Heliostat robust adaptive neural network sliding mode dynamic surface control method and system

Abstract

The invention discloses a robust adaptive neural network sliding mode dynamic surface control method and system for a heliostat, and relates to the technical field of heliostat control. The problems that a control structure can be effectively simplified and'differential explosion 'can be solved by adopting an existing neural network dynamic surface method are solved. However, perturbation of a low-pass filter time constant and a self-adaptive parameter is very fragile, and system divergence is easily caused. The method comprises the following steps: constructing a first surface error, and introducing an error conversion function and a performance function; constructing a second surface error, and introducing an error conversion function and a performance function; constructing a sliding mode surface according to the first surface error and the second surface error, and obtaining a control law according to the sliding mode surface; and the first surface error, the second surface error, the sliding mode surface and parameter signals in the control law are constrained through a Lyapunov function, so that all parameter signals in the controller are finally consistent and bounded and convergent to any small. The method is suitable for the design of the heliostat control system.

Description

Technical Field

[0001] The invention relates to the technical field of heliostat control, and in particular to a heliostat robust adaptive neural network sliding mode dynamic surface control method. Background Art

[0002] With the rapid development of society, human demand for energy has increased rapidly, and the market for solar thermal power generation has ushered in an explosive growth period. The control of a solar thermal power station is roughly divided into three parts: the concentrating and distributing system, the heat storage and exchange system, and the conventional power generation system. Among them, the concentrating and collecting system is the key to the success of the entire power plant. The cost of the concentrating and collecting system accounts for about 50% of the total investment of the entire tower solar thermal power station. The main function of the heliostat is to track the sun, collect and reflect sunlight into the absorber.

[0003] Although the heliostat is being studied continuously, the existing neural network dynamic surface method can effectively simplify the control structure and solve the "differential explosion" problem. However, the perturbation of its low-pass filter time constant and adaptive parameters is very fragile. Swaroop et al. discovered this problem when they proposed the dynamic surface theory, and gave a simulation example to verify that a slightly larger low-pass filter time constant will cause the system to diverge. In actual engineering applications, the low-pass filter time constant and neural network adaptive parameters are usually selected based on experience. These parameters usually take values ​​within a very small range. Slightly inappropriate parameter selection may cause system oscillation or even divergence. The main reason is that the low-pass filter introduced by the dynamic surface control method makes the control performance greatly affected by the change of the filter time constant. Summary of the invention

[0004] The present invention is used to solve the existing problem that the neural network dynamic surface method can effectively simplify the control structure and solve the "differential explosion" problem. However, the perturbation of the low-pass filter time constant and adaptive parameters is very fragile and easily causes system divergence.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The present invention provides a heliostat robust adaptive neural network sliding mode dynamic surface control method, the method comprising the following steps:

[0007] Step 1: Construct the first surface error and introduce the error conversion function and performance function;

[0008] Step 2: Construct the second surface error and introduce the error conversion function and performance function;

[0009] Step 3: construct a sliding surface according to the first surface error and the second surface error, and obtain the control law according to the sliding surface;

[0010] Step 4: Constrain the first surface error, the second surface error, the sliding surface and the parameter signals in the control law through the Lyapunov function, so that all parameter signals in the controller are ultimately uniformly bounded and converge to arbitrarily small.

[0011] Furthermore, in another preferred embodiment, the above step 1 is specifically as follows:

[0012] Step 1.1: Construct the system tracking error, and construct the performance function and error conversion function based on the system tracking error;

[0013] Step 1.2: Construct the first surface error according to the performance function and the error conversion function, and perform derivative and parameter conversion on the first surface error;

[0014] Step 1.3: Derivative the system tracking error, combine the first surface error derivative result, parameter conversion and system tracking error derivative result, and introduce the quadratic function and derive it;

[0015] Step 1.4: According to the dynamic surface control algorithm and the derivative result of the quadratic function, the first surface error virtual control law is obtained;

[0016] Step 1.5: Use a first-order low-pass filter to process the first error virtual control law and obtain a new variable z 2 .

[0017] Furthermore, in another preferred embodiment, the first surface error is:

[0018]

[0019] Where e(t) is the error conversion function, is the performance function, Φ -1 is a smooth decreasing function.

[0020] Furthermore, in another preferred embodiment, the above step 2 is specifically as follows:

[0021] Step 2.1: Based on the new variable z 2 Construct a second surface error and take the derivative of the second surface error;

[0022] Step 2.2: Introduce the quadratic function and take its derivative;

[0023] Step 2.3: Use RBFNNs network to approximate the unknown term in the derivative of quadratic function;

[0024] Step 2.4: According to the results of step 2.3, the second surface error virtual control law and parameter adjustment law are obtained;

[0025] Step 2.5: Use a first-order low-pass filter to process the second surface error virtual control law to obtain a new variable z 3 .

[0026] Furthermore, in another preferred embodiment, the second surface error is:

[0027] S 2 =x 2 -z 2

[0028] Among them, x 2 Represents the second status variable returned by the sensor.

[0029] Furthermore, in another preferred embodiment, the above step 3 is specifically as follows:

[0030] Step 3.1: According to the first surface error S 1 , the second surface error S 2 and the new variable z 3 Construct the sliding surface and take its derivative;

[0031] Step 3.2: Introduce the quadratic equation and take its derivative;

[0032] Step 3.3: Use RBFNNs network to approximate the unknown term in the derivative of quadratic function;

[0033] Step 3.4: Perform parameter conversion on the result in step 3.3;

[0034] Step 3.5: Substitute the results of step 3.3 and step 3.4 into the sliding surface to obtain the actual control law and parameter adjustment law. Further, there is another preferred embodiment, the sliding surface is:

[0035] S m =m 1 S 1 +m 2 S 2 +S 3

[0036] S 3 =x 3 -z 3

[0037] Among them, m 1 ,m 2 are all positive design parameters, x 3 Represents the third status variable returned by the sensor.

[0038] The robust adaptive neural network sliding mode dynamic surface control method for a heliostat described in the present invention can be fully implemented by computer software. Therefore, correspondingly, the present invention also provides a robust adaptive neural network sliding mode dynamic surface control system for a heliostat, the system comprising:

[0039] Storage means for constructing a first surface error and introducing an error conversion function and a performance function;

[0040] A storage device for constructing a second surface error and introducing an error conversion function and a performance function;

[0041] A storage device for constructing a sliding surface according to the first surface error and the second surface error, and obtaining a control law according to the sliding surface;

[0042] It is used to constrain the first surface error, the second surface error, the sliding surface and the parameter signals in the control law through the Lyapunov function, so that all parameter signals in the controller are ultimately uniformly bounded and converge to an arbitrarily small storage device.

[0043] The present invention also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, any one of the above-mentioned robust adaptive neural network sliding mode dynamic surface control methods for a heliostat is executed.

[0044] The present invention also provides a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes any one of the above-mentioned robust adaptive neural network sliding mode dynamic surface control methods for heliostats.

[0045] The beneficial effects of the present invention are:

[0046] 1. The present invention introduces an error conversion function and a sliding mode variable structure control method on the basis of adaptive neural network dynamic surface control to solve the problem that the perturbation of the low-pass filter time constant and adaptive parameters is very fragile and easily causes system divergence. Specifically: two dynamic surfaces are defined respectively by the error conversion function to ensure the predetermined tracking performance index. By introducing the sliding surface in the last step design of the dynamic surface control, and taking the tracking errors of the first two steps into consideration in the design of the actual control law, the design of the control law comprehensively considers each of the previous dynamic surface errors to solve the problem of decreased control performance caused by the change of the low-pass filter time constant in the process of adaptive dynamic surface design, and improve the system tracking performance and reduce overshoot.

[0047] Furthermore, the present invention combines the error performance function with the sliding mode control, and the RBF neural network is used as a neural network approximator to estimate dynamic uncertainty and nonlinear terms. The dynamic surface adaptive control algorithm enables the tower solar heliostat system to achieve semi-global final uniform boundedness, making the system run stably and reliably.

[0048] The invention is suitable for the design of a heliostat control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of the heliostat robust adaptive neural network sliding mode dynamic surface control method of the present invention;

[0050] Figure 2 is a tracking performance diagram of the altitude angle control subsystem of the present invention;

[0051] Figure 3 is the tracking error of the altitude angle control subsystem of the present invention, and the performance index function

[0052] Figure 4 is a comparison diagram of tracking errors of the altitude angle control subsystem of the present invention;

[0053] Figure 5 is a control input diagram of the altitude angle control subsystem of the present invention;

[0054] Figure 6 is the estimated norm value of the neural network weights described in the present invention

[0055] Figure 7 is a tracking performance diagram of the azimuth control subsystem of the present invention;

[0056] Figure 8 is the tracking error of the azimuth control subsystem of the present invention, and the performance index function

[0057] Fig. 9 is the tracking error of the azimuth control subsystem of the present invention;

[0058] Fig.10 is a control input diagram of the azimuth control subsystem of the present invention;

[0059] Fig.11 is the estimated norm value of the neural network weights described in the present invention DETAILED DESCRIPTION

[0060] The specific embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

[0061] Embodiment 1: This embodiment provides a robust adaptive neural network sliding mode dynamic surface control method for heliostats, which is used to solve the problem that although the existing neural network dynamic surface method can effectively simplify the control structure and solve the "differential explosion" problem, the perturbation of the low-pass filter time constant and adaptive parameters is very fragile, which easily causes the system divergence problem.

[0062] The method comprises the following steps:

[0063] Step 1: Construct the first surface error and introduce the error conversion function and performance function;

[0064] Step 2: Construct the second surface error and introduce the error conversion function and performance function;

[0065] Step 3: construct a sliding surface according to the first surface error and the second surface error, and obtain the control law according to the sliding surface;

[0066] Step 4: Constrain the first surface error, the second surface error, the sliding surface and the parameter signals in the control law through the Lyapunov function, so that all parameter signals in the controller are ultimately uniformly bounded and converge to arbitrarily small.

[0067] This embodiment introduces an error conversion function and a sliding mode variable structure control method on the basis of the adaptive neural network dynamic surface control to solve the problem that the perturbation of the low-pass filter time constant and the adaptive parameters is very fragile and easily causes the system to diverge. Specifically: two dynamic surfaces are defined respectively by the error conversion function to ensure the predetermined tracking performance index. By introducing the sliding surface in the last step of the dynamic surface control design, and taking the tracking errors of the first two steps into consideration in the design of the actual control law, the design of the control law comprehensively considers each of the previous dynamic surface errors to solve the problem of decreased control performance caused by the change of the low-pass filter time constant in the adaptive dynamic surface design process, and improve the system tracking performance and reduce overshoot.

[0068] Implementation 2: This implementation is to specifically describe the steps of a heliostat robust adaptive neural network sliding mode dynamic surface control method described in Implementation 1;

[0069] Step 1: Construct the first surface error and introduce the error conversion function and performance function;

[0070] The specific steps include:

[0071] Step 1.1: Construct the system tracking error, and construct the performance function and error conversion function based on the system tracking error;

[0072] Step 1.2: Construct the first surface error according to the performance function and the error conversion function, and perform derivative and parameter conversion on the first surface error;

[0073] Step 1.3: Derivative the system tracking error, combine the first surface error derivative result, parameter conversion and system tracking error derivative result, and introduce the quadratic function and derive it;

[0074] Step 1.4: According to the dynamic surface control algorithm and the derivative result of the quadratic function, the first surface error virtual control law is obtained;

[0075] Step 1.5: Use a first-order low-pass filter to process the first error virtual control law and obtain a new variable z 2 .

[0076] Step 2: Construct the second surface error and introduce the error conversion function and performance function;

[0077] The specific steps include:

[0078] Step 2.1: Based on the new variable z 2 Construct a second surface error and take the derivative of the second surface error;

[0079] Step 2.2: Introduce the quadratic function and take its derivative;

[0080] Step 2.3: Use RBFNNs network to approximate the unknown term in the derivative of quadratic function;

[0081] Step 2.4: According to the results of step 2.3, the second surface error virtual control law and parameter adjustment law are obtained;

[0082] Step 2.5: Use a first-order low-pass filter to process the second-surface error virtual control law to obtain a new variable z 3 .

[0083] Step 3: Construct a sliding surface based on the first surface error and the second surface error, and obtain the control law based on the sliding surface.

[0084] The specific steps include:

[0085] Step 3.1: According to the first surface error S 1 , the second surface error S 2 and the new variable z 3 Construct the sliding surface and take its derivative;

[0086] Step 3.2: Introduce the quadratic equation and take its derivative;

[0087] Step 3.3: Use RBFNNs network to approximate the unknown term in the derivative of quadratic function;

[0088] Step 3.4: Perform parameter conversion on the result in step 3.3;

[0089] Step 3.5: Substitute the results of step 3.3 and step 3.4 into the sliding surface to obtain the actual control law and parameter adjustment law.

[0090] Step 4: Constrain the first surface error, the second surface error, the sliding surface and the parameter signals in the control law through the Lyapunov function, so that all parameter signals in the controller are ultimately uniformly bounded and converge to arbitrarily small.

[0091] The specific steps include:

[0092] In the process of stability analysis, stability analysis is performed by designing a suitable Lyapunov function. The designed parameters and control signals are globally bounded, making the system more stable.

[0093] Implementation method 3: This implementation method is an example of a heliostat robust adaptive neural network sliding mode dynamic surface control method described in implementation method 2;

[0094] Firstly, in order to ensure the pre-given tracking performance indicators, the error conversion function and performance function are constructed.

[0095] Build system tracking error:

[0096] e:=x 1 -y r (1)

[0097] In the formula, y r is the ideal tracking trajectory, x 1 Represents the first status variable returned by the sensor.

[0098] According to the system tracking error, the performance function and error conversion function are defined as follows:

[0099] Performance functions: is defined as a smoothly decreasing positive function such that for all t ≥ 0, it satisfies:

[0100]

[0101] In the formula, 0<σ<1, and It is the maximum tracking error value allowed when the system is stable.

[0102] In order to convert the above formula (2) into an equivalent function, an error conversion function is introduced. The error conversion function is as follows:

[0103]

[0104] In the formula, s 1 is the conversion error after conversion by the error conversion function, Φ(s 1 ) is a smooth and strictly monotonically increasing function, and its inverse function has the following properties:

[0105]

[0106] and

[0107]

[0108] From the above system tracking error formula (1), we can know that if s 1 ∈L ∞ , then formula (4) holds, and then consider And formula (3), we can get:

[0109] (when e(0)>0) or (When e(0)<0), that is: formula (2) holds.

[0110] Therefore, from the above analysis, we can see that if we want to achieve a given performance indicator, we only need to prove that s 1 ∈L ∞ Then, Φ(s 1 ), we can obtain the strictly monotonically increasing property of

[0111]

[0112] In practical applications, the case when e(0) = 0 is included in the case when e(0) > 0 or e(0) < 0. At the same time, σ cannot be zero, because this will make s 1 (0)Unbounded.

[0113] Secondly, the design method of sliding mode variable structure control includes two steps: 1. Select the sliding surface κ(x). The design of the sliding surface will directly affect the asymptotic stability of the system when it enters the sliding mode. 2. Design the control law u of the system. This process involves the arrival condition.

[0114] Consider the following nonlinear system with the following relationship:

[0115]

[0116] In the above formula (7), a mathematical analytical relationship of a nonlinear system is constructed, in which x represents the state variable of the system, u represents the control variable of the system, and t represents time.

[0117] Therefore, according to the above content, the sliding surface is defined and the sliding mode variable structure control law u is obtained:

[0118] The sliding surface is defined as:

[0119] In the servo system, the system can be single-input or multi-input, but the difference between the two is not big. The heliostat control system described in this embodiment only involves the single-input case. Therefore, the single-input case is analyzed:

[0120] The switching function form for a single input is:

[0121] κ=c 1 x 1 +c 2 x 2 +…c n-1 x n-1 +x n (8)

[0122] In formula (8), c i ,i=1,2,...,n-1 are all constants. When selecting these constants, it is necessary to ensure that the controller has a certain stability and good dynamic performance.

[0123] The specific method for obtaining the sliding mode variable structure control law u is:

[0124] The control law u is mainly used to realize the movement of the state point of the system on the sliding surface. In the process of realizing control, u generally has the following basic forms:

[0125] 1) Constant value switching control law:

[0126] u=u 0 sgn(κ) (9)

[0127] In the formula, u 0 is the quantity to be determined, and sgn is the sign function. The process of determining the control law u is to design a suitable u 0 process.

[0128] 2) Function switching control law:

[0129] u=u eq +u 0 sgn(κ) (10)

[0130] In the formula, u eq is the equivalent control quantity when the state point moves stably on the sliding surface.

[0131] 3) Proportional switching control law:

[0132]

[0133] In the formula, k i is a constant and sgn is a sign function.

[0134] Take the design of the altitude angle control subsystem controller as an example:

[0135] Step 1: Construct the first surface error S 1 The above formula (6) is derived as follows:

[0136]

[0137] In the formula, represents the performance function, represents the dynamic uncertainty term, e 1 (t) represents the error transfer function, The symbol represents the partial derivative, not the variable in the formula.

[0138] make

[0139]

[0140] By derivatizing the above system tracking error formula (1), we can obtain:

[0141]

[0142] Combine the above first surface error S 1 The derivative formula (12), parameter conversion formula (13), and system tracking error derivative formula (14) can be obtained:

[0143]

[0144] In the formula, x 2d Represents the virtual control law.

[0145] Introduce the following quadratic function:

[0146]

[0147] V 1 The derivative is:

[0148]

[0149] According to the dynamic surface control algorithm and the above formula (17), the virtual control law x is selected 2d for:

[0150]

[0151] In the formula, k 1 is a positive design parameter.

[0152] In order to avoid repeated derivatives of the virtual control signal, let the virtual control law x 2d The new variable z obtained by first-order low-pass filtering 2 , which is expressed as follows:

[0153]

[0154] In the formula, τ 2 is the filter time constant, and in the next second step z 2 Replace x 2d .

[0155] By introducing a new variable z 2 , which can avoid the subsequent virtual control law x 2d Repeated derivation of .

[0156] Step 2: Construct the second surface error S 2 , specifically:

[0157] S 2 =x 2 -z 2 (20)

[0158] In the formula, x 2 Represents the second status variable returned by the sensor.

[0159] The error of the second surface S 2 Taking the derivative, we get:

[0160]

[0161] Introduce the following quadratic function:

[0162]

[0163] For the above quadratic function formula (22) V 2 The derivation yields:

[0164]

[0165] In the formula, yes The estimated value of γ 2 is a positive design parameter.

[0166] RBFNNs are used to approximate the unknown terms in formula (23).

[0167]

[0168] In the formula, is the optimal weight vector, ξ 2 =(x 1 ,x 2 ,z 2 )∈R 3 ,|ε 2 (ξ 2 )|≤ε 2m .make From Young's inequality we can get:

[0169]

[0170] In the formula, α 2 is a positive design parameter, ε 2m is the upper bound of the approximation error.

[0171] Substituting the above formulas (24) to (26) into formula (23), we can obtain:

[0172]

[0173] In the formula, x 3d is the virtual control law to be designed.

[0174] According to the above formula (27), the virtual control law x 3d The design is as follows:

[0175]

[0176] In the formula, k 2 is a positive design parameter, parameter tuning law The design is as follows:

[0177]

[0178] In the formula, γ 2 ,σ 2 is a positive design parameter.

[0179] Let the virtual control law x 3d Through a first-order low-pass filter, we get a new variable z 3

[0180]

[0181] In the formula, τ 3 is the filter time constant.

[0182] By introducing a new variable z 3 , which can avoid the subsequent virtual control law x 3d Repeated derivation of .

[0183] Step 3: Construct the following sliding surface:

[0184] S m =m 1 S 1 +m 2 S 2 +S 3 (31)

[0185] and

[0186] S 3 =x 3 -z 3 (32)

[0187] For the above sliding surface formula S m The derivative is:

[0188]

[0189] Introduce the following quadratic equation:

[0190]

[0191] In the formula, yes The estimated value of γ 3 is a positive design parameter.

[0192] By estimating the norm of the N-dimensional optimal weight vector, where N is the number of neuron nodes, the estimated number of unknown neuron nodes is reduced from N to 1, which greatly reduces the computational burden and is more suitable for real-time control than existing technologies.

[0193] V 3 The derivative is:

[0194]

[0195] In the tight set Ω 3 We use RBFNNs to approximate the unknown terms:

[0196]

[0197] In the formula, is the optimal weight vector, ξ 3 =(x 2 ,x 3 ,z 3 )∈R 3 ,|ε 3 (ξ 3 )|≤ε 3m .

[0198] make From Young's inequality we can get:

[0199]

[0200] Substituting the above formulas (36), (37) and (38) into the above formula (31), we can obtain:

[0201]

[0202] The actual control law can be obtained from the above formula (39):

[0203]

[0204] Parameter tuning law:

[0205]

[0206] In the formula, k 3 ,γ 3 ,σ 3 is a positive design parameter.

[0207] Take the azimuth control subsystem controller design as an example:

[0208] Step 1: Construct the first surface error Γ 1 And taking the derivative we get:

[0209]

[0210] Introduce the following quadratic equation:

[0211]

[0212] Deriving the above formula (43), the virtual control law y is selected according to the principle of dynamic surface control algorithm: 2d for:

[0213]

[0214] In the formula, l 1 is a positive design parameter, let y 2d The new variable c obtained by passing through a first-order low-pass filter 2 .

[0215] By introducing a new variable c 2 , which can avoid the subsequent virtual control law y 2d Repeated derivation of .

[0216] Step 2: Construct the second surface error

[0217] Γ 2 =y 2 -c 2(45)

[0218] Introduce the following quadratic equation:

[0219]

[0220] In the formula, yes The estimated value of γ 4 is a positive design parameter. Derivative it and use RBFNNs to approximate the unknown term, and select the virtual control law y 3d for:

[0221]

[0222] Parameter Tuning Law The design is as follows:

[0223]

[0224] In the formula, l 2 ,γ 4 ,σ 4 is a positive design parameter. And let y 3d Through a first-order low-pass filter, we get a new variable c 3 .

[0225] By introducing a new variable c 3 , which can avoid the subsequent virtual control law y 3d Repeated derivation of .

[0226] Step 3: Construct the following sliding surface:

[0227] Γ m =ω 1 Γ 1 +ω 2 Γ 2 +Γ 3 (49)

[0228] Introduce the following quadratic equation:

[0229]

[0230] In the formula, yes The estimated value of γ 5 is a positive design parameter. By taking its derivative and using RBFNNs to approximate the unknown term, the actual control law can be obtained:

[0231]

[0232] The parameter tuning law is:

[0233]

[0234] In the formula, l 3 ,γ 5 ,σ 5 is a positive design parameter.

[0235] This embodiment uses a first-order low-pass filter to process the virtual control law to obtain new variables, which can avoid repeated derivation of the virtual control law. Therefore, it can not only overcome the differential "explosion problem" in the inversion method, but also make the calculation of the control rate simpler than the inversion method in the prior art.

[0236] This embodiment estimates the norm of the N-dimensional optimal weight vector, as shown in the above formula: and N is the number of neuron nodes. The estimated number of unknown neuron nodes is reduced from N to 1, which greatly reduces the computational burden and is more suitable for real-time control than the existing technology.

[0237] Step 4: Constrain the first surface error, the second surface error, the sliding surface and the parameter signals in the control law through the Lyapunov function, so that all parameter signals in the controller are ultimately uniformly bounded and converge to arbitrarily small, realizing the stability and tracking performance analysis of the heliostat controller.

[0238] For the altitude angle control subsystem, first construct the error y 2e ,y 3e :

[0239]

[0240]

[0241] In the formula, the virtual control law x 2d and virtual control law x 3d It has been given in the above formulas (18) and (28). According to the above formulas (10) and (13), it can be obtained that:

[0242]

[0243] Similarly, according to the above formulas (32) and (14), we can get

[0244]

[0245] Then, the derivatives of the above formulas (13) and (14) are as follows:

[0246]

[0247] in

[0248]

[0249] And B 2 ,B 3 is a continuous function.

[0250] The Lyapunov function is defined as follows:

[0251]

[0252] Among them, V 1 ,V 2 and V 3 are functions defined by the above formulas (16), (22), and (34) respectively.

[0253] Therefore, considering the closed-loop system consisting of equations (12), (21), (33), (13), (16), for a given positive constant ε im Satisfy |ε i (ξ i )|≤ε im ,i=2,3, formulas (24) and (36) are in the compact set and If the given positive constant p satisfies:

[0254] V(0)≤p (62)

[0255] Then, by choosing a suitable design parameter k 1 , k 2 , k 3 , γ 2 , γ 3 , σ 2 , σ 3 , m 1 , m 2 Make all variables in the closed-loop system as s 1 ,s 2 ,s 3 , v 2 , v 3 Ultimately, it is uniformly bounded. And the tracking error of the system can converge to an arbitrarily small residual set. Proof: Taking the derivative of V in formula (61), we can obtain:

[0256]

[0257] According to the above formulas (20) and (13), we can get:

[0258] x 2 =s 2 +y 2e +x 2d (64)

[0259] Considering formula (64), the virtual control law x in the above formula (18) is 2d Substituting into formula (17), we can get:

[0260]

[0261] Using Young's inequality we can have:

[0262]

[0263] Substituting the above formulas (66) and (67) into formula (61), we can obtain:

[0264]

[0265] Similar to formula (64), from formula (32) and (14), we can get:

[0266] x 3 =s 3 +y 3e +x 3d (69)

[0267] Considering formula (19), the virtual control law x in formula (28) is 3d Substituting into formula (27), we can get:

[0268]

[0269] Considering formula (131), using Young's inequality we can get:

[0270]

[0271] Substitute formula (29) and formulas (71)-(73) into formula (70):

[0272]

[0273] Substituting formula (40), (41) into formula (39), we can obtain:

[0274]

[0275] Using Young's inequality we can have:

[0276]

[0277] Substituting formula (76) into formula (71):

[0278]

[0279] Considering assumption 1, we can reasonably define a compact set:

[0280]

[0281] belong And B 0 > 0. Let M 2 and M 3 It is B 2 and B 3 The maximum value on the compact set Θ, then for any p>0, using Young's inequality, we can get:

[0282]

[0283] μ is a positive constant. Let

[0284]

[0285] Substituting formulas (68), (74), (77) and (79)-(84) into formula (63), we can obtain

[0286]

[0287] and

[0288]

[0289] Now, define the positive design parameter α 0 satisfy:

[0290]

[0291] make:

[0292]

[0293] Then, considering equations (81) and (87), (88), we can get

[0294]

[0295] make

[0296]

[0297] Then, V = p, when , it means that V≤p is an invariant set, that is, if V(0)≤p, for all t≥0, V(t)≤p.

[0298] By solving formula (74), we can get

[0299]

[0300] The above formula explains:

[0301] lim t→∞ V(t)=C * / 2α 0 (92)

[0302] Therefore, through the above analysis, it can be obtained that for any initial condition, by choosing appropriate design parameters, all signals of the closed-loop system such as s 1 ,s 2 ,s 3 , y 2e ,y 3e are eventually uniformly bounded. In addition, by choosing appropriate design parameters, namely k 1 , k 2 , k 3 , γ 2 , γ 3 , σ 2 , σ 3 , m 1 , m 2 Can make α 0 infinite, so that all signals in closed-loop systems such as s 1 ,s 2 ,s 3 , y 2e ,y 3e can converge to an arbitrarily small value.

[0303] The stability analysis of the azimuth control subsystem is similar to that of the altitude control subsystem.

[0304] First, define the error y 4e ,y 5e , and define the following Lyapunov function:

[0305]

[0306] By taking the derivative of the above formula (93), similar to formula (81), we can get:

[0307]

[0308] and

[0309]

[0310] Define the positive design parameter β 0 Satisfying the form of formula (87) and designing appropriate parameters: we can get

[0311]

[0312] From the above analysis process, we can see that for any initial condition, by choosing appropriate design parameters, all signals of the closed-loop system such as Γ1 , Γ 2 , Γ 3 , y 4e ,y 5e are ultimately uniformly bounded. In addition, by selecting appropriate design parameters, namely, l 1 , l 2 , l 3 , γ 4 , γ 5 , σ 4 , σ 5 , m 1 , m 2 Can make β 0 infinite, so that all signals in closed-loop systems such as Γ 1 , Γ 2 , Γ 3 , y 4e ,y 5e Can converge to any small size and satisfy L ∞ Performance indicators.

[0313] Implementation method 4: See Figures 2 to 11 This embodiment is described. This embodiment uses the heliostat robust adaptive neural network sliding mode dynamic surface control method described in the above embodiment to simulate and analyze the servo control system of the heliostat:

[0314] In the servo control system of the heliostat, the servo motor parameters are shown in the following table.

[0315] Altitude angle motor Azimuth motor <![CDATA[Stator resistance r 1 > 0.34Ω 0.34Ω <![CDATA[Rotor resistance r 2 > 0.191Ω 0.191Ω <![CDATA[Magnetic flux linkage λ 2s > 0.9378Wb 0.9378Wb <![CDATA[Number of pole pairs n 1 > 1 1 <![CDATA[Stator inductance L 1 > 0.1078H 0.1078H <![CDATA[Rotor inductance L 2 > 0.1077H 0.1077H <![CDATA[Mutual inductance L m > 0.1042H 0.1042H

[0316] In simulation, β 1 =0.15,β 2 =0.25; m 1 =m 2 =0.5, l 1 = l 2 =0.5 reference signal y r1 = sin(t),y r2 =cos(t) design parameter k 1 =35, k 2 =60, k 3 =75; l 1 =15,l 2 =35,l 3 =55; the time constant of the low-pass filter in each step is: τ 2 =τ 3 =0.007, τ 4 =τ 5=0.015; the parameter of the parameter adjustment law is: γ 2 =0.75,σ 2 =0.075;γ 3 =0.75,σ 3 =0.075;γ 4 =0.75,σ 4 =0.5;γ 5 =0.75,σ 5 =0.5; α 2 =5.5,α 3 =4; α 4 =3,α 5 = 2. Gaussian basis function They are basis functions ζ 1j∈ R 3 , 2j ∈R 3 , 3j ∈R 3 , 4j ∈R 3 Select 21 center points, evenly distributed in [-1, +1] × [-1, +1] × [-1, +1], and the base width η 1j =η 2j =1,η 3j =η 4j =1,j=1,...,21. The initial value of each state of the system is x 1 (0) = 0.01, x 2 (0) = 0, x 3 (0) = 0; y 1 (0) = 1, y 2 (0) = 0.015, y 3 (0)=0.

[0317] Simulation analysis such as Figures 2 to 11 As shown, Figure 2 and Figure 7 They represent the tracking performance of the altitude control subsystem and the azimuth control subsystem respectively. It can be seen from the figure that the system output can accurately track the reference signal; Figure 3 and Figure 8 This shows that by using the performance indicator function The tracking error of the system does not exceed 0.4 and the tracking performance remains on the pre-set tracking performance function. Figure 4 It shows the tracking error comparison curve of the altitude angle control subsystem using the neural network dynamic surface and the neural network sliding mode dynamic surface control technology. Fig. 9It shows the tracking error comparison curve of the azimuth control subsystem using the neural network dynamic surface and the neural network sliding mode dynamic surface control technology. It can be seen from the figure that the introduction of the sliding mode surface in the neural network dynamic surface control technology improves the system tracking performance, reduces overshoot and shortens the time it takes for the system to reach a steady state. Figure 5 and Fig.10 It represents the controller output value (control signal). Figure 6 and Fig.11 The estimated values ​​of the norm of neural network weights are given respectively.

[0318] In summary, the sliding surface is introduced on the basis of the adaptive neural network dynamic surface control technology to complete the design of the heliostat controller. In the first step of the controller design process, the error conversion function and the performance index function are introduced to ensure the preset tracking performance index of the system. In the last step, the sliding surface is introduced to improve the tracking performance of the system. In the process of stability analysis, the stability analysis is carried out by designing a suitable Lyapunov function. The designed parameters and control signals are globally bounded. The rationality and effectiveness of the controller design are verified by simulation experiments using Matlab. The simulation results show the effectiveness of this method and can ensure the semi-global stability of the closed-loop system.

[0319] Embodiment 5: The robust adaptive neural network sliding mode dynamic surface control method for a heliostat described in the above embodiments can be implemented entirely by computer software. Therefore, correspondingly, the present invention also provides a robust adaptive neural network sliding mode dynamic surface control system for a heliostat, the system comprising:

[0320] Storage means for constructing a first surface error and introducing an error conversion function and a performance function;

[0321] A storage device for constructing a second surface error and introducing an error conversion function and a performance function;

[0322] A storage device for constructing a sliding surface according to the first surface error and the second surface error, and obtaining a control law according to the sliding surface;

[0323] It is used to constrain the first surface error, the second surface error, the sliding surface and the parameter signals in the control law through the Lyapunov function, so that all parameter signals in the controller are ultimately uniformly bounded and converge to an arbitrarily small storage device.

[0324] Embodiment 6: This embodiment provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, any one of the above-mentioned robust adaptive neural network sliding mode dynamic surface control methods for a heliostat is executed.

[0325] Embodiment 7. This embodiment provides a computer device, which includes a memory and a processor. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes the heliostat robust adaptive neural network sliding mode dynamic surface control method described in any one of the above.

[0326] For the computer device provided in this embodiment, the hardware device in this part is of a general model and is not shown in the form of a diagram. The system includes a processor and a memory. The processor and the memory can be connected through a bus or other means. The memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, as well as corresponding program instructions / modules. The processor executes various functional applications and data processing of the processor by running the non-transitory software programs, instructions, and modules stored in the memory, so as to implement the heliostat robust adaptive neural network sliding mode dynamic surface control method and steps in the above method embodiments.

[0327] The above is only the embodiment of the present invention and does not limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A heliostat robust adaptive neural network sliding mode dynamic surface control method, characterized in that: The method is: Step 1: Construct the first surface error and introduce the error conversion function and performance function; Step 2: Construct the second surface error and introduce the error conversion function and performance function; Step 3: construct a sliding surface according to the first surface error and the second surface error, and obtain the control law according to the sliding surface; Step 4: Constrain the first surface error, the second surface error, the sliding surface and the parameter signals in the control law through the Lyapunov function, so that all parameter signals in the controller are ultimately uniformly bounded and converge to arbitrarily small.

2. The heliostat robust adaptive neural network sliding mode dynamic surface control method according to claim 1, characterized in that: Step 1 is as follows: Step 1.1: Construct the system tracking error, and construct the performance function and error conversion function based on the system tracking error; Step 1.2: Construct the first surface error according to the performance function and the error conversion function, and perform derivative and parameter conversion on the first surface error; Step 1.3: Derivative the system tracking error, combine the first surface error derivative result, parameter conversion and system tracking error derivative result, and introduce the quadratic function and derive it; Step 1.4: According to the dynamic surface control algorithm and the derivative result of the quadratic function, the first surface error virtual control law is obtained; Step 1.5: Use a first-order low-pass filter to process the first-side error virtual control law to obtain a new variable z2.

3. The heliostat robust adaptive neural network sliding mode dynamic surface control method according to claim 2, characterized in that: The first surface error is: Where e(t) is the error conversion function, is the performance function, Φ -1 is a smooth decreasing function.

4. The heliostat robust adaptive neural network sliding mode dynamic surface control method according to claim 2, characterized in that: Step 2 is as follows: Step 2.1: Construct the second surface error based on the new variable z2 and take the derivative of the second surface error; Step 2.2: Introduce the quadratic function and take its derivative; Step 2.3: Use RBFNNs network to approximate the unknown term in the derivative of quadratic function; Step 2.4: According to the results of step 2.3, the second surface error virtual control law and parameter adjustment law are obtained; Step 2.5: Use a first-order low-pass filter to process the second surface error virtual control law to obtain a new variable z3.

5. The heliostat robust adaptive neural network sliding mode dynamic surface control method according to claim 1, characterized in that: The second surface error is: S2=x2-z2 Among them, x2 represents the second state variable.

6. The heliostat robust adaptive neural network sliding mode dynamic surface control method according to claim 4, characterized in that: Step 3 is as follows: Step 3.1: Construct the sliding surface according to the first surface error S1, the second surface error S2 and the new variable z3, and take its derivative; Step 3.2: Introduce the quadratic equation and take its derivative; Step 3.3: Use RBFNNs network to approximate the unknown term in the derivative of quadratic function; Step 3.4: Perform parameter conversion on the result in step 3.3; Step 3.5: Substitute the results of step 3.3 and step 3.4 into the sliding surface to obtain the actual control law and parameter adjustment law.

7. The heliostat robust adaptive neural network sliding mode dynamic surface control method according to claim 1, characterized in that: The sliding surface is: S m =m1S1+m2S2+S3 S3=x3-z3 Among them, m1 and m2 are both positive design parameters, and x3 represents the third state variable.

8. Heliostat robust adaptive neural network sliding mode dynamic surface control system, characterized in that: The system includes: Storage means for constructing a first surface error and introducing an error conversion function and a performance function; A storage device for constructing a second surface error and introducing an error conversion function and a performance function; A storage device for constructing a sliding surface according to the first surface error and the second surface error, and obtaining a control law according to the sliding surface; It is used to constrain the first surface error, the second surface error, the sliding surface and the parameter signals in the control law through the Lyapunov function, so that all parameter signals in the controller are ultimately uniformly bounded and converge to an arbitrarily small storage device.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the heliostat robust adaptive neural network sliding mode dynamic surface control method according to any one of claims 1 to 7 is executed.

10. A computer device, characterized in that: The device includes a memory and a processor, wherein a computer program is stored in the memory, and when the processor runs the computer program stored in the memory, the processor executes the heliostat robust adaptive neural network sliding mode dynamic surface control method according to any one of claims 1 to 7.

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