Design and application method of sliding mode deadbeat reaching law

Abstract

The invention provides a design and application method of a sliding-mode deadbeat reaching law, and relates to the technical field of electrical engineering, and the method comprises the steps: designing a sliding-mode deadbeat reaching law SMDRL, designing a control strategy through a deadbeat control principle, defining a state change law on a sliding-mode surface through a sign function, and achieving the design of the sliding-mode deadbeat reaching law SMDRL. It is ensured that the system state converges to the sliding mode surface at the fastest speed in a control period; an improved sliding mode deadbeat reaching law ISMDRL is designed, a traditional sign function is replaced with a hyperbolic tangent function, and parameters of the hyperbolic tangent function are adjusted according to the system state; the SMDRL and the ISMDRL are applied to a speed driving system of a permanent magnet synchronous motor (PMSM), and the speed driving system comprises a PMSM mathematical model, a sliding mode speed controller with a speed disturbance observer and model prediction current control. The SMDRL is introduced from the traditional sliding mode reaching law for the first time through theoretical derivation, the convergence time of the SMDRL is the shortest, and the SMDRL is applied to a permanent magnet synchronous motor speed driving system.

Description

Technical Field

[0001] The present application relates to the field of electrical engineering technology, and in particular to a design and application method of a sliding mode deadbeat reaching law. Background Art

[0002] The permanent magnet synchronous motor (PMSM) is a key motor in electrical engineering, widely used in industrial automation, electric vehicles, robotics, and other fields. The classic proportional-integral (PI) controller is popular in PMSM control systems due to its simplicity. While the PI controller effectively suppresses system fluctuations, it suffers from slow dynamic response and requires adjustment of two parameters, which must be readjusted when the system is subject to disturbances. These shortcomings can cause the control system to deviate from its intended objectives, limiting its effectiveness in high-performance control applications.

[0003] In order to overcome the limitations of traditional PI controllers, people have proposed various modern control theories, such as fuzzy control, state feedback control, predictive control, internal model control and sliding mode control (SMC). Among them, sliding mode control has become a popular choice in the field of motor control because of its relatively simple design and implementation, and its ability to provide faster dynamic response, excellent robustness and accuracy. In the development of SMC, scholars have discovered and constructed a variety of sliding mode reaching laws. The constant speed reaching law mentioned in a certain document controls the response time and chattering suppression of the system by artificially setting parameters. The exponential reaching law mentioned in a certain document adds an exponential term on the basis of the equivalent reaching law, which greatly improves the dynamic response speed and system stability. The power function reaching law discussed in the literature

[17] replaces a parameter in the equivalent reaching law with a power function to achieve smoother state changes, reduce possible chattering during the control process, and make the state converge faster. In addition, the terminal sliding mode reaching law (TSMRL) discussed in a certain document replaces the parameter k of the exponential reaching law with a power function, so that the system approaches the equilibrium point more smoothly. A variable exponential reaching law proposed in one paper uses a saturation function to further reduce chattering in the q-axis current output. Meanwhile, a new reaching law (NRL) proposed in another paper utilizes a hyperbolic tangent saturation function and an adjustable boundary layer to improve the response speed and system robustness during sliding mode soft switching.

[0004] With the further development of sliding mode reaching laws, a hybrid reaching law in one paper introduced a terminal factor to achieve rapid global convergence. It then combined a power function of the system state variables with the terminal sliding mode to create a variable terminal reaching law. This approach effectively reduces sliding chattering and mitigates the impact of the switching function term in traditional sliding mode reaching laws on system performance. Similarly, the adaptive sliding mode reaching law (ASCDO) and NRL in one paper both incorporate system state variables to create sliding mode variable structure reaching laws. This approach balances convergence speed and chatter suppression. In another paper, an adaptive reaching law adjusts the bandwidth based on the state error, effectively reducing chatter compared to an equivalent reaching law. These sliding mode reaching laws, all combinations of constant velocity, exponential, power function, and general function reaching laws, help plan the convergence of the sliding mode to a curved surface, thereby significantly improving control performance. However, none of these reaching laws can reflect the minimum time required to converge to the sliding mode surface, nor can a standardized measurement of the convergence time of different reaching laws be established. In addition, although the planning and design of existing sliding mode convergence law models are consistent, they are diverse in form and lack theoretical unity. Summary of the Invention

[0005] The present application aims to solve one of the technical problems in the related art at least to a certain extent.

[0006] To this end, the first objective of this application is to propose a design and application method for a sliding mode deadbeat reaching law.

[0007] The second objective of this application is to propose a design and application device for a sliding mode deadbeat reaching law.

[0008] The third objective of this application is to provide an electronic device.

[0009] The fourth object of this application is to provide a computer-readable storage medium.

[0010] A fifth object of this application is to provide a computer program product.

[0011] To achieve the above objectives, the first embodiment of the present application proposes a design and application method for a sliding mode deadbeat reaching law, including:

[0012] Design the deadbeat reaching law (SMDRL) of the sliding mode, design the control strategy based on the deadbeat control principle, and use the symbolic function to define the state change law on the sliding surface to ensure that the system state converges to the sliding surface at the fastest speed within one control cycle;

[0013] An improved sliding mode deadbeat reaching law (ISMDRL) is designed, in which the traditional sign function is replaced by a hyperbolic tangent function, and the parameters of the hyperbolic tangent function are adjusted according to the system state.

[0014] The SMDRL and ISMDRL are applied to a speed drive system of a permanent magnet synchronous motor (PMSM). The speed drive system includes a PMSM mathematical model, a sliding mode speed controller with a speed disturbance observer, and a model predictive current control.

[0015] Optionally, the design of a sliding mode deadbeat reaching law (SMDRL) includes designing a control strategy based on the deadbeat control principle, defining a state change law on a sliding mode surface using a sign function, and ensuring that the system state converges to the sliding mode surface at the fastest speed within a control cycle, including:

[0016] The designed sliding mode deadbeat reaching law is:

[0017]

[0018] Among them, S is the sliding surface state, T sc is the control cycle, and the symbolic function sgn is used to guide the system state to converge and ensure that the system state reaches the sliding surface within one control cycle. is the time variation speed of the sliding surface state S in the sliding mode control system.

[0019] Optionally, the improved sliding mode deadbeat reaching law ISMDRL replaces the traditional sign function with a hyperbolic tangent function, and adjusts the parameters of the hyperbolic tangent function according to the system state, including:

[0020] The designed improved sliding mode deadbeat reaching law is:

[0021]

[0022] Where k is a tuning parameter and tanh(kS) is a hyperbolic tangent function that replaces the sign function sgn.

[0023] Optionally, the mathematical model of PMSM on the dq axis is:

[0024]

[0025] Where u d and u q Represent the dq axis stator voltage respectively; i d and i q Represent the dq axis current respectively; ω m is the electrical angular velocity; T e is the electromagnetic torque; T L is the load torque; p is the number of pole pairs; ψ f is the permanent magnet flux connection; J is the moment of inertia; B is the viscous friction coefficient; L is the stator capacitance; R is the stator resistance.

[0026] Optionally, the model predicts current control, including:

[0027] The current prediction model is used to predict the current based on the motor status information. The calculation formula for the one-step delay current value is:

[0028]

[0029] Among them, i d (t+1) and i q (t+1) represents i d (t) and i d (t) one-step delay current value;

[0030] The current at time t+1 is introduced into the current prediction model, and the prediction formula of the current prediction model is obtained as follows:

[0031]

[0032] Among them, i d (t+2) and i q (t+2) represents i d (t) and i d (t) future predicted value;

[0033] The cost function is used to select the optimal voltage vector for the PMSM, with the goal of minimizing the deviation between the current prediction value and the expected current value. The cost function is:

[0034]

[0035] in, Set to 0, The output value is taken from the sliding mode controller in the speed loop.

[0036] The design process for an optional sliding mode speed controller with a speed disturbance observer includes:

[0037] The sliding surface is defined according to the motor speed error, and the formula is:

[0038]

[0039] Calculating the time derivative of the sliding surface, we get:

[0040]

[0041] According to the dynamic equation of the motor, when considering the parameter changes, the dynamic equation of the motor is obtained:

[0042]

[0043] Among them, a=a n +Δa=3p2 ψ f / 2J,b=b n +Δb=P / K,c=c n +Δc=pB / J, Δa, Δb and Δc are parameter changes, r(t)=Δqi q -Δcω-bT L represents an integer perturbation and |r(t)|≤l, where l is the upper limit of r(t);

[0044] get:

[0045]

[0046] The control input designed by this for:

[0047]

[0048] Taking r(t) as the extended state variable of the system, the extended dynamic equation is obtained as follows:

[0049]

[0050] Where d(t) is the rate of change of r(t);

[0051] A speed disturbance observer is designed to estimate and compensate for external disturbances. The dynamic equation of the speed disturbance observer is:

[0052]

[0053] in, is the speed ω m The estimated value of is the estimated value of r(t), g is the sliding mode parameter, u smo Represents a switching signal;

[0054] Subtracting the dynamic equation of the velocity disturbance observer from the expanded dynamic equation yields the error equation:

[0055]

[0056] in, is the velocity estimation error, is the interference estimation error;

[0057] The disturbance compensator is designed using ISMDRL and the control input is optimized using the following formula:

[0058]

[0059] Further we get:

[0060]

[0061] Taking e2 as the interference in the control function, the switching signal is designed through ISMDRL, and the formula is:

[0062]

[0063] The interference estimation error e2 is obtained by the following formula:

[0064] e2=e -gt [C+∫d(t)·e gt dt]

[0065] Where C is a constant, g is a sliding mode parameter, and e2 converges to zero over time;

[0066] The calculation formula of the discretized disturbance observer is as follows:

[0067]

[0068] in, represents the future forecast value of the estimated speed, represents the future predicted value of the estimated interference.

[0069] To achieve the above objectives, the second embodiment of the present application proposes a design and application device for a sliding mode deadbeat reaching law, including:

[0070] The deadbeat reaching law design module is used to design the deadbeat reaching law (SMDRL) of the sliding mode. The control strategy is designed based on the deadbeat control principle, and the state change law on the sliding surface is defined using a symbolic function to ensure that the system state converges to the sliding surface at the fastest speed within a control cycle.

[0071] An improvement module is used to design an improved sliding mode deadbeat reaching law (ISMDRL), replace the traditional sign function with a hyperbolic tangent function, and adjust the parameters of the hyperbolic tangent function according to the system state;

[0072] An application module is provided for applying the SMDRL and ISMDRL to a speed drive system of a permanent magnet synchronous motor (PMSM). The speed drive system includes a PMSM mathematical model, a sliding mode speed controller with a speed disturbance observer, and a model predictive current control.

[0073] To achieve the above-mentioned purpose, a third embodiment of the present application provides an electronic device, comprising: a processor, and a memory communicatively connected to the processor;

[0074] The memory stores computer-executable instructions;

[0075] The processor executes the computer-executable instructions stored in the memory to implement the method as described in any one of the first aspects above.

[0076] To achieve the above-mentioned purpose, the fourth embodiment of the present application proposes a computer-readable storage medium, in which computer-executable instructions are stored. When the computer-executable instructions are executed by a processor, they are used to implement the method as described in any one of the above-mentioned first aspects.

[0077] To achieve the above-mentioned purpose, the fifth embodiment of the present application proposes a computer program product, including a computer program, which, when executed by a processor, implements the method as described in any one of the above-mentioned first aspects.

[0078] The technical solutions provided by the embodiments of this application bring at least the following beneficial effects:

[0079] This application proposes the concept of a dead-zone sliding mode reaching law (SMDRL) and discovers the theoretical consistency of various traditional sliding mode reaching laws within the theoretical framework of minimum convergence time, theoretically unifying the various traditional sliding mode reaching laws. Specifically, all traditional sliding mode reaching laws are theoretically equivalent to SMDRL, achieving a unified form of sliding mode reaching law. This application also designs a PMSM speed drive system based on the proposed dead-zone reaching law to verify its effectiveness and superiority.

[0080] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0082] Figure 1 A flowchart of a method for designing and applying a deadbeat reaching law for a sliding mode provided in an embodiment of the present application;

[0083] Figure 2 A schematic diagram of the development process of the traditional sliding mode reaching law provided in the embodiments of the present application;

[0084] Figure 3 A schematic diagram of the derivation of the deadbeat reaching law of the sliding mode provided in the embodiment of the present application;

[0085] Figure 4 A graphical diagram of the hyperbolic tangent function provided in an embodiment of the present application;

[0086] Figure 5 A schematic diagram of the trajectory of the proportional parameters provided in the embodiment of the present application;

[0087] FIG6( a ) shows K, S and T when k=0.01 provided in an embodiment of the present application. SC Schematic diagram of the numerical relationship between ;

[0088] FIG6( b ) shows K, S and T when k=0.1 provided in an embodiment of the present application. SC Schematic diagram of the numerical relationship between ;

[0089] FIG6( c ) shows K, S and T when k=1 provided in an embodiment of the present application. sC Schematic diagram of the numerical relationship between ;

[0090] FIG7( a ) is a schematic diagram of components of a PMSM speed regulation drive system provided in an embodiment of the present application;

[0091] FIG7( b ) is a discrete block diagram of an SDO in a PMSM speed regulation drive system according to an embodiment of the present application;

[0092] FIG7( c ) is a discrete block diagram of the SMSC in the PMSM speed regulation drive system provided in an embodiment of the present application. DETAILED DESCRIPTION

[0093] The following describes in detail embodiments of the present application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0094] In order to solve the problems existing in the prior art, the present invention provides a method for designing and applying a deadbeat reaching law for a sliding mode. Figure 1 This is a flow chart of a design and application method of a sliding mode deadbeat reaching law provided in an embodiment of the present application. Figure 1 As shown, the method includes the following steps:

[0095] Step 101 , designing a deadbeat reaching law (SMDRL) for a sliding mode, designing a control strategy based on the deadbeat control principle, and using a sign function to define the state change law on the sliding surface to ensure that the system state converges to the sliding surface at the fastest speed within one control cycle.

[0096] Figure 2 Schematic diagram of the development process of the traditional sliding mode reaching law provided in the embodiments of the present application.

[0097] It should be noted that traditional sliding mode convergence laws include constant velocity, exponential, power function, and general function convergence laws. All of these convergence laws satisfy convergence conditions and ensure dynamic characteristics during the convergence process. All convergence rates have a minimum convergence time, or the fastest convergence rate. In digital control systems, this minimum convergence time is equivalent to one control cycle. Therefore, the embodiments of the present application propose the concept of a sliding mode deadbeat convergence law.

[0098] The following will study its derivation process in detail to deepen our understanding of the sliding mode reaching law.

[0099] First, as shown in (1), the constant velocity convergence law ensures that the equilibrium point is approached at a consistent speed during the motion convergence phase. The convergence speed can be changed by adjusting the parameter k1. Formula (1) is:

[0100]

[0101] After Euler discretization of formula (1), we can obtain:

[0102]

[0103] Among them, T sc For the control cycle.

[0104] After applying the deadbeat principle (S(t+1)=0), (2) can be simplified and updated as:

[0105]

[0106] Substituting k1 back into k1, we get the deadbeat form of the isokinetic reaching law, which is expressed as:

[0107]

[0108] Among them, S is the sliding surface state, T SC is the control cycle, and the symbolic function sgn is used to guide the system state to converge and ensure that the system state reaches the sliding surface within one control cycle. is the time variation speed of the sliding surface state S in the sliding mode control system.

[0109] When dV / dt satisfies dV / dt=S·dS / dt≤0, the Lyapunov function V=S is selected. 2 / 2 to verify that the sliding mode reaches the condition, and then we can get When the conditions are met, the deadbeat form satisfies the sliding mode arrival condition, ensuring that the system trajectory reaches the sliding mode surface within a finite time.

[0110] The following discussion will explore whether other traditional sliding mode reaching laws also conform to this deadbeat form.

[0111] Secondly, as shown in (5), the exponential reaching law fine-tunes the overall convergence rate by independently adjusting the parameters k2 and ε.

[0112]

[0113] After discretizing (5), we get:

[0114] S(t+1)-S(t)=-k2T sc sgn[S(t)]-εT sc S(t) (6)

[0115] Set S(t+1)=0 and obtain the parameter k2 using formula (6):

[0116]

[0117] Substituting (7) into (5) yields:

[0118]

[0119] Similarly, formula (9) is a power series law, and its convergence rate is determined by the power function. The formula is:

[0120]

[0121] Discretize (9) and rewrite it as

[0122] S(t+1)-S(t)=-k3T sc |S(t)| α sgn[S(t)] (10)

[0123] According to (10), the parameter k3 can be solved:

[0124]

[0125] Substituting (11) into (9) yields:

[0126]

[0127] Finally, through the proofs of Equations (2), (6), and (9), the deadbeat form of the general function convergence law (13) can be solved. The convergence rate of (13) is closely related to f(S).

[0128]

[0129] By performing Euler discretization calculation on (13), we can obtain:

[0130] S(t+1)-S(t)=-k4T sc sgn[S(t)]-f(S)Tsc (14)

[0131] It can be understood that the parameter k4 can be easily obtained from (14):

[0132]

[0133] Substituting (15) into k4 in (13) yields:

[0134]

[0135] According to the above proof, observing (4), (8), (12) and (16), we can conclude that no matter which sliding mode reaching law is adopted, the minimum convergence time (one control cycle T sc ), the expression of the sliding mode reaching law is unique, that is, (5), which is defined as SMDRL in the embodiment of this application. Figure 3 shown.

[0136] Step 102 : Design an improved sliding mode deadbeat reaching law ISMDRL, replace the traditional sign function with a hyperbolic tangent function, and adjust the parameters of the hyperbolic tangent function according to the system state.

[0137] Judging from the expression of SMDRL, its convergence speed is related to the system state, and it shows a certain ability to suppress chattering. However, when the system state is close to the sliding mode surface, the existence of the sign function often has an adverse effect on the chattering suppression effect. In order to enhance the chattering suppression ability while maintaining a fast convergence speed, the embodiment of the present application chooses to use the hyperbolic tangent function instead of the traditional sign function. This method retains the convergence speed of the sliding mode control to the greatest extent and enhances its ability to suppress chattering. The improved SMDRL (ISMDRL) is shown below:

[0138]

[0139] Among them, k is a tuning parameter used to adjust the conflicting relationship between convergence speed and chattering suppression, and tanh(kS) is a hyperbolic tangent function used to replace the sign function sgn. Figure 4 shown.

[0140] From formula (17) and Figure 4 As can be seen, when |S| is large, tanh(kS) approaches 1, making ISMDRL similar to SMDRL and thus achieving the fastest convergence speed. Conversely, when |S| is small, tanh(kS) approaches 0, which helps improve the system's chattering suppression. Based on these characteristics, the following compares the convergence speed and chattering suppression of ISMDRL and ASMDRL to evaluate their speed and stability.

[0141] In order to prove that ISMDRL has better convergence speed and good chattering suppression ability, the embodiment of this application theoretically compares it with ASCDO. The expression of ASCDO is:

[0142]

[0143] Among them, K>0, δ>0, λ>0 and 0<ε<1.

[0144] It can be understood that the speed of (18) and its effect on chatter suppression also vary with the size of |S|. When |S| is large, the variable M converges to K / ε. When |S| is small, the variable M converges to K / (1+1 / |S|).

[0145] A common method for comparing the advantages and disadvantages of two convergence laws is to calculate the convergence time of the two convergence laws, then subtract them, and find the point where the convergence time is the same to compare the chattering effect, thereby highlighting the superiority of one convergence law. However, the present embodiment chooses to directly divide the two convergence laws and compare them under different circumstances, thereby highlighting the superiority of one convergence law.

[0146] To verify the superiority of ISMDRL, we can divide (18) by (17) to obtain:

[0147]

[0148] Here, c is the scale parameter.

[0149] When |S| is large, the embodiment of the present application simplifies (19) to:

[0150]

[0151] observe Figure 5 From (20), we can see that only when λ = 1 / T sc Only when , ASCDO has the same fast convergence speed as ISMDRL.

[0152] When |S| is small, (19) becomes:

[0153]

[0154] Observe (21), only K = |tanh(kS) / T is needed sc | can make ISMDRL achieve the same chattering suppression effect as ASCDO. As shown in Figure 6(a), (b) and (c), the value of parameter K is related to k, S and T SC Therefore, the choice of K will be a challenge. It is worth noting that when K and λ become larger at the same time, the contradiction between convergence speed and chattering will be aggravated.

[0155] In summary, when ASCDO converges at the same speed as ISMDRL, chattering is weaker; conversely, when ASCDO's chattering effect is the same as ISMDRL's, convergence time is longer. ASCDO's parameters are complex and difficult to tune, while ISMDRL has only one parameter, k, making it easier to tune. Therefore, ISMDRL is theoretically superior to ASCDO.

[0156] Step 103 : Applying the SMDRL and ISMDRL to a speed drive system of a permanent magnet synchronous motor (PMSM). The speed drive system includes a PMSM mathematical model, a sliding mode speed controller with a speed disturbance observer, and a model predictive current control.

[0157] To verify the theoretical feasibility of the proposed dead-zone convergence law, this embodiment of the present application applies it to the speed control of a PMSM. The speed drive system primarily consists of a speed control component and a current control component. The speed control component includes a sliding mode speed controller (SMSC) and a speed disturbance observer (SDO), while the current control component utilizes a simple, easy-to-control model predictive current control (MPCC). Figure 7(a) shows the discrete block diagram of the PMSM speed drive system.

[0158] The following describes each part of the speed drive system.

[0159] In the embodiment of the present application, the mathematical model of the PMSM on the dq axis is:

[0160]

[0161] Where u d and u q Represent the dq axis stator voltage respectively; i d and i q Represent the dq axis current respectively; ω m is the electrical angular velocity; T e is the electromagnetic torque; T L is the load torque; p is the number of pole pairs; ψ f is the permanent magnet flux connection; J is the moment of inertia; B is the viscous friction coefficient; L is the stator capacitance; R is the stator resistance.

[0162] Because the MPCC control structure is simple, has fast dynamic response, and is easy to implement, the present embodiment selects the MPCC method to drive the system. Traditional MPCC typically includes one-step delay compensation, a current prediction model, and a cost function. Therefore, the dq axis current after one-step delay is as follows:

[0163]

[0164] Among them, i d (t+1) and iq (t+1) represents i d (t) and i d (t) is the one-step delay current value.

[0165] Furthermore, the current at time t+1 is introduced into the current prediction model, and the prediction formula of the current prediction model is obtained as follows:

[0166]

[0167] Among them, i d (t+2) and i q (t+2) represents i d (t) and i d The future predicted value of (t).

[0168] Finally, the cost function is shown below, which is used to select the optimal voltage vector for PMSM with the goal of minimizing the deviation between the current prediction value and the expected current value. The cost function is:

[0169]

[0170] in, Set to 0, The output value is taken from the sliding mode controller in the speed loop.

[0171] Next, the design process of the sliding mode speed controller with speed disturbance observer will be described in detail.

[0172] To facilitate the design of SMSC and reduce its complexity, the embodiment of the present application defines the sliding mode surface according to the motor speed error, and the formula is:

[0173]

[0174] Then the time derivative of the sliding surface is calculated to obtain:

[0175]

[0176] In addition, according to formula (22), when considering the parameter changes, the dynamic equation of the motor can be obtained:

[0177]

[0178] Among them, a=a n +Δa=3p 2 ψ f / 2J,b=b n +Δb=p / J,c=c n +Δc=pB / J, Δa, Δb and Δc are parameter changes, r(t)=Δqi q-Δcω-bT L Denotes integer perturbations, including internal parameter changes, friction, and external load perturbations, all of which are assumed to be bounded, then:

[0179] |r(t)|≤l (29)

[0180] where l is the upper limit of r(t).

[0181] Combining the above equations (4), (27), and (28), we can obtain:

[0182]

[0183] The control input designed according to (30) is for:

[0184]

[0185] In (31), only r(t) and mtanh(kS) change with time. mtanh(kS) can be obtained through system feedback, but accurately measuring r(t) is challenging. Although methods such as error control and experiments can determine them, they are often time-consuming. To solve this problem, the embodiment of the present application designs an SDO based on ISMDRL for fast estimation and compensation of r(t). The discrete block diagram of SMSC is shown in Figure 7(c). Taking r(t) as the extended state variable of the system, the extended dynamic equation can be obtained, that is,

[0186]

[0187] where d(t) is the rate of change of r(t).

[0188] Next, a speed disturbance observer is designed according to Equation (32) to estimate and compensate for external disturbances. The dynamic equation of the speed disturbance observer is:

[0189]

[0190] in, is the speed ω m The estimated value of is the estimated value of r(t), g is the sliding mode parameter, u smo Represents a switching signal.

[0191] Next, subtract the dynamic equation (33) of the velocity disturbance observer from the expanded dynamic equation (32) to obtain the error equation:

[0192]

[0193] in, is the velocity estimation error, is the interference estimation error.

[0194] In addition, in order to improve the response speed and observation accuracy of SDO, the embodiment of the present application adopts ISMDRL design. ISMDRL transformation obtains:

[0195]

[0196] Substituting (35) into (34), we can further obtain:

[0197]

[0198] In the embodiment of the present application, e2 is used as the interference in the control function, and the switching signal is designed through ISMDRL. The formula is:

[0199]

[0200] The ISMDRL-based SDO can reach and maintain the sliding surface in a finite time, indicating that the error and its derivative can converge to zero. The disturbance estimation error e2 can be obtained by (38)

[0201] e2=e -gt [C+∫d(t)·e gt dt] (38)

[0202] Where C is a constant, g is a sliding mode parameter, and e2 converges to zero over time.

[0203] In addition, to ensure that the disturbance estimation error e2 converges to zero, the sliding mode parameters should be selected so that g> 0. Therefore, it can be noted that the selection of SDO parameters is only restricted by the relationship between k and g.

[0204] It should be noted that the transfer function of the disturbance observation error e2 acts like a low-pass filter, which can effectively suppress high-frequency signals, and the parameter g represents the cutoff frequency. Therefore, the disturbance estimate can be used directly in the control system without the need for an additional low-pass filter, which helps to avoid amplitude and phase changes. The chattering suppression effect can be fine-tuned by adjusting the cutoff frequency g to meet the requirements of the control system. In addition, it should be noted that the disturbance observer is calculated at discrete moments and applied during the sampling interval, resulting in the discrete expression of the discretized disturbance observer:

[0205]

[0206] in, represents the future forecast value of the estimated speed, represents the future prediction value of the estimated interference. The SDO discrete block diagram is shown in Figure 7(b).

[0207] In addition, in order to verify the effectiveness and superiority of the composite speed control system based on ISMDRL, the embodiments of the present application also carried out steady-state and dynamic experiments under various operating conditions on a certain experimental platform. The experimental platform consists of a laptop, an isolation transformer, a voltage regulator, a direct current (DC) power supply, an oscilloscope, a motor, a control board, a load controller and a driver board with an inverter. With a digital signal processor (DSP) as the center, steady-state and dynamic experiments were carried out under various working conditions. The results of the proposed ISMDRL method were compared with those of the composite speed drive system based on ASCDO. Specifically, the adjustment of ASCDO-I parameters was matched with the jitter of ISMDRL, while the adjustment of ASCDO-II parameters was to obtain similar dynamic response time. The control frequency of all experiments was set to 15kHz. The experimental results were compared with the results of the composite speed control system based on ASMDRL.

[0208] Experimental results show that ISMDRL not only has good steady-state performance, but also excellent dynamic performance. Compared with ASCDO, ISMDRL has fewer parameters and can be easily adjusted to achieve good results. At the same time, it also proves the advantages of SMDRL in terms of convergence time and convergence speed.

[0209] To implement the above embodiment, the present application also proposes a design and application device for a sliding mode deadbeat reaching law. The device includes:

[0210] The deadbeat reaching law design module is used to design the deadbeat reaching law (SMDRL) of the sliding mode. The control strategy is designed based on the deadbeat control principle, and the state change law on the sliding surface is defined using a symbolic function to ensure that the system state converges to the sliding surface at the fastest speed within a control cycle.

[0211] An improvement module is used to design an improved sliding mode deadbeat reaching law (ISMDRL), replace the traditional sign function with a hyperbolic tangent function, and adjust the parameters of the hyperbolic tangent function according to the system state;

[0212] An application module is provided for applying the SMDRL and ISMDRL to a speed drive system of a permanent magnet synchronous motor (PMSM). The speed drive system includes a PMSM mathematical model, a sliding mode speed controller with a speed disturbance observer, and a model predictive current control.

[0213] Regarding the apparatus in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0214] In order to implement the above embodiments, the present application also proposes an electronic device, comprising: a processor, and a memory communicatively connected to the processor; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory to implement the method provided by the above embodiments.

[0215] In order to implement the above embodiments, the present application also proposes a computer-readable storage medium, in which computer-executable instructions are stored. When the computer-executable instructions are executed by a processor, they are used to implement the methods provided by the above embodiments.

[0216] In order to implement the above embodiments, the present application also proposes a computer program product, including a computer program, which implements the methods provided by the above embodiments when executed by a processor.

[0217] The collection, storage, use, processing, transmission, provision and disclosure of user personal information involved in this application are in compliance with relevant laws and regulations and do not violate public order and good morals.

[0218] It is important to note that personal information collected from users should be used for legitimate and reasonable purposes and should not be shared or sold beyond these legitimate uses. Furthermore, such collection / sharing should be conducted only after receiving the user's informed consent, including but not limited to notifying the user to read the user agreement / user notice and sign an agreement / authorization that includes the relevant user information before using the feature. Furthermore, any necessary steps must be taken to safeguard and secure access to such personal information and ensure that others with access to personal information comply with its privacy policy and procedures.

[0219] This application contemplates providing implementations that allow users to selectively block the use or access of personal information data. Specifically, this disclosure contemplates providing hardware and / or software to prevent or block access to such personal information data. Risks can be minimized by limiting data collection and deleting data once it is no longer needed. Furthermore, where applicable, such personal information can be de-identified to protect user privacy.

[0220] In the descriptions of the foregoing embodiments, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are mutually inconsistent.

[0221] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. Throughout the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0222] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application belong.

[0223] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and a portable compact disc read-only memory (CDROM). Furthermore, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or processing it in another suitable manner if necessary, and then storing it in a computer memory.

[0224] It should be understood that various parts of the present application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used to implement: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0225] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0226] In addition, the functional units in the various embodiments of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into a module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0227] The storage medium mentioned above may be a read-only memory, a magnetic disk, or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application. Persons skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

[0228] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this application can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solution of this application can be achieved. This is not limited herein.

[0229] The above specific embodiments do not constitute a limitation on the scope of protection of this application. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application shall be included within the scope of protection of this application.

Claims

1. A design and application method of a deadbeat reaching law for a sliding mode, characterized in that: include: Design the deadbeat reaching law (SMDRL) of the sliding mode, design the control strategy based on the deadbeat control principle, and use the symbolic function to define the state change law on the sliding surface to ensure that the system state converges to the sliding surface at the fastest speed within one control cycle; An improved sliding mode deadbeat reaching law (ISMDRL) is designed, in which the traditional sign function is replaced by a hyperbolic tangent function, and the parameters of the hyperbolic tangent function are adjusted according to the system state. The SMDRL and ISMDRL are applied to a speed drive system of a permanent magnet synchronous motor (PMSM). The speed drive system includes a PMSM mathematical model, a sliding mode speed controller with a speed disturbance observer, and a model predictive current control.

2. The method according to claim 1, characterized in that The deadbeat reaching law (SMDRL) of the sliding mode is designed. The control strategy is designed based on the deadbeat control principle. The state change law on the sliding mode surface is defined by the sign function to ensure that the system state converges to the sliding mode surface at the fastest speed within a control cycle. The method includes: The designed sliding mode deadbeat reaching law is: Among them, S is the sliding surface state, T sc is the control cycle, and the symbolic function sgn is used to guide the system state to converge and ensure that the system state reaches the sliding surface within one control cycle. is the time variation speed of the sliding surface state S in the sliding mode control system.

3. The method according to claim 2, characterized in that The improved sliding mode deadbeat reaching law ISMDRL replaces the traditional sign function with a hyperbolic tangent function and adjusts the parameters of the hyperbolic tangent function according to the system state, including: The designed improved sliding mode deadbeat reaching law is: Where k is a tuning parameter and tanh(kS) is a hyperbolic tangent function that replaces the sign function sgn.

4. The method according to claim 3, characterized in that The mathematical model of PMSM on the dq axis is: Where u d and u q Represent the dq axis stator voltage respectively; i d and i q Represent the dq axis current respectively; ω m is the electrical angular velocity; T e is the electromagnetic torque; T L is the load torque; p is the number of pole pairs; ψ f is the permanent magnet flux connection; J is the moment of inertia; B is the viscous friction coefficient; L is the stator capacitance; R is the stator resistance.

5. The method according to claim 4, characterized in that The model predicts current control, including: The current prediction model is used to predict the current based on the motor status information. The calculation formula for the one-step delay current value is: Among them, i d (t+1) and i q (t+1) represents i d (t) and i d (t) one-step delay current value; The current at time t+1 is introduced into the current prediction model, and the prediction formula of the current prediction model is obtained as follows: Among them, i d (t+2) and i q (t+2) represents i d (t) and i d (t) future predicted value; The cost function is used to select the optimal voltage vector for the PMSM, with the goal of minimizing the deviation between the current prediction value and the expected current value. The cost function is: in, Set to 0, The output value is taken from the sliding mode controller in the speed loop.

6. The method according to claim 5, characterized in that The design process of the sliding mode speed controller with speed disturbance observer includes: The sliding surface is defined according to the motor speed error, and the formula is: Calculating the time derivative of the sliding surface, we get: According to the dynamic equation of the motor, when considering the parameter changes, the dynamic equation of the motor is obtained: Among them, a=a n +Δa=3p 2 ψ f / 2J,b=b n +Δb=p / J,c=c n +Δc=pB / J, Δa, Δb and Δc are parameter changes, r(t)=Δqi q -Δcω-bT L represents an integer perturbation and |r(t)|≤l, where l is the upper limit of r(t); get: The control input designed by this for: Taking r(t) as the extended state variable of the system, the extended dynamic equation is obtained as follows: Where d(t) is the rate of change of r(t); A speed disturbance observer is designed to estimate and compensate for external disturbances. The dynamic equation of the speed disturbance observer is: in, is the speed ω m The estimated value of is the estimated value of r(t), g is the sliding mode parameter, u smo Represents a switching signal; Subtracting the dynamic equation of the velocity disturbance observer from the expanded dynamic equation yields the error equation: in, is the velocity estimation error, is the interference estimation error; The disturbance compensator is designed using ISMDRL and the control input is optimized using the following formula: Further we get: Taking e2 as the interference in the control function, the switching signal is designed through ISMDRL, and the formula is: The interference estimation error e2 is obtained by the following formula: e2=e -gt [C+∫d(t)·e gt [dt] Where C is a constant, g is a sliding mode parameter, and e2 converges to zero over time; The calculation formula of the discretized disturbance observer is as follows: in, represents the future forecast value of the estimated speed, represents the future predicted value of the estimated interference.

7. A design and application device for a deadbeat reaching law of a sliding mode, characterized in that: include: The deadbeat reaching law design module is used to design the deadbeat reaching law (SMDRL) of the sliding mode. The control strategy is designed based on the deadbeat control principle, and the state change law on the sliding surface is defined using a symbolic function to ensure that the system state converges to the sliding surface at the fastest speed within a control cycle. An improvement module is used to design an improved sliding mode deadbeat reaching law (ISMDRL), replace the traditional sign function with a hyperbolic tangent function, and adjust the parameters of the hyperbolic tangent function according to the system state; An application module is provided for applying the SMDRL and ISMDRL to a speed drive system of a permanent magnet synchronous motor (PMSM). The speed drive system includes a PMSM mathematical model, a sliding mode speed controller with a speed disturbance observer, and a model predictive current control.

8. An electronic device, characterized in that: include: a processor, and a memory communicatively connected to the processor; The memory stores computer-executable instructions; The processor executes the computer-executable instructions stored in the memory to implement the method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions, which are used to implement the method according to any one of claims 1 to 6 when executed by a processor.

10. A computer program product, characterized in that The invention comprises a computer program, which implements the method according to any one of claims 1 to 6 when being executed by a processor.

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