A nonlinear control method for an electric machine system

Abstract

The present application belongs to the technical field of motor nonlinear control, and particularly relates to a nonlinear control method for a motor system. The method first constructs an improved adaptive neural network backstepping controller, in the process of which a composite observer is constructed, the composite observer including a state observer and a disturbance observer to respectively achieve estimation of system states and external disturbances, and then the improved adaptive neural network backstepping controller constructed is used to control the motor system. The present application combines the composite observer with the adaptive neural network finite-time command filter control scheme, can estimate the unmeasurable states and disturbances in the system, and thus better controls the system, which is more practical in actual systems with many restrictions, so that the method of the present application can be more generally applicable in actual engineering.

Description

Technical Field

[0001] This invention belongs to the field of nonlinear control technology for motors, and specifically relates to a nonlinear control method for motor systems. Background Technology

[0002] In recent years, with the rapid development of artificial intelligence, human life has become increasingly intelligent, and various AI products are ubiquitous. Robotic arms are a typical example of intelligent products because they can repeatedly complete various expected tasks without ever getting tired, and are widely used in industrial production. Robotic arms combine the advantages of both humans and machines in their structure and performance, reflecting human intelligence and adaptability. Given these advantages, robotic arms have broad development prospects in all sectors of the national economy.

[0003] There are four main types of drive methods for robotic arms: hydraulic, pneumatic, electric, and mechanical. Electric drives are widely used in practical production due to their advantages such as convenient power supply, fast response, large driving force, and ease of signal detection, transmission, and processing. Among electric drives, the DC motors driving the robotic arm can be divided into brushed DC motors and brushless DC motors. Because brushless DC motors have multiple input characteristics, and there is a significant nonlinear coupling between their phase winding current and rotor speed, controlling brushless DC motors presents a significant challenge. Therefore, brushed DC motors are more widely used in robotic arm drive systems.

[0004] The aforementioned nonlinear motor system for a robotic arm driven by a brushed DC motor suffers from issues such as load variations, module malfunctions, external disturbances, and component losses. These problems introduce uncertainties into motor control, potentially rendering the original design methods ineffective. Furthermore, current technologies typically use state observers or disturbance observers to handle unmeasurable states and disturbances in the system. This approach can only handle individual unmeasurable parameters and has limited practicality. Summary of the Invention

[0005] The purpose of this invention is to provide a nonlinear control method for motor systems, which solves the problem of low practicality caused by the use of state observers or disturbance observers in the prior art to handle unmeasurable states and disturbances in the system.

[0006] To solve the above-mentioned technical problems, the technical solution provided by this invention and the corresponding beneficial effects of the technical solution are as follows:

[0007] The present invention provides a nonlinear control method for a motor system, comprising the following steps:

[0008] 1) Construct an improved backstepping controller based on an adaptive neural network. The process includes:

[0009] 1.1) Establish a mathematical model of the motor system and determine its state-space expression based on the mathematical model of the motor system;

[0010] 1.2) Construct a composite observer, which includes a state observer and a disturbance observer to estimate the system state x and the external disturbance φ, respectively;

[0011] 1.3) Using the constructed composite observer, the state-space expression is transformed to obtain the error equation of the motor system;

[0012] 1.4) Construct the Lyapunov function and design the virtual control law, the actual control law, and the adaptive law of the ideal weight vector of the neural network to stabilize the system;

[0013] 2) The improved adaptive neural network-based backstepping controller constructed in step 1) is used to control the motor system.

[0014] The beneficial effects of the above technical solution are as follows: This invention combines a composite observer with an adaptive neural network finite-time command filter control scheme, which can simultaneously estimate the unmeasurable states and disturbances in the system, thereby better controlling the system. This is more practical and general in real systems with many constraints, making the method of this invention more widely applicable in practical engineering.

[0015] Furthermore, the state observer and disturbance observer constructed in step 1.2) are respectively:

[0016]

[0017]

[0018] In the formula, Represents the i-th system state x i The estimated value; express The first derivative; ε i >0 represents a design parameter; W represents the ideal weight vector of the i-th neural network. i * The estimated value of S; i (·) represents the known basis functions of the i-th neural network; Represents the system state vector. express The estimated values; k1, k2, and k3 all represent constants; This represents the estimated value of the output signal y; Describes the i-th composite perturbation d i The estimated value; Denotes the i-th intermediate auxiliary variable e i The estimated value, e i =d i -ε i x i i = 1, 2, 3; H represents armature inductance; J represents the rotor inertia, K t Γ represents the conversion factor, m represents the link quality, P0 represents the link length, Γ0 represents the load quality, and t represents time.

[0019] Furthermore, the error equation of the motor system obtained in step 1.3) is as follows:

[0020]

[0021] In the formula, Represents the i-th system state x i The estimation error, Denotes the i-th intermediate auxiliary variable e i The estimation error, express The first derivative; This represents the estimation error of the ideal weight vector of the i-th neural network. d i The first derivative.

[0022] Furthermore, the method described in step 1.4) for designing the virtual control law, the actual control law, and the adaptive law for the unknown parameters of the neural network to stabilize the system includes:

[0023] 1.4.1) Utilizing the first compensated tracking error signal υ1 and the estimation error of the ideal weight vector of the first neural network Construct the first Lyapunov function V1, design the second virtual control law α2 to stabilize the system, and estimate the error of the ideal weight vector of the first neural network. Adaptive law

[0024] 1.4.2) Utilizing the second compensation tracking error signal υ2 and the estimation error of the ideal weight vector of the second neural network Construct the second Lyapunov function V2, design the third virtual control law α3 to stabilize the system, and estimate the error of the ideal weight vector of the second neural network. Adaptive law

[0025] 1.4.3) Estimation error using the third compensated tracking error signal υ3 and the ideal weight vector of the third neural network Construct the third Lyapunov function V3, design the actual control law v that stabilizes the system, and estimate the error of the ideal weight vector of the third neural network. Adaptive law

[0026] Furthermore, the estimation errors of the first Lyapunov function V1, the second virtual control law α2, and the ideal weight vector of the first neural network... Adaptive law They are respectively:

[0027]

[0028]

[0029]

[0030] In the formula, ε1, h1, k b1 σ1 and W1 both represent positive constants. * S1 represents the ideal weight vector of the first neural network; S1(·) represents the basis functions of the first neural network. Represents the state vector of the first system The estimated value; This represents the estimated value of the first composite disturbance d1; λ represents the design parameters; λ1 represents the output of the first auxiliary system; z1 represents the state error of the first system; l represents a positive constant and 0 < l < 1; This represents the estimated ideal weight vector of the first neural network.

[0031] The beneficial effects of the above technical solution are as follows: the barrier Lyapunov function (IBF) is introduced, that is, the Lyapunov function is constructed in logarithmic form, which can effectively constrain the state of the system within a certain range, making it more practical in actual engineering applications.

[0032] Furthermore, the estimation errors of the second Lyapunov function V2, the third virtual control law α3, and the ideal weight vector of the second neural network... Adaptive law They are respectively:

[0033]

[0034]

[0035]

[0036] In the formula, ε2>0, h2>0, k b2 >0 and σ2>0 both represent design parameters; S1 represents the ideal weight vector of the second neural network; S2(·) represents the basis functions of the second neural network; Represents the state vector of the second system The estimated value; This represents the estimated value of the first composite disturbance d2; α2 represents the first derivative of the output signal of the fractional-order filter corresponding to the second virtual control signal α2; z2 represents the second system state error; λ2 represents the output of the second auxiliary system. This represents the estimated ideal weight vector of the second neural network.

[0037] The beneficial effects of the above technical solution are as follows: the barrier Lyapunov function (IBF) is introduced, that is, the Lyapunov function is constructed in logarithmic form, which can effectively constrain the state of the system within a certain range, making it more practical in actual engineering applications.

[0038] Furthermore, the estimation errors of the third Lyapunov function V3, the actual control law v, and the ideal weight vector of the third neural network are... Adaptive law They are respectively:

[0039]

[0040]

[0041]

[0042] In the formula, ε3>0, h3>0, k b3 >0、 σ3>0 all represent design parameters; S3 represents the ideal weight vector of the third neural network; S3(·) represents the basis functions of the third neural network. Represents the state vector of the third system The estimated value; This represents the estimated value of the third composite disturbance d3; This represents the first derivative of the output signal of the fractional filter corresponding to the actual control signal v; Indicates the reference signal y r The third derivative; z3 represents the state error of the third system; λ3 represents the output of the second auxiliary system; This represents the estimated ideal weight vector of the third neural network.

[0043] The beneficial effects of the above technical solution are as follows: the barrier Lyapunov function (IBF) is introduced, that is, the Lyapunov function is constructed in logarithmic form, which can effectively constrain the state of the system within a certain range, making it more practical in actual engineering applications.

[0044] Furthermore, prior to step 1.4), an error compensation mechanism is introduced to address the issue of the fractional-order filter τ. i D q ω i +ω i =α i Filtering error (ω) i -α i The error compensation mechanism is as follows, taking into account the influence of ( ).

[0045]

[0046] In the formula, τ i Let D represent the time constant at time i. q This represents the fraction operator, where q represents a positive constant and 0 < q < 1; ω i α represents the output signal of the i-th fractional-order filter; i ξ represents the input signal of the i-th fractional-order filter; i h represents the i-th error compensation signal; i Represents positive integers; Indicates ξ i The first derivative of ; i = 1, 2, 3.

[0047] The beneficial effects of the above technical solution are as follows: the introduction of a fractional-order filter overcomes the problem of repeated differentiation of the virtual control signal in the traditional adaptive backstepping control framework, thereby reducing the corresponding computational burden, and the introduction of an error compensation mechanism solves the influence of filtering error. It has wide applicability and greater research value.

[0048] Furthermore, an auxiliary system is introduced to reduce the impact of system input saturation. This auxiliary system is:

[0049]

[0050]

[0051] In the formula, λ1 and λ2 represent the outputs of the first and second auxiliary systems, respectively; Denote the first derivatives of λ1 and λ2; The design parameters are represented by Δu = u(v) - v, where u(v) represents the actual control input and v represents the control input to be designed.

[0052] The beneficial effect of the above technical solution is that introducing an auxiliary system can reduce the impact of system input saturation.

[0053] Further, the state-space expression described in step 1.1) is:

[0054]

[0055] In the formula, x i Indicates the state of the i-th system; x represents i The first derivative; v represents the control input to be designed; y represents the system output; K D R represents the back electromotive force coefficient; R0 represents the armature resistance; H represents the armature inductance; J represents the rotor inertia, K t Γ0 represents the conversion factor, m represents the link quality, P0 represents the link length, and Γ0 represents the load quality. B0 represents the coefficient of viscous friction; G represents the gravity coefficient; t represents time; u(v) represents the actual control input of the system affected by asymmetric saturated nonlinearity, and is influenced by the following formula:

[0056]

[0057] In the formula, u M >0,u m <0 indicates that the input saturation constant is known. Attached Figure Description

[0058] Figure 1 This is a flowchart of the nonlinear control method for motor systems according to the present invention;

[0059] Figure 2 This is a control block diagram of the motor system of the present invention;

[0060] Figure 3 This is a diagram showing the reference signal, tracking trajectory, and estimated tracking trajectory values ​​of the present invention.

[0061] Figure 4 This is a tracking error diagram of the motor system of the present invention;

[0062] Figure 5 This invention provides a state estimation and constraint diagram for the first system.

[0063] Figure 6 This is the second system state estimation and constraint diagram of the present invention. Detailed Implementation

[0064] This invention is based on an adaptive neural network backstepping control strategy and combines an adaptive finite-time command filter with a composite observer to apply to a fully state-constrained motor system, thereby realizing a nonlinear control method for motor systems. Its control block diagram is shown below. Figure 2 As shown. The overall design goal is to design a controller v such that the output y can asymptotically track the reference signal y. r And ensure that the tracking error j = yy rIt converges to a small set of residuals that are zero within a fixed time interval, thus effectively reducing the computational load and accelerating the convergence speed. The overall process is as follows: Figure 1 As shown below, a detailed introduction will follow.

[0065] Step 1: Establish a mathematical model of the motor system. Considering that the actual physical system is affected by external disturbances and input saturation, modeling errors are inevitable. Based on the mathematical model of the motor system, obtain the state-space expression of the motor system.

[0066] 1. Express the mathematical model of the motor system using the following formula:

[0067]

[0068] In the formula, r represents the position of the angle motor; I represents the armature current of the motor; V Τ Indicates the input control voltage; Other parameters are detailed in Table 1 below.

[0069] Table 1

[0070]

[0071]

[0072] 2. Based on the mathematical model of the motor system, the state-space expression of the motor system is obtained:

[0073]

[0074] In the formula, x1 represents the i-th system state; Let represent the first derivative of the i-th system state; i = 1, 2, 3; y represent the system output; v represent the control input to be designed; u(v) represent the actual control input, and is affected by the following formula: In the formula, u M >0, u m <0 indicates that the input saturation constant is known.

[0075] Step 2: Construct a composite observer, which includes a state observer and a disturbance observer. Use the constructed composite observer to estimate the unmeasurable system states and external disturbances in the state-space expression of the motor system, so as to better control the system.

[0076] 1. Construct a state observer.

[0077] The state-space expression of the motor system in step one can be rewritten in the following form:

[0078]

[0079] In the formula, u(v) represents the actual control input; Represents the system state vector. express The estimated value; Let i represent the i-th unknown smooth function; i = 1, 2, 3.

[0080] Using neural networks Approximating an unknown smooth function Let ε represent the minimum approximation error of the i-th neural network. i W represents the design parameters. i * Let S represent the ideal weight vector of the i-th neural network. i (·) represents the known basis functions of the i-th neural network. Represents the system state vector; express From the estimated value, we can further obtain:

[0081]

[0082] In the formula, d i Let i represent the i-th composite perturbation.

[0083] Based on the above, the following state observer is constructed:

[0084]

[0085] In the formula, Let x represent the i-th system state respectively. i The i-th composite disturbance d i The ideal weight vector W of the i-th neural network i * The system output is an estimated value of y; k1, k2, and k3 are all constants and satisfy A T P+PA≤-Q, P = P T It is a positive definite matrix; Q = Q T >0.

[0086] 2. Construct a disturbance observer.

[0087] make Based on the above, the state error system can be obtained as follows:

[0088]

[0089] In the formula, and

[0090] To design a disturbance observer to estimate the disturbance, an i-th intermediate auxiliary variable e is introduced. i Let e1 = d1 - ε1x1, e2 = d2 - ε2x2, and e3 = d3 - ε3x3, respectively. Taking their derivatives, we get:

[0091]

[0092] Further estimates of the various intermediate auxiliary variables can be obtained:

[0093]

[0094] The perturbation observer can then be represented as:

[0095]

[0096] 3. Using the constructed composite observer, the state-space expression is transformed to obtain the error equation of the motor system.

[0097]

[0098] In the formula, z i υ represents the tracking error of the i-th digit; i This indicates that the i-th compensation tracking error is being compensated. Indicates the reference signal y r The (i-1)th derivative; λ i ξ represents the output of the i-th auxiliary system; i ω represents the i-th error compensation signal; i This represents the output signal of the i-th fractional-order filter.

[0099] make The error system equation can then be expressed as:

[0100]

[0101] 4. Prove that in the composite error system consisting of (6) and (11), there exists a positive definite Lyapunov function. Its first derivative satisfies Where, P = P T It is a positive definite matrix; Q = Q T >0. Q represents a matrix and Q = Q T >0, ε M =max{ε1,ε2,ε3}, ε i Indicate design parameters; a0 represents the design parameter, and a0 > 0. b0 = max{b1,b2,b3}; diM >0 and satisfy Specifically:

[0102] Based on the system's state estimation error The estimation error of the introduced auxiliary variable e Constructing Lyapunov functions Differentiating it, we get:

[0103]

[0104] Using Young's inequality, we can obtain:

[0105]

[0106] In the formula, b0 = max{b1,b2,b3}; ε m =min{ε1,ε2,ε3}, ε M =max{ε1,ε2,ε3}; ||·|| denotes the Euclidean norm of a vector.

[0107] Substituting equation (13) into equation (12), we get:

[0108]

[0109] In the formula,

[0110] Step 3: Introduce a fractional-order filter τ i D q ω i +ω i =α i This overcomes the problem of repetitive differentiation of the virtual control signal in the traditional adaptive backstepping control framework, thereby reducing the corresponding computational burden, and ω i (0)=α i (0). The following error compensation mechanism is introduced to solve the filtering error (ω). i -α i The influence of ω i Let α represent the output signal of the i-th fractional-order filter. i Let τ represent the input signal of the i-th fractional-order filter. i Let D represent the time constant at time i. q This represents the fraction operator, where q represents a positive constant and 0 < q < 1.

[0111]

[0112] In the formula, ξ i h represents the i-th error compensation signal; i Represents positive integers; Indicates ξ i The first derivative of ; i = 1, 2, 3.

[0113] Furthermore, an auxiliary system needs to be introduced to reduce the impact of input saturation. The error between the saturated input and the actual control input is used as the input to this system, λ. i As the output of the auxiliary system, this system can be represented by the following formula:

[0114]

[0115] In the formula, The parameter to be designed is Δu = u(v) - v.

[0116] For the first compensated tracking error signal υ i Differentiation yields:

[0117]

[0118] In the formula, ε1>0, h1>0, k1>0, All of these represent design parameters.

[0119] Step four: Utilize the first compensated tracking error signal υ1 and the estimation error of the ideal weight vector of the first neural network. Construct the first Lyapunov function V1, and design the second virtual control law α2 to stabilize the system and the estimation error of the ideal weight vector of the first neural network. Adaptive law Specifically:

[0120] 1. Construct the first Lyapunov function in, k b1 Represents the positive constants of the design; This represents the parameter estimation error.

[0121] 2. Differentiating the first Lyapunov function V1 yields:

[0122]

[0123] In the formula, ξ1 represents the first error compensation signal; express The transpose of .

[0124] 3. Estimation errors of the designed second virtual control law α2 and the ideal weight vector of the first neural network. Adaptive law They are respectively:

[0125]

[0126]

[0127] In the formula, ε1, h1, k b1 σ1 and σ1 both represent positive constants; z1 represents the first system state error; l represents a positive constant and 0 < l < 1.

[0128] 4. Substituting the designed virtual control law and adaptive law into equation (18), we can obtain:

[0129]

[0130] 5. Using Young's inequality, we can obtain:

[0131]

[0132]

[0133]

[0134] In the formula, ||·|| represents the Euclidean norm of the vector.

[0135] Substituting equations (22) to (24) into equation (21), we get:

[0136]

[0137] Step 5: Utilize the second compensated tracking error signal υ2 and the estimation error of the ideal weight vector of the second neural network. Construct the second Lyapunov function V2, and design the third virtual control law α3 to stabilize the system and estimate the ideal weight vector of the second neural network. Adaptive law Specifically:

[0138] 1. Construct the second Lyapunov function in, k b2 For the design of positive constants; For parameter estimation error; the first derivative of the second compensation tracking error signal υ2 for:

[0139]

[0140] In the formula, ε2>0, h2>0, k2>0, All represent the design parameters; S2 represents the basis functions of the second neural network; Represents the ideal weight vector of the second neural network The estimated value; This represents the estimated value of d2; υ3 represents the first derivative of the output signal of the fractional-order filter corresponding to the second virtual control signal α2; υ3 represents the third tracking compensation signal; and ξ2 represents the second error compensation signal.

[0141] 2. Differentiate the second Lyapunov function V² and use a neural network. Approximating an unknown smooth function We can obtain:

[0142]

[0143] In the formula, ξ2 represents the second error compensation signal.

[0144] 3. Design the third virtual control law α3 and estimate the ideal weight vector of the second neural network. Adaptive law They are respectively:

[0145]

[0146]

[0147] In the formula, ε2, h2, k b2 σ2 and σ2 both represent positive constants; z2 represents the second system state error.

[0148] 4. Design the third virtual control law α3 and the adaptive law. Substituting into equation (27), we get:

[0149]

[0150] 5. Using Young's inequality, we can obtain:

[0151]

[0152]

[0153]

[0154] In the formula, ||·|| represents the Euclidean norm of the vector.

[0155] Substituting equations (31) to (33) into equation (30), we get:

[0156]

[0157] Step 6: Utilize the third compensated tracking error signal υ3 and the estimation error of the ideal weight vector of the third neural network. Construct the third Lyapunov function V3, and design the actual control signal v that stabilizes the system and the estimation error of the ideal weight vector of the third neural network. Adaptive law Specifically:

[0158] 1. Construct the third Lyapunov function in, k b3 For the design of positive constants; For parameter estimation error; the first derivative of the third compensation tracking error signal υ3 for:

[0159]

[0160] In the formula, ε3>0, h3>0, k3>0, All represent design parameters; S3 represents the basis functions of the third neural network; Represents the ideal weight vector of the third neural network The estimated value; This represents the estimated value of d3; ξ3 represents the first derivative of the output signal of the fractional filter corresponding to the actual control signal v; ξ3 represents the third error compensation signal. Indicates the reference signal y r The third derivative of .

[0161] 2. Differentiate the third Lyapunov function V3 and use a neural network. Approximating an unknown smooth function We can obtain:

[0162]

[0163] In the formula, ξ3 represents the third error compensation signal.

[0164] 3. The estimation error of the actual control signal v and the ideal weight vector of the third neural network. Adaptive law They are respectively:

[0165]

[0166]

[0167] In the formula, ε3, h3, k b3 σ3 and z3 both represent positive constants; z3 represents the state error of the third system.

[0168] 4. Substituting the actual control law and adaptive law of the design into equation (36), we can obtain:

[0169]

[0170] 5. Using Young's inequality, we can obtain:

[0171]

[0172]

[0173] In the formula, ||·|| represents the Euclidean norm of the vector.

[0174] Substituting equations (40) to (41) into equation (39), we get:

[0175]

[0176] Step 7: Construct the Lyapunov function V = V0 + V1 + V2 + V3 using V0, V1, V2, and V3, that is:

[0177]

[0178] Taking its derivative, we get:

[0179]

[0180] Based on Lemma 1: Where z, μ, α, θ, and ι all represent positive constants. Let z = 1, μ = 1 - l, θ = l, We can obtain:

[0181]

[0182] Similarly, we can obtain:

[0183]

[0184]

[0185] Substituting equations (45), (46), and (47) into equation (40) yields:

[0186]

[0187] Based on Lemma 2: for any υ i Satisfy |υ i |<k bi ,but Where, k bi >0, we can get:

[0188]

[0189] According to equations (30) to (36), let:

[0190]

[0191]

[0192]

[0193] Therefore, we can obtain:

[0194]

[0195] According to Lemma 3: Suppose V(x) is a positive definite function and has the following form:

[0196]

[0197] Among them, π1, π2>0, 0<l<1, 0<ρ<∞.

[0198] This proves that the origin of the system has achieved practical finite-time stability.

[0199] Therefore, the motor system can be concluded that it meets the actual finite-time stability requirement.

[0200] Step eight: Following the methods in steps one through seven, the adaptive neural network-based backstepping controller of this invention can be designed and applied to the motor system to control the motor system.

[0201] When the method of this invention is applied to a motor system, the reference signal, tracking trajectory, and trajectory tracking conditions are as follows: Figure 3 As shown, the tracking error is as follows Figure 4 As shown, the estimation and constraints of the system state are as follows: Figure 5 and Figure 6 As shown in the figure, the designed control method can effectively constrain and estimate the system state, and has good tracking performance.

[0202] In summary, the method of the present invention has the following characteristics:

[0203] 1) This invention utilizes the finite-time command filtering method and, by combining the approximation capability of neural networks and the method of composite observers, establishes a finite-time adaptive controller, which enables the tracking error to strictly converge to the zero neighborhood range within a finite time.

[0204] 2) This invention combines a composite observer with an adaptive neural network finite-time command filtering control scheme, which can estimate the unmeasurable states and disturbances in the system, thereby better controlling the system. This is more practical in real systems with many constraints, making the method of this invention more widely applicable in practical engineering.

[0205] 3) This invention proposes a novel finite-time command filter, which not only successfully avoids the problem of "computational complexity", but also introduces an improved error compensation mechanism to effectively reduce the error impact of fractional-order filters. This method has wide applicability and greater research value.

[0206] 4) This invention introduces the barrier Lyapunov function (IBF), that is, the Lyapunov function is constructed in logarithmic form, which can effectively constrain the state of the system within a certain range, which is more common and practical in actual engineering applications.

[0207] 5) For the processing of unknown functions, this invention uses a neural network to approximate the unknown terms, which has better approximation ability.

Claims

1. A nonlinear control method for a motor system, characterized in that, include: 1) Constructing an adaptive neural network-based backstepping controller, the process includes: Establish a mathematical model of the motor system, and determine its state-space expression based on the mathematical model of the motor system; Construct a composite observer that includes a state observer and a disturbance observer to separately monitor the system state. and external disturbances The estimate; Using the constructed composite observer, the state-space expression is transformed to obtain the error equation of the motor system; Construct the Lyapunov function, and design the virtual control law and actual control input to stabilize the system based on the following process. The adaptive law of the ideal weight vector in a neural network: Using the first compensation tracking error signal The estimation error of the ideal weight vector of the first neural network Constructing the first Lyapunov function Design a second virtual control law to stabilize the system. And adaptive law : Using the second compensation tracking error signal Estimation error of the ideal weight vector of the second neural network Constructing the second Lyapunov function The design of a third virtual control law to stabilize the system. And adaptive law : Using the third compensation tracking error signal The estimation error of the ideal weight vector of the third neural network Constructing the third Lyapunov function The design makes the system stable And adaptive law : All are positive numbers; , , , , These are all design parameters; , , These are the ideal weight vectors for the first, second, and third neural networks, respectively. , , These are the basis functions of the first, second, and third neural networks, respectively. , , These are the state vectors of the first system. Second system state vector The third system state vector The estimated value; , , The first composite disturbance Second composite disturbance Third composite disturbance The estimated value; For design parameters; , , The outputs are for the first, second, and third auxiliary systems, respectively. , , These are the first, second, and third system state errors, respectively. are positive numbers and ; , , ; , , These are the estimated values ​​of the ideal weight vectors for the first, second, and third neural networks, respectively. for The first derivative of the output signal of the corresponding fractional-order filter; for The first derivative of the output signal of the corresponding fractional-order filter; Reference signal The third derivative; 2) Use the results of 1) to control the motor system.

2. The nonlinear control method for a motor system according to claim 1, characterized in that, The constructed state observer is: In the formula, Indicates the first System status The estimated value; express The first derivative; For design parameters; Indicates the first Ideal weight vector of a neural network The estimated value; Represents the known first Basis functions of neural networks; Represents the system state vector. ; express The estimated value; , , Both represent constants; Indicates the output signal The estimated value; Indicates the first Composite disturbance The estimated value; ; Indicates armature inductance; , Indicates rotor inertia. Indicates the conversion factor. Indicates link quality. Indicates the link length. Indicates load quality; Indicates time; Indicates saturated input. This represents the actual control input.

3. The nonlinear control method for a motor system according to claim 2, characterized in that, The constructed perturbation observer is: In the formula, Indicates the first intermediate auxiliary variables The estimated value, .

4. The nonlinear control method for a motor system according to claim 3, characterized in that, The error equation of the motor system obtained by conversion is: In the formula, Indicates the first System status The estimation error, ; Indicates the first intermediate auxiliary variables The estimation error, ; express The first derivative; Indicates the first The estimation error of the ideal weight vector of a neural network. ; express The first derivative.

5. The nonlinear control method for a motor system according to claim 1, characterized in that, The mathematical model of the motor system is: In the formula, ; Indicates the angular position of the motor; ; ; Indicates the armature current of the motor; Indicates armature inductance; Indicates the input control voltage; Indicates armature resistance; Indicates the back electromotive force coefficient; Indicates rotor inertia; Indicates the conversion factor; Indicates link quality; Indicates the link length; Indicates load quality; Indicates the coefficient of viscous friction; This represents the gravity coefficient.

6. The nonlinear control method for a motor system according to claim 1, characterized in that, The goal of constructing the improved adaptive neural network-based backstepping controller is to make the output... Able to progressively track reference signal And ensure tracking error Within a small set of residuals that converge to zero over a fixed time interval.

7. The nonlinear control method for a motor system according to claim 1, characterized in that, Before constructing the Lyapunov function, an error compensation mechanism is also introduced to solve the problem of fractional-order filters. To mitigate the impact of filtering errors, the error compensation mechanism is as follows: In the formula, Indicates the first Time constant, Represents fraction operators, Represents positive numbers and ; Indicates the first The output signal of a fractional-order filter; Indicates the first Error compensation signal; Represents positive numbers; express The first derivative; .

8. The nonlinear control method for a motor system according to claim 7, characterized in that, An auxiliary system is also introduced to reduce the impact of system input saturation. The auxiliary system is as follows: In the formula, These represent the outputs of the first auxiliary system and the second auxiliary system, respectively. They represent The first derivative; Indicate design parameters; , Indicates saturated input. This represents the actual control input.

9. The nonlinear control method for a motor system according to claim 1, characterized in that, The state-space expression is: In the formula, Indicates the first System status; express The first derivative; This indicates the control input to be designed; Indicates the actual output of the system; Indicates the back electromotive force coefficient; Indicates armature resistance; Indicates armature inductance; , Indicates rotor inertia. Indicates the conversion factor. Indicates link quality. Indicates the link length. Indicates load quality; , Indicates the coefficient of viscous friction; , Indicates the gravity coefficient; Indicates time; This indicates saturated input.

10. The nonlinear control method for a motor system according to claim 9, characterized in that, for: In the formula, This represents the known input saturation constant.

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