Asynchronous motor finite time adaptive control method and system considering preset performance and input saturation

Abstract

The invention belongs to the technical field of asynchronous motor position tracking control, discloses an asynchronous motor finite time adaptive control method and system considering preset performance and input saturation, and aims at the control precision requirement of an asynchronous motor random system and the problems of random disturbance and nonlinearity. And designing an asynchronous motor random system finite time self-adaptive controller considering preset performance and input saturation so as to track a target position. According to the control method, a Lyapunov function is constructed to ensure that state variables such as current and rotating speed do not violate physical constraint conditions, unknown nonlinear terms in an asynchronous motor random system are processed by utilizing a fuzzy logic theory, and a method of combining an instruction filtering technology and an error compensation mechanism is adopted; the problem of calculation explosion in a traditional backstepping method is solved, meanwhile, the influence of filtering errors is eliminated, the influence of input saturation and random disturbance can be effectively restrained, rapid convergence of system tracking errors is achieved, and the control performance of the system is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of asynchronous motor position tracking control, and in particular relates to a finite-time adaptive control method and system for an asynchronous motor taking into account preset performance and input saturation. Background Art

[0002] In recent years, with the rapid development of power electronics technology, the comprehensive performance of asynchronous motors has been significantly improved. With its simple structure, strong practicality and high reliability, it has been widely used in production and transportation. However, the dynamic model of asynchronous motors has the characteristics of strong coupling, multivariable, nonlinear and high order. In order to overcome the above shortcomings, scholars have proposed many effective nonlinear control methods for the controller design problem of asynchronous motor systems, such as backstepping, sliding mode control, fuzzy adaptive and other advanced control methods.

[0003] Among them, the backstepping control method is an effective control method for nonlinear systems, but in the process of designing the controller, there will be a problem of computational explosion caused by repeated derivation. To address this problem, scholars have proposed dynamic surface control technology, which is to introduce a first-order filter to approximate the derivative of the virtual control function, thereby simplifying the calculation process. However, the dynamic surface control technology has the problem of reducing the control accuracy of the system due to the filtering error generated by the first-order filter. Compared with the dynamic surface control technology, the instruction filtering technology introduces an error compensation mechanism, which not only solves the problem of computational explosion, but also compensates for the filtering error, making the system more accurate.

[0004] However, the above method does not take into account the actual situation of motor operation. In fact, during the actual operation of asynchronous motors, relevant parameters such as motor torque and winding resistance will change due to factors such as damping torque and magnetic saturation. Such random disturbances will reduce the performance of asynchronous motors. At the same time, in actual operation, the saturation of input voltage should be considered according to the physical constraints and mechanical design of asynchronous motors to keep the voltage within a reasonable range.

[0005] Secondly, compared with the method of gradual convergence to obtain asymptotically stable results, the finite-time control method has greater advantages. It can improve the response speed and convergence speed and ensure that the system state trajectory converges to the origin or the neighborhood near the origin within a finite time.

[0006] In addition, the design of typical control systems mainly focuses on the stability of the equilibrium point and the convergence time of the system, but pays less attention to the instantaneous performance and steady-state performance of the system, and can only improve the system performance by optimizing parameters later. In response to this, scholars have proposed the concept of a preset performance function, which ensures that the tracking error is constrained within a pre-set arbitrarily small neighborhood and that the instantaneous performance and steady-state performance of the system meet the pre-set conditions, thereby greatly improving the performance of the system.

[0007] Therefore, it is of great significance to realize the finite-time preset performance control of the random system of asynchronous motor considering input saturation. Summary of the invention

[0008] The purpose of the present invention is to propose a finite-time adaptive control method for an asynchronous motor taking into account preset performance and input saturation. The method can constrain the tracking error of the system, improve the performance of the asynchronous motor, and enable the asynchronous motor random system to quickly track the desired signal while fully considering input saturation and random disturbances.

[0009] In order to achieve the above object, the present invention adopts the following technical scheme:

[0010] A method for finite-time adaptive control of an asynchronous motor considering preset performance and input saturation, characterized in that it comprises the following steps:

[0011] Step 1. Establish a dynamic mathematical model of the asynchronous motor considering random interference;

[0012] Step 2. Based on the dynamic mathematical model of the asynchronous motor constructed in step 1, design a finite-time adaptive controller for a random system of an asynchronous motor for realizing position tracking control of the asynchronous motor taking into account preset performance and input saturation;

[0013] Step 3. Use the finite-time adaptive controller of the asynchronous motor random system to realize the position tracking control of the asynchronous motor.

[0014] In addition, based on the finite-time adaptive control method of an asynchronous motor considering preset performance and input saturation, the present invention also proposes a finite-time adaptive control system of an asynchronous motor considering preset performance and input saturation, and its technical solution is as follows:

[0015] An asynchronous motor finite time adaptive control system considering preset performance and input saturation includes the following modules:

[0016] A model building module is used to build a dynamic mathematical model of the asynchronous motor taking into account random interference;

[0017] A controller design module is used to design a finite-time adaptive controller of a random system of an asynchronous motor for realizing position tracking control of the asynchronous motor based on a dynamic mathematical model of the asynchronous motor, taking into account preset performance and input saturation;

[0018] And a tracking control module is used to realize the position tracking control of the asynchronous motor by using the finite time adaptive controller of the asynchronous motor random system.

[0019] In addition, based on the above-mentioned method for adaptive control of an asynchronous motor in a limited time considering preset performance and input saturation, the present invention further proposes a computer device, which includes a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it is used to implement the steps of the above-mentioned method for adaptive control of an asynchronous motor in a limited time considering preset performance and input saturation.

[0020] In addition, based on the above-mentioned method for adaptive control of an asynchronous motor in a limited time considering preset performance and input saturation, the present invention further proposes a computer-readable storage medium on which a program is stored. When the program is executed by a processor, it is used to implement the steps of the above-mentioned method for adaptive control of an asynchronous motor in a limited time considering preset performance and input saturation.

[0021] The present invention has the following advantages:

[0022] (1) The method of the present invention is aimed at the random system of asynchronous motors, and takes input saturation into consideration in the controller design, thereby avoiding damage to the motor caused by the input saturation problem. At the same time, the preset performance function and the finite time control strategy are combined to strictly constrain the system tracking error within the actual required range and converge within a finite time, thereby improving the convergence speed of the system, reducing the overshoot of the system tracking error, and improving the transient response performance of the system.

[0023] (2) The present invention adopts the fuzzy logic system approximation method to deal with the unknown nonlinear function in the random system of the asynchronous motor, simplifies the structure of the controller, and effectively solves the problem of position tracking control of the asynchronous motor under the conditions of parameter uncertainty and load torque disturbance.

[0024] (3) The present invention combines instruction filtering technology with error compensation mechanism, which not only fundamentally solves the problem of computational explosion, but also reduces the impact of filtering error on system performance, thereby improving the control accuracy of the system.

[0025] (4) The present invention takes into account the random interference occurring during the operation of the motor when designing the controller, thereby improving the robustness and stability of the system and making the designed finite-time adaptive controller for the random system of the asynchronous motor more conducive to practical application. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 The flowchart of the finite-time adaptive control method of an asynchronous motor considering preset performance and input saturation in an embodiment of the present invention.

[0027] Figure 2 The system block diagram of the finite-time adaptive control method for an asynchronous motor considering preset performance and input saturation in an embodiment of the present invention.

[0028] Figure 3 This is a simulation diagram of the rotor angle and rotor angle setting value tracking using the control method of the present invention.

[0029] Figure 4 The figure is a simulation diagram of the rotor angle, angle tracking error and its constraints using the control method of the present invention.

[0030] Figure 5 It is a simulation diagram of rotor flux and rotor flux set value tracking using the control method of the present invention.

[0031] Figure 6 The figure is a simulation diagram of the D-axis stator voltage of an asynchronous motor using the control method of the present invention.

[0032] Figure 7 The figure is a simulation diagram of the q-axis stator voltage of an asynchronous motor using the control method of the present invention.

[0033] Figure 8 is the state quantity x of the asynchronous motor using the control method of the present invention 2 Simulation diagram of .

[0034] Fig. 9 is the state quantity x of the asynchronous motor using the control method of the present invention 3 Simulation diagram of .

[0035] Fig.10 is the state quantity x of the asynchronous motor using the control method of the present invention 5 Simulation diagram of . DETAILED DESCRIPTION

[0036] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0037] Example 1

[0038] This embodiment provides a finite-time adaptive control method based on the random system model of the asynchronous motor. This method aims at the performance improvement problem in the position tracking control of the random system of the asynchronous motor, and constructs a finite-time preset performance function to constrain the position tracking error of the asynchronous motor. Secondly, the fuzzy logic system is used to deal with the random disturbance problem in the system to improve the robustness of the system. Furthermore, based on the finite-time control strategy and taking the voltage saturation phenomenon of the asynchronous motor into consideration, the system controller is designed so that the tracking error of the system converges within a finite time. Finally, the instruction filtering technology is used to solve the computational explosion problem in the backstepping method, and the error compensation mechanism is introduced to eliminate the influence of the filtering error.

[0039] like Figure 1 As shown, the finite time adaptive control method of an asynchronous motor considering preset performance and input saturation includes the following steps:

[0040] Step 1. Establish a dynamic mathematical model of the asynchronous motor considering random interference.

[0041] The dq coordinate axis dynamic mathematical model of the asynchronous motor is established, as shown in formula (1):

[0042]

[0043] Among them, θ represents the rotor angle of the asynchronous motor, ω represents the rotor angular velocity, and θ and ω are both state variables of the asynchronous motor system. p represents the number of pole pairs, L m represents mutual inductance, J represents moment of inertia, L r and L s They represent the rotor leakage inductance and the stator leakage inductance respectively, represents the rotor flux, i d and i q denote the d-axis and q-axis stator currents respectively, T L Represents load torque, R r and R s They represent the rotor resistance and stator resistance respectively, u d and u q represent the d-axis and q-axis stator voltages respectively.

[0044] In order to simplify the dq axis dynamic mathematical model of the asynchronous motor, the following variables are defined:

[0045]

[0046] When random interference is considered, the dynamic mathematical model of the dq coordinate axis of the asynchronous motor is shown in formula (2):

[0047]

[0048] in, is an unknown smooth disturbance function.

[0049] Step 2. Based on the dynamic mathematical model of the asynchronous motor constructed in step 1, design a finite-time adaptive controller for a random system of an asynchronous motor for realizing position tracking control of the asynchronous motor taking into account preset performance and input saturation.

[0050] Based on the command filtering technology and the principle of adaptive backstepping, a finite-time adaptive controller for a random asynchronous motor system is designed considering preset performance and input saturation. Its control goal is to design the input signal u of the random asynchronous motor system. d and u q , so that the position tracking error of the system converges within a finite time and reduces its overshoot, and the system input is constrained within a preset range to achieve position tracking control of the asynchronous motor.

[0051] Before specifically introducing step 2 of the control method of the present invention, the following concepts are first explained:

[0052] For the following asynchronous motor random system: dx=g(x)dt+μ(x)dw.

[0053] in, is the state variable of the asynchronous motor random system, Indicates n 0 dimensional real vector set, w∈R r is the standard Brownian motion, R r represents a set of r-dimensional real vectors. g(x) and μ(x) are local Lipschitz functions, and satisfy the initial value of g(x) g(0)=μ(0)=0, where g(0) represents the initial value of g(x) and μ(0) represents the initial value of μ(x).

[0054] Any given V(x)∈C 2 , where V(x) represents the Lyapunov function of the system, C 2 represents the set of complex numbers and defines the differential function Depend on The differential law tells us:

[0055]

[0056] in, express The correction term, Tr, represents the sum of the diagonal elements.

[0057] Take any real number λ 1 >0,λ 2>0, 0<τ<1, 0<η<∞, if the asynchronous motor random system satisfies:

[0058]

[0059] Then the system is actually finite-time stable and converges to a tight set Ω:

[0060]

[0061] Among them, T r represents the convergence time of the asynchronous motor random system, 0<θ 0 <1.

[0062] Convergence time T r for:

[0063]

[0064] Among them, t 0 represents the starting time, V(t 0 ) indicates t 0 The value of the Lyapunov function at time .

[0065] Assume f(x) is a continuous function defined on a compact set Ω, there exists a constant δ(z)>0 and a fuzzy logic system W T S(x), so that f(x) = W T S(x)+δ(z), and for any ε>0, we have Where ε is a constant, δ(z) is the approximation error, W is the fuzzy weight vector, S(x) is the basis function vector, S(x) = [p 1 (x),…,p N (x)] T . p m (x) is a Gaussian function used to select fuzzy sets, that is η m is the center vector, ρ m is the width of the Gaussian function, m=1,...,N, where N is a positive integer.

[0066] For real numbers κ and χ, and arbitrary real variables z, o, and s, we have:

[0067]

[0068] The above formula is used for stability proof.

[0069] Treat the constraint error signal e(t), the continuous function ρ(t): R + →R + The performance function is preset for a finite time, where R + represents the set of positive real numbers, for which the following conditions hold:

[0070] ρ(t) is positive and strictly monotonically decreasing, t∈(0,T 0 ].

[0071]

[0072] Among them, T 0 represents the convergence time of the finite-time preset performance function, and denote the initial conditions and convergence boundaries of the finite-time preset performance function, respectively, and e(0) is the initial value of e(t).

[0073] In this embodiment, step 2 of the finite-time adaptive control method for an asynchronous motor considering preset performance and input saturation is specifically as follows:

[0074] For formula (2), considering that the input signal of the asynchronous motor random system is affected by saturation nonlinearity, u is used to represent u d and u q :

[0075]

[0076] Where u is the control input in actual application, v is the actual control input voltage of the stator, sat(v) represents the input saturation function, and u max with u min is the unknown saturation constant, u max >0,u min <0.

[0077] Define a smooth piecewise function s(v) as shown in formula (4) to approximate the saturation function:

[0078]

[0079] From formula (3) and formula (4), we can get u = sat(v) = s(v) + d(v), and:

[0080] |d(v)|=|sat(v)-s(v)|≤max{u max (1-tanh(1)),u min (tanh(1)-1)}=D, where D represents a positive constant.

[0081] Then there exists a constant λ:

[0082]

[0083] Among them, v 0 Represents the initial value of the actual control input voltage v of the stator.

[0084] v λ =λv+(1-λ)v 0 , 0<λ<1.

[0085] When v 0 =0, When , we get:

[0086]

[0087] When on the q axis, use Refers to d 1 (v) refers to d(v), where b 11 is a positive constant. When on the d-axis, use Refers to d 2 (v) refers to d(v), where b 12 Is a normal number.

[0088] In design d and v q During the process, u d and u q is regarded as the input signal of the asynchronous motor system. Designing a controller is actually designing the output signal of the controller, which is u d and u q In actual environment, the input signal of the system is the output signal of the designed controller. There are many output signals of the system, such as the position and speed of the motor. When designing the system, the actual control input voltage v of the stator on the d-axis is d and the actual control input voltage v of the stator on the q axis q As the real control rate, but in actual situations, the purpose of considering input saturation is to make u d and u q Keep it within a reasonable range.

[0089] Define the command filter as shown in formula (7):

[0090]

[0091] Among them, α i is the input signal of the command filter, i=1,2,3. 11 , l 12 are the output signals of the command filter, and l 11 The initial value of l 11 (0) = α i (0), α i (0) is α iThe initial value of l 12 The initial value of l 12 (0) = 0. If there are two constants θ 1 >0,θ 2 > 0, for any time t≥0, it can simultaneously satisfy Then for any There is always n >0 and Make are all bounded, among which ω n , is a positive number, represents any positive number, ω n represents any positive number, Represents any positive number less than or equal to 1.

[0092] According to the principle of backstepping, the tracking error variable and compensation error variable are defined as follows:

[0093]

[0094] Among them, v y represents the compensation error variable, y=1,2,3,4,5. j represents the tracking error variable, j = 0, 2, 3, 4, 5. 1 Represents the conversion error. ξ y is the filter error compensation signal, x 1d 、x 4d is the preset expected signal, x i,c is the output signal of the command filter, i=1,2,3.

[0095] The process of constructing the preset performance function and converting the position error is as follows: the finite time preset performance function ρ(t) is constructed as shown in formula (8):

[0096]

[0097] Among them, T 0 represents the convergence time of the finite-time preset performance function, and denote the initial conditions and convergence boundaries of the finite-time preset performance function, ρ 0 is a constant. The finite time preset performance function can be 0 Rapid internal convergence to ensure the convergence speed of the system.

[0098] The difference between the rotor angle and the set value is the angle tracking error. The angle tracking error, i.e. the rotor position tracking error, has the following inequality constraints:

[0099]

[0100] Where n and h are real numbers and satisfy 0<n≤1 and 0 <h≤1。

[0101] Introducing the smooth reversible function H(z 1 ):

[0102]

[0103] in, The smooth reversible function H(z 1 ) transforms the constraints into:

[0104] z 0 =ρ(t)H(z 1 ) (11)

[0105] According to formula (10) and formula (11), we can perform inverse transformation and obtain the following derivative:

[0106]

[0107] in,

[0108] Design virtual control function α 1 and filter error compensation signal ξ 1 The process is as follows: Select the Lyapunov function V 1 for:

[0109] Design virtual control function α 1 and filter error compensation signal ξ 1 for:

[0110]

[0111] Among them, k 1 is the system control gain, k 1 >0,β,l 1 is a constant.

[0112] By using formula (14) and formula (15), we can get:

[0113]

[0114] Design virtual control function α 2 and filter error compensation signal ξ 2 The process is as follows: Select the Lyapunov function V 2 for:

[0115] Load torque TL The upper limit is a positive number d, satisfying 0≤|T L |≤d.

[0116] According to Young's inequality:

[0117]

[0118] Among them, l 2 is a constant, l 2 >0.

[0119] make where f 2 (Z 2 ) represents the nonlinear fuzzy term in the asynchronous motor random system, Z 2 represents the fuzzy term f 2 (Z 2 ), is a fuzzy logic system, W 2 is the fuzzy weight vector, S 2 (Z 2 ) is the basis function vector, δ 2 (Z 2 ) is the approximation error, we get:

[0120]

[0121] Among them, h 2 is a constant. 2 Represents an arbitrarily small positive number.

[0122] definition is the fuzzy weight vector, i 1 =2,4, for The estimated value, estimated error for:

[0123] Construct virtual control function α 2 and filter error compensation signal ξ 2 for:

[0124]

[0125] Among them, k 2 is the system control gain, k 2 >0.

[0126] Through formula (18) to formula (21), we can get:

[0127]

[0128] make

[0129] Among them, v q represents the real control input voltage of the stator on the q axis, and|d 1 (v)|≤D H , where D H With b 11 All are positive numbers.

[0130] Select the Lyapunov function V as shown in formula (23) 3 :

[0131]

[0132] in, ||W 3 || is the vector W 3 The norm of γ 3 is a constant, for The estimated value of Denotes the estimation error, and we get:

[0133]

[0134] According to Young's inequality:

[0135]

[0136] Among them, l 3 is a constant, l 3 >0.

[0137] make where f 3 (Z 3 ) represents the nonlinear fuzzy term in the asynchronous motor random system, Z 3 represents the fuzzy term f 3 (Z 3 ), is a fuzzy logic system, W 3 is the fuzzy weight vector, S 3 (Z 3 ) is the basis function vector, δ 3 (Z 3 ) is the approximation error, we get:

[0138]

[0139] Among them, h 3 is a constant, m 3 is a constant, ε 3 Represents an arbitrarily small positive number.

[0140] Construct the real control law v as shown in formula (27)q and Adaptive Law

[0141]

[0142] Among them, the design parameters Pick k 3 Denotes the system control gain, and we get:

[0143]

[0144] Select the Lyapunov function V 4 for:

[0145]

[0146] According to Young's inequality:

[0147]

[0148] Among them, l 4 is a constant, l 4 >0.

[0149] make where f 4 (Z 4 ) represents the nonlinear fuzzy term in the asynchronous motor random system, Z 4 represents the fuzzy term f 4 (Z 4 ), is a fuzzy logic system, W 4 is the fuzzy weight vector, S 4 (Z 4 ) is the basis function vector, δ 4 (Z 4 ) is the approximation error, we get:

[0150]

[0151] Among them, h 4 is a constant. 4 Represents an arbitrarily small positive number.

[0152] Construct virtual control function α 3 and filter error compensation signal ξ 4 for:

[0153]

[0154] Among them, k 4 >0,k 4 is the system control gain, and we get:

[0155]

[0156] make

[0157] Among them, v d represents the actual control input voltage of the stator on the d-axis, and|d 2 (v)|≤D d , D d With b 12 All are positive numbers.

[0158] Select the Lyapunov function V as shown in formula (35) 5 :

[0159]

[0160] in, ||W 5 || is the vector W 5 The norm of γ 5 is a constant, for The estimated value of Expressing the estimated error is:

[0161]

[0162] According to Young's inequality:

[0163]

[0164] Among them, l 5 is a constant, l 5 >0.

[0165] make where f 5 (Z 5 ) represents the nonlinear fuzzy term in the asynchronous motor random system, Z 5 represents the fuzzy term f 5 (Z 5 ), is a fuzzy logic system, W 5 is the fuzzy weight vector, S 5 (Z 5 ) is the basis function vector, δ 5 (Z 5 ) is the approximation error, we get:

[0166]

[0167] Among them, m 5 is a constant, h5 is a constant, ε 5 Represents an arbitrarily small positive number.

[0168] Construct the real control law v d and Adaptive Law As shown in formula (39):

[0169]

[0170] Among them, the design parameters Pick k 5 Denotes the system control gain, and we get:

[0171]

[0172] The finite-time adaptive controller for the random system of asynchronous motors considering the preset performance and input saturation is designed as:

[0173]

[0174] After completing the design of the finite-time adaptive controller for the random system of the asynchronous motor in step 2, this embodiment also performs stability analysis on the asynchronous motor controlled by the finite-time adaptive controller for the random system of the asynchronous motor. The specific process is as follows:

[0175] Define the Lyapunov function V of the asynchronous motor stochastic system:

[0176]

[0177] Among them, r 1 is a positive number, we get:

[0178]

[0179] Construct the adaptive law as shown in formula (43)

[0180] Among them, k 0 is a constant, k 0 >0,h 2 >0,h 4 >0. According to Young's inequality:

[0181]

[0182] Then formula (42) becomes:

[0183]

[0184] in:

[0185]

[0186]

[0187] According to formula (34), v y , It will converge to the following region in a finite time:

[0188]

[0189] Among them, θ 0 is a constant and satisfies 0<θ 0 <1.

[0190] Convergence time T 1 for:

[0191]

[0192] Among them, V(0) represents the Lyapunov function value at the initial moment of V.

[0193] Select the Lyapunov function V as shown in formula (49) ξ Used to prove the boundedness of the compensation signal:

[0194] Derivative of formula (49) yields:

[0195]

[0196] Among them, |x i,c -α i |≤μ,μ>0.

[0197] According to Young's inequality:

[0198]

[0199] Then formula (50) becomes:

[0200]

[0201] in:

[0202] n 0 =min{K 1 ,K 2 ,K 3 ,K 4 ,K 5},

[0203] K 1 =k 1 -r 0,

[0204] K 4 =k 4 -b 4 ,

[0205] According to formula (34), ξ y Will converge to the following region in finite time:

[0206]

[0207] Among them, V ξ Lyapunov function representing the system compensation signal.

[0208] Convergence time T 2 for:

[0209]

[0210] Among them, V ξ (0) indicates V ξ The value of the Lyapunov function at the initial time.

[0211] Because v y and y The boundedness of v y =z j -ξ y , signal z j It is also bounded, that is, the system position tracking error converges to the equilibrium point within a finite time.

[0212] Step 3. Use the finite-time adaptive controller of the asynchronous motor random system to realize the position tracking control of the asynchronous motor.

[0213] like Figure 2 As shown, α and β represent the axes of the two-phase stationary coordinate system. represents the voltage of the α-axis of the two-phase stationary coordinate system, represents the voltage of the β axis in the two-phase stationary coordinate system, and a, b, and c represent the axes in the three-phase coordinate system. The actual position x of the asynchronous motor 1 That is, the rotor angle θ, the desired position x 1d The desired rotor angle θ * . is an unknown smooth disturbance function, include

[0214] First, define the angle tracking error z 0 , real-time acquisition of the actual position x of the asynchronous motor1 and the expected position x 1d Formation error z 0 , the conversion error z is obtained by presetting the performance function in a finite time 1 , using the asynchronous motor random system finite time adaptive controller, combined with fuzzy logic, finite time convergence design controller input signal, controller output u d 、u q , decomposed into u through coordinate transformation α * 、u β * . Using SVPWM modulation, i.e. space vector pulse width modulation, u α * 、u β * Converted into a three-phase PWM waveform, i.e. a pulse width modulation waveform, drives the inverter to generate AC voltage, controls the operation of the asynchronous motor, and detects the three-phase current i in real time a 、i b 、i c , the output torque is adjusted through the current closed loop, and the actual position x of the asynchronous motor 1 Feedback to the controller through encoder and other sensors forms a closed loop to achieve x 1 Tracking x 1d The effect is achieved by completing the position tracking control of the asynchronous motor.

[0215] The method of the present invention adopts command filtering control technology, and eliminates the influence of filtering error by introducing compensation signal, thereby reducing system error. At present, many existing adaptive control methods are used to solve nonlinear deterministic systems, but the preset performance problem of random systems is not involved. The present invention proposes a reasonable control method. On the other hand, the input saturation problem is taken into account during the design, making the designed system more suitable for engineering applications.

[0216] The proposed finite-time adaptive control method for an asynchronous motor considering preset performance and input saturation is simulated in a virtual environment to verify the feasibility of the control method proposed in the present invention:

[0217] The motor parameters are: n p =1,L m =0.068H, J = 0.0586kg·m 2 , L r =0.0699H,L s =0.0699H, R r =0.15Ω, R s =0.1Ω.

[0218] The selected fuzzy sets are: g∈N 1 , N 1 represents an integer, and g∈[-5,5].

[0219] The initial state of the asynchronous motor simulation is selected as [0.1, 0, 0, 1, 0].

[0220] The parameters of the fuzzy adaptive controller are selected as:

[0221] k 1 =17, k 2 =2.2, k 3 =60, k 4 =125, k 5 =40.

[0222] m 1 =m 3 =m 5 =0.005, r 1 =0.02, β=0.9, h 1 =h 2 =h 3 =h 4 =h 5 =0.5.

[0223] The relevant parameters of the finite time preset performance function are: 0 =1rad, T 0 =0.4s.

[0224] The constraint boundary parameters are: h=0.1, n=0.003.

[0225] Load torque: T L =1.0N·m, the expected position signal is: x 1d =sint,x 4d =1.

[0226] The random perturbation term is selected as:

[0227]

[0228] The simulation results of the finite time adaptive control method for asynchronous motors considering preset performance and input saturation are shown in Figure 2. Figures 3 to 10 As shown. Among them, the rotor position signal x 1 That is, the rotor angle and the desired position signal x d That is, the tracking simulation diagram of the rotor angle setting value is as follows Figure 3 As shown, the rotor position error z 1 =x 1 -x d , the preset upper and lower bounds of the performance function are as follows Figure 4As shown. Figure 3 It can be seen that the position signal of the system can quickly track the expected signal, Figure 4 It can be seen that the tracking error of the system converges to a small range near the origin after a finite time preset performance function constraint, and the system has a good tracking effect and high tracking accuracy. Figure 5 It can be seen that the system rotor flux can quickly track the expected flux, and the steady-state error is small. The d-axis stator voltage and the q-axis stator voltage are as follows: Figure 6 and Figure 7 As shown by Figure 6 and Figure 7 It can be seen that in the asynchronous motor random system using the control method of the present invention, u d and u q The state of the asynchronous motor is limited to a reasonable area, avoiding damage to the motor due to excessive starting voltage, and ensuring the safe and reliable operation of the system. 2 、x 3 、x 5 Respectively Figures 8 to 10 The above simulation results show that the finite time adaptive control method for asynchronous motors considering preset performance and input saturation in the present invention can track the reference signal efficiently, and therefore has practical implementation significance.

[0229] The control method of the present invention is aimed at the control accuracy requirements of the asynchronous motor random system considering preset performance and input saturation, as well as the existing random disturbances and nonlinear problems, and designs a finite time adaptive controller of the asynchronous motor random system considering preset performance and input saturation to achieve tracking of the target position and performance improvement. The method uses a fuzzy logic system to process the unknown nonlinear terms of the high-order nonlinear terms in the asynchronous motor random system, and combines the adaptive control method to solve the unknown parameters and input saturation problems in the system, constructs a Lyapunov function to ensure that the state quantities such as current and speed do not violate the physical constraints, introduces a finite time preset performance function to constrain the tracking error, improves the control accuracy, and adopts a method combining the command filtering technology with the error compensation mechanism to construct a finite time adaptive controller of the asynchronous motor random system, which not only solves the calculation explosion problem in the traditional backstepping method, but also eliminates the influence of the filtering error. The method of the present invention can effectively suppress the influence of input saturation and random disturbance, realize the rapid convergence of the system tracking error, and improve the control performance of the system.

[0230] Example 2

[0231] This embodiment 2 describes a finite-time adaptive control system for an asynchronous motor considering preset performance and input saturation, which is based on the same inventive concept as the finite-time adaptive control method for an asynchronous motor considering preset performance and input saturation in the above embodiment 1. The system of the present invention specifically includes the following modules:

[0232] The model building module is used to build a dynamic mathematical model of the asynchronous motor taking random interference into consideration.

[0233] The controller design module is used to design a finite-time adaptive controller of a random system of an asynchronous motor for realizing position tracking control of the asynchronous motor, taking into account preset performance and input saturation, based on the dynamic mathematical model of the asynchronous motor.

[0234] And a tracking control module is used to realize the position tracking control of the asynchronous motor by using the finite time adaptive controller of the asynchronous motor random system.

[0235] It should be noted that the implementation process of the functions and effects of each functional module in the finite-time adaptive control system of an asynchronous motor taking into account preset performance and input saturation is specifically described in the implementation process of the corresponding steps in the finite-time adaptive control method of an asynchronous motor taking into account preset performance and input saturation in the above-mentioned embodiment 1, and will not be repeated here.

[0236] Example 3

[0237] This embodiment 3 describes a computer device, which is used to implement the asynchronous motor finite-time adaptive control method considering preset performance and input saturation described in the above embodiment 1.

[0238] Specifically, the computer device includes a memory and one or more processors.

[0239] An executable code is stored in the memory. When the processor executes the executable code, the steps of the asynchronous motor finite time adaptive control method considering preset performance and input saturation are implemented.

[0240] In this embodiment, the computer device is any device or apparatus with data processing capability, which will not be described in detail here.

[0241] Example 4

[0242] This embodiment 4 describes a computer-readable storage medium, which is used to implement the asynchronous motor finite-time adaptive control method considering preset performance and input saturation described in the above embodiment 1.

[0243] Specifically, the computer-readable storage medium in this embodiment 4 stores a program thereon, and when the program is executed by the processor, it is used to implement the steps of the above-mentioned asynchronous motor finite-time adaptive control method considering preset performance and input saturation.

[0244] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart memory card (SmartMediaCard, SMC), SD card, flash memory card (FlashCard), etc. equipped on the device.

[0245] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the essential scope of this specification and should be protected by the present invention.

Claims

1. A finite-time adaptive control method for an asynchronous motor considering preset performance and input saturation, characterized in that: The steps include: Step 1. Establish a dynamic mathematical model of the asynchronous motor considering random interference; Step 2. Based on the dynamic mathematical model of the asynchronous motor constructed in step 1, design a finite-time adaptive controller for a random system of an asynchronous motor for realizing position tracking control of the asynchronous motor taking into account preset performance and input saturation; Step 3. Use the finite-time adaptive controller of the asynchronous motor random system to realize the position tracking control of the asynchronous motor.

2. The method for finite-time adaptive control of an asynchronous motor considering preset performance and input saturation according to claim 1, characterized in that: The step 1 is specifically as follows: The dq coordinate axis dynamic mathematical model of the asynchronous motor is established, as shown in formula (1): Wherein, θ represents the rotor angle of the asynchronous motor, ω represents the rotor angular velocity, and θ and ω are both state variables of the asynchronous motor system; n p represents the number of pole pairs, L m represents mutual inductance, J represents moment of inertia, L r and L s They represent the rotor leakage inductance and the stator leakage inductance respectively, represents the rotor flux, i d and i q denote the d-axis and q-axis stator currents respectively, T L Represents load torque, R r and R s They represent the rotor resistance and stator resistance respectively, u d and u q denote the d-axis and q-axis stator voltages respectively; In order to simplify the dq axis dynamic mathematical model of the asynchronous motor, the following variables are defined: When random interference is considered, the dynamic mathematical model of the dq coordinate axis of the asynchronous motor is shown in formula (2): in, is an unknown smooth disturbance function.

3. The method for finite-time adaptive control of an asynchronous motor considering preset performance and input saturation according to claim 1, characterized in that: In step 2, based on the command filtering technology and the principle of adaptive backstepping, a finite-time adaptive controller for a random system of an asynchronous motor is designed considering preset performance and input saturation. The control objective is to design the input signal u of the random system of the asynchronous motor. d and u q , so that the position tracking error of the system converges within a finite time and reduces its overshoot, and the system input is constrained within a preset range to achieve position tracking control of the asynchronous motor.

4. The method for finite-time adaptive control of an asynchronous motor considering preset performance and input saturation according to claim 2, characterized in that: The step 2 is specifically as follows: For formula (2), considering that the input signal of the asynchronous motor random system is affected by saturation nonlinearity, u is used to represent u d and u q : Where u is the control input in actual application, v is the actual control input voltage of the stator, sat(v) represents the input saturation function, and u max with u min is the unknown saturation constant, u max >0,u min <0; Define a smooth piecewise function s(v) as shown in formula (4) to approximate the saturation function: From formula (3) and formula (4), we can get u = sat(v) = s(v) + d(v), and: |d(v)|=|sat(v)-s(v)|≤max{u max (1-tanh(1)),u min (tanh(1)-1)}=D, where D represents a positive constant; Then there exists a constant λ: Wherein, v0 represents the initial value of the real control input voltage v of the stator; v λ =λv+(1-λ)v0,0<λ<1; When v0=0, When , we get: When on the q axis, use Refers to d1(v) refers to d(v), where b 11 is a positive constant; when on the d-axis, Refers to d2(v) refers to d(v), where b 12 is a positive constant; Define the command filter as shown in formula (7): Among them, α i is the input signal of the command filter, i=1,2,3; l 11 , l 12 are the output signals of the command filter, and l 11 The initial value of l 11 (0) = α i (0), α i (0) is α i The initial value of l 12 The initial value of l 12 (0) = 0; if there are two constants θ1>0 and θ2>0, for any time t≥0, Then for any There is always n >0 and Make are all bounded, among which ω n , is a positive number; According to the principle of backstepping, the tracking error variable and compensation error variable are defined as follows: Among them, v y represents the compensation error variable, y=1,2,3,4,5; z j represents the tracking error variable, j = 0, 2, 3, 4, 5; z1 represents the conversion error; ξ y is the filter error compensation signal, x 1d 、x 4d is the preset expected signal, x i,c is the output signal of the command filter; Construct a finite time preset performance function ρ(t) as shown in formula (8): Where T0 represents the convergence time of the finite time preset performance function, and They represent the initial conditions and convergence boundaries of the finite-time preset performance function, respectively, and ρ0 is a constant; For the angle tracking error, that is, the rotor position tracking error, there is the following inequality constraint: Where n and h are real numbers and satisfy 0<n≤1 and 0 <h≤1; Introduce the smooth reversible function H(z1) shown in formula (10): Convert the constraints to: z0=ρ(t)H(z1) (11) According to formula (10) and formula (11), we can perform inverse transformation and obtain the following derivative: in, Select the Lyapunov function V1 as: Design the virtual control function α1 and the filtering error compensation signal ξ1 as: Where k1 is the system control gain, k1>0, β and l1 are constants; By using formula (14) and formula (15), we can get: Select the Lyapunov function V2 as: Load torque T L The upper limit of is a positive number d, satisfying 0≤|T L |≤d; According to Young's inequality: Among them, l2 is a constant, l2>0; make Where f2(Z2) represents the nonlinear fuzzy term in the asynchronous motor random system, Z2 represents the variable set in the fuzzy term f2(Z2), is a fuzzy logic system, W2 is the fuzzy weight vector, S2(Z2) is the basis function vector, δ2(Z2) is the approximation error, and we get: Among them, h2 is a constant; ε2 represents an arbitrarily small positive number; definition is the fuzzy weight vector, i1=2,4, for The estimated value, estimated error for: The virtual control function α2 and the filtering error compensation signal ξ2 are constructed as: Wherein, k2 is the system control gain, k2>0; Through formula (18) to formula (21), we can get: make Among them, v q represents the real control input voltage of the stator on the q axis, and |d1(v)|≤D H , where D H With b 11 are all positive numbers; Select the Lyapunov function V3 as shown in formula (23): in, ||W3|| is the norm of vector W3, γ3 is a constant, for The estimated value of Denotes the estimation error, and we get: According to Young's inequality: Among them, l3 is a constant, l3>0; make Where f3(Z3) represents the nonlinear fuzzy term in the asynchronous motor random system, Z3 represents the variable set in the fuzzy term f3(Z3), is a fuzzy logic system, W3 is the fuzzy weight vector, S3(Z3) is the basis function vector, δ3(Z3) is the approximation error, and we get: Among them, h3 is a constant, m3 is a constant, and ε3 represents an arbitrarily small positive number; Construct the real control law v as shown in formula (27) q and adaptive law Among them, the design parameters Pick k3 represents the system control gain, and we get: Select the Lyapunov function V4 as: According to Young's inequality: Among them, l4 is a constant, l4>0; make Where f4(Z4) represents the nonlinear fuzzy term in the asynchronous motor random system, Z4 represents the variable set in the fuzzy term f4(Z4), is a fuzzy logic system, W4 is the fuzzy weight vector, S4(Z4) is the basis function vector, δ4(Z4) is the approximation error, and we get: Among them, h4 is a constant; ε4 represents an arbitrarily small positive number; The virtual control function α3 and the filtering error compensation signal ξ4 are constructed as: Where k4>0, k4 is the system control gain, and we get: make Among them, v d represents the actual control input voltage of the stator on the d-axis, and |d2(v)|≤D d , D d With b 12 are all positive numbers; Select the Lyapunov function V5 as shown in formula (35): in, ||W5|| is the norm of vector W5, γ5 is a constant, for The estimated value of Expressing the estimated error is: According to Young's inequality: Among them, l5 is a constant, l5>0; make Where f5(Z5) represents the nonlinear fuzzy term in the asynchronous motor random system, Z5 represents the variable set in the fuzzy term f5(Z5), is a fuzzy logic system, W5 is the fuzzy weight vector, S5(Z5) is the basis function vector, δ5(Z5) is the approximation error, and we get: Among them, m5 is a constant, h5 is a constant, and ε5 represents an arbitrarily small positive number; Construct the real control law v d and adaptive law As shown in formula (39): Among them, the design parameters Pick k5 represents the system control gain, and we get: The finite-time adaptive controller for the random system of asynchronous motors considering the preset performance and input saturation is designed as:

5. The method for finite-time adaptive control of an asynchronous motor considering preset performance and input saturation according to claim 4, characterized in that: In the step 2, after the design of the finite-time adaptive controller for the random system of the asynchronous motor is completed, a stability analysis is performed on the asynchronous motor controlled by the finite-time adaptive controller for the random system of the asynchronous motor.

6. The method for finite-time adaptive control of an asynchronous motor considering preset performance and input saturation according to claim 5, characterized in that: In step 2, the process of performing stability analysis on the asynchronous motor controlled by the asynchronous motor random system finite time adaptive controller is specifically as follows: Define the Lyapunov function V of the asynchronous motor stochastic system: Where r1 is a positive number, we get: Construct the adaptive law as shown in formula (43) Among them, k0 is a constant, k0>0, h2>0, h4>0; According to Young's inequality: Then formula (42) becomes: in: According to formula (34), v y , It will converge to the following region in a finite time: Wherein, θ0 is a constant and satisfies 0<θ0<1; The convergence time T1 is: Where V(0) represents the Lyapunov function value at the initial time of V; Select the Lyapunov function V as shown in formula (49) ξ Used to prove the boundedness of the compensation signal: Derivative of formula (49) yields: among them,|x i,c -a i |≤μ,μ>0; According to Young's inequality: Then formula (50) becomes: in: According to formula (34), ξ y Will converge to the following region in finite time: Among them, V ξ Lyapunov function representing the system compensation signal; The convergence time T2 is: Among them, V ξ (0) indicates V ξ The value of the Lyapunov function at the initial moment; Because v y and y The boundedness of v y =z j -ξ y , signal z j It is also bounded, that is, the system position tracking error converges to the equilibrium point within a finite time.

7. The method for finite-time adaptive control of an asynchronous motor considering preset performance and input saturation according to claim 4, characterized in that: The step 3 is specifically as follows: First, define the angle tracking error, and collect the actual position x1 and the expected position x1 of the asynchronous motor in real time. 1d The error z0 is formed, and the conversion error z1 is obtained through the finite time preset performance function. The finite time adaptive controller of the asynchronous motor random system is used, and the controller input signal is designed by combining fuzzy logic and finite time convergence. d 、u q Decomposed into u by coordinate transformation α * 、u β * ,in represents the voltage of the α-axis of the two-phase stationary coordinate system, Represents the voltage of the β axis of the two-phase stationary coordinate system; using SVPWM modulation to convert u α * 、u β * Convert it into a three-phase PWM waveform, drive the inverter to generate AC voltage, control the operation of the asynchronous motor, and detect the three-phase current i in real time a 、i b 、i c , the output torque is adjusted through the current closed loop; the actual position x1 of the asynchronous motor is fed back to the controller through the sensor to form a closed loop, so that x1 tracks x 1d , and then complete the position tracking control of the asynchronous motor.

8. A finite-time adaptive control system for an asynchronous motor taking into account preset performance and input saturation, characterized in that: Includes the following modules: A model building module is used to build a dynamic mathematical model of the asynchronous motor taking into account random interference; A controller design module is used to design a finite-time adaptive controller of a random system of an asynchronous motor for realizing position tracking control of the asynchronous motor based on a dynamic mathematical model of the asynchronous motor, taking into account preset performance and input saturation; And a tracking control module is used to realize the position tracking control of the asynchronous motor by using the finite time adaptive controller of the asynchronous motor random system.

9. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, the steps of the asynchronous motor finite-time adaptive control method considering preset performance and input saturation as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps of the finite-time adaptive control method for an asynchronous motor considering preset performance and input saturation as described in any one of claims 1 to 7 are implemented.

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