Sliding mode control method for permanent magnet synchronous linear motor based on reaching law and disturbance compensation

Abstract

This invention relates to a sliding mode control method for a permanent magnet synchronous linear motor based on a reaching law and disturbance compensation. It includes: in the speed control loop of the permanent magnet synchronous linear motor, a sliding mode speed controller for speed control and a sliding mode disturbance observer for observing disturbances during speed control; the sliding mode disturbance observer feeds forward the observed disturbance values ​​to the sliding mode speed controller for compensation; and the sliding mode speed controller is based on a mover speed setpoint v. * The actual value of the mover speed v and the disturbance observation value fed forward by the sliding mode disturbance observer are used to generate the given current for the q-axis of the permanent magnet synchronous linear motor. During speed control, a reaching law for the speed sliding surface is configured within the sliding mode speed controller. This invention, based on the reaching law and disturbance compensation, effectively improves response speed, reduces chattering, and minimizes the impact of disturbances, resulting in better static and dynamic performance of the permanent magnet synchronous linear motor.

Description

Technical Field

[0001] This invention relates to a sliding mode control method, and more particularly to a sliding mode control method for a permanent magnet synchronous linear motor based on a reaching law and disturbance compensation. Background Technology

[0002] Permanent magnet synchronous linear motors are characterized by simple structure, high thrust density, low mechanical loss, high precision, high efficiency, and fast dynamic response. Therefore, direct drive systems represented by permanent magnet synchronous linear motors have broad application prospects in high-precision industrial production fields such as high-end CNC machine tools, lithography machines, and logistics transportation.

[0003] Permanent magnet synchronous linear motors are complex nonlinear, strongly coupled, and multivariable systems. Their physical structure exhibits cogging, edge, and saturation effects. Furthermore, during operation, they are affected by changes in temperature rise parameters and external uncertain disturbances. Therefore, it is necessary to design reasonable control strategies to achieve high-performance control of permanent magnet synchronous linear motors.

[0004] Traditional PI (proportional-integral) control algorithms are simple and can eliminate steady-state errors, making them widely used in motor control systems. However, when the internal parameters of the motor are mismatched or the external disturbances are too large, a set of fixed PI parameters cannot adapt well to changes in operating conditions, making it difficult to achieve satisfactory control requirements throughout the entire operating range.

[0005] In order to achieve high-performance control of permanent magnet synchronous linear motors, advanced control strategies such as sliding mode control, predictive control, and intelligent control have been proposed and applied to the control system of permanent magnet synchronous linear motors in recent years.

[0006] Sliding mode control, with its fast response, insensitivity to parameter changes and disturbances, and simple physical implementation, has proven to be an effective method for improving the anti-interference and robustness of motor control systems. However, traditional sliding mode control requires a large switching gain to ensure robustness, which is accompanied by chattering problems. Excessive chattering can trigger a series of chain reactions that degrade control performance.

[0007] Currently, researchers have proposed methods such as boundary layer method, improved reaching law, combination with intelligent control methods, high-order sliding mode control, and disturbance compensation to suppress chattering. Among them, the combined approach of improved reaching law and disturbance compensation is of great research significance for reducing system chattering and improving control performance. However, how to effectively improve the response speed of permanent magnet synchronous linear motor, weaken chattering, and reduce the impact of disturbances during control has always been a technical problem that urgently needs to be solved. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a sliding mode control method for permanent magnet synchronous linear motors based on the reaching law and disturbance compensation. The sliding mode control based on the reaching law and disturbance compensation effectively improves the response speed, weakens chattering, reduces the impact of disturbances, and enables the permanent magnet synchronous linear motor to have better static and dynamic performance.

[0009] According to the technical solution provided by this invention, a sliding mode control method for a permanent magnet synchronous linear motor based on reaching law and disturbance compensation is provided. The sliding mode control method for the permanent magnet synchronous linear motor includes:

[0010] In the speed control loop of the permanent magnet synchronous linear motor, a sliding mode speed controller for speed control and a sliding mode disturbance observer for observing disturbances during speed control are configured. The sliding mode disturbance observer feeds forward the observed disturbance values ​​to the sliding mode speed controller, which is based on the mover speed setpoint v. * The actual value of the mover velocity v and the disturbance observation value fed forward by the sliding mode disturbance observer generate the given current for the q-axis of the permanent magnet synchronous linear motor. in,

[0011] When performing speed control, a reaching law for the speed sliding surface is configured within the sliding mode speed controller. The configured reaching law for the speed sliding surface is as follows:

[0012]

[0013] In the formula, s is the velocity sliding surface within the sliding mode speed controller. Let x be the speed sliding surface approach law, k be the speed error, ε be the exponential coefficient, α be the switching gain coefficient, β be the approach law parameters, t be the working time of the permanent magnet synchronous linear motor, and sgn() be the sign function.

[0014] When speed control is performed using a sliding mode speed controller based on a reaching law, the q-axis current of the permanent magnet synchronous linear motor output by the sliding mode speed controller is... for:

[0015]

[0016] Where τ is the pole pitch of the permanent magnet synchronous linear motor. Given a velocity value v * The derivative of ψ f p is the permanent magnet flux linkage of a permanent magnet synchronous linear motor. n This represents the number of pole pairs in a permanent magnet synchronous linear motor. denoted as the disturbance observation value observed by the sliding mode disturbance observer, B as the viscous friction coefficient, m as the mover mass of the permanent magnet synchronous linear motor, and c as the sliding surface coefficient with c>0.

[0017] Within the sliding mode perturbation observer, the sliding surface s1 is selected as the observer velocity error e1, and a perturbation observation sliding mode reaching law is configured on the sliding surface s1. in,

[0018]

[0019] In the formula, For the observed mover speed of the permanent magnet synchronous linear motor, k1 is the coefficient of the exponential term, ε1 is the coefficient of the switching gain term, and α1, β1, and γ1 are all reaching law parameters.

[0020] For perturbation-observed sliding mode reaching laws A sliding mode perturbation observer, wherein the design method of the sliding mode perturbation observer includes:

[0021] Step 100: Establish the mechanical equations of the permanent magnet synchronous linear motor, specifically as follows:

[0022]

[0023] Among them, F L Let ξ(t) be the total uncertain disturbance of the permanent magnet synchronous linear motor, and i be the change in the total uncertain disturbance of the permanent magnet synchronous linear motor. q This refers to the current along the q-axis of the permanent magnet synchronous linear motor.

[0024] Step 110: Based on the mechanical equations of the permanent magnet synchronous linear motor, establish a sliding mode disturbance observer for the permanent magnet synchronous linear motor. The established sliding mode disturbance observer is as follows:

[0025]

[0026] Where g is the observer coefficient; u smo The control law for the disturbance observer to be designed;

[0027] Step 120: Define the observation velocity error e1 and observation disturbance error e2 of the sliding mode disturbance observer, specifically as follows:

[0028]

[0029] Step 130: Based on the above mechanical equations and the established sliding mode disturbance observer, generate the observer error equation:

[0030]

[0031] Step 140: Select sliding mode surface s1 as the observer velocity error e1, and configure the perturbation observation sliding mode reaching law. Then we have:

[0032]

[0033] Step 150, Order The control law for the sliding mode disturbance observer is given, and the observer parameters satisfy... When g>0 and k1>0, the observation velocity error e1=0, the observation disturbance error e2=0, and the observation disturbance value are achieved. for

[0034] When using a sliding mode speed controller based on the reaching law for speed control, the speed error x can enter the speed sliding surface s, and the speed sliding surface s can converge to the equilibrium point s = 0. The time for the speed sliding surface s to converge to the equilibrium point is less than [T1 + T2].

[0035]

[0036] Where s0 is the initial value of the sliding surface s, and x0 is the initial velocity error.

[0037] When performing sliding mode control on a permanent magnet synchronous linear motor, a current control loop located within the speed control loop is also included.

[0038] The current control loop includes a q-axis current regulator, a d-axis current regulator, a Park transform, an inverse Park transform, a Clark transform, and SVPWM control.

[0039] For a three-phase inverter adapted to a permanent magnet synchronous linear motor, the q-axis current i in the rotating coordinate system is obtained by sequentially performing Clark transformation and Park transformation. q and d-axis current i d ;

[0040] q-axis current i q The current is applied to the sliding mode perturbation observer and compared with the given current along the q-axis. Both are used as inputs to the q-axis current regulator, and the d-axis current i d With respect to the given current along the d-axis This is applied as input to the d-axis current regulator;

[0041] The q-axis current regulator and d-axis current regulator are connected to the three-phase inverter via inverse Park conversion and SVPWM control in sequence.

[0042] For a permanent magnet synchronous linear motor, the actual value of the mover velocity v and the angle θ of the permanent magnet synchronous linear motor are obtained based on a grating ruler, where,

[0043] The obtained angle θ is simultaneously applied to both the Park transform and the inverse Park transform.

[0044] The given current along the d-axis Keep it at 0.

[0045] Advantages of this invention: It transforms the variable function e of the speed error... -β|x| By introducing a reaching law, the reaching speed adapts to the speed error, resulting in a faster reaching speed when far from the speed sliding surface, thus reducing chattering during sliding. A sliding mode disturbance observer observes and feeds forward to compensate for disturbances, improving the system's anti-disturbance capability and further reducing chattering. Compared with methods based on traditional reaching laws, this approach offers faster response, better anti-disturbance performance, and less chattering, improving the dynamic and static response performance of the permanent magnet synchronous linear motor speed control system. Attached Figure Description

[0046] Figure 1 This is a system block diagram of the sliding mode control of a permanent magnet synchronous linear motor based on the sliding mode approach law and disturbance compensation according to the present invention;

[0047] Figure 2 This is a flowchart of the sliding mode control of a permanent magnet synchronous linear motor with sliding mode approach law and disturbance compensation designed according to the present invention;

[0048] Figure 3 This is a structural diagram of the sliding mode speed controller for a permanent magnet synchronous linear motor based on the reaching law of the present invention;

[0049] Figure 4 This is a simulation comparison of the speed response of a permanent magnet synchronous linear motor sliding mode control scheme based on the approaching law of this invention and schemes based on traditional exponential and power approaching laws after no-load start-up with added load.

[0050] Figure 5 This is a simulation comparison of the current response of a permanent magnet synchronous linear motor sliding mode control scheme based on the approaching law of this invention and a scheme based on traditional exponential and power approaching laws after no-load start-up with added load.

[0051] Figure 6 This is a simulation diagram of the velocity tracking and perturbation value estimation of the extended sliding mode perturbation observer based on the novel reaching law of this invention. Detailed Implementation

[0052] The present invention will be further described below with reference to specific accompanying drawings and embodiments.

[0053] To effectively improve response speed, reduce chattering, and mitigate the impact of disturbances, thereby enabling the permanent magnet synchronous linear motor control system to possess better static and dynamic performance, a sliding mode control method for permanent magnet synchronous linear motors based on reaching laws and disturbance compensation is provided in one embodiment of the present invention. The sliding mode control method for the permanent magnet synchronous linear motor includes:

[0054] In the speed control loop of the permanent magnet synchronous linear motor, a sliding mode speed controller for speed control and a sliding mode disturbance observer for disturbance observation during speed control are configured. The sliding mode disturbance observer feeds forward the observed disturbance values ​​to the sliding mode speed controller, which is based on the mover speed setpoint v. * The actual value of the mover velocity v and the disturbance observation value fed forward by the sliding mode disturbance observer generate the given current for the q-axis of the permanent magnet synchronous linear motor. in,

[0055] When performing speed control, a reaching law for the speed sliding surface is configured within the sliding mode speed controller. The configured reaching law for the speed sliding surface is as follows:

[0056]

[0057] In the formula, s is the velocity sliding surface within the sliding mode speed controller. Let x be the speed sliding surface approach law, k be the speed error, ε be the exponential coefficient, α be the switching gain coefficient, β be the approach law parameters, t be the working time of the permanent magnet synchronous linear motor, and sgn() be the sign function.

[0058] Figure 1 The diagram shows a control system block diagram of a permanent magnet synchronous linear motor. As can be seen from the diagram, sliding mode control of the permanent magnet synchronous linear motor generally employs a speed-current dual closed-loop control method. The speed control loop includes a sliding mode speed controller and a sliding mode disturbance controller. The sliding mode disturbance controller is connected to the sliding mode speed controller and is based on the actual mover speed value v and the q-axis current i of the permanent magnet synchronous linear motor. q It can generate perturbation observations. The generated perturbation observations Feedforward compensation is provided to the sliding mode speed controller.

[0059] Figure 1 In the process, the sliding mode speed controller is based on the mover speed setpoint v. * The actual value of the mover velocity v and the perturbation observations fed forward by the sliding mode perturbation observer. Generate the given current for the q-axis of a permanent magnet synchronous linear motor. In one embodiment of the present invention, a reaching law for the speed sliding surface is configured within the sliding mode speed controller. The reaching law for the configured speed sliding surface is as follows:

[0060]

[0061] Approach law of the configured velocity sliding surface Because the variable function e of velocity error x is introduced. -β|x|, it can make the reaching law adaptively change according to the velocity error x, solving the problems that the traditional reaching law has a slow reaching speed when far from the velocity sliding surface and a large chattering when approaching the velocity sliding surface.

[0062] In specific implementation, for the reaching law Then: when the velocity error x is far from the velocity sliding surface, that is, when s >> 1 and |x| >> 0, e -β|x| → 0. At this time, the reaching law is actually composed of -ε|s| α sgn(s) - ε|s| γ sgn(s) - ks. Therefore, according to the composition of the reaching law, it can be known that the reaching speed can be increased. When the velocity error x approaches the velocity sliding surface, that is, 0 < s < 1, especially when |x| → 0, at this time, the reaching law is actually dominated by -ε|s| γ sgn(s) - ks. When the velocity error x approaches 0 and at the same time the sliding surface s also approaches the equilibrium point, at this time, the reaching law is actually composed of -ε|s| γ sgn(s). From the composition of the reaching law, it can be known that the reaching speed slows down, so the chattering can be effectively weakened.

[0063] Based on the reaching law of the above velocity sliding surface expression, it can be specifically obtained that: the reaching law satisfies When and only when s = 0, there is That is, it satisfies the proof of the existence and reachability of the sliding mode. The following is a detailed description of the process of satisfying the existence and reachability of the sliding mode.

[0064] For the proof of the existence and reachability of the sliding mode, there is:

[0065] According to the definition of the reaching law, it can be obtained that:

[0066]

[0067] Thus, when and only when s = 0, there is Then the proposed reaching law satisfies the existence and reachability conditions of the continuous system sliding mode reaching law. That is, under the action of the proposed reaching law, the velocity error x can enter the velocity sliding surface, and the velocity sliding surface s can converge to the equilibrium point s = 0 of the sliding surface s. When the velocity error x is 0, then s = 0

[0068] In an embodiment of the present invention, when performing speed control based on the sliding mode speed controller of the reaching law, the velocity error x can enter the velocity sliding surface s, and the velocity sliding surface s can converge to the equilibrium point s = 0 of the sliding surface s. The time for the velocity sliding surface s to converge to the equilibrium point is less than [T1 + T2], where

[0069]

[0070] Where s0 is the initial value of the sliding surface s, and x0 is the initial speed error of the permanent magnet synchronous linear motor in its initial state.

[0071] The process of converging to the equilibrium point s = 0 in a finite time is described below. Specifically, assuming the initial value of the sliding surface s is s0 >> 1, the convergence process is divided into two stages:

[0072] 1) From s0 to s(t1)=1, where s(t1)=1 means that at time t1, the sliding surface s is 1.

[0073] The law of convergence can be written as: At this point, the approach law contains two power terms, making the equation solution somewhat difficult. Considering 0 < γ < 1, the approach rate at this stage is mainly affected by -ε(1-e^(-γ / γ)). -β|x| )s α Due to the influence of -ks, the approach time must be less than The solution to the equation is as follows:

[0074]

[0075] Let the intermediate variable be y = s 1-α , Equation (1) can then be written as:

[0076]

[0077] Solving equation (2), we get:

[0078]

[0079] Where C1 is a constant;

[0080] Substitute equation (3) back into the equation y = s 1-α We can obtain:

[0081]

[0082] Since s = s0 when t = 0, the constant C1 can be obtained as:

[0083]

[0084] Combining equations (4) and (5), the original equation can be obtained. The solution is:

[0085]

[0086] The time required to reach s(t1) = 1 from s0 is:

[0087]

[0088] Therefore, the time required for the system to reach s(t1) = 1 from s0 is less than t1.

[0089] 2) From s(t1) = 1 to s(t2) = 0, where s(t2) = 0 means that at time t2, the sliding surface s is 0.

[0090] At this point, the reaching law can be written as: Considering α>1, the approach rate in this stage is mainly affected by -εs γ Due to the influence of -ks, the approach time must be less than The solution to the equation is as follows:

[0091]

[0092] Let the intermediate variable z = s 1-γ , Then equation (8) above can be written as:

[0093]

[0094] Solving equation (9), we get:

[0095]

[0096] Where: C2 is a constant;

[0097] Substituting equation (10) back into the equation z = s 1-γ We can obtain:

[0098]

[0099] Since s = 1 when t = 0, the constant C2 can be obtained from equation (11):

[0100]

[0101] Combining equations (11) and (12), the original equation can be obtained. The solution is:

[0102]

[0103] The time required to go from s(t1) = 1 to s(t2) = 0 is:

[0104]

[0105] Therefore, the time required for the system to go from s(t1) = 1 to s(t2) = 0 is less than t2.

[0106] Furthermore, if the initial value of the sliding surface s is s0 << -1, then... The required time is less than in:

[0107]

[0108]

[0109] In summary, by combining s0>>1 and s0<<-1, for the approach law of the velocity sliding surface, the convergence time of the system state (the system state refers to the convergence of the sliding surface s to 0) is less than [T1+T2]. The specific cases of T1 and T2 can be referred to the above explanation, and will not be repeated here.

[0110] Based on the above explanation, when using a sliding mode speed controller based on the reaching law for speed control, the given current of the permanent magnet synchronous linear motor q-axis output by the sliding mode speed controller can be obtained. for:

[0111]

[0112] Where τ is the pole pitch of the permanent magnet synchronous linear motor, and ψ f p is the permanent magnet flux linkage of a permanent magnet synchronous linear motor. n This represents the number of pole pairs in a permanent magnet synchronous linear motor. denoted as , where is the disturbance observation value observed by the sliding mode disturbance observer; B is the viscous friction coefficient; m is the mover mass of the permanent magnet synchronous linear motor; and c is the sliding surface coefficient, where c > 0.

[0113] In practical implementation, after configuring the sliding mode speed controller, a system is formed. Figure 1 Therefore, the sliding mode speed controller in this invention is a sliding mode speed controller based on the reaching law. Specifically, the control law for the sliding mode speed controller based on the reaching law is to generate the given current for the q-axis of the permanent magnet synchronous linear motor. The specific method.

[0114] right Figure 1 The following describes a design method for a sliding mode speed controller based on a reaching law. Specifically, the design steps include:

[0115] Step 1: Perform coordinate transformation to establish the mathematical model of the permanent magnet synchronous linear motor in the dq coordinate system, then we have:

[0116]

[0117] Where: i d i q These represent the d-axis current and q-axis current of the permanent magnet synchronous linear motor, respectively; R is the primary resistance of the permanent magnet synchronous linear motor, u du q These are the d-axis voltage and q-axis voltage of the permanent magnet synchronous linear motor, respectively; L d L q These are direct-axis inductance and quadrature-axis inductance, respectively; ψ f Let L represent the flux linkage of the permanent magnet; for a surface-mounted permanent magnet synchronous linear motor, then: L = L d =L q .

[0118] The electromagnetic thrust equation of a permanent magnet synchronous linear motor in the dq coordinate system is:

[0119]

[0120] The mechanical motion equations of a permanent magnet synchronous linear motor in the dq coordinate system are:

[0121]

[0122] Wherein: F L Let F be the total uncertain disturbance of the permanent magnet synchronous linear motor; generally, the total uncertain disturbance F of the permanent magnet synchronous linear motor is... L It can generally include load thrust, nonlinear friction force, and thrust fluctuation, etc.

[0123] Step 2: Define the rotational speed error x

[0124] x = e = v * -v (20)

[0125] Step 3: To improve the dynamic response of the system and eliminate the steady-state error, select the velocity sliding surface s for integration, then we have:

[0126] s=x+c∫xdt (21)

[0127] Differentiating the integral sliding surface and substituting the mechanical motion equation (19) and electromagnetic thrust equation (18) of the permanent magnet synchronous linear motor, we obtain:

[0128]

[0129] Using the reaching law:

[0130]

[0131] Substituting the selected approach law (23) into the derivative equation (22) of the velocity sliding surface s, the given current of the permanent magnet synchronous linear motor q-axis output by the sliding speed controller can be obtained.

[0132]

[0133] Among them, FL Obtained through a sliding mode perturbation observer, that is Equation (24) can be further written as:

[0134]

[0135] The above describes one design method for a sliding mode speed controller based on the reaching law. Of course, other methods and steps can be used to design the required sliding mode speed controller based on the reaching law in practice; these specific design methods and steps will not be listed here. For the structural form of a sliding mode speed controller based on the reaching law, please refer to [reference needed]. Figure 3 The structural form shown is shown.

[0136] In one embodiment of the present invention, within the sliding mode perturbation observer, the sliding surface s1 is selected as the observer velocity error e1, and a perturbation observation sliding mode reaching law is configured on the sliding surface s1. in,

[0137]

[0138] In the formula, For the observed mover speed of the permanent magnet synchronous linear motor, k1 is the coefficient of the exponential term, ε1 is the coefficient of the switching gain term, and α1, β1, and γ1 are all reaching law parameters.

[0139] In practical implementation, to reduce the impact of disturbances on the control of the permanent magnet synchronous linear motor, a sliding mode disturbance observer is designed to observe the disturbances and record the observed disturbance values. Feedforward to the sliding mode speed controller, and observe the sliding mode reaching law by perturbation. The approach law of the velocity sliding surface mentioned above has the same approach law form, that is, we obtain Figure 1 The extended sliding mode perturbation observer in the model, specifically, the perturbation observes the sliding mode reaching law. The coefficients k1 of the exponential term, etc., can be found in the above explanation and will not be repeated here.

[0140] For perturbation-observed sliding mode reaching laws The sliding mode disturbance observer can be designed through the following steps. Specifically, the design method of the sliding mode disturbance observer includes:

[0141] Step 100: Establish the mechanical equations of the permanent magnet synchronous linear motor, specifically as follows:

[0142]

[0143] Among them, F L Let ξ(t) be the total uncertain disturbance of the permanent magnet synchronous linear motor, and i be the change in the total uncertain disturbance of the permanent magnet synchronous linear motor. qThis refers to the current along the q-axis of the permanent magnet synchronous linear motor.

[0144] In practice, based on the principle of the extended sliding mode observer, the extended equations of the permanent magnet synchronous linear motor are established, which can also be used to establish the mechanical equations in step 100.

[0145] Step 110: Based on the mechanical equations of the permanent magnet synchronous linear motor, establish a sliding mode disturbance observer for the permanent magnet synchronous linear motor. The established sliding mode disturbance observer is as follows:

[0146]

[0147] Where g is the observer coefficient; u smo The control law for the disturbance observer to be designed;

[0148] Step 120: Define the observation velocity error e1 and observation disturbance error e2 of the sliding mode disturbance observer, specifically as follows:

[0149]

[0150] Step 130: Based on the above mechanical equations and the established sliding mode disturbance observer, generate the observer error equation:

[0151]

[0152] Step 140: Select sliding mode surface s1 as the observer velocity error e1, and configure the perturbation observation sliding mode reaching law. Then we have:

[0153]

[0154] Step 150, Order The control law for the sliding mode disturbance observer is given, and the observer parameters satisfy... When g>0 and k1>0, the observation velocity error e1=0, the observation disturbance error e2=0, and the observation disturbance value are achieved. for

[0155] Specifically, due to Therefore, when e2 = 0, we can obtain

[0156] Figure 2 The diagram shows the approaching law of the velocity sliding surface and the approaching law of the perturbation observation sliding surface. A schematic diagram of a specific design process; the specific design methods and steps can be found by referring to... Figure 2 The diagram and the steps described above.

[0157] Figure 4 , Figure 5 This invention presents a sliding mode speed control scheme for a permanent magnet synchronous linear motor based on a reaching law, compared with schemes based on traditional power-law and exponential-law reaching laws, under no-load start-up and load application simulation. The initial given speed is 0.2 m / s, and a 20 N·m load is applied at 0.5 s. Figure 4 and Figure 5 It can be seen that the sliding mode speed control of the present invention has a fast response speed at initial start-up, reaches the given speed as quickly as possible, and has good speed tracking performance. Figure 5 It can be seen that, in steady state, the solution of the present invention has less chattering, while the traditional exponential approach law solution has a rapid speed response but obvious current chattering, and the traditional power approach law solution has a very slow overall response. When disturbed, the speed fluctuation of the present invention is the smallest and can quickly recover to the given speed, while the solution based on the traditional power approach law has a long recovery time after being disturbed. Figure 4 and Figure 5 In this invention, the novel approach law is the approach law adopted by the present invention, which is also the sliding speed control method based on the approach law adopted.

[0158] Figure 6 The results of the extended sliding mode disturbance observer based on the novel reaching law of this invention for tracking velocity and observing disturbance values ​​show that the extended sliding mode disturbance observer of this invention tracks velocity very quickly. When subjected to a 20 N·m load disturbance, it can accurately estimate the disturbance load value and provide feedforward compensation, thereby improving the reliability of the system.

[0159] As explained above, sliding mode control of a permanent magnet synchronous linear motor also includes a current control loop located within the speed control loop.

[0160] The current control loop includes a q-axis current regulator, a d-axis current regulator, a Park transform, an inverse Park transform, a Clark transform, and SVPWM control.

[0161] For a three-phase inverter adapted to a permanent magnet synchronous linear motor, the q-axis current i in the rotating coordinate system is obtained by sequentially performing Clark transformation and Park transformation. q and d-axis current i d ;

[0162] q-axis current i q The current is applied to the sliding mode perturbation observer and compared with the given current along the q-axis. Both are used as inputs to the q-axis current regulator, and the d-axis current i d With respect to the given current along the d-axis This is applied as input to the d-axis current regulator;

[0163] The q-axis current regulator and d-axis current regulator are connected to the three-phase inverter via inverse Park conversion and SVPWM control in sequence.

[0164] In practice, the specific form of the current control loop and the method of current closed-loop control can be consistent with the existing ones. Figure 1 The PMLSM mentioned here refers to a permanent magnet synchronous linear motor. The three-phase stator currents of a permanent magnet synchronous linear motor are: i a i b and i c Generally, the three-phase stator current can be detected by a current sensor, which is consistent with the existing method.

[0165] The three-phase stator current is converted into the dq-axis current i in the rotating coordinate system through a Clarke transformer and a Park transform. d and current i q The actual value of the mover velocity v and the angle θ can be obtained through the grating ruler. In specific implementation, the given current on the d-axis in the current loop... Keep it at 0, that is, use Vector control, which is related to the d-axis current i d The difference is used to obtain the input of the d-axis PI current regulator and the setpoint current of the q-axis. The output of the sliding mode speed controller based on the reaching law is obtained, and is related to the measured q-axis current i. q The input to the q-axis PI current regulator is obtained by taking the difference, and the two current regulators output the setpoint value of the stator voltage in the rotating coordinate system. and The stator voltage in the two-phase stationary coordinate system is obtained by inverse Park transformation. and As input to the voltage space vector modulation, it generates switching signals that act on the power devices in the power conversion circuit, ultimately driving the permanent magnet synchronous linear motor to run.

[0166] The q-axis current regulator, d-axis current regulator, Park transform, inverse Park transform, Clark transform, and SVPWM control in the aforementioned current loop can all adopt existing commonly used forms. For specific operational coordination processes, please refer to [reference needed]. Figure 1 And explanations.

[0167] The stability of the aforementioned sliding mode speed controller can be verified using the following method. Specifically:

[0168] Define the Lyapunov function V

[0169]

[0170] Assuming the current loop is efficient The effectiveness of the sliding mode perturbation observer satisfies Differentiating the Lyapunov function in the above equation, we get:

[0171]

[0172] By the definition of the reaching law, we know that k>0, ε>0, and |s| α (1-e -β|e| )+|s| γ If >0, we can obtain: Furthermore, V = 0 if and only if s = 0, meaning that the sliding mode speed controller based on the reaching law satisfies stability.

[0173] Regarding the stability assessment and parameter selection of the sliding mode disturbance observer, specifically: defining the Lyapunov function V2, we have:

[0174]

[0175] Differentiating the Lyapunov function V², we have:

[0176]

[0177] make Since η > 0, the expression for the derivative above can be further written as:

[0178]

[0179] According to the Lyapunov criterion, for the observer to converge stably... Right now:

[0180] That is to say:

[0181] when Then:

[0182] At this point, the above formula can be further written as: That is, we get: The solution is: e2 = e -gt [∫ξ(t)e gt dt+C3], where C3 is an arbitrary constant.

[0183] As can be seen from the above formula, g>0 can achieve the convergence of error e2 to 0, which means that the observation disturbance error e2 is 0.

[0184] In summary: the observer parameters satisfy... When g>0 and k1>0, asymptotic convergence of the observer can be achieved, making

[0185] The above embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A sliding mode control method for a permanent magnet synchronous linear motor based on reaching law and disturbance compensation, characterized in that, The sliding mode control method for the permanent magnet synchronous linear motor includes: In the speed control loop of the permanent magnet synchronous linear motor, a sliding mode speed controller for speed control and a sliding mode disturbance observer for observing disturbances during speed control are configured. The sliding mode disturbance observer feeds forward the observed disturbance values ​​to the sliding mode speed controller, which is based on the mover speed setpoint v. * The actual value of the mover velocity v and the disturbance observation value fed forward by the sliding mode disturbance observer generate the given current for the q-axis of the permanent magnet synchronous linear motor. in, When performing speed control, a reaching law for the speed sliding surface is configured within the sliding mode speed controller. The configured reaching law for the speed sliding surface is as follows: In the formula, s is the velocity sliding surface within the sliding mode speed controller. Let x be the speed sliding surface approach law, k be the speed error, ε be the exponential coefficient, α be the switching gain coefficient, β be the approach law parameters, t be the working time of the permanent magnet synchronous linear motor, and sgn() be the sign function.

2. The sliding mode control method for permanent magnet synchronous linear motors based on reaching law and disturbance compensation according to claim 1, characterized in that, When speed control is performed using a sliding mode speed controller based on a reaching law, the q-axis current of the permanent magnet synchronous linear motor output by the sliding mode speed controller is... for: Where τ is the pole pitch of the permanent magnet synchronous linear motor. Given a velocity value v * The derivative of ψ f p is the permanent magnet flux linkage of a permanent magnet synchronous linear motor. n This represents the number of pole pairs in a permanent magnet synchronous linear motor. denoted as the disturbance observation value observed by the sliding mode disturbance observer, B as the viscous friction coefficient, m as the mover mass of the permanent magnet synchronous linear motor, and c as the sliding surface coefficient with c>

0.

3. The sliding mode control method for permanent magnet synchronous linear motors based on reaching law and disturbance compensation according to claim 2, characterized in that, Within the sliding mode perturbation observer, the sliding surface s1 is selected as the observer velocity error e1, and a perturbation observation sliding mode reaching law is configured on the sliding surface s1. in, In the formula, For the observed mover speed of the permanent magnet synchronous linear motor, k1 is the coefficient of the exponential term, ε1 is the coefficient of the switching gain term, and α1, β1, and γ1 are all reaching law parameters.

4. The sliding mode control method for permanent magnet synchronous linear motors based on reaching law and disturbance compensation according to claim 3, characterized in that, For perturbation-observed sliding mode reaching laws A sliding mode perturbation observer, wherein the design method of the sliding mode perturbation observer includes: Step 100: Establish the mechanical equations of the permanent magnet synchronous linear motor, specifically as follows: Among them, F L Let ξ(t) be the total uncertain disturbance of the permanent magnet synchronous linear motor, and i be the change in the total uncertain disturbance of the permanent magnet synchronous linear motor. q This refers to the current along the q-axis of the permanent magnet synchronous linear motor. Step 110: Based on the mechanical equations of the permanent magnet synchronous linear motor, establish a sliding mode disturbance observer for the permanent magnet synchronous linear motor. The established sliding mode disturbance observer is as follows: Where g is the observer coefficient; u smo The control law for the disturbance observer to be designed; Step 120: Define the observation velocity error e1 and observation disturbance error e2 of the sliding mode disturbance observer, specifically as follows: Step 130: Based on the above mechanical equations and the established sliding mode disturbance observer, generate the observer error equation: Step 140: Select sliding mode surface s1 as the observer velocity error e1, and configure the perturbation observation sliding mode reaching law. Then we have: Step 150, Order The control law for the sliding mode disturbance observer is given, and the observer parameters satisfy... When g>0 and k1>0, the observation velocity error e1=0, the observation disturbance error e2=0, and the observation disturbance value are achieved. for 5. The sliding mode control method for permanent magnet synchronous linear motors based on reaching law and disturbance compensation according to any one of claims 1 to 4, characterized in that, When using a sliding mode speed controller based on the reaching law for speed control, the speed error x can enter the speed sliding surface s, and the speed sliding surface s can converge to the equilibrium point s = 0. The time for the speed sliding surface s to converge to the equilibrium point is less than [T1 + T2]. Where s0 is the initial value of the sliding surface s, and x0 is the initial velocity error.

6. The sliding mode control method for permanent magnet synchronous linear motors based on reaching law and disturbance compensation according to any one of claims 1 to 4, characterized in that, When performing sliding mode control on a permanent magnet synchronous linear motor, a current control loop located within the speed control loop is also included. The current control loop includes a q-axis current regulator, a d-axis current regulator, a Park transform, an inverse Park transform, a Clark transform, and SVPWM control. For a three-phase inverter adapted to a permanent magnet synchronous linear motor, the q-axis current i in the rotating coordinate system is obtained by sequentially performing Clark transformation and Park transformation. q and d-axis current i d ; q-axis current i q The current is applied to the sliding mode perturbation observer and compared with the given current along the q-axis. Both are used as inputs to the q-axis current regulator, and the d-axis current i d With respect to the given current along the d-axis This is applied as input to the d-axis current regulator; The q-axis current regulator and d-axis current regulator are connected to the three-phase inverter via inverse Park conversion and SVPWM control in sequence.

7. The sliding mode control method for permanent magnet synchronous linear motors based on reaching law and disturbance compensation according to claim 6, characterized in that, For a permanent magnet synchronous linear motor, the actual value of the mover velocity v and the angle θ of the permanent magnet synchronous linear motor are obtained based on a grating ruler, where, The obtained angle θ is simultaneously applied to both the Park transform and the inverse Park transform.

8. The sliding mode control method for permanent magnet synchronous linear motors based on reaching law and disturbance compensation according to claim 6, characterized in that, The given current along the d-axis Keep it at 0.

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