Permanent magnet synchronous motor nonlinear integral compound control method based on novel reaching law

Abstract

The invention discloses a permanent magnet synchronous motor nonlinear integral compound control method based on a novel reaching law. The method comprises the following steps: detecting a motor rotating speed omega and position angle information theta; calculating a rotating speed deviation e; transforming to obtain id and iq; calculating a nonlinear integral sliding mode surface s and a novel reaching law to observe a motor rotating speed omega and a load torque TL; calculating an output current given value iq *; performing Park inverse transformation to obtain u alpha and u beta; and performing voltage space vector pulse width modulation to obtain three switching signals of a three-phase inverter, and controlling the permanent magnet synchronous motor. According to the permanent magnet synchronous motor control method, the load disturbance observer and the nonlinear integral sliding mode controller are combined to construct the novel composite sliding mode controller, unknown disturbance can be estimated and compensated timely and accurately, the degree of dependence on high gain is effectively reduced, and the robustness of dealing with the unknown disturbance is remarkably improved.

Description

TECHNICAL FIELD

[0001] The application relates to a permanent magnet synchronous motor control method, in particular to a nonlinear integral compound control method for a permanent magnet synchronous motor based on a new reaching law. BACKGROUND

[0002] Permanent magnet synchronous motors (PMSM) are widely used in new energy transportation, aerospace, robots, logistics, high-precision servo and other fields due to their simple structure, low noise, high power density and various control strategies. However, as a complex system, PMSM has characteristics such as multivariable, strong coupling and nonlinearity. In actual operation, it will show nonlinear characteristics such as saturation effect and eddy current loss. The traditional proportional integral (PI) control strategy is difficult to ensure good dynamic and static performance and robustness when facing such complex situations.

[0003] In order to solve the problem of traditional PI control, domestic and foreign scholars have proposed and developed some nonlinear control theories, such as fuzzy control, adaptive control, neural network control and sliding mode variable structure control. Among them, the sliding mode variable structure control (SMC) has been widely used in the control of permanent magnet synchronous motors due to its remarkable characteristics such as no need for accurate modeling of the control object, good control performance and strong robustness. However, the traditional sliding mode control has exposed many serious problems in actual application scenarios: (1) its overshoot is too large, resulting in large fluctuations in system output when approaching the target value, which seriously affects the control accuracy; (2) the response speed is slow, which cannot track the system state change in time, resulting in poor dynamic performance of the system; (3) most notably, there is a chattering phenomenon, which not only causes high-frequency oscillation of the control signal, but also may cause wear of mechanical parts, greatly reducing the stability and reliability of the system. These problems together constitute a huge barrier to the widespread application of SMC in the industrial field. SUMMARY

[0004] The application aims to provide a nonlinear integral compound control method for a permanent magnet synchronous motor based on a new reaching law, which can effectively improve the response speed and accuracy of the system and greatly improve the performance of the permanent magnet synchronous motor control system.

[0005] Technical scheme: The nonlinear integral compound control method for a permanent magnet synchronous motor based on a new reaching law provided by the application comprises the following steps:

[0006] Step 1, detecting the motor speed ω and position angle information θ of the permanent magnet synchronous motor;

[0007] Step 2, calculate the speed deviation e of the motor speed ω and the given motor speed ω*;

[0008] Step 3, collect three-phase alternating current signals i a , i b , and i c in the a-b-c stationary coordinate system α , i β , i α , i β , and i d , i q , ;

[0009] Step 4, design a sliding mode controller to calculate the nonlinear integral sliding surface s and the new reaching law according to the speed deviation e

[0010] Step 5, design a disturbance observer to observe the motor speed ω and the load torque T L in real time

[0011] Step 6, design a composite sliding mode controller to calculate the output current given value i q * according to the nonlinear integral sliding surface s, the new reaching law , the motor speed ω, and the load torque T L ;

[0012] Step 7, calculate the stator current deviation value i q *-i q of the q-axis stator current component i q and the output current given value i q *, and take the stator current deviation value i q *-i q as the input of the q-axis PI current controller, while taking i d * = 0 as the input of the d-axis PI controller, and then convert the output voltage signals u α * and u β * of the q-axis PI current controller and the d-axis PI controller into voltage components u α and u β in the α-β stationary coordinate system through Park inverse transformation α , u β ;

[0013] Step 8, calculate the voltage components u α and u βThe voltage space vector pulse width modulation is performed to generate three switching signals of a three-phase inverter, and smooth control of the permanent magnet synchronous motor is realized by controlling the output of the inverter.

[0014] Further, in step 4, a nonlinear integral sliding mode surface s and a novel reaching law are calculated according to the speed deviation e The specific steps are as follows:

[0015] Step 4.1, the mechanical motion equation and the torque equation of the surface-mounted permanent magnet synchronous motor in the d-q rotating coordinate system are established as follows:

[0016]

[0017] In formula (1) and (2), ω is the motor speed, J is the motor moment of inertia, B is the friction coefficient, T e is the electromagnetic torque, T L is the load torque, ψ f is the permanent magnet flux linkage amplitude, i q is the component of the stator current on the q-axis, p n is the number of pole pairs;

[0018] Step 4.2, the state variables of the PMSM system are defined as follows:

[0019]

[0020] In formula (3), x1 and x2 are the speed deviation and the first derivative of the speed deviation respectively, and the derivative of formula (3) is obtained as follows:

[0021]

[0022] Step 4.3, the speed deviation e is used as the input of the nonlinear integral sliding mode controller based on the novel reaching law by using the sliding mode controller, and the nonlinear integral sliding mode surface s and the novel reaching law are designed as follows:

[0023]

[0024] In formula (5) and (6), c and k1 are normal number parameters, β∈R + is an error adjustment factor, k2 is a basic reaching gain, k2>0, ε is a variable speed adjustment factor, 0<ε<1, λ is a speed deviation power term coefficient, λ>0, s is a nonlinear integral sliding mode surface, is a novel reaching law, and tanh() is a hyperbolic tangent function.

[0025] Further, in step 4.3, the function expression of tanh(s) is as follows:

[0026]

[0027] where q is a tunable parameter and q > 0.

[0028] Further, in step 5, the motor speed ω and the load torque T L of the permanent magnet synchronous motor are observed in real time, and the specific steps are as follows:

[0029] Step 5.1, the system disturbance is regarded as the load torque T L After the load torque is expanded into a state variable, the system model is obtained as follows:

[0030]

[0031] In equation (8), θ(t) is an unknown function, so an extended sliding mode disturbance observer can be constructed as follows:

[0032]

[0033] In equation (9), u is the control law of the state observer, L is the gain of the observer, and are the speed observation value and the load torque observation value, respectively;

[0034] Step 5.2, the observation error is defined as:

[0035]

[0036] In equation (10), e ω is the speed observation error, is the electromagnetic torque observation error, and the first derivative of the tracking error is obtained as:

[0037]

[0038] By introducing a nonlinear integral sliding surface and a traditional constant reaching law, the observer control law is obtained as:

[0039]

[0040] In equation (12), η is the reaching gain, s ω is a nonlinear integral sliding surface based on the speed observation error, k3 and c1 are normal number parameters, is the first derivative of the speed observation error.

[0041] Further, in step 6, the specific steps for calculating the output current given value i q of the compound sliding mode controller are as follows:

[0042] Step 6.1, the nonlinear integral sliding surface s, the new reaching law Motor speed ω and load torque T L ;

[0043] Step 6.2, the output current given value i of the composite sliding mode controller is calculated q * is:

[0044]

[0045] In formula (13), the load torque observation value is:

[0046]

[0047] Further, in step 3, three-phase alternating current signals i a , i b and i c are obtained by current sensor acquisition.

[0048] Compared with the prior art, the present application has the beneficial effects that: the present application combines a load disturbance observer and a nonlinear integral sliding mode controller to construct a new type of composite sliding mode controller, which can estimate and compensate unknown disturbances in time and accurately, effectively reduces the dependence of sliding mode control on high gain, and significantly improves the robustness of the control system in response to unknown disturbances. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 is the control method flowchart of the present application;

[0050] Figure 2 is the permanent magnet synchronous motor control system block diagram of the present application;

[0051] Figure 3 is the nonlinear function curve with "small error amplification and large error saturation" referred to by the sliding surface of the present application;

[0052] Figure 4 is the comparison diagram of the trajectory approaching process of the traditional constant speed reaching law and the new reaching law of the present application;

[0053] Figure 5 is the permanent magnet synchronous motor composite sliding mode variable structure control system block diagram of the present application based on nonlinear function;

[0054] Figure 6 is the comparison diagram of the speed response of the composite control proposed by the present application and the traditional PI control and the conventional SMC at a given speed and at a certain time when a load is suddenly added. DETAILED DESCRIPTION

[0055] The technical solutions of the present application will be described in detail below in conjunction with the drawings, but the protection scope of the present application is not limited to the described embodiments.

[0056] like Figure 1 and 2 As shown, the nonlinear integral composite control method for permanent magnet synchronous motors based on a novel reaching law disclosed in this invention includes the following steps:

[0057] Step 1: Detect the motor speed ω and position angle information θ of the permanent magnet synchronous motor, such as... Figure 2 As shown, the motor speed ω and position angle information θ are obtained through sensor detection;

[0058] Step 2: Calculate the deviation between the motor speed ω and the given motor speed ω* to obtain the speed deviation e, e = ω* - ω;

[0059] Step 3: Acquire the three-phase AC current signal i in the abc stationary coordinate system. a i b and i c Then, through Clark transformation, the two-phase current i in the α-β stationary coordinate system is obtained. α and i β The two-phase current i α and i β Further, using the position and angle information θ, a Park transformation is performed to obtain i in the dq rotating coordinate system. d and i q ,like Figure 2 As shown;

[0060] Step 4: Design a nonlinear integral sliding mode controller to calculate the nonlinear integral sliding surface s and the novel reaching law based on the rotational speed deviation e.

[0061] Step 5: Design a load disturbance observer to monitor the motor speed ω and load torque T of the permanent magnet synchronous motor. L Conduct real-time observation;

[0062] Step 6: Design a novel composite sliding mode controller based on the nonlinear integral sliding surface s and a novel reaching law. Motor speed ω and load torque T L The output current setpoint i of the composite sliding mode controller is calculated. q *;

[0063] Step 7, calculate the q-axis stator current component i in the dq rotating coordinate system. q With the output current setpoint i q * Stator current deviation value i q *-i q And the stator current deviation value i q *-i q As the input to the q-axis PI current controller, and simultaneously id *=0 as the input of the d-axis PI controller, and the output voltage signals u α * and u β * are converted into voltage components u α and u β in the alpha-beta stationary coordinate system through Park inverse transformation.

[0064] Step 8, voltage space vector pulse width modulation is performed on the voltage components u α and u β to generate three switching signals of the three-phase inverter, and smooth control of the permanent magnet synchronous motor is realized by controlling the output of the inverter.

[0065] The application can estimate and compensate unknown disturbances in time and accurately by combining a load disturbance observer and a nonlinear integral sliding mode controller, effectively reduces the dependence of sliding mode control on high gain, and significantly improves the robustness of the control system in response to unknown disturbances.

[0066] Further, in step 4, the nonlinear integral sliding mode surface s and the novel reaching law are calculated according to the speed deviation e.

[0067] Step 4.1, the mechanical motion equation and torque equation of the surface-mounted permanent magnet synchronous motor in the d-q rotating coordinate system are established as follows:

[0068]

[0069] In formula (1) and (2), ω is the motor speed, J is the motor moment of inertia, B is the friction coefficient, T e is the electromagnetic torque, T L is the load torque, ψ f is the permanent magnet flux linkage amplitude, i q is the component of the stator current in the q-axis, and p n is the number of pole pairs.

[0070] Step 4.2, the state variables of the PMSM system are defined as:

[0071]

[0072] In formula (3), x1 and x2 are the speed deviation and the first-order derivative of the speed deviation, respectively, and the derivation of formula (3) is as follows:

[0073]

[0074] Step 4.3: Using the sliding mode controller, the rotational speed deviation e is used as the input to a nonlinear integral sliding mode controller based on a novel reaching law. The nonlinear integral sliding surface s and the novel reaching law are designed. They are respectively:

[0075]

[0076] like Figure 3 As shown, the nonlinear integral sliding surface s constructed in this invention introduces a nonlinear function curve with the characteristics of "small error amplification and large error saturation." This function can change in real time according to the dynamic changes of the system error. Under small error conditions, the accumulation rate of the integral term g(e) is significantly faster than that of traditional integral sliding mode control, thereby prompting the system to quickly approach a stable state. Under large error conditions, it performs integral operation according to the set error adjustment factor β, which reduces the accumulation of error and effectively solves the integral saturation problem caused by the large initial error. At the same time, due to its nonlinear characteristics, the system error converges to zero within a finite time.

[0077] By introducing a nonlinear function with the ability to amplify small errors and saturate large errors as the integral term, the integral term can be dynamically adjusted according to changes in error, thereby improving the system's response speed and enabling the system error to converge to zero within a finite time. This also effectively solves the problem of integral term saturation when the initial error is large. Introducing an integral term related to the error signal into the sliding surface design avoids the requirement for acceleration signals in the control quantity, reducing the system's steady-state error.

[0078]

[0079] In equations (5) and (6), c and k1 are positive constant parameters, and β∈R + ε is the error adjustment factor, k2 is the basic approaching gain (k2>0), ε is the speed regulation factor (0<ε<1), λ is the coefficient of the power term of the speed deviation (λ>0), and s is the nonlinear integral sliding surface. For a new type of reaching law, tanh() is the hyperbolic tangent function.

[0080] like Figure 4 As shown, the novel approach law of this invention designs a variable-speed function coefficient term f(x1,s) by introducing system state variables, thus associating the approach velocity with the system state variables. When the system moves away from the sliding surface, the approach velocity decreases because 0 < ε < 1, making... Therefore, the system's approach speed is improved. As the system approaches the sliding surface, the approach speed decreases as the system state variable |x1| continuously decreases and approaches zero, thereby accelerating the approach and suppressing chattering. Simultaneously, the hyperbolic tangent function tanh() is used instead of the discontinuous sign function sgn(), further suppressing chattering and ultimately improving the system's control performance.

[0081] Furthermore, in step 4.3, the functional expression for tanh(s) is:

[0082]

[0083] In the formula, q is an adjustable parameter, and q>0.

[0084] Furthermore, in step 5, the motor speed ω and load torque T of the permanent magnet synchronous motor are... L The specific steps for conducting real-time observation are as follows:

[0085] Step 5.1, treat the system disturbance as the load torque T L After expanding the load torque into state variables, the system model is obtained as follows:

[0086]

[0087] In equation (8), θ(t) is an unknown function, therefore an extended sliding mode perturbation observer can be constructed as follows:

[0088]

[0089] In equation (9), u is the control law of the state observer, and L is the gain of the observer. and These are the observed values ​​of rotational speed and load torque, respectively.

[0090] Step 5.2, define the observation error as:

[0091]

[0092] In equation (10), e ω For speed observation error, For the electromagnetic torque observation error, the first derivative of the tracking error is obtained as follows:

[0093]

[0094] By introducing a nonlinear integral sliding surface and a traditional isorhythmic reaching law to design the observer, the observer control law can be obtained as follows:

[0095]

[0096] In equation (12), η is the approach gain, and s ω For a nonlinear integral sliding surface based on rotational speed observation error, k3 and c1 are both positive constant parameters. This is the first derivative of the rotational speed observation error.

[0097] Furthermore, in step 6, the output current setpoint i of the composite sliding mode controller is calculated. q The specific steps are as follows:

[0098] Step 6.1: Obtain the nonlinear integral sliding surface s and the novel reaching law. Motor speed ω and load torque T L ;

[0099] Step 6.2: Calculate the output current setpoint i of the composite sliding mode controller. q *for:

[0100]

[0101] In equation (13), the observed load torque value is:

[0102]

[0103] Furthermore, in step 3, the three-phase alternating current signal i a i b and i c Data is collected through a current sensor.

[0104] like Figure 6 As shown, the simulation waveforms of the nonlinear integral composite sliding mode variable structure control of a permanent magnet synchronous motor based on a novel reaching law, proposed in this invention, are compared with those of traditional PI control and conventional SMC under a given speed and with a sudden load increase to 10 N·m at t = 0.2 s. The results show that the proposed composite control effectively eliminates overshoot during system operation, accelerates system convergence speed, suppresses inherent chattering, and enhances system robustness, exhibiting faster convergence speed and smaller overshoot, thus improving the dynamic and static characteristics of the system. Compared with traditional PI control and traditional sliding mode control, this invention demonstrates higher accuracy, faster response speed, and stronger stability when tracking a given speed signal, and exhibits excellent robustness to external disturbances.

[0105] As described above, although the invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A nonlinear integral composite control method for permanent magnet synchronous motors based on a novel reaching law, characterized in that, Includes the following steps: Step 1: Detect the motor speed ω and position angle information θ of the permanent magnet synchronous motor; Step 2: Calculate the deviation between the motor speed ω and the given motor speed ω* to obtain the speed deviation e, e = ω* - ω; Step 3: Acquire the three-phase AC current signal i in the abc stationary coordinate system. a i b and i c Then, through Clark transformation, the two-phase current i in the α-β stationary coordinate system is obtained. α and i β The two-phase current i α and i β Further, using the position and angle information θ, a Park transformation is performed to obtain i in the dq rotating coordinate system. d and i q ; Step 4: Design a sliding mode controller to calculate the nonlinear integral sliding surface s and the novel reaching law based on the rotational speed deviation e. Step 5: Design a disturbance observer to monitor the motor speed ω and load torque T of the permanent magnet synchronous motor. L Conduct real-time observation; Step 6: Design a composite sliding mode controller to utilize the nonlinear integral sliding surface s and a novel reaching law. Motor speed ω and load torque T L The output current setpoint i of the composite sliding mode controller is calculated. q *; Step 7, calculate the q-axis stator current component i in the dq rotating coordinate system. q With the output current setpoint i q * Stator current deviation value i q *-i q and the stator current deviation value i q *-i q As the input to the q-axis PI current controller, and simultaneously i d * = 0 is used as the input to the d-axis PI controller, and then the output voltage signal u of the q-axis PI current controller and the d-axis PI controller is used. α * and u β *Converted to voltage component u in α-β stationary coordinate system via inverse Park transform. α and u β ; Step 8, for the voltage component u α and u β Voltage space vector pulse width modulation is performed to generate three switching signals for the three-phase inverter. By controlling the output of the inverter, the permanent magnet synchronous motor can be smoothly controlled.

2. The nonlinear integral composite control method for permanent magnet synchronous motors based on a novel reaching law according to claim 1, characterized in that, In step 4, the nonlinear integral sliding surface s and the novel reaching law are calculated based on the rotational speed deviation e. The specific steps are as follows: Step 4.1, establish the mechanical motion equations and torque equations of the surface-mounted permanent magnet synchronous motor in the dq rotating coordinate system as follows: In equations (1) and (2), ω is the motor speed, J is the motor moment of inertia, B is the coefficient of friction, and T is the coefficient of friction. e For electromagnetic torque, T L For the load torque, ψ f i represents the flux linkage amplitude of the permanent magnet. q p is the component of the stator current on the q-axis. n It is the extreme logarithm; Step 4.2, define the state variables of the PMSM system as follows: In equation (3), x1 and x2 are the speed deviation and the first derivative of the speed deviation, respectively. Taking the derivative of equation (3) yields: Step 4.3: Using the sliding mode controller, the rotational speed deviation e is used as the input to a nonlinear integral sliding mode controller based on a novel reaching law. The nonlinear integral sliding surface s and the novel reaching law are designed. They are respectively: In equations (5) and (6), c and k1 are positive constant parameters, and β∈R + ε is the error adjustment factor, k2 is the basic approaching gain (k2>0), ε is the speed regulation factor (0<ε<1), λ is the coefficient of the power term of the speed deviation (λ>0), and s is the nonlinear integral sliding surface. For a new type of reaching law, tanh() is the hyperbolic tangent function.

3. The nonlinear integral composite control method for permanent magnet synchronous motors based on a novel reaching law according to claim 2, characterized in that, In step 4.3, the functional expression of tanh(s) is: In the formula, q is an adjustable parameter, and q>0.

4. The nonlinear integral composite control method for permanent magnet synchronous motors based on a novel reaching law according to claim 2, characterized in that, In step 5, the motor speed ω and load torque T of the permanent magnet synchronous motor are... L The specific steps for conducting real-time observation are as follows: Step 5.1, treat the system disturbance as the load torque T L After expanding the load torque into state variables, the system model is obtained as follows: In equation (8), θ(t) is an unknown function, therefore an extended sliding mode perturbation observer can be constructed as follows: In equation (9), u is the control law of the state observer, and L is the gain of the observer. and These are the observed values ​​of rotational speed and load torque, respectively. Step 5.2, define the observation error as: In equation (10), e ω For speed observation error, For the electromagnetic torque observation error, the first derivative of the tracking error is obtained as follows: By introducing a nonlinear integral sliding surface and a traditional isorhythmic reaching law to design the observer, the observer control law can be obtained as follows: In equation (12), η is the approach gain, and s ω For a nonlinear integral sliding surface based on rotational speed observation error, k3 and c1 are both positive constant parameters. This is the first derivative of the rotational speed observation error.

5. The nonlinear integral composite control method for permanent magnet synchronous motors based on a novel reaching law according to claim 4, characterized in that, In step 6, the output current setpoint i of the composite sliding mode controller is calculated. q The specific steps are as follows: Step 6.1: Obtain the nonlinear integral sliding surface s and the novel reaching law. Motor speed ω and load torque T L ; Step 6.2: Calculate the output current setpoint i of the composite sliding mode controller. q *for: In equation (13), the observed load torque value is:

6. The nonlinear integral composite control method for permanent magnet synchronous motors based on a novel reaching law according to claim 1, characterized in that, In step 3, the three-phase alternating current signal i a i b and i c Data is collected through a current sensor.

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