Referring to fig. 3, a tracking performance diagram provided for a dynamic surface control method is shown, and the abscissa represents simulation time in seconds; the ordinate represents the voltage value in volts; the solid black line represents the desired signal, which has a value of 450V; the red dashed line represents the output voltage of the system. Referring to fig. 4, a tracking error diagram provided for a dynamic surface control method, the abscissa represents simulation time in seconds; the ordinate represents the voltage value in volts; the black solid line represents the performance function p (t) = ± (1.2 e) -0.8t +0.1); the red dashed line represents the tracking error of the system. Experimental results show that the dynamic surface control methodThe control strategy can achieve effective tracking performance with tracking errors eventually stabilized around 0.03V. It is noted that the tracking error curve is always included in the performance function p (t) = ± (1.2 e) during the simulation time -0.8t +0.1).
The working process comprises the following steps: firstly, taking the difference value between the actual voltage value of the battery side measured by a sensor and the expected voltage value as an error signal, taking the error signal as an input signal of the self-adaptive dynamic surface controller, outputting a control signal to an executing mechanism in a Buck circuit by the controller according to a designed control algorithm, regulating the battery side voltage of a controlled object, namely the Buck circuit, by the executing mechanism, measuring the actual voltage signal of the controlled object by the sensor, feeding back the signal to the input end of a closed loop system, calculating the difference value between the closed loop system and the expected voltage value again, if the difference value is 0, ending the control, and if the difference value still exists, continuing to execute the process. The control objective of the invention is to stabilize the energy storage system side voltage in the Buck circuit near the expected voltage value by adopting the self-adaptive dynamic surface control algorithm under the condition of considering the unknown time delay and external interference generated in the measuring process of the sensor, all signals in the closed loop system are consistent and finally bounded, and the tracking error can be converged into one residual set.
Compared with the existing Buck circuit controller designed by using a back-stepping method, the dynamic surface control method introduces a first-order low-pass filter to calculate the derivative of the virtual control law, so that the differential explosion phenomenon is avoided; introducing a performance function and an error conversion function to realize a given performance index; the neural network system is combined with the finite coverage primer, so that not only can an unknown smooth function be approximated, but also the time delay generated by the system can be compensated, and the tracking error is reduced; the control law u (t) designed by the dynamic surface control method can avoid differential explosion phenomenon generated by a back-stepping method, and stability analysis shows that the designed self-adaptive controller can ensure that all update laws, design parameters and the like in a control system are semi-globally consistent and finally bounded, and tracking errors of the system can be converged to an adjustable tight set by means of an initialization skill.
Claims (3)
1. The self-adaptive dynamic surface control method of the Buck circuit based on the energy storage system is characterized in that given performance indexes are realized by introducing a performance function and an error conversion function, and a neural network system with limited coverage primer is combined to compensate time delay generated in the measuring process of a sensor; by adjusting the parameters of the controller, the tracking error can be converged into any small residue, so that the output voltage of the Buck circuit is stabilized;
the dynamic surface control method is realized based on the following steps:
s1, adopting mathematical transformation to transform a state space equation of a Buck DC/DC converter into a mathematical model in a general form, and using the mathematical model as a controlled object of the dynamic surface control method;
s2, adopting a performance function and an error conversion function to ensure a given tracking performance index;
s3, approximating an unknown function with time delay in a mathematical model of the controlled object by adopting a mode of combining a neural network and a finite coverage primer;
s4, designing a dynamic surface controller, enabling the virtual control law to pass through a first-order low-pass filter, enabling the input of a neural network to be known, adopting the neural network to compensate time delay by combining a technology of limited coverage quotients, combining a performance function and an error conversion function in the step S2 to ensure a given tracking performance index, and designing the self-adaptive dynamic surface controller of the Buck circuit with time delay compensation.
2. The energy storage system-based Buck circuit adaptive dynamic surface control method according to claim 1, wherein the state space equation of the Buck class DC/DC converter in step S1 is shown in formula (1):
in the formula (1), u H A unit V representing a battery side voltage; i.e L Representing inductor current, unit a;U de the direct current busbar voltage of the direct current micro-grid is represented by a unit V; l is battery energy storage inductance, unit mH; c (C) H The unit mF is a battery side filter capacitor; r is the internal resistance of the battery, and is the unit omega; without loss of generality, considering external disturbance, the state space equation of the Buck circuit can be rewritten into a mathematical model shown as a formula (2) in a mathematical transformation mode, and the mathematical model is used as a controlled object of the dynamic surface control method:
in the formula (2), the amino acid sequence of the compound,
it is emphasized that the value is unknown during the controller design process; τ i ，/>
And d i I=1, 2, respectively represent an unknown time delay constant generated during the sensor measurement, a time delay and a battery side voltage u H The related unknown nonlinear function is smooth and the external disturbance of the system;
in the formula (2), u is the duty ratio of the MOS tube, namely the control input signal of the system;
representing an output of the system;
for the mathematical model of the controlled object of the dynamic surface control method, the following assumptions are specified:
suppose 1: g i Not equal to 0, i=1, 2, is an unknown normal number, and satisfies g i ≥g imin ：
Suppose 2: desired tracking y r Is a smooth and bounded function;
belonging to a tight set:
suppose 3: τ i I=1, 2, unknownA positive constant and satisfies 0.ltoreq.τ i ≤τ M Wherein τ M Denoted τ i Is the maximum value of (2):
suppose 4: unknown external disturbance d i I=1, 2, satisfy
To introduce the adoption of the performance function and the error transfer function described in step S2, the tracking error e is defined as shown in equation (3):
e＝x 1 -y r (3)
for any moment when t is greater than or equal to 0, the performance function p (t) is a smooth and decreasing positive function, and the specific form is as shown in the formula (4):
in the formula (4), 0 < sigma < 1 and lim t→∞ ＝p ∞ ＞0，p ∞ Is the maximum value of the tracking error allowed when the system is stable; to convert equation (4) to an equivalent function, an error transfer function of the form is introduced as shown in equation (5):
e(t):＝p(t)Φ(S 1 ), (5)
in the formula (5), S 1 Is a conversion error converted by an error conversion function, Φ (S 1 ) Is a smooth and strictly monotonically increasing function whose inverse has the following properties:
and is also provided with
As can be seen from formula (7), if
Then equation (6) holds; taking further consideration of p (t) > 0 and formula (5), it is possible to obtain- σp (t) < p (t) Φ (S 1 ) =p (t) < 1 (when e (0) > 0) or-p (t) < Φ (S) 1 ) =p (t) < σp (t) (when e (0) < 0), i.e., formula (4) holds; thus, from the above analysis, it is only necessary to prove +.>
The preparation method is finished; from phi (S) 1 ) The strictly monotonically increasing nature of (2) can give a conversion error S 1 The method comprises the following steps:
adopting the neural network in the step S3 to approach the unknown smooth function in the mathematical model of the controlled object on line
Wherein (1)>
Representing a tight set, q being the dimension of the input vector; the neural network approximates the expression of the unknown function as shown in equation (9):
f i (ζ i )＝W i *T ψ i (ζ i )+ε i , (9)
in the formula (9), the amino acid sequence of the compound,
is an input vector to the neural network; />
Is an optimal weight vector, and N is the number of nodes of the neuron, as shown in formula (10):
in the formula (10), the amino acid sequence of the compound,
is a weight vector function; kappa (kappa) j (ζ i ) Is a radial basis function, as shown in equation (11):
κ j (ζ i )＝exp[-||ζ i -ξ j ||/2μ j 2 ],j＝1,...,N (11)
in the formula (11): zeta type toy j Is the center of the j-th basis function, mu j Is the width of the basis function; epsilon i Is the estimated error of the neural network;
suppose 5: epsilon i |≤υ i ，
Wherein v i An upper bound value representing an estimation error;
annotation 1: it should be emphasized that when the unknown smoothing function has an unknown time delay constant τ i When, for example, f i (ζ i ,ζ i (t-τ i ) A direct approximation cannot be made using a neural network; however, due to the tight set
Can be used to determine the unknown function using a neural network combined with a finite coverage primer>
Performing approximation;
lemma 1: assume an input vector ζ i ＝(ζ i ,ζ i (t-τ i ) In line with time t, where τ i ∈[0,τ M ]Is an unknown time delay constant; then, for any given error
There is a finite interval [0, τ ] independent of time t M ]In the form shown in the formula (12):
0＜t 1 ＜…＜t m ＜τ M (12)
from one time point in formula (12), the following is satisfied:
the method can obtain:
combining lemma 1 and hypothesis 3, there are multiple time points τ 1/1 ,...,τ n/n ∈{t 1 ,...,t m -representing the unknown smooth function with time delay as shown in equation (15):
in formula (15):
the estimation error representing the finite coverage theory, combined with the expression of the neural network approximation unknown function, equation (15) can be approximated as the one shown in equation (16):
in delta i The sum of the upper bound value representing the neural network estimation error and the estimation error of the finite coverage primer;
and input vector
Θ i ＝(x 1 ,...,x i ,...,x 1 (t-t 1 ),...,x k (t-τ k/k ),...,x i (t-t m )) (17)。
3. The energy storage system-based Buck circuit adaptive dynamic surface control method according to claim 1, wherein step S4 designs the adaptive dynamic surface controller, and the method comprises the following steps:
s41, combining a mathematical model of the controlled object, and converting the error S 1 The first derivative with respect to time t is shown in equation (18):
in formula (18):
x 2d is a virtual control law;
from the formula (18), as shown in the formula (19):
in the formula (19), the amino acid sequence of the compound,
combining formula (16), the unknown term in formula (19)
Can be written as shown in formula (20):
and input vector theta 1 ＝(x 1 ,x 1 (t-t 1 ),...,x 1 (t-τ k/k ),...,x 1 (t-t m ),Ψ)；
With the help of the young's inequality, the following holds:
constructing a first candidate lyapunov function as shown in formula (23):
in the formula (23), the amino acid sequence of the compound,
and->
Is a positive parameter of the design, estimation error +.>
And->
Wherein (1)>
And->
Respectively express theta 1 And v 1 * Is a function of the estimated value of (2);
deriving a first candidate lyapunov function by combining the correlation calculation obtained in the formulas (19) - (22) to obtain:
the virtual control quantity and the self-adaptive law are designed as follows:
wherein k is 1 ，
And->
Are all positive parameters of the design;
substituting the designed virtual control quantity and the adaptive law into the derivative of the first candidate lyapunov function can be obtained as shown in formula (28):
a first order low pass filter as shown in equation (29) is introduced to calculate the derivative of the virtual control quantity:
in formula (29), τ and z 1 The time constant and the output of the filter, respectively;
will filter the error y 1 Is defined as shown in formula (30):
y 1 ＝z 1 -x 2d (30)
dynamic face error S 2 Is defined as shown in formula (31):
S 2 ＝x 2 -z 1 (31)
by filtering error y 1 And dynamic surface error S 2 The expression (32) can be obtained as follows:
x 2 -x 2d ＝S 2 +z 1 -x 2d ＝S 2 +y 1 (32)
consider the following inequality:
in combination with formula (32), it can be demonstrated that as shown in formula (38):
s42, according to the mathematical model of the controlled object, the dynamic surface error S 2 As shown in formula (39):
in formula (39): ,
obtainable by formula (39), as shown in formula (40):
in the formula (40), the amino acid sequence of the compound,
constructing a second candidate lyapunov function as shown in formula (41):
in the formula (41),
and->
Is a positive parameter of the design, estimation error +.>
And->
Wherein->
And->
Respectively is theta 2 And v 2 * Is a function of the estimated value of (2);
combining equation (40), deriving a second candidate lyapunov function is available as shown in equation (42):
combining formula (16), the unknown term in formula (42)
Can be written as shown in formula (43): :
and input vector theta 2 The same as defined in formula (17);
in the same way as step S41, the derivative of the second candidate lyapunov function can be rewritten as shown in the formula (44) using the inequality of the formulas (21) - (22):
the design control law and the update law are as follows:
wherein k is 2 ，
And->
Is a positive parameter of the design;
the designed control law and update law are brought into the derivative of the second candidate lyapunov function as shown in equation (48):
in the same way as in step S41, according to the young' S inequality, the formula (48) can be written as:
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