Nonlinear active disturbance rejection control method based on RBF neural network

Abstract

The invention discloses a nonlinear active-disturbance-rejection control method based on an RBF neural network, and belongs to the field of motion control, and the method comprises the steps: 1, constructing a nonlinear active-disturbance-rejection controller and a radial basis function neural network identifier which comprises an input layer, a hidden layer and an output layer; step 2, acquiring a given speed v (k) and a feedback speed y (k) of a controlled object; through the good self-learning capability of the radial basis function neural network identifier, the influence of external disturbance on the system is reduced by using a nonlinear active-disturbance-rejection control method, system control parameters are adaptively adjusted in real time according to internal and external disturbance of the system, and compared with an original fixed parameter mode, overshoot can be remarkably reduced, and the stability of the system is improved. The anti-interference capability of the system is enhanced, the control precision of the system is improved, and the technical problem that the two key parameters beta 4 and beta 5 of the disturbance compensation error feedback control rate module of the active disturbance rejection controller in the prior art are difficult to set is solved.

Description

Technical Field

[0001] The present invention belongs to the field of motion control, relates to a nonlinear active disturbance rejection control method, and specifically is a nonlinear active disturbance rejection control method based on an RBF neural network. Background Technique

[0002] At present, scholars have conducted a large number of studies on the linear active disturbance rejection control (LADRC) method, which simplifies the process of controller parameter tuning. Compared with the application limitations brought by the complex parameter tuning of the nonlinear active disturbance rejection control (NLADRC), the linear active disturbance rejection control has become the first choice for engineering applications. The control strategy of double-position-loop Lagrange-LADRC has been studied for various severe nonlinear disturbances, and its research results have achieved relatively ideal effects based on linear active disturbance rejection. Good suppression has been obtained for the fluctuations caused by harmonic cogging, motor torque fluctuations, and resonances. However, the "bandwidth method" is usually used for parameter tuning in linear ADRC, which has certain limitations for non-minimum phase systems.

[0003] Considering that there are still serious nonlinear interferences such as wind resistance and wire winding in the actual application of the GI Lidar system, which affect the platform line-of-sight stabilization accuracy, and the nonlinear ADRC has advantages such as a wide application range, high tracking accuracy, and strong anti-interference ability compared with the linear ADRC. It is necessary to conduct targeted research on the nonlinear active disturbance rejection control in this system. Some scholars have tried to switch between the linear ADRC and the nonlinear ADRC to obtain better dynamic performance and anti-interference ability, but it is more difficult to implement, and there is still a certain distance from further experimental implementation. Therefore, how to use the nonlinear ADRC to achieve better control effects and better solve the problem of parameter tuning has become the research direction of many scholars.

[0004] The nonlinear active disturbance rejection controller has excellent control characteristics such as strong robustness and no static error, but its adjustable parameters are too many and not easy to adjust, which greatly limits its engineering application. The active disturbance rejection controller consists of three parts, and each part has parameters that need to be tuned. The combination of the sizes of each parameter will lead to different effects, so it is more difficult to adjust them together. The traditional second-order nonlinear ADRC has as many as 11 parameters to be tuned, and tuning the parameters will consume a lot of time and energy. Therefore, in order to give full play to the advantages of NLADRC, a suitable parameter tuning method must be designed. The existing parameter tuning methods can be roughly divided into four categories, namely the separation method, the index optimization method, the structure optimization method, the artificial intelligence method, etc.

[0005] 1) Separation method

[0006] In the traditional parameter tuning process, engineers mainly rely on the empirical trial-and-error method. By separately adjusting each module and then integrating them, the parameters of the entire active disturbance rejection controller are tuned. This method is also called the separation method, but the obtained control effect is not satisfactory. To address this issue, some scholars have started to study the relationships between the controller parameters, aiming to find a simple parameter tuning method, but with little success.

[0007] 2) Index optimization method

[0008] Based on the separation method, some scholars have studied the influence of different controller parameters on the system performance, treating one or several parameters as a whole and optimizing the specific indices of the system. Existing documents have analyzed the expected performance indices of time-delay systems, compensated for the modeling errors using the active disturbance rejection controller, and proposed a parameter tuning method based on the quantitative feedback theory, enabling the control system to have good disturbance rejection ability. However, this method has a high complexity and requires offline parameter tuning, resulting in poor system adaptability.

[0009] 3) Structure optimization method

[0010] In the research on methods for tuning the controller parameters, existing documents have addressed the problems of parameter tuning and response speed in the traditional active disturbance rejection control method, and have improved the structures of the extended state observer and the nonlinear error feedback control law. From the perspective of simplifying the controller parameters, the number of adjustable parameters has been reduced, but at the same time, a new chattering problem has been introduced. On this basis, existing documents have addressed the chattering problem in the sliding mode control algorithm, and have improved the structure of the sliding mode controller using a new saturation function, thereby optimizing the control law module in the active disturbance rejection controller, solving the chattering problem, and enhancing the disturbance rejection ability. However, its network structure is fixed and the learning speed is slow, affecting the dynamic performance of the system.

[0011] 4) Artificial intelligence method

[0012] The parameter tuning strategies based on artificial intelligence methods can be divided into offline and online tuning strategies according to the different offline iterative properties of the algorithms. Existing documents have proposed using the large mutation genetic algorithm to online tune the parameters of the active disturbance rejection controller for online tuning, achieving a certain optimization effect. However, the convergence speed of this algorithm is limited, and it often requires a lot of training time to obtain an accurate solution.

[0013] Since the advent of neural networks, scholars have conducted in-depth research in combination with specific actual systems. Initially, neural networks were used to tune the parameters of PID controllers. Since the advent of the active disturbance rejection controller (ADRC) in 1998, Professors Zhang Rong and Han Jingqing first proposed a control scheme that combines neural networks and ADRC by drawing on this idea. Subsequently, scholars have made a large number of attempts in this direction. Existing documents use a radial basis function (RBF) neural network to real-time tune the parameters of a second-order ADRC, enhancing the anti-interference ability of the servo control system while improving the control accuracy. However, the network structure adopted in the literature is relatively complex, difficult to implement, and not very practical. Summary of the Invention

[0014] Aiming at the deficiencies of the existing technology, the purpose of the present invention is to provide a non-linear active disturbance rejection control method based on an RBF neural network, so as to solve the technical problem that it is difficult to tune the two key parameters, β4 and β5, of the disturbance compensation error feedback control rate module of the active disturbance rejection controller in the existing technology.

[0015] To solve the above technical problems, the present invention is implemented by adopting the following technical solutions:

[0016] A non-linear active disturbance rejection control method based on an RBF neural network specifically includes the following steps:

[0017] Step 1: Construct a non-linear active disturbance rejection controller and an RBF neural network identifier, and set the initial values of the weight vector, basis width vector, and center vector of the RBF neural network identifier to 0;

[0018] The RBF neural network identifier includes an input layer, a hidden layer, and an output layer;

[0019] The input layer is used to receive the input signal and transfer it to the hidden layer;

[0020] The hidden layer is used to process the input signal by using the radial basis function as the transfer function;

[0021] The output layer is used to linearly transform the processing result of the hidden layer and then output it;

[0022] The non-linear active disturbance rejection controller includes a tracking differentiator, an extended state observer, and a disturbance compensation error feedback control rate;

[0023] Step 2: Collect the given speed v(k) and the feedback speed y(k) of the controlled object;

[0024] Step 3: Input the given speed v(k) and the feedback speed y(k) obtained in Step 2 into the RBF neural network identifier to obtain the output speed y m (k);

[0025] Step 4: Calculate the output speed y m (k) obtained in Step 3 and the difference between the feedback speed y(k) collected in Step 2;

[0026] Step 5: Determine whether the difference obtained in Step 4 meets the preset threshold. If yes, proceed to Step 6; otherwise, correct the weight vector, basis width vector, and center vector of the radial basis neural network identifier, and then proceed to Step 6;

[0027] Step 6: Calculate the Jacobian information in real time based on the results obtained in Step 2 and Step 3, and online adjust the parameters of the disturbance compensation error feedback control rate of the nonlinear active disturbance rejection controller according to the Jacobian information;

[0028] Step 7: Based on the parameters of the disturbance compensation error feedback control rate adjusted in Step 6, the disturbance compensation error feedback control rate outputs the control quantity u0(k), and returns to Step 2.

[0029] The present invention further includes the following technical features:

[0030] In Step 1, constructing the nonlinear active disturbance rejection controller specifically includes the following steps: Step 1.1, constructing a second-order tracking differentiator;

[0031]

[0032] Wherein:

[0033] fh is the fastest control synthesis function;

[0034] x1(k) is the tracking signal of the k-th discrete point of the given speed v(k);

[0035] x2(k) is the differential signal of x1(k);

[0036] r is the speed factor;

[0037] h is the sampling period of the system, i.e., the integration step size;

[0038] h0 is the filtering factor parameter;

[0039] Step 1.2, constructing an extended state observer;

[0040]

[0041] Wherein:

[0042] Both z1(k) and z2(k) are state variables observed by the observer;

[0043] z3(k) is the estimated total disturbance;

[0044] β1, β2, β3, a1, a2 are specific non - linear parameters of the adjustable parameter function fal;

[0045] δ1 is the length of the non - linear interval, 0 < δ1 < 1;

[0046] b is the compensation coefficient;

[0047] δ is the length of the non - linear interval, 0 < δ < 1;

[0048] y(k) is the feedback speed, m / s;

[0049] u(k) is the k - th control quantity input to the controlled object;

[0050] sign is the sign function;

[0051] ε1(k) is the error between the state variable z1(k) observed by the extended state observer and the feedback speed y(k);

[0052] Step 1.3, construct the non - linear state error feedback control law;

[0053]

[0054] Where:

[0055] β4(k), β5(k), a3 and a4 are specific non - linear parameters of the adjustable parameter function fal;

[0056] u0(k) is the k - th control quantity output by the disturbance compensation error feedback control law;

[0057] e1(k) is the error between the tracking signal x1(k) output by the tracking differentiator and the state variables z1(k) and z2(k) observed by the extended state observer;

[0058] e2(k) is the error between the differential signal x2(k) of the tracking signal x1(k) and the state variable z2(k) observed by the extended state observer.

[0059] The sixth step specifically includes the following steps:

[0060] Step 6.1, select the performance index function E1(k);

[0061]

[0062] Where:

[0063] r(k) is the input of the radial basis neural network identifier, which is the given speed v(k) and the feedback speed y(k);

[0064] ym (k) is the output speed of the radial basis neural network identifier;

[0065] Step 6.2, calculate the Jacobian information Take the calculation result as the Jacobian information;

[0066] Step 6.3, use the following formula to calculate the adjustment values Δβ4(k) and Δβ5(k) of β4 and β5,

[0067]

[0068] where:

[0069] η is the learning rate, and 0 < η < 1;

[0070] Step 6.4, input the adjustment values Δβ4(k) and Δβ5(k) obtained in Step 6.3 into the following formulas respectively to obtain the adjusted values of β4(k) and β5(k);

[0071] β4(k) = β4(k - 1) + Δβ4(k)

[0072] β5(k) = β5(k - 1) + Δβ5(k).

[0073] In Step 7, according to the parameters of the disturbance compensation error feedback control rate adjusted in Step 6, the control quantity u0(k) output by the disturbance compensation error feedback control rate is specifically:

[0074] u0(k) = β4(k)·fal(e1(k), a3, δ) + β5(k)·fal(e2(k), a4, δ)

[0075]

[0076] Compared with the prior art, the beneficial technical effects of the present invention are:

[0077] (Ⅰ) Through the good self-learning ability of the radial basis neural network identifier, the nonlinear active disturbance rejection control method is used to reduce the influence of external disturbances on the system. At the same time, the system control parameters are adaptively adjusted in real time according to the internal and external disturbances of the system. Compared with its original fixed parameter mode, overshoot can be significantly reduced, the anti-interference ability of the system is enhanced, and the control accuracy of the system is improved. The technical problem of difficult tuning of the two key parameters β4 and β5 of the disturbance compensation error feedback control rate module of the active disturbance rejection controller in the prior art is solved.

[0078] (Ⅱ) In the prior art, the parameters are fixedly set before the system works and cannot be adaptively changed in real time according to the real-time state of the system. The real-time parameter adjustment method proposed by the present invention can adjust the parameters in real time according to the system state, enabling the parameters to intelligently adapt to the internal and external disturbances of the system, so that the system can achieve higher control precision. While effectively reducing overshoot, it reduces the influence of external non-linear disturbances on the system speed stability and position tracking accuracy, and this method is not sensitive to flexible joint disturbances and typical non-linear disturbance problems, having strong system adaptability.

[0079] (Ⅲ) Nonlinear active disturbance rejection control is used in the present invention. The advantage of this method is strong anti-disturbance ability, but adjusting parameters is time-consuming and laborious. Since this method adaptively adjusts parameters β4 and β5 through artificial intelligence algorithms, the process of manual parameter adjustment is omitted, which can effectively improve the work efficiency of debuggers in engineering and is easy to implement in engineering. Brief Description of the Drawings

[0080] Figure 1 is the method flow chart of the present invention;

[0081] Figure 2 is the non-linear active disturbance rejection control structure diagram based on RBF neural network;

[0082] Figure 3 is the non-linear active disturbance rejection control simulation diagram based on RBF neural network;

[0083] Figure 4 is the change curve of parameters (without interference);

[0084] Figure 5 Change curve of parameters (with interference);

[0085] Figure 6 Comparison of sine target tracking position curves;

[0086] Figure 7 Position tracking comparison curves of different control methods under disturbance.

[0087] The following further elaborates on the specific content of the present invention in conjunction with embodiments. Detailed Embodiment

[0088] It should be noted that all components in the present invention, without special instructions, are components known in the art.

[0089] The following gives specific embodiments of the present invention. It should be noted that the present invention is not limited to the following specific embodiments, and all equivalent transformations made on the basis of the technical solutions of the present application fall within the protection scope of the present invention.

[0090] The present invention provides a non - linear active disturbance rejection control method based on an RBF neural network, which specifically includes the following steps:

[0091] Step 1: Construct a non - linear active disturbance rejection controller and a radial basis function neural network identifier, and set the initial values of the weight vector, basis width vector, and center vector of the radial basis function neural network identifier to 0;

[0092] The radial basis function neural network identifier includes an input layer, a hidden layer, and an output layer;

[0093] The input layer is used to receive the input signal and transfer it to the hidden layer;

[0094] The hidden layer is used to process the input signal by using the radial basis function as the transfer function;

[0095] The output layer is used to linearly transform and output the processing result of the hidden layer;

[0096] The non - linear active disturbance rejection controller includes a tracking differentiator, an extended state observer, and a disturbance compensation error feedback control law;

[0097] Step 2: Collect the given speed v(k) and the feedback speed y(k) of the controlled object;

[0098] Step 3: Input the given speed v(k) and the feedback speed y(k) obtained in Step 2 into the radial basis function neural network identifier to obtain the output speed y m (k);

[0099] Step 4: Calculate the difference between the output speed y m (k) obtained in Step 3 and the feedback speed y(k) collected in Step 2;

[0100] Step 5: Determine whether the difference obtained in Step 4 meets the preset threshold. If it does, go to Step 6; otherwise, correct the weight vector, basis width vector, and center vector of the radial basis function neural network identifier, and then go to Step 6;

[0101] Step 6: Calculate the Jacobian information in real - time according to the results obtained in Step 2 and Step 3, and online - adjust the parameters of the disturbance compensation error feedback control law of the non - linear active disturbance rejection controller according to the Jacobian information;

[0102] Step 7: According to the parameters of the disturbance compensation error feedback control law adjusted in Step 6, the disturbance compensation error feedback control law outputs the control quantity u0(k), and return to Step 2.

[0103] In the above technical solution, by virtue of the good self-learning ability of the radial basis function neural network identifier (RBFNNI), the nonlinear active disturbance rejection control method is utilized to reduce the influence of external disturbances on the system. Meanwhile, the control parameters of the system are adaptively adjusted in real time according to the internal and external disturbances of the system. Compared with its original fixed-parameter mode, overshoot can be significantly reduced, the anti-interference ability of the system is enhanced, and the control accuracy of the system is improved, solving the technical problem of difficult tuning of the two key parameters, β4 and β5, in the disturbance compensation error feedback control rate module of the active disturbance rejection controller in the prior art.

[0104] In the prior art, the parameters are fixedly set before the system works and cannot be adaptively changed in real time according to the real-time state of the system. The parameter real-time adjustment method proposed by the present invention can adjust the parameters in real time according to the system state, enabling the parameters to intelligently adapt to the internal and external disturbances of the system, so that the system can achieve higher control accuracy. While effectively reducing overshoot, the influence of external nonlinear disturbances on the speed stability and position tracking accuracy of the system is reduced, and this method is insensitive to flexible joint disturbances and typical nonlinear disturbance problems, having strong system adaptability.

[0105] The nonlinear active disturbance rejection control is used. The advantage of this method is strong anti-disturbance ability, but the adjustment of parameters is time-consuming and laborious. Since this method adaptively adjusts the parameters β4 and β5 through an artificial intelligence algorithm, the process of manually adjusting parameters is omitted, which can effectively improve the work efficiency of debugging personnel in engineering and is easy to implement in engineering.

[0106] The preset threshold can be based on empirical values or can be selected as one-fifth of the speed stability value, and the speed stability value is generally 0.05. When the radial basis function neural network identifier (RBFNNI) performs real-time tuning of the parameters β4(k) and β5(k) of the nonlinear state error feedback control rate (NLSEF), the control quantity u0(k) is adjusted in real time according to the disturbance compensation error feedback control rate, so that the feedback speed tracks the target speed, achieving the purpose of controlling speed stability.

[0107] In step one, constructing the nonlinear active disturbance rejection controller specifically includes the following steps:

[0108] Step 1.1, constructing a second-order tracking differentiator;

[0109]

[0110] Wherein:

[0111] fh is the fastest control synthesis function;

[0112] x1(k) is the tracking signal of the k-th discrete point of the given speed v(k);

[0113] x2(k) is the differential signal of x1(k);

[0114] r is the speed factor;

[0115] h is the sampling period of the system, i.e., the integration step size;

[0116] h0 is the filter factor parameter;

[0117] Step 1.2, construct the extended state observer;

[0118]

[0119] Where:

[0120] z1(k) and z2(k) are both state variables observed by the observer;

[0121] z3(k) is the estimated total disturbance;

[0122] β1, β2, β3, a1, a2 are specific nonlinear parameters of the adjustable parameter function fal;

[0123] δ1 is the length of the nonlinear interval, 0 < δ1 < 1;

[0124] b is the compensation coefficient;

[0125] δ is the length of the nonlinear interval, 0 < δ < 1;

[0126] y(k) is the feedback speed, m / s;

[0127] u(k) is the kth control quantity input to the controlled object;

[0128] sign is the sign function;

[0129] ε1(k) is the error between the state variable z1(k) observed by the extended state observer and the feedback speed

[0130] y(k);

[0131] Step 1.3, construct the nonlinear state error feedback control law;

[0132]

[0133] Where:

[0134] β4(k), β5(k), a3 and a4 are specific nonlinear parameters of the adjustable parameter function fal, the value range of a3 is 0 to 1, and the value range of a4 is 0 to 2;

[0135] u0(k) is the kth control quantity output by the disturbance compensation error feedback control law;

[0136] e1(k) is the error between the tracking signal x1(k) output by the tracking differentiator and the state variables z1(k) and z2(k) observed by the extended state observer of the extended state;

[0137] e2(k) is the error between the differential signal x2(k) of the tracking signal x1(k) and the state variable z2(k) observed by the extended state observer of the extended state.

[0138] In the above technical solution, r determines the tracking speed of the system; h reduces the influence of noise on the system by reducing the integration step size.

[0139] A non - linear transformation is set between the input layer and the hidden layer of the radial basis neural network identifier, and a linear transformation is set between the hidden layer and the output layer of the radial basis neural network identifier.

[0140] In the above technical solution, in order to make the RBF neural network better approximate the objective function.

[0141] Step six specifically includes the following steps:

[0142] Step 6.1, select the performance index function E1(k);

[0143]

[0144] Among them:

[0145] r(k) is the input of the radial basis neural network identifier, which is the given speed v(k) and the feedback speed y(k);

[0146] y m (k) is the output speed of the radial basis neural network identifier;

[0147] Step 6.2, calculate the Jacobian information Take the calculation result as the Jacobian information;

[0148] Step 6.3, use the following formula to calculate the adjustment values Δβ4(k) and Δβ5(k) of β4 and β5,

[0149]

[0150] Among them:

[0151] η is the learning rate, and 0 < η < 1;

[0152] Step 6.4, input the adjustment values Δβ4(k) and Δβ5(k) obtained in step 6.3 into the following formulas respectively to obtain the adjusted values of β4(k) and β5(k);

[0153] β4(k) = β4(k - 1) + Δβ4(k)

[0154] β5(k) = β5(k - 1) + Δβ5(k).

[0155] In step seven, according to the parameters of the disturbance compensation error feedback control rate adjusted in step six, the control quantity u0(k) output by the disturbance compensation error feedback control rate is specifically:

[0156] u0(k) = β4(k)·fal(e1(k), a3, δ) + β5(k)·fal(e2(k), a4, δ)

[0157]

[0158] Simulation Experiment One:

[0159] To study the performance characteristics of the present invention, models of linear ADRC, Lagrange - LADRC, and the nonlinear active disturbance rejection control method based on RBF neural network are successively built and analyzed in the MATLAB simulation environment. By comparing with similar methods, the anti - interference ability, speed, and position tracking performance of the proposed RBF - based nonlinear active disturbance rejection control method are verified. The built simulation model is as Figure 3 shown:

[0160] In the existing turntable nonlinear active disturbance rejection controller, the parameter values used are as follows:

[0161] The parameters in TD are: r0 = 10, h0 = 0.01;

[0162] The parameters in the extended state observer are: δ1 = 0.05, a1 = 0.5, a2 = 0.25, b = 1.5; β1 = 3ω0, ω0 is the observer bandwidth.

[0163] The parameters in NLSEF are: δ2 = 0.05, a3 = 0.75, a4 = 1.25, β4 = 1.84, β5 = 2.76.

[0164] When the turntable is under the nonlinear active disturbance rejection control based on RBF neural network, the parameters in the nonlinear active disturbance rejection controller basically remain unchanged. The number of input nodes in the first layer of the RBF neural network identifier is 3, the number of nodes in the second - layer hidden layer is 5, the number of output nodes in the third - layer output layer is 2, the learning rate η1 = 0.3, and the momentum factor α = 0.032; in the state error feedback control rate of the nonlinear active disturbance rejection controller, the learning rate η = 0.15.

[0165] Simulation Experiment Two:

[0166] To verify the anti-disturbance performance of the present invention, the simulation analysis of the speed step response is carried out under two conditions: without interference and with interference.

[0167] During the operation of the turntable, the parameter tuning change process of the nonlinear active disturbance rejection controller based on the RBF neural network is as Figure 4 shown.

[0168] Table 1 Performance indicators of speed control (without interference)

[0169]

[0170] It can be obtained from Table 1 that for the three control methods, the adjustment time and overshoot of the turntable speed stability control are very small in an environment without external interference. However, it can be seen from the simulation results that the response speed of the RBF-based nonlinear active disturbance rejection control is faster. The adjustment time of this method is shortened by 0.024 s compared with the Lagrange-LADRC control method, and the overshoot is reduced by 28%.

[0171] To verify the anti-interference performance of the present invention, when setting a step of the given speed of 1° / s, external environmental interference is added to the feedback curve of the system. Among them, the interference of the wind is obtained through white noise and then superimposed on the output angle feedback of the turntable.

[0172] It can be concluded from the simulation results in Table 2 that the turntable controller based on the RBF-based nonlinear active disturbance rejection control requires a shorter adjustment time in an environment with external interference, and the speed stability is also better than that of the Lagrange-LADRC control method. This shows that the dynamic and steady-state performance of the coarse tracking two-dimensional turntable of the control method based on the RBF-based nonlinear active disturbance rejection is better. In addition, since this method can optimize the controller parameters in real time according to the changes of internal and external disturbances of the system and has a certain adaptive ability, the control accuracy and anti-interference ability of the system can be improved.

[0173] Table 2 Performance indicators of speed control (with interference)

[0174]

[0175] Simulation experiment three:

[0176] When the system gives a sine target curve, the comparison of the position feedback tracked by different control methods is as Figure 6 shown.

[0177] Table 3 Performance indicators of position control without interference

[0178]

[0179] As can be seen from Table 3, under the condition of no interference, the position tracking performance of the RBF nonlinear active disturbance rejection control method is better than that of Lagrange-LADRC. Figure 7 The following figure shows the comparison curves of position tracking after the system is disturbed. It can be seen that the accuracy of various methods is good without interference, and the advantages of this method can be reflected when there is interference. The adaptive adjustment process of the two parameters of this control system can also be seen from the parameter change curves.

[0180] Table 4 Position Tracking Control Performance Index

[0181]

[0182] As can be seen from Table 4, after the turntable system is disturbed, the error amplitude of the Lagrange-LADRC control method is 0.213°, while the error amplitude of the RBF nonlinear active disturbance rejection control method is 0.032°. Therefore, compared with the Lagrange-LADRC method, the turntable position tracking error of the RBF nonlinear active disturbance rejection control method is reduced by 85%, and it has better anti-interference and position tracking performance.

[0183] According to the above simulation experiment data, it can be seen that since the RBF-based nonlinear active disturbance rejection control method enables the parameters in the control system to be optimized in real time according to the changes of internal and external disturbances, this method has higher control accuracy, stronger anti-interference performance and certain adaptive ability compared with similar methods.

Claims

1. A nonlinear auto-disturbance rejection control method based on RBF neural network, characterized in that: The specific steps include: Step 1: construct a nonlinear active disturbance rejection controller and a radial basis function neural network identifier, and set the initial values ​​of the weight vector, basis width vector and center vector of the radial basis function neural network identifier to 0; The radial basis neural network identifier comprises an input layer, a hidden layer and an output layer; The input layer is used to receive input signals and pass them to the hidden layer; The hidden layer is used to process the input signal using a radial basis function as a transfer function; The output layer is used to output the processing result of the hidden layer after linear transformation; The nonlinear active disturbance rejection controller includes a tracking differentiator, an extended state observer and a disturbance compensation error feedback control rate; Step 2: Collect the given speed v(k) and feedback speed y(k) of the controlled object; Step 3: Input the given speed v(k) and feedback speed y(k) obtained in step 2 into the radial basis neural network identifier to obtain the output speed y m (k); Step 4: Calculate the output speed y obtained in step 3 m The difference between the feedback speed y(k) and the feedback speed y(k) collected in step 2; Step 5, judging whether the difference obtained in step 4 meets the preset threshold, if yes, proceeding to step 6, otherwise, correcting the weight vector, basis width vector and center vector of the radial basis neural network identifier, and proceeding to step 6; Step 6, calculating the Jacobian information in real time according to the results obtained in step 2 and step 3, and adjusting the parameters of the disturbance compensation error feedback control rate of the nonlinear active disturbance rejection controller online in real time according to the Jacobian information; Step 7: According to the parameters of the disturbance compensation error feedback control rate adjusted in step 6, the disturbance compensation error feedback control rate outputs the control amount u0(k), and returns to step 2.

2. The nonlinear auto-disturbance rejection control method based on RBF neural network as claimed in claim 1, characterized in that: In step 1, building a nonlinear active disturbance rejection controller specifically includes the following steps: Step 1.1, construct a second-order tracking differentiator; in: fh is the fastest control comprehensive function; x1(k) is the tracking signal of the kth discrete point with a given velocity v(k); x2(k) is the differential signal of x1(k); r is the speed factor; h is the sampling period of the system, that is, the integration step length; h0 is the filter factor parameter; Step 1.2, construct an extended state observer; in: z1(k) and z2(k) are both state variables observed by the observer; z3(k) is the estimated total disturbance; β1, β2, β3, a1, a2 are specific nonlinear parameters of the adjustable parameter function fal; δ1 is the length of the nonlinear interval, 0<δ1<1; b is the compensation coefficient; δ is the length of the nonlinear interval, 0<δ<1; y(k) is the feedback speed, m / s; u(k) refers to the Kth control quantity input to the controlled object; sign is the sign function; ε1(k) is the error between the state variable z1(k) observed by the extended state observer and the feedback speed y(k); Step 1.3, construct the nonlinear state error feedback control rate; in: β4(k), β5(k), a3 and a4 are specific nonlinear parameters of the adjustable parameter function fal; u0(k) is the Kth control quantity output by the disturbance compensation error feedback control rate; e1(k) is the error between the tracking signal x1(k) output by the tracking differentiator and the state variables z1(k) and z2(k) observed by the extended state observer; e2(k) is the error between the differential signal x2(k) of the tracking signal x1(k) and the state variable z2(k) observed by the expanded state observer.

3. The nonlinear auto-disturbance rejection control method based on RBF neural network as claimed in claim 1, characterized in that: A nonlinear transformation is arranged between the input layer and the hidden layer of the radial basis neural network identifier, and a linear transformation is arranged between the hidden layer and the output layer of the radial basis neural network identifier.

4. The nonlinear auto-disturbance rejection control method based on RBF neural network as claimed in claim 2, characterized in that: The step six specifically includes the following steps: Step 6.1, select the performance indicator function E1(k); in: r(k) is the input of the radial basis neural network identifier, which is the given speed v(k) and the feedback speed y(k); y m (k) is the output speed of the radial basis neural network identifier; Step 6.2, calculate Jacobian information The calculation result is used as Jacobian information; Step 6.3, use the following formula to calculate the adjustment values ​​Δβ4(k) and Δβ5(k) of β4 and β5, in: η is the learning rate, and 0<η<1; Step 6.4, input the adjusted values ​​Δβ4(k) and Δβ5(k) obtained in step 6.3 into the following formulas to obtain the adjusted values ​​of β4(k) and β5(k); β4(k)=β4(k-1)+Δβ4(k) β5(k)=β5(k-1)+Δβ5(k).

5. The nonlinear auto-disturbance rejection control method based on RBF neural network as claimed in claim 2, characterized in that: In step 7, according to the parameters of the disturbance compensation error feedback control rate adjusted in step 6, the disturbance compensation error feedback control rate output control amount u0(k) is specifically: u0(k)=β4(k)·fal(e1(k),a3,δ)+β5(k)·fal(e2(k),a4,δ)

Images