A Model Predictive Control Method and Device for Suppressing Multiple Nonlinear Disturbances

Abstract

The present invention discloses a model predictive control method and device for suppressing various nonlinear disturbances. First, a state-space model of the servo system is established, and the constraint conditions of the model and the nonlinear disturbance constraint conditions are analyzed; secondly, through the optimization and improvement of the system model, various nonlinear disturbances can be directly incorporated into the novel predictive control strategy designed in this paper; in order to better handle various nonlinear disturbances of the servo system dynamic model, the constraint conditions are adjusted and transformed into a new cost function, which is more in line with the actual servo system dynamic model compared with the traditional constraint conditions and cost functions; then the control law is designed and the stability is analyzed. The model predictive control (MPC) control method proposed by the present invention has high-precision speed tracking ability and anti-interference ability, has a good compensation effect on the coupling effect of various nonlinear disturbances, and has the characteristics of high precision, fast speed and strong robustness.

Description

Technical Field

[0001] The present invention relates to the field of servo control, and in particular, to a model predictive control method and device for suppressing multiple non - linear disturbances. Background Art

[0002] Servo systems are widely used in motion control systems such as telescopes, radar antennas, and inertial navigation platforms. In applications in the military and astronomical fields, extremely high requirements are placed on the tracking accuracy of electro - mechanical servo systems. At present, in order to achieve high - performance control effects, advanced control strategies such as sliding - mode control, robust control, and adaptive control have been introduced. However, servo systems will inevitably be disturbed by non - linear factors. For example, friction in the transmission mechanism, dead zones in the drive circuit, torque rotation, and backlash will all have a great impact.

[0003] Nowadays, rich achievements have been made in the modeling and compensation of single - input non - linear disturbances. However, in the actual use process of servo systems, it is impossible to be disturbed only by a single non - linear disturbance. Often, it is simultaneously disturbed by multiple non - linear disturbances. In the prior art, the vast majority of scholars and engineering and technical personnel have studied single - input non - linear disturbances, and the research on multi - input non - linear disturbance systems is very limited. In particular, almost no researchers have explored the coupling effects generated by multi - input non - linear disturbances. The multi - input non - linear disturbances and the coupling effects generated by multi - input non - linear disturbances often have a huge impact on other performance such as the accuracy of servo systems. Summary of the Invention

[0004] In view of the problems existing in the above - mentioned prior art, the present invention provides a model predictive control method and device for suppressing multiple non - linear disturbances, so as to solve the technical problems of the reduction of the accuracy and other performances of the servo system caused by the coupling effects of multiple non - linear disturbances in the prior art.

[0005] To achieve the above object, the present invention provides a model predictive control method for suppressing non - linear disturbances, and the method includes:

[0006] Construct a state - space model of the electro - mechanical servo system including multiple non - linear disturbances;

[0007] Discretize the state - space model to obtain a discretized state - space model that simultaneously includes inputs, outputs, and the multiple non - linear disturbances, and constrain the inputs and the multiple non - linear disturbances of the discretized state - space model;

[0008] Based on the discretized state - space model, predict the output of the servo system under the prediction time domain of the non - linear disturbance to obtain a series of predicted values of the output speed at different times;

[0009] Calculate the error caused by the multiple non - linear perturbations according to the predicted speed value and the actual speed value of the output;

[0010] Construct a cost function to handle the non - linear perturbations and then compensate for the error.

[0011] In an alternative embodiment of the present invention, the non - linear perturbations include load torque perturbation, friction torque perturbation, and pulsating torque perturbation.

[0012] In an alternative embodiment of the present invention, the state - space model is specifically as follows:

[0013]

[0014] y = cx (1b);

[0015] Where:

[0016] The state variable x = [x1 x2 x3] T , where x1 represents the motor current, x2 represents the motor speed, and x3 represents the output angular velocity;

[0017] The non - linear perturbation w = [T f T r T L T , where T f represents the friction torque perturbation, T r represents the pulsating torque perturbation, T L represents the load torque perturbation;

[0018] c = [0 0 1],

[0019]

[0020] Where, T s represents the inertia time constant, K s represents the drive device amplification factor, K t represents the torque constant, J m represents the moment of inertia of the motor, J L represents the moment of inertia of the load, B L represents the damping constant of the load, K e represents the back electromotive force, T L represents the load torque perturbation, T f represents the friction torque perturbation, T r represents the pulsating torque perturbation.

[0021] ​In an alternative embodiment of the present invention, the discretization process of the state space model to obtain a discretized state space model that simultaneously includes inputs, outputs, and the multiple non-linear disturbances specifically includes:

[0022] Let u a =[u w] T , B a =[b B d , then formula (1a) is transformed into

[0023]

[0024] Use the Euler method to discretize formula (2), and the following is obtained

[0025] x(k + 1)=Gx(k)+H a u a (k) (3),

[0026] where G = TA + I, H a =TB a , I is the identity matrix, and T is the sampling time;

[0027] Let then formula (3) becomes as follows:

[0028] x(k + 1)=Gx(k)+hu(k)+H w w(k) (4a);

[0029] Thus, the following discretized state space model is obtained:

[0030] x(k + 1)=Gx(j)+hu(k)+H w w(k) (4a);

[0031] y(k)=cx(k)(4b).

[0032] In an alternative embodiment of the present invention, based on the discretized state space model, the output of the servo system is predicted under the prediction time domain of the non-linear disturbance to obtain a series of predicted velocity values of the output at different times, which specifically includes:

[0033] Predict according to the discretized state space model in the prediction time domain to obtain a series of predicted velocity values of the output at different times;

[0034] A series of predicted velocity values of the output at different times form a predicted velocity sequence, where the predicted velocity sequence is specifically as follows:

[0035]

[0036] wherein, is the control sequence in the control time domain, and the specific formula is as follows:

[0037] U(k) = [u(k) u(k + 1)... u(k + d - 1)]^T (6);

[0038] The predicted output Y(k + 1|k) = [y(k + 1|k)... y(k + n|k)] T (7);

[0039] Composed of disturbances constitute

[0040] The specific formula of W(k) is as shown in (8):

[0041] W(k) = [w^T(k) w^T(k + 1)... w^T(k + d - 1)] T (8);

[0042] The specific expression is as shown in (9):

[0043]

[0044] The specific formula is as shown in (10):

[0045]

[0046] The specific formula is as shown in (11):

[0047]

[0048] In an alternative embodiment of the present invention, a cost function is constructed to process the non - linear disturbance and thereby compensate the error, specifically including:

[0049] Construct a cost function including the error sequence, the control sequence in the control time domain, and the non - linear disturbance to process the non - linear disturbance;

[0050] Process the cost function to obtain an optimal control sequence, and use the optimal control sequence as an output feed - forward to control the servo system for error compensation.

[0051] In an alternative embodiment of the present invention, the cost function is specifically as follows:

[0052]

[0053] wherein, represents the error sequence between the predicted speed sequence and the reference speed sequence, To ensure that the value of the control sequence is small, it plays a role in reducing the interference effects brought by the frictional torque disturbance, torque ripple disturbance, and load torque disturbance. The symmetric positive definite matrix is a weighting matrix.

[0054] In an alternative embodiment of the present invention, the cost function is processed to obtain an optimal control sequence, and the optimal control sequence is used as an output feedforward to control the servo system for error compensation, specifically including:

[0055] Substitute Equation (5) into Equation (12), then Equation (12) is converted into the equation shown in (13):

[0056]

[0057] Differentiate Equation (13) with respect to U(k) to obtain the equation shown in (14):

[0058]

[0059] Let Equation (14) be 0 to obtain the optimal control sequence shown in (15) below:

[0060] where

[0061] can be regarded as output feedforward and state feedback, which is used to perform feedback compensation on the disturbance of the controller.

[0062] In an alternative embodiment of the present invention, the mathematical model of the pulsating torque disturbance is:

[0063]

[0064] where N s is the number of slots, θ is the rotor position of the driving motor, A rn and are respectively the amplitude and phase angle of the nth-order torque ripple harmonic.

[0065] To achieve the above and other objectives, the present invention also discloses a model predictive control device for suppressing multiple nonlinear disturbances, including:

[0066] A state space model component module for constructing a state space model of the electro-mechanical servo system including multiple nonlinear disturbances;

[0067] The state - space model discretization processing module is used to discretize the state - space model to obtain a discretized state - space model that simultaneously includes inputs, outputs, and the multiple non - linear disturbances, and to constrain the inputs and the multiple non - linear disturbances of the discretized state - space model;

[0068] The prediction module is used to predict the output of the servo system based on the discretized state - space model in the prediction time domain of the non - linear disturbances, and obtain a series of predicted velocity values of the output at different times;

[0069] The error calculation module is used to calculate the error caused by the multiple non - linear disturbances according to the predicted velocity value of the output and the actual velocity value;

[0070] The error compensation module is used to construct a cost function to handle the non - linear disturbances and then compensate the error.

[0071] Advantageous effects:

[0072] The model predictive control method for suppressing multiple non - linear disturbances applied to an electro - mechanical servo system provided by the present invention first constructs a state - space model of the electro - mechanical servo system that includes multiple non - linear disturbances; then discretizes the state - space model to obtain a discretized state - space model that simultaneously includes inputs, outputs, and the multiple non - linear disturbances, and constrains the inputs and the multiple non - linear disturbances of the discretized state - space model; then predicts the output of the servo system based on the discretized state - space model in the prediction time domain of the non - linear disturbances, and obtains a series of predicted velocity values of the output at different times; then calculates the error caused by the multiple non - linear disturbances according to the predicted velocity value of the output and the actual velocity value; finally, constructs a cost function to handle the non - linear disturbances and then compensates the error. The method provided by this application effectively solves the problems such as reduced accuracy caused by the coupled action of multiple non - linear disturbances in the servo system. At the same time, it has high - precision speed tracking ability and anti - interference ability, has a good compensation effect on the coupled effect of multiple non - linear disturbances, and has the characteristics of high precision, fast speed, and strong robustness. Description of the Drawings

[0073] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0074] Figure 1Schematic flow chart of a model predictive control method for suppressing multiple non - linear disturbances provided in an embodiment of the present invention.

[0075] Figure 2 Open - loop block diagram of the speed of a multi - disturbance servo motor system in an embodiment of the present invention.

[0076] Figure 3a Speed response curves of different control strategies under the condition of a given rotational speed of 100 rmp in an embodiment of the present invention.

[0077] Figure 3b Speed response curves of different control strategies under the condition of a given rotational speed of 100 rmp in an embodiment of the present invention.

[0078] Figure 4a Speed response curves of different control strategies under the condition of a given rotational speed of 500 rmp in an embodiment of the present invention.

[0079] Figure 4b Speed response curves of different control strategies under the condition of a given rotational speed of 500 rmp in an embodiment of the present invention.

[0080] Figure 5a Speed response curves of different control strategies under the condition of a given rotational speed of 1000 rmp in an embodiment of the present invention.

[0081] Figure 5b Speed response curves of different control strategies under the condition of a given rotational speed of 1000 rmp in an embodiment of the present invention.

[0082] Figure 6 Comparison chart of the tracking performance of the servo system under different control strategies in an embodiment of the present invention.

[0083] Figure 7 Schematic structure diagram of a model predictive control device for suppressing multiple non - linear disturbances in an embodiment of the present invention. Detailed implementation manners

[0084] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0085] It should be noted that the terms "including" and "having" and any variations thereof in the description, claims and above-mentioned drawings of the present invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device including a series of steps or units is not necessarily limited to those clearly listed steps or units, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0086] Nowadays, rich achievements have been made in the modeling and compensation of single-input non-linear disturbances. However, in the actual use process of the servo system, it is impossible to be disturbed only by a single non-linear disturbance. It is often disturbed by multiple non-linear disturbances simultaneously. In the prior art, most scholars and engineers have studied single-input non-linear disturbances, and the research on the model of multi-input non-linear disturbance system is very limited. In particular, almost no researcher has dabbled in the coupling effect generated by multi-input non-linear disturbances. The multi-input non-linear disturbances and the coupling effect generated by multi-input non-linear disturbances often have a huge impact on other performances such as the accuracy of the servo system.

[0087] In view of the problems existing in the above-mentioned prior art, the purpose of the present application is to provide a model predictive control method and device for suppressing non-linear disturbances. The following will describe these embodiments in detail.

[0088] Please refer to Figure 1 as shown in Figure 1 is a flowchart of a model predictive control method for suppressing multiple non-linear disturbances shown in an exemplary embodiment of the present application. Combining Figure 1 as shown in

[0089] Step 101, constructing a state space model of the electro-mechanical servo system including multiple non-linear disturbances;

[0090] Step S102, discretizing the state space model to obtain a discretized state space model including inputs, outputs and the multiple non-linear disturbances, and constraining the inputs and the multiple non-linear disturbances of the discretized state space model;

[0091] Step S103, predicting the output of the servo system based on the discretized state space model in the prediction time domain of the non-linear disturbance to obtain a series of predicted velocity values of the output at different times;

[0092] Step S104, calculating the error generated by the multiple non-linear disturbances according to the predicted velocity value of the output and the actual velocity value;

[0093] Step S105: Construct a cost function to handle the non - linear disturbances and thus compensate for the error.

[0094] The model predictive control method for suppressing multiple non - linear disturbances provided by the embodiments of the present disclosure first constructs a state - space model of the electro - mechanical servo system including multiple non - linear disturbances; then discretizes the state - space model to obtain a discretized state - space model that simultaneously includes inputs, outputs, and the multiple non - linear disturbances, and constrains the inputs and the multiple non - linear disturbances of the discretized state - space model; then predicts the output of the servo system based on the discretized state - space model under the prediction time domain of the non - linear disturbances to obtain a series of predicted speed values of the output at different times; then calculates the error caused by the multiple non - linear disturbances according to the predicted speed values of the output and the actual speed values; finally, constructs a cost function to handle the non - linear disturbances and thus compensate for the error. The method provided herein effectively solves problems such as reduced accuracy caused by the coupled action of multiple non - linear disturbances in the servo system. At the same time, it has high - precision speed tracking ability, has a good compensation effect on the coupled effect of multiple non - linear disturbances, and has the characteristics of high precision, fast speed, and strong robustness.

[0095] Now, in combination with the attached Figure 1 and the attached Figure 2 we will detail the implementation process of each step:

[0096] First, execute step S101 to construct a state - space model of the electro - mechanical servo system including multiple non - linear disturbances.

[0097] Please refer to Figure 2 as shown, Figure 2 which is the speed open - loop block diagram of the multi - disturbance electro - mechanical servo system provided in a specific embodiment of the present application.

[0098] Combined with Figure 2 as shown, in this embodiment, the multiple non - linear disturbances include load torque disturbance T L , frictional torque disturbance T f , and pulsating torque disturbance T r . It can be understood that in other embodiments, the non - linear disturbances can also be backlash, mechanical deflection, noise, vibration, etc. In short, in other embodiments, the disturbance factors to be processed can be expanded according to the constructed disturbance mathematical model.

[0099] According to Figure 2 the speed open - loop block diagram of the multi - disturbance electro - mechanical servo system shown, construct the following continuous state - space model:

[0100]

[0101] y = cx (1b);

[0102] Among them, the state variable \(x = [x_1\ x_2\ x_3]\), T , where \(x_1\) represents the motor current, \(x_2\) represents the motor speed, and \(x_3\) represents the output angular velocity;

[0103] The non - linear disturbance \(w=[T\) f \(T\) r \(T\) L \), T , where \(T\) f represents the frictional torque disturbance, \(T\) r represents the pulsating torque disturbance, \(T\) L represents the load torque disturbance;

[0104] \(c = [0\ 0\ 1]\),

[0105]

[0106] Among them, \(T\) s represents the inertia time constant, \(K\) s represents the drive device amplification factor, \(K\) t represents the torque constant, \(J\) m represents the moment of inertia of the motor, \(J\) L represents the moment of inertia of the load, \(B\) L represents the damping constant of the load, \(K\) e represents the back - electromotive force, \(T\) L represents the load torque disturbance, \(T\) f represents the frictional torque disturbance, \(T\) r represents the pulsating torque disturbance.

[0107] Then, step S102 is executed to discretize the state - space model to obtain a discretized state - space model that simultaneously includes inputs, outputs, and the various non - linear disturbances, and to constrain the inputs and the various non - linear disturbances of the discretized state - space model.

[0108] In a specific embodiment, step S102 specifically includes:

[0109] Let \(u\) a \(=[u\ w]\) T , \(B\) a \(=[b\ B\) d , then formula (1a) is transformed into

[0110]

[0111] Using the Euler method to discretize formula (2), the following formula (3) is obtained:

[0112] x(k + 1) = Gx(k) + h a u a (k) (3),

[0113] where G = TA + I, H a = TB a , I is the identity matrix, and T is the sampling time;

[0114] Let then formula (3) becomes as shown in (4a):

[0115] x(k + 1) = Gx(k) + hu(k) + H w w(k) (4a);

[0116] Thus, the following discretized state - space model is obtained:

[0117] x(k + 1) = Gx(k) + hu(k) + H w w(k) (4a);

[0118] y(k) = cx(k) (4b).

[0119] Controlling input limits and minimizing non - linear disturbances are two constraint conditions of model predictive control (MPC). Optimizing the future control input sequence u = [u(k),..., u(k + N - 1)] T can keep the predicted future output constrained within the expected range r = [r(k + 1),..., r(k + N)] T , where N is the control horizon.

[0120] In a specific embodiment of the present application, the constraints on the input of the discretized state - space model and the various non - linear disturbances are as follows:

[0121]

[0122]

[0123]

[0124] min T f (k) = T f (x(k), k), (17d)

[0125] min T r (k) = T r (x(k), k), (17e)

[0126] min T L (k) = TL (k), (17f)

[0127]

[0128] In a specific embodiment of the present application, when an elastoplastic friction model is adopted, the mathematical model of the frictional torque disturbance is as follows:

[0129]

[0130] Where:

[0131]

[0132]

[0133] Where z is the average deformation of the rigid bristles, x3 is the output angular velocity, and z ss (x3) is the Stribeck influence function, σ0, σ1, and σ2 are the stiffness, micro-damping, and viscous friction coefficients of the bristles, v s is the Stribeck angular velocity, T c and T s are the Coulomb frictional torque and the maximum static frictional torque respectively, and z ss is the effect function.

[0134] In this embodiment, z ba and z ss satisfy a linear relationship. In a preferred embodiment, z ba = 0.7169z ss .

[0135] Among the numerous non-linear disturbance interferences suffered by the electro-mechanical servo system, torque ripple will affect the dynamic performance of the electro-mechanical servo system, resulting in fluctuations in the motor output speed. Considering factors such as cogging torque, flux linkage harmonics, current measurement error, and inverter dead-time effect that cause speed pulsation, in a specific embodiment of the present application, the mathematical model of the pulsating torque disturbance is as follows:

[0136]

[0137] Where N s is the number of slots, θ is the rotor position of the driving motor, and A rn and are the amplitude and phase angle of the nth-order torque ripple harmonic respectively.

[0138] Furthermore, for the convenience of calculation, it can be assumed that the initial rotor position is 0. When the motor speed is, the mathematical model of the periodic torque fluctuation is approximately described as:

[0139]

[0140] Next, step S103 is executed to predict the output of the servo system based on the discretized state - space model in the prediction time domain of the non - linear perturbation, and a series of predicted velocity values of the output at different times are obtained.

[0141] In a specific embodiment, step S103 specifically includes:

[0142] Perform prediction in the prediction time domain according to the discretized state - space model to obtain a series of predicted velocity values of the output at different times;

[0143] A series of predicted velocity values of the output at different times form a predicted velocity sequence, where the predicted velocity sequence is specifically as follows:

[0144]

[0145] Among them, is the control sequence in the control time domain, which is composed of the perturbation constitutes

[0146] In this embodiment, the prediction time domain is nT, and the control time domain is dT. n and d are non - negative integers, n≥1 and n≥d≥1.

[0147] In the prior art, the prediction of the output variable does not consider the non - linear perturbation. In this paper, the output is predicted in the prediction time domain of the control variable u and the perturbation vector w.

[0148] U(k) = [u(k) u(k + 1) … u(k + d - 1)] T (6),

[0149] y(k + 1|k) = [y(k + 1|k) … y(k + n|k)] T (7),

[0150] w(k) = [w T (k) w T (k + 1)... w T (k + d - 1)] T (8),

[0151]

[0152]

[0153]

[0154] Next, step S104 is executed to calculate the error caused by the multiple non - linear disturbances according to the predicted speed value and the actual speed value outputted.

[0155] The model error is and y(k + 1) are the predicted speed and the actual speed of the electro - mechanical servo system respectively.

[0156] Finally, step S105 is executed to construct a cost function to handle the non - linear disturbances and thus compensate for the error.

[0157] In a specific embodiment of the present application, step S105 specifically includes:

[0158] First, construct a cost function including the error sequence, the control sequence in the control time domain, and the non - linear disturbances to handle the non - linear disturbances;

[0159] Specifically, the cost function is shown as the following formula:

[0160]

[0161] Among them, the first term in the cost function represents the error sequence between the predicted speed sequence and the reference speed sequence. The second term in the cost function is used to ensure that the value of the control sequence is small. The third term in the cost function plays a role in reducing the interference effects brought by the friction torque disturbance, the torque ripple disturbance, and the load torque disturbance. The symmetric positive definite matrix is a weighting matrix.

[0162] Compared with the prior art, the present application effectively handles non - linear disturbances by creatively introducing the third term so as to reduce the interference effects brought by the friction torque disturbance, the torque ripple disturbance, and the load torque disturbance.

[0163] Secondly, process the cost function to obtain the optimal control sequence;

[0164] Specifically, first substitute formula 5 into formula 12, then the expression of formula (12) is deformed as shown in (13):

[0165]

[0166] Take the derivative of formula (13) with respect to U(k) to obtain the formula as shown in (14):

[0167]

[0168] Let formula (14) be 0 to obtain the optimal control sequence, that is, the formula as shown in (15):

[0169]

[0170] Finally, use the optimal control sequence as output feedforward to control the servo system for error compensation.

[0171] It can be regarded as state feedback of output feedforward, and then perform feedback compensation on the disturbance of the controller. Under the combined action of these control laws, the model predictive control method provided by this application has high-precision speed tracking ability and anti-interference ability.

[0172] In addition, the model predictive control method provided by the present invention further includes stability analysis, which is specifically as follows:

[0173] Let Then formula (15) can be simplified to:

[0174]

[0175] From formula (4a) and formula (15), the state equation of the closed-loop electro-mechanical servo system is as shown in formula (16):

[0176]

[0177] If the eigenvalues of are inside the unit circle, then the closed-loop system is stable, and the eigenvalues can be determined by Q1 and Q2. Therefore, selecting appropriate matrices Q1 and Q2 can ensure the stability of the electro-mechanical servo system. In addition, the tracking performance is also related to the second and third terms.

[0178] In order to verify that the model predictive control method provided by the present invention has very good performance in suppressing various nonlinear disturbances, a simulation experiment is built in the simulation software matlab / simulink for testing, which is specifically as follows:

[0179] The state-space equation of the prediction model is:

[0180]

[0181] where C = [0 0 1].

[0182] Traditional MPC control usually adopts a fixed time domain, that is, the prediction step length output in each cycle is the same. Due to various uncertain factors and non-linear disturbances in the actual system, there are inevitably deviations between the output waveform based on predictive control and the output of the actual system, which can be compensated by feedback correction. However, when the system state changes rapidly, the length of the prediction step will affect the magnitude of the prediction deviation. The longer the step, the greater the deviation. To solve the above problems, in the servo system, according to the relationship between the prediction time domain and the speed deviation, a variable prediction time domain model predictive control can be designed in the speed loop of the servo system.

[0183] Determine the constraint conditions based on the servo system itself, and let the time domain N c = 1, the weighting coefficient matrix is a constant R = r, the error matrix Q = q * diag(1…1), and the speed deviation is e = ω * - ω. Then the control time domain at the k-th step is:

[0184]

[0185]

[0186] Among them, represents rounding up, M min and N max represent the lower and upper limits of the time domain.

[0187] Given the rotational speed ω * = 100, 150, 200, …, 1500, determine the optimal N p and r for tracking performance. Based on their fitting relationship, this paper sets the fitting relationship on the experimental platform as: r = R c *(N p / N min ) 4 , and determine the N p and r with the highest fitting degree, where R c is the initial value of r.

[0188] To verify the effectiveness of the algorithm in this paper, under the same optimal parameter conditions, different control algorithms are compared for the speed loop. Through PI control, the control effects of traditional MPC and the novel MPC designed in this paper are compared, and the controller parameters are kept the same during this process. The results are as shown in Figure 3a , 3b , 4a, 4b, 5a, 5b. Figure 3a is the speed response curve of different control strategies under the given rotational speed of 100 rmp in an embodiment of the present invention. Figure 3b is the speed response curve of different control strategies under the given rotational speed of 100 rmp in an embodiment of the present invention. Figure 4aSpeed response curves of different control strategies at a given rotational speed of 500 rmp in an embodiment of the present invention Figure 4b Speed response curves of different control strategies at a given rotational speed of 500 rmp in an embodiment of the present invention Figure 5a Speed response curves of different control strategies at a given rotational speed of 1000 rmp in an embodiment of the present invention Figure 5b Speed response curves of different control strategies at a given rotational speed of 1000 rmp in an embodiment of the present invention

[0189] By adopting different control strategies for the speed loop at rotational speeds of 100, 500, and 1000 respectively, and adding a non - linear disturbance at 0.15 s. It can be seen from the analysis of the simulation results that compared with the traditional PI control, the traditional MPC control and the MPC control proposed in this paper have better dynamic performance and stronger anti - interference ability. At different rotational speeds, when the improved MPC proposed in this paper is applied to the servo system, whether in the high - speed region or the low - speed region, the overshoot is smaller, the response speed is faster, and the anti - interference ability is stronger.

[0190] In order to further verify the effectiveness and practicality of the improved MPC control strategy, an experimental verification is carried out on the X - axis motion platform of the servo turntable. The PWM frequency is set to 10 KHZ, and the sampling period is 0.0001 S. Given a position signal, the traditional MPC and the improved MPC are respectively used for the tracking experiment, and the comparison of the tracking performance is as follows Figure 6 as shown

[0191] By comparing the position tracking curves under two different control methods, it can be concluded that compared with the traditional MPC control strategy, the improved MPC control strategy has higher position tracking accuracy and at the same time improves the response speed in the reciprocating motion of the servo system.

[0192] As Figure 7As shown in the figure, this embodiment also discloses a model predictive control device for suppressing multiple non-linear disturbances. The device includes a state space model construction module 701, a state space model discretization processing module 702, a prediction module 703, an error calculation module 704, and an error compensation module 705. The state space model construction module 701 is used to construct a state space model of the electro-mechanical servo system including multiple non-linear disturbances; the state space model discretization processing module 702 is used to discretize the state space model to obtain a discretized state space model that simultaneously includes inputs, outputs, and the multiple non-linear disturbances, and to constrain the inputs and the multiple non-linear disturbances of the discretized state space model; the prediction module 703 is used to predict the output of the servo system based on the discretized state space model in the prediction time domain of the non-linear disturbances to obtain a series of predicted velocity values of the output at different times; the error calculation module 704 is used to calculate the error caused by the multiple non-linear disturbances according to the predicted velocity value of the output and the actual velocity value; the error compensation module 705 is used to construct a cost function to process the non-linear disturbances and then compensate the error.

[0193] The foregoing description of the embodiments of the present invention (including what is described in the abstract of the specification) is not intended to be exhaustive or to limit the invention to the precise forms disclosed herein. Although specific embodiments of the invention and examples of the invention have been described herein for illustrative purposes only, various equivalent modifications will be apparent to and can be made by those skilled in the art within the spirit and scope of the invention. As noted, these modifications can be made to the invention in accordance with the foregoing description of the embodiments of the invention, and these modifications will be within the spirit and scope of the invention.

[0194] The systems and methods have been described generally herein to assist in understanding the details of the invention. In addition, various specific details have been given to provide a general understanding of embodiments of the invention. However, those skilled in the relevant art will recognize that embodiments of the invention may be practiced without one or more of the specific details, or with other devices, systems, components, methods, materials, parts, etc. In other instances, well-known structures, materials, and / or operations have not been shown or described in detail to avoid obscuring aspects of the embodiments of the invention.

[0195] Accordingly, while the present invention has been described herein with reference to its specific embodiments, modifications, various changes and substitutions are also within the above disclosure, and it should be understood that in some cases, some features of the present invention will be employed without corresponding use of other features, without departing from the scope and spirit of the claimed invention. Therefore, many modifications may be made to adapt a particular environment or material to the essential scope and spirit of the present invention. The present invention is not intended to be limited to the specific terms used in the following claims and / or to the specific embodiments disclosed as the best mode contemplated for carrying out the present invention, but the present invention will include any and all embodiments and equivalents falling within the scope of the appended claims. Accordingly, the scope of the present invention will be determined only by the appended claims.

Claims

1. A model predictive control method for suppressing multiple non - linear disturbances, characterized in that, Applied to an electro-mechanical servo system, the method includes: Construct a state space model of the electro-mechanical servo system that includes multiple non-linear disturbances; Discretize the state space model to obtain a discretized state space model that simultaneously includes inputs, outputs, and the multiple non-linear disturbances, and impose constraints on the inputs and the multiple non-linear disturbances of the discretized state space model; Based on the discretized state space model, predict the output of the servo system under the prediction time domain of the non-linear disturbances to obtain a series of predicted velocity values of the output at different times; Calculate the error caused by the multiple non-linear disturbances according to the predicted velocity values of the output and the actual velocity values; Construct a cost function to handle the non-linear disturbances and thereby compensate for the error; Wherein, the cost function is specifically as follows: Where: It represents the error sequence between the predicted speed sequence and the reference speed sequence, to ensure that the value of the control sequence is small, which plays a role in reducing the interference effects caused by frictional torque disturbance, torque ripple disturbance and load torque disturbance. The symmetric positive definite matrix is the weighting matrix; Constructing a cost function to handle the non-linear disturbances and thereby compensate for the error specifically includes: Construct a cost function that includes an error sequence, a control sequence in the control time domain, and non-linear disturbances to handle the non-linear disturbances; Process the cost function to obtain an optimal control sequence, and use the optimal control sequence as an output feedforward to control the servo system to perform error compensation.

2. The model predictive control method for suppressing multiple non-linear disturbances according to claim 1, wherein The non-linear disturbances include load torque disturbance, friction torque disturbance, and pulsating torque disturbance.

3. The model predictive control method for suppressing multiple non-linear disturbances according to claim 2, characterized in that The state space model is specifically as follows: y = cx (1b); Among them, the state variable \(x = [x_1\ x_2\ x_3]\) T , where \(x_1\) represents the motor current, \(x_2\) represents the motor speed, and \(x_3\) represents the output angular velocity; The non - linear perturbation w = [T f T r T L T , T f represents the frictional torque perturbation, T r represents the pulsating torque perturbation, T L represents the load torque perturbation;​ c＝[0 0 1]， Among them, T s represents the inertia time constant, K s represents the driving device amplification factor, K t represents the torque constant, J m represents the moment of inertia of the motor, J L represents the moment of inertia of the load, B L represents the damping constant of the load, K e represents the back electromotive force, T L represents the load torque disturbance, T f represents the frictional torque disturbance, T r represents the pulsating torque disturbance.

4. The model predictive control method for suppressing multiple non - linear disturbances according to claim 3, characterized in that, The discretizing the state space model to obtain a discretized state space model that simultaneously includes inputs, outputs, and the multiple non-linear disturbances specifically includes: Let u a = [u w] T , B a = [b B d , then formula (1a) is transformed into Use the Euler method to discretize formula (2) to obtain the following: x(k + 1) = Gx(k) + H a u a (k)(3), where G = TA + I, H a = TB a , I is the identity matrix, and T is the sampling time; Let Then formula (3) becomes as follows: x(k + 1) = Gx(k) + hu(k) + H w w(k) (4a); Thus, the following discretized state space model is obtained: x(k + 1) = Gx(k) + hu(k) + H w w(k) (4a); y(k) = cx(k) (4b).

5. The model predictive control method for suppressing multiple non-linear disturbances according to claim 3, characterized in that, Based on the discretized state space model, predicting the output of the servo system under the prediction time domain of the non-linear disturbances to obtain a series of predicted velocity values of the output at different times specifically includes: Perform prediction based on the discretized state space model in the prediction time domain to obtain a series of predicted velocity values of the output at different times; A series of predicted velocity values of the output at different times form a predicted velocity sequence, where the predicted velocity sequence is specifically as follows: Among them, is the control sequence in the control time domain, and the specific formula is as follows: U(k) = [u(k) u(k + 1)... u(k + d - 1)] T (6); The predicted output Y(k + 1|k) = [y(k + 1|k)...y(k + n|k)] T (7); caused by disturbance constitute The specific formula of W(k) is as shown in (8): W(k) = [w T (k) w T (k + 1)... w T (k + d - 1)] T (8); The specific expression is as shown in (9): The specific formula is as shown in (10): The specific formula is as shown in (11):

6. The model predictive control method for suppressing multiple non-linear disturbances according to claim 5, characterized in that Processing the cost function to obtain an optimal control sequence, and using the optimal control sequence as an output feedforward to control the servo system to perform error compensation specifically includes: Substitute formula (5) into formula (12), then formula (12) is converted into the formula shown in (13): Take the derivative of formula (13) with respect to U(k) to obtain the formula shown in (14): Let formula (14) be 0 to obtain the following optimal control sequence shown in (15): Among them, it can be regarded as output feedforward and state feedback, which is used to perform feedback compensation on the disturbance of the controller.

7. The model predictive control method for suppressing multiple non-linear disturbances according to claim 3, characterized in that, The mathematical model of the pulsating torque disturbance is: Among them, N s is the number of slots, θ is the rotor position of the drive motor, A rn and are respectively the amplitude and phase angle of the nth torque ripple harmonic.

8. A model predictive control device for suppressing multiple non-linear disturbances, characterized in that, Applied to an electro-mechanical servo system, includes: A state space model construction module for constructing a state space model of the electro-mechanical servo system that includes multiple non-linear disturbances; The state space model discretization processing module is used to discretize the state space model to obtain a discretized state space model that simultaneously includes inputs, outputs, and the multiple non-linear disturbances, and to constrain the inputs and the multiple non-linear disturbances of the discretized state space model; The prediction module is used to predict the output of the servo system based on the discretized state space model under the prediction time domain of the non-linear disturbance, and obtain a series of predicted speed values of the output at different times; The error calculation module is used to calculate the error caused by the multiple non-linear disturbances according to the predicted speed value of the output and the actual speed value; The error compensation module is used to construct a cost function to process the non-linear disturbance and then compensate the error; Wherein, the cost function is specifically as follows: Where: It represents the error sequence between the predicted speed sequence and the reference speed sequence, to ensure that the value of the control sequence is small, which plays a role in reducing the interference effects caused by frictional torque disturbance, torque ripple disturbance and load torque disturbance. The symmetric positive definite matrix is the weighting matrix; Constructing a cost function to process the non-linear disturbance and then compensate the error specifically includes: Constructing a cost function that includes an error sequence, a control sequence in the control time domain, and a non-linear disturbance to process the non-linear disturbance; Processing the cost function to obtain an optimal control sequence, and using the optimal control sequence as an output feedforward to control the servo system for error compensation.

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