High-frequency motor driving multi-rate control method for time sequence disturbance compensation

Abstract

The invention discloses a high-frequency motor drive multi-rate control method for time sequence disturbance compensation, and the core principle of the method is that low-rate disturbance compensation and a reference tracking trajectory are improved and converted into a time sequence processing process matched with a high-rate control instruction; specifically, a single disturbance compensation value which can be known only at a sampling moment Ts is expanded into time sequence prediction of disturbance changes on N control points in the future through a generalized proportional-integral observer; meanwhile, a low-frequency single reference instruction is constructed into a smooth high-frequency reference trajectory covering N control points through a Lagrange interpolation method, and closed-loop correction of disturbance compensation and reference tracking is achieved on each high-frequency control point Tc. The problem that open-loop prediction errors are continuously accumulated and spread due to mismatching of information updating rates in traditional multi-rate control is fundamentally solved, and therefore high-precision robust control over the high-frequency motor driving system is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-frequency motor drive control, and more specifically, relates to a high-frequency motor drive multi-rate control method with time series disturbance compensation. Background Art

[0002] In recent years, wide-bandgap semiconductor device technology, represented by silicon carbide (SiC), has developed rapidly, enabling power converters to operate at extremely high switching frequencies. This has brought revolutionary breakthroughs in improving the power density of motor drive systems, reducing system size, and improving energy efficiency. However, high switching frequencies pose a severe challenge to digital controllers, and extremely short interrupt cycles limit the execution of complex control algorithms. To address this challenge, a multi-rate model predictive control scheme has emerged. This scheme decouples the sampling and control frequencies, allowing the controller to operate at a longer sampling period T s Calculate N control sequences within the time and use a higher control frequency T c This solution not only relieves the computing pressure of the processor but also achieves high switching frequency control.

[0003] However, although the above scheme successfully achieves high-frequency control, its control performance is highly dependent on the accuracy of the system model. Due to its multi-step prediction mechanism, when there is a mismatch between the model parameters and the actual system, the prediction error will continue to propagate and accumulate at N control points with time series characteristics within a sampling period. To solve this problem, a common solution is to introduce a disturbance observer to equate the model mismatch and external disturbances to a lumped disturbance for compensation. However, the traditional disturbance observer can only perform disturbance compensation once at each sampling moment. It cannot provide real-time disturbance suppression for the time series composed of multiple control inputs within the sampling period. As a result, the cumulative effect of the error still exists within a sampling period, limiting the control accuracy and robustness of the system. Therefore, there is an urgent need for a new control method that can accurately compensate for time series disturbances within the sampling period. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the existing technology and propose a high-frequency motor drive multi-rate control method with time series disturbance compensation. When the system model is inaccurate, the time series disturbance within the sampling period is effectively compensated and suppressed, thereby achieving high-performance control of the high-frequency motor drive system.

[0005] To achieve the above-mentioned object of the invention, the present invention provides a high-frequency motor drive multi-rate control method with time series disturbance compensation, characterized by comprising the following steps:

[0006] (1) Obtain the motor system status and low-frequency reference instructions: The motor three-phase current ia 、i b 、i c Converted to the actual current i in the αβ stationary coordinate system α 、i β ; Obtain the reference current of the motor in the αβ stationary coordinate system through the speed loop PI controller and T2 coordinate transformation module The actual current i of the motor in the αβ stationary coordinate system α 、i β , as the state vector x(k) = [i α ,i β ] T ;

[0007] (2) Estimation of time series disturbance and model compensation: Use the generalized proportional integral observer to estimate k and k+N p The time series disturbance between the moments is then embedded into the current prediction model of the motor system;

[0008] (3) Generate high-frequency reference trajectory: Based on the low-frequency reference current at the current k moment Electrical angle θ e and electrical angular velocity ω e , predict k+N p The reference current at the moment; then the Lagrange interpolation method is used to interpolate k and k+N p The reference current between the moments is interpolated to generate a smooth high-dimensional reference trajectory vector Y * ;

[0009] (4) Solve the optimal control sequence: predict the output vector of the motor system at the next moment based on the current prediction model Y ; Combined with the high-dimensional reference trajectory vector generated in step (3) Y * , by minimizing the cost function J, we can obtain an optimal control sequence u (k);

[0010] (5) Drive execution: The optimal control sequence u (k) Input to the space vector pulse width modulation module of the motor system, in N p Sampling period T s The high-frequency switching signal is generated by the space vector pulse width modulation module to control the motor.

[0011] The object of the invention of the present invention is achieved like this:

[0012] The core principle of the multi-rate control method for high-frequency motor drive based on time series disturbance compensation proposed in this paper is to improve and transform the low-rate disturbance compensation and reference tracking trajectory into a time-series processing process that matches the high-rate control instruction; specifically, the generalized proportional-integral observer is used to convert the low-rate disturbance compensation and reference tracking trajectory into a time-series processing process that matches the high-rate control instruction. s The known single disturbance compensation value is expanded to the time series prediction of disturbance changes at N control points in the future; at the same time, the low-frequency single reference instruction is constructed into a smooth high-frequency reference trajectory covering N control points through the Lagrange interpolation method. c Both of them realize closed-loop correction of disturbance compensation and reference tracking, which fundamentally solves the problem of continuous accumulation and propagation of open-loop prediction errors caused by information update rate mismatch in traditional multi-rate control, thereby realizing high-precision robust control of high-frequency motor drive systems.

[0013] At the same time, the high-frequency motor drive multi-rate control method based on time series disturbance compensation of the present invention also has the following beneficial effects:

[0014] (1) In the present invention, by adopting a generalized proportional-integral observer, real-time estimation and compensation of the timing disturbance of each control point within the sampling period are achieved; this method fundamentally solves the problem of propagation and accumulation of prediction errors caused by model mismatch in traditional multi-rate predictive control methods during multi-step prediction, and significantly improves the control accuracy;

[0015] (2) To address the data dimension mismatch problem of high-frequency reference trajectories in multi-rate control, the present invention uses Lagrange interpolation to generate smooth high-frequency reference trajectories, which enables the system to have faster dynamic response speed and higher steady-state tracking accuracy;

[0016] (3) The present invention provides effective timing compensation for disturbances caused by uncertainties such as parameter mismatch, so that the control system can maintain stable and high-quality control performance when the key parameters of the motor change significantly;

[0017] (4) By decoupling the sampling and control frequencies, the controller is allowed to complete the complex calculations of multiple future control sequences within a longer sampling period; this method alleviates the computational pressure of the digital processor at high switching frequencies and provides sufficient time margin for executing the precise disturbance compensation algorithm proposed in the present invention, ensuring the reliable implementation of the control strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is an overall structural diagram of a multi-rate control system for time series disturbance compensation according to the present invention;

[0019] Figure 2 It is a detailed flow chart of the time series disturbance compensation control algorithm;

[0020] Figure 3 It is a digital implementation method based on the time series disturbance compensation control algorithm;

[0021] Figure 4 This is a waveform comparison diagram of the present invention under the condition of motor inductance parameter mismatch. DETAILED DESCRIPTION

[0022] The following describes the specific embodiments of the present invention in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when detailed descriptions of known functions and designs may dilute the main content of the present invention, such descriptions will be omitted here.

[0023] Example

[0024] Figure 1 This is the overall structural diagram of a multi-rate control system for time series disturbance compensation according to the present invention.

[0025] In this embodiment, we first briefly introduce the overall structure of the multi-rate control system for time series disturbance compensation. Figure 1 As shown, it includes: a high-frequency motor driver 1 based on silicon carbide (SiC), a three-phase permanent magnet synchronous motor (PMSM) 2, a DC power supply 3, a current sampling module 4, a position encoding module 5 and a disturbance compensation multi-rate controller 6.

[0026] The high-frequency motor driver 1 is a three-phase voltage source inverter (VSI), whose DC side is powered by a DC power supply 3 and whose AC side is connected to a three-phase permanent magnet synchronous motor 2;

[0027] The three-phase permanent magnet synchronous motor 2 is the final controlled object of this control system. In this embodiment, it is a surface-mounted permanent magnet synchronous motor. Its stator three-phase winding receives three-phase alternating current from the high-frequency motor driver 1.

[0028] The DC power supply 3 is the energy source of the entire motor drive system, and its function is to provide a stable and continuous DC voltage for the high-frequency motor driver 1;

[0029] The current sampling module 4 is provided between the driver 1 and the permanent magnet synchronous motor 2 and is used to collect the three-phase AC current i in real time. abc And feed it back to the multi-rate controller 6;

[0030] The position encoding module 5 is installed on the shaft of the motor 2 and is used to detect the electrical angle θ of the motor rotor in real time. e And feed it back to the multi-rate controller 6;

[0031] The disturbance compensation multi-rate controller 6 is the core of the present invention. It receives the signals from the current sampling module 4 and the position encoding module 5, and after a series of internal algorithm processing, outputs the space vector pulse width modulation (SVPWM) signal S abc To the high-frequency motor driver 1; the disturbance compensation multi-rate controller 6 internally includes: a speed calculation module 7, a difference operation unit 8, a speed loop PI controller 9, a T1 / T2 coordinate transformation module 10, a Lagrange interpolation module 11, a time series disturbance observation module 12, a prediction model module 13, a control law solving module 14 and a space vector pulse width modulation module 15;

[0032] The input end of the speed calculation module 7 is connected to the position encoding module 5, and is used to calculate the speed of the position according to the input electrical angle θ. e Calculate the current actual angular velocity ω of the motor e ;

[0033] The input end of the difference operation unit 8 is connected to the external reference angular velocity ω e * and the actual angular velocity ω from the velocity calculation module 7 e , used to calculate the difference between the two and obtain the speed error signal;

[0034] The input end of the speed loop PI controller 9 is connected to the output end of the difference operation unit 8, receives the speed error signal, and outputs the q-axis reference current through proportional integral (PI) control. In addition, the d-axis reference current In this embodiment, it is set to zero;

[0035] The T1 / T2 coordinate transformation module 10 is responsible for converting the three-phase actual current i abc Converted to the actual current i in the αβ stationary coordinate system αβ And convert the dq axis reference current into the reference current in the αβ stationary coordinate system

[0036] The input end of the Lagrange interpolation module 11 is connected to the T1 coordinate transformation module 10 to receive the low-frequency reference current Fit the low-frequency reference command to generate a high-dimensional reference trajectory that matches the future N high-frequency control points Y * and output it to the prediction model module 13;

[0037] The input end of the time series disturbance observation module 12 is connected to the T2 coordinate transformation module 10 to receive the actual current i αβ ; This module is used to online estimate the time series disturbance information within the sampling period caused by uncertainties such as model parameter mismatch

[0038] The prediction model module 13 receives the actual current i from the T2 coordinate transformation module 10 αβ and the time series disturbance information of the time series disturbance observation module 12 This module embeds the estimated time series disturbance into the system's discretized state space model to form a more accurate prediction model that is compensated in real time.

[0039] The control law solving module 14 has its input end connected to the Lagrange interpolation module 11 and the prediction model module 13; the module is based on the compensated prediction model and the high-dimensional reference trajectory. Y * By minimizing the cost function J, an optimal control sequence containing the future N control inputs is obtained online. u (k);

[0040] The input end of the space vector pulse width modulation module 15 is connected to the control law solving module 14; the module generates the driving signal S in turn at a higher control frequency within a sampling period. abc , used to control the high-frequency motor driver 1.

[0041] Figure 2 The detailed flow chart of the time series disturbance compensation control algorithm of the present invention is characterized in that it includes the following steps:

[0042] (1) Obtain the motor status and low-frequency reference trajectory;

[0043] (1.1) Obtain the motor three-phase current i through the current sampling module a ,i b ,i c ;

[0044] (1.2) Obtain the real-time electrical angle θ of the motor through the position encoding module e ;

[0045] (1.3) The three-phase actual current i is converted into abc Converted to the actual current i in the αβ stationary coordinate system αβ , the T1 coordinate transformation formula is expressed as follows:

[0046]

[0047] (1.4) Using the speed calculation module to find the derivative, the electrical angle θ e Converted into electrical angular velocity ω e ;

[0048] (1.5), given reference speed The electrical angular velocity error is calculated using the difference operation unit and input into the speed loop PI controller to obtain the q-axis reference current. To achieve maximum torque current ratio control, the d-axis reference current Set to zero;

[0049] (1.6) To obtain the low-frequency current reference trajectory, the reference current of the dq rotating coordinate system is converted into the reference current of the αβ stationary coordinate system through the T2 coordinate transformation module. The T2 coordinate transformation formula is expressed as follows:

[0050]

[0051] (2) Time series disturbance observation and compensation;

[0052] (2.1) All errors caused by uncertainties such as inaccurate model parameters and unmodeled dynamics are unified into a time series disturbance term f(mT c |k), the constructed system discretization state equation can be expressed as follows:

[0053]

[0054] Among them, f(mT c |k) is the system in mT c The time series disturbance term at time |k can be specifically expressed as:

[0055] f(mT c |k)=ΔA d x(mT c |k)+ΔB d u(mT c |k)+ΔD d ;

[0056] Where ΔA d , ΔB d , ΔD d Represent the system matrix A respectively d , input matrix B d , the perturbation matrix D d In the uncertain part at the current moment, that is, x=[i α ,i β ] T ,u=[u α ,u β ] T

[0057]

[0058] i α ,i β ,u α,u β are the current and voltage under α and β axes respectively, R s , ψ f and L s The resistance, flux linkage and inductance of the motor respectively;

[0059] (2.2), estimate each sampling period T through the reduced-order generalized proportional integral observer s Time series disturbance within;

[0060] (2.2.1) First, a high-order difference model of discrete-time disturbance is constructed, which can be expressed as follows:

[0061]

[0062] Among them, h1(k),…,h n (k) represents the high-order difference term of the time series disturbance f(k);

[0063] (2.2.2) Design a discretized reduced-order generalized proportional-integral observer:

[0064]

[0065] Where r(k)=Ax(k)+Bu(k)+D, where A, B and D are matrices in the continuous domain of the system; α i is the gain of the observer, z i is the state vector of the observer, where i = 0,...,n-1;

[0066] (2.2.3) The state vector at the current k moment x(k) = [i α ,i β ] T Input to the generalized proportional integral observer to estimate k and k+N p Time series disturbances between moments

[0067]

[0068] In this embodiment, the designed lifting time series disturbance matrix It will be combined with the subsequent control rate calculation process and compensate for the uncertainty components in the model;

[0069] (2.3), model compensation;

[0070] Perturb the time series Time series disturbance information in Embedded into the current state equation, the compensated current state prediction equation is obtained:

[0071]

[0072] Among them, y(mT c |k) is mT c |The output vector at time k, C is the second-order unit matrix, and N is the frequency increase multiple.

[0073] (3) Lagrangian interpolation of high-frequency reference trajectory;

[0074] In order to obtain the lifting reference trajectory vector Y * In this embodiment, the Lagrange interpolation method is used to obtain the high-frequency reference trajectory data within the sampling period. The specific process is as follows:

[0075] First, construct N p The interpolation polynomial of order -1 can be expressed as follows:

[0076]

[0077] Among them, P(x) is the interpolation polynomial, L j (x) is the Lagrange interpolation basis function and satisfies:

[0078]

[0079] Among them, x is the interpolation point within the sampling period, x j =θ+jω e T s ,y j =y * (T c |k+j), j=0,1,…,N p -1,y * Contains the reference current at each sampling cycle

[0080] Next, for k and k+N p The reference current between the moments is interpolated to generate a high-dimensional reference trajectory vector Y * It is expressed as follows:

[0081]

[0082] (4) Obtaining the optimal control sequence;

[0083] (4.1) To obtain a high-dimensional control sequence, the following cost function is constructed:

[0084] J=Δ Y (k+1|k) T Θ Δ Y (k+1|k)+ U(k) T ΥU (k);

[0085] Among them, Δ Y is the tracking error, i.e. Δ Y (k+1|k)= Y (k+1|k)- Y * (k+1|k), Θ and Υ are Δ Y and boost control vector U The weight coefficient of

[0086] (4.2), by making the cost function J U The partial derivative of is equal to zero, and the lifting control vector is obtained as follows:

[0087] U (k)=( C d T TH d + Υ ) -1 C d T Θ [ Y * - Oh d x(k)- X d ];

[0088] Among them, the improvement matrix C d and Oh d They are expressed as follows:

[0089]

[0090]

[0091] Improvement Matrix X d Expressed as:

[0092]

[0093] Among them, the lifting matrix ∑ represents:

[0094]

[0095] Where, To improve the time series disturbance matrix;

[0096] (5) Output the optimal control sequence in an orderly manner;

[0097] Improve the control vector according to the extended rolling optimization strategy UThe first N sequences of (k) are applied to the system, and the optimal control sequence is expressed as:

[0098] u (k)=Ψ U (k);

[0099] in, The dimension is N×N p N;

[0100] Finally, the optimal control sequence u (k) Space vector pulse modulation is performed in sequence, and the generated switching signal drives the high-frequency silicon carbide motor driver.

[0101] like Figure 3 The specific implementation of the control algorithm of the present invention on the digital controller is demonstrated. The core of the invention is to use a dual-rate interrupt mechanism to balance the computing load and the control frequency; low-rate interrupt: the interrupt is based on the sampling frequency 1 / T s Execution, in a longer sampling period T s The controller completes all complex computational tasks in sequence, including: acquiring the state x(k) through sampling; generating high-dimensional references through the Lagrange interpolation module; estimating the disturbance time series through the time series disturbance observation module; and calculating the optimal control sequence containing the next N instructions through the control law solution module; high-rate interrupt: the interrupt is at N times the control frequency 1 / T c Execution; in each control cycle T c Initially, only pre-calculated control sequences are interrupted at a low rate u In (k), a control instruction is sequentially retrieved; the modulation module compares the modulated wave with the triangular carrier wave to generate the switching signal for that control cycle. This approach separates time-consuming computational tasks from high-speed instruction execution, enabling the present invention to achieve high switching frequencies while ensuring sufficient computational redundancy in the digital controller.

[0102] This embodiment is described with reference to examples. Figure 4 The following are experimental comparison waveforms under the condition of motor inductance parameter mismatch. The inductance value set in the controller is 50% of the actual value. From top to bottom, they are motor speed n r , electromagnetic torque T e and phase current i ab ; (a) is the traditional multi-rate control scheme (b) is the control scheme proposed by the present invention. It can be seen that under the condition of parameter mismatch, the total harmonic distortion of the current of the traditional multi-rate control scheme is as high as 7.21%, and there are obvious fluctuations in the speed and electromagnetic torque; while the total harmonic distortion of the current of the control scheme proposed by the present invention is reduced to 2.67%, with better current quality, and effectively suppresses the disturbance within the sampling period, thereby improving the robustness of the system.

[0103] Although the above describes the illustrative specific embodiments of the present invention to facilitate understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concepts of the present invention are protected.

Claims

1. A high-frequency motor drive multi-rate control method for time series disturbance compensation, characterized in that: The following steps are involved: (1) Obtain the motor system status and low-frequency reference instructions: The motor three-phase current i a 、i b 、i c Converted to the actual current i in the αβ stationary coordinate system α 、i β ; Obtain the reference current of the motor in the αβ stationary coordinate system through the speed loop PI controller and T2 coordinate transformation module The actual current i of the motor in the αβ stationary coordinate system α 、i β , as the state vector x(k) = [i α ,i β ] T ; (2) Estimation of time series disturbance and model compensation: Use the generalized proportional integral observer to estimate k and k+N p The time series disturbance between the moments is then embedded into the current prediction model of the motor system; (3) Generate high-frequency reference trajectory: Based on the low-frequency reference current at the current k moment Electrical angle θ e and electrical angular velocity ω e , predict k+N p The reference current at the moment; then the Lagrange interpolation method is used to interpolate k and k+N p The reference current between the moments is interpolated to generate a smooth high-dimensional reference trajectory vector Y * ; (4) Solve the optimal control sequence: predict the output vector of the motor system at the next moment based on the current prediction model Y ; Combined with the high-dimensional reference trajectory vector generated in step (3) Y * , by minimizing the cost function J, we can obtain an optimal control sequence u (k); (5) Drive execution: The optimal control sequence u (k) Input to the space vector pulse width modulation module of the motor system, in N p Sampling period T s The high-frequency switching signal is generated by the space vector pulse width modulation module to control the motor.

2. The high-frequency motor drive multi-rate control method for time series disturbance compensation according to claim 1, characterized in that: The actual current i α 、i β With reference current The specific method to obtain is: (2.1) Obtain the motor three-phase current i through the current sampling module a 、i b 、i c ; ( 2.2) Obtain the real-time electrical angle θ of the motor through the position encoding module e ; (2.3), through the T1 coordinate transformation module, the three-phase current i a 、i b 、i c Converted to the actual current i in the αβ stationary coordinate system α 、i β , the T1 coordinate transformation formula is expressed as follows: (2.4) Using the speed calculation module to find the derivative, the electrical angle θ e Converted into electrical angular velocity ω e ; (2.5), given reference speed The electrical angular velocity error is calculated using the difference operation unit and input into the speed loop PI controller to obtain the q-axis reference current. To achieve maximum torque current ratio control, the d-axis reference current Set to zero; (2.6) To obtain the low-frequency current reference trajectory, the reference current of the dq rotating coordinate system is converted into the reference current of the αβ stationary coordinate system through the T2 coordinate transformation module. The T2 coordinate transformation formula is as follows:

3. The high-frequency motor drive multi-rate control method for time series disturbance compensation according to claim 1, characterized in that: The estimation method of the time series disturbance is: (3.1), in T c Construct the motor current state equation of a sampling period on the time scale: Among them, f(mT c |k) is the motor system in mT c The time series disturbance term at time |k, m=0,1,…,N-1, is specifically expressed as: f(mT c |k)=ΔA d x(mT c |k)+ΔB d u(mT c |k)+ΔD d ; Where ΔA d , ΔB d , ΔD d Represent the system matrix A respectively d , input matrix B d , perturbation matrix D d In the uncertain part at the current moment, that is, x(k)=[i α ,i β ] T ,u(k)=[u α ,u β ] T , Among them, i α 、i β 、u α 、u β are the current and voltage under α and β axes respectively, R s , ψ f and L s The resistance, flux linkage and inductance of the motor respectively; (3.2), estimate N by using the reduced-order generalized proportional integral observer p Time series disturbance within a sampling period; (3.2.1) and construct a high-order difference model of discrete-time disturbance, which is expressed as follows: Among them, h1(k),h2(k),…,h n (k) represents the high-order difference term of the time series disturbance f(k), and n represents the order; (3.2.2) and design a discretized generalized proportional integral observer, which can be expressed as: Wherein, the variable r(k)=Ax(k)+Bu(k)+D, A, B and D are matrices in the continuous domain of the motor system; α i is the gain of the observer, z i is the state vector of the observer, i=0,1,…,n-1; (3.2.3), the state vector x(k) at the current time k = [i α ,i β ] T Input to the generalized proportional integral observer to estimate k and k+N p Time series disturbances between moments 4. The high-frequency motor drive multi-rate control method for time series disturbance compensation according to claim 1, characterized in that: The method of model compensation in step (2) is: Perturb the time series Time series disturbance information in Embedded into the current state equation, the compensated current state prediction equation is obtained: Among them, y(mT c |k) is mT c |The output vector at time k, C is the second-order unit matrix, and N is the frequency increase multiple.

5. The high-frequency motor drive multi-rate control method for time series disturbance compensation according to claim 1, characterized in that: The high-dimensional reference trajectory vector Y * The generation method is: (5.1), constructed N p -1 order interpolation polynomial, expressed as: Among them, P(x) is the interpolation polynomial, L j (x) is the Lagrange interpolation basis function and satisfies: Among them, x is the interpolation point within the sampling period, x j =θ+jω e T s ,y j =y * (T c |k+j), j=0,1,…,N p -1,y * Contains the reference current at each sampling cycle (5.2), for k and k+N p The reference current between the moments is interpolated to generate a high-dimensional reference trajectory vector Y * It is expressed as follows:

6. The high-frequency motor drive multi-rate control method for time series disturbance compensation according to claim 1, characterized in that: The optimal control sequence u The method for obtaining (k) is: (6.1) Construct the cost function: J=Δ Y (k+1|k) T Θ Δ Y (k+1|k)+ U (k) T ΥU (k); Among them, Δ Y is the tracking error, i.e. Δ Y (k+1|k)= Y (k+1|k)- Y * (k+1|k), Θ and Υ are Δ Y and boost control vector U The weight coefficient of (6.2), by making the cost function J U The partial derivative of is equal to zero, and the lifting control vector is obtained as follows: U (k)=( C d T TH d + Υ ) -1 C d T Θ [ Y * - Oh d x(k)- X d ]; Among them, the improvement matrix Γ d and Ω d They are expressed as follows: Improvement Matrix X d Expressed as: Among them, the lifting matrix Σ represents: Where, To improve the time series disturbance matrix; (6.3) According to the extended rolling optimization strategy, the control vector is improved U The first N sequences of (k) are applied to the system, and the optimal control sequence is expressed as: u (k)=Ψ U (k); in, The dimension is N×N p N.

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