Permanent magnet synchronous motor enhanced active-disturbance-rejection control method based on superhelix control law

Abstract

The invention relates to the field of motor control, and discloses a permanent magnet synchronous motor enhanced active-disturbance-rejection control method based on a superhelix control law, which comprises the following steps of: firstly, establishing a permanent magnet synchronous motor mathematical model by considering load disturbance, current sampling disturbance and flux linkage parameter change disturbance in actual motor operation; according to the mathematical model of the permanent magnet synchronous motor and the mathematical characteristics of the active disturbance rejection controller, constructing an observer equation by using a differential relationship, and solving the problem of observation error accumulation through the differential relationship; a lumped disturbance compensation function is introduced into the observer, the anti-interference capacity of the control system is enhanced, and decoupling of steady-state and dynamic performance control parameters is achieved; and finally, designing a state error feedback control law by adopting a super-spiral sliding mode control law, so that the anti-interference capability of the active-disturbance-rejection controller is further improved, and the inherent buffeting of the system is weakened. A simulation result shows that compared with a traditional PI control method, the control method has better dynamic response performance and anti-interference performance.

Description

Technical Field

[0001] The present invention relates to the field of motor control, and in particular to a permanent magnet synchronous motor self-disturbance rejection control method based on a super-helical control law. Background Art

[0002] Permanent magnet synchronous motor (PMSM) uses a sturdy motor housing and special fixing devices, which can effectively reduce the impact of vibration and shock on the internal components of the motor. PMSM has no excitation current and excitation loss, high efficiency and high power density. At the same time, due to its brushless design, it reduces mechanical wear and failure points. Therefore, PMSM has been widely used in ship propulsion, new energy vehicles, mining transport vehicles and other fields.

[0003] Conventional PMSM drive systems mainly use vector control, which mainly includes PI speed loop and PI current loop control. The speed loop mainly affects the motor speed and determines the performance of the drive system. The traditional PI controller has the advantages of easy tuning and low dependence on the motor model. However, the PMSM drive system is affected by mechanical disturbances such as load disturbances and electrical disturbances such as motor parameter mismatch. The effect of running the motor based on the traditional PI controller is not ideal and cannot give full play to the advantages of PMSM.

[0004] Active disturbance rejection control has the advantages of strong robustness and is widely used in permanent magnet synchronous motor disturbance suppression. However, the current active disturbance rejection control has the problems of insufficient fast time-varying disturbance observation capability, limited observation accuracy, and weak medium-frequency disturbance observation and rejection performance. It is necessary to improve the traditional active disturbance rejection controller to improve the disturbance observation performance and control robustness of the drive system under complex working conditions. Summary of the invention

[0005] The purpose of the present invention is to solve the technical problems existing in the prior art and to propose a permanent magnet synchronous motor self-disturbance rejection control method based on a super-helical control law.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A permanent magnet synchronous motor enhanced active disturbance rejection control method based on a super helical control law, characterized in that it comprises the following steps:

[0008] Step 1, in the control of the permanent magnet synchronous motor, the influence of load disturbance, current sampling disturbance and flux parameter change disturbance in the actual motor operation is considered, and a mathematical model of the permanent magnet synchronous motor is established;

[0009] Step 2, improve the algorithm of the extended state observer (ESO) in the active disturbance rejection control (ADRC), add a lumped disturbance compensation function, and use the compensation function to achieve accurate observation of the disturbance in the mathematical model of the permanent magnet synchronous motor in step 1;

[0010] Step 3: Improve the linear state error feedback control law (LSEF) algorithm by introducing the super-twisting sliding mode (STSM) control law and using the hyperbolic tangent function to weaken the inherent jitter of the sliding mode. Based on the information such as the lumped disturbance observation value provided by the improved ESO in step 2, the disturbance in the mathematical modeling of step 1 is suppressed to achieve fast and accurate control of the system state.

[0011] As a further preferred solution, in step 1, the established permanent magnet synchronous motor mathematical model is converted into the permanent magnet synchronous motor motion equation:

[0012] The motion equation of the interior PMSM (Interior Permanent Magnet Synchronous Motor, IPMSM) set under load disturbance is expressed as:

[0013]

[0014] Where, T L is the load torque converted to the motor spindle end, B is the PMSM damping coefficient, ω m is the mechanical angular velocity of the PMSM, J is the moment of inertia of the entire mechanical load converted to the motor spindle end, T e is the electromagnetic torque, and its expression is:

[0015]

[0016] Where P em is the electromagnetic power, n p is the number of PMSM pole pairs; ψ f Represents the permanent magnet flux of the motor, L d , L q Respectively represent the direct-axis and quadrature-axis inductances of the motor, i d 、i q They represent the direct-axis current and quadrature-axis current of the motor respectively.

[0017] According to equations (1) and (2), considering the disturbance caused by current sampling and flux parameters, the motion equation is transformed into:

[0018]

[0019] Where, T A , T fluxThey are the disturbances caused by current sampling and flux parameters, and b 0 =J, f represents the total disturbance including current sampling disturbance, flux change disturbance, load disturbance and other disturbances.

[0020] As a further preferred solution, in step 2, the speed loop anti-disturbance controller adopts a compensation function observer, and introduces the lumped disturbance compensation function into the state expansion observer, thereby improving the system's observation capability of load disturbances;

[0021] Let x 1 =θ m 、x 2 =ω m 、u=T e , then the state space equation of the system is:

[0022]

[0023] In the traditional LADRC, LESO is a non-derivative observer, and only uses the velocity feedback signal. The relationship between the position and velocity feedback signals is established. The observer is designed as follows:

[0024]

[0025] In the formula, z 1 、z 2 They are the positions θ m and the mechanical angular velocity ω m The observed value of is the lumped disturbance observation value of the control system, L v1 , L v2 is the observer gain, and e 1 =x 1 -z 1 、e 2 =x 2 -z 2 ;

[0026] Subtracting equation (5) from equation (4) yields the differential relation of the error:

[0027]

[0028] The problem of observation error accumulation is solved through the differential relationship;

[0029] In addition, it can be seen from formula (6) that the estimation error is also affected by the lumped disturbance of the system. The compensation function of the lumped disturbance is introduced, and the observer equation is applied with the lumped disturbance compensation function as follows:

[0030]

[0031] In the formula, is the lumped disturbance compensation function.

[0032] Subtracting equation (7) from equation (4) yields the observer error after adding the compensation function:

[0033]

[0034] According to formula (8), the closer the compensation function of the lumped disturbance is to the lumped disturbance, the smaller the observer error is. and the aggregate disturbance observation The goal is to approach the lumped disturbance. The two are connected through a low-pass filter, and the expression is:

[0035]

[0036] Where λ = 2πf c , f c is the cutoff frequency of the low-pass filter; therefore, the observer expression with compensation function can be changed to:

[0037]

[0038] Assume compensation function For z 3 , after rearranging formula (10), we can get:

[0039]

[0040] In the formula, is the lumped disturbance observation value after compensation.

[0041] The improved compensation function observer (CFO) in step 2 can more accurately track medium and high frequency nonlinear disturbances, as well as mechanical disturbances and electrical disturbances including load disturbances, making the controller more anti-interference capable.

[0042] As a further preferred solution, in step 3, the speed loop anti-disturbance control controller adopts a super-helical sliding mode error feedback control law to weaken the chattering of the anti-disturbance control controller and enhance the dynamic response capability, thereby enhancing the anti-disturbance capability and dynamic performance of the anti-disturbance control controller;

[0043] Design the super-helical sliding mode state error feedback control law and define the sliding surface function:

[0044]

[0045] Where s is the sliding surface function, is the mechanical angular velocity observation value, ω mref is the mechanical angular velocity reference value.

[0046] According to the basic principle of the second-order sliding mode of the super spiral algorithm, we can get:

[0047]

[0048] In the formula, u 0 、u s represents the state variable, and tanh(s) is the hyperbolic tangent function. k p , k i is the parameter to be designed of the super-helical sliding mode controller and is greater than zero, and r is the coefficient to be designed.

[0049] Then the super-helical sliding mode state error feedback control law is:

[0050]

[0051] Where u represents the PMSM control variable.

[0052] The introduction of the STSM algorithm in step 3 reduces the inherent jitter of the system and has strong robustness. Compared with the sgn sign function, the hyperbolic tangent function can make the switching of the sliding mode controller smoother, thereby further reducing the system jitter.

[0053] Compared with the prior art, the present invention has the following advantages:

[0054] 1. In the design process of the super-helical enhanced anti-disturbance controller for a permanent magnet synchronous motor, the present invention takes into account the load disturbance, current sampling disturbance and flux parameter change disturbance in actual motor operation, and constructs an observer equation using a differential relationship based on the mathematical model of the permanent magnet synchronous motor and the mathematical characteristics of the anti-disturbance controller. The problem of observation error accumulation is solved through the differential relationship; the lumped disturbance compensation function is introduced into the observer to achieve accurate observation of medium and high frequency nonlinear disturbances, enhance the anti-disturbance capability of the control system, and achieve decoupling of steady-state and dynamic performance control parameters; the super-helical sliding mode control law is used to design the state error feedback control law, which further improves the anti-disturbance capability of the anti-disturbance controller and weakens the system jitter in steady state.

[0055] 2. The present invention uses the Matlab-Simulink simulation environment to conduct a comparative study on the PMSM vector control system based on the superhelical enhanced anti-disturbance controller and the PMSM vector control system based on the traditional PI controller. The simulation results show that the control system based on the superhelical enhanced anti-disturbance controller has better anti-disturbance performance and dynamic performance than the PI system. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A distribution diagram of the roots of the observer characteristic equation in a specific implementation scheme of the present invention;

[0057] Figure 2A structural diagram of an enhanced active disturbance rejection control method for a permanent magnet synchronous motor based on a super-helical control law according to the present invention;

[0058] Figure 3 It is a structural block diagram of the super-helix enhanced active disturbance rejection controller system in the present invention;

[0059] Figure 4 It is a comparison diagram of the speed waveforms of the super-helical enhanced active disturbance rejection controller system and the PI system when the speed suddenly changes in an embodiment of the present invention;

[0060] Figure 5 This is a comparison diagram of the speed waveforms of the super-helical enhanced active disturbance rejection controller system and the PI system when the load is suddenly increased / reduced in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0062] In a permanent magnet synchronous motor self-disturbance rejection control method based on a super-helical control law of the present invention:

[0063] The compensation disturbance observer expression is:

[0064]

[0065] In the formula, z 1 、z 2 They are the positions θ m and the mechanical angular velocity ω m The observed value, z 3 is the lumped disturbance compensation function, is the lumped disturbance observation value of the control system, λ is the relationship between With z 3 The low-pass filter cutoff frequency, L v1 , L v2 is the observer gain, and e 1 =x 1 -z 1 、e 2 =x 2 -z 2 , x 1 、x 2 They are the positions θ m and the mechanical angular velocity ω m The actual value of .

[0066] Then the super-helical sliding mode state error feedback control law is:

[0067]

[0068] In the formula, u 0 、u s represents the state variable, u represents the PMSM control variable, and tanh(s) is the hyperbolic tangent function. p , k i is the design parameter of the super-helical sliding mode controller and is greater than zero, r is the design coefficient, ω mref is the mechanical angular velocity reference value, b 0 =J, J is the moment of inertia.

[0069] Define the Lyapunov function:

[0070]

[0071] Its derivative is:

[0072]

[0073] According to Lyapunov's stability theorem, k i k p >0 o'clock, The super-helical sliding mode state error feedback control law makes the system stable.

[0074] According to formula (11), the compensated observer transfer function can be obtained:

[0075]

[0076] From formula (11), the characteristic equation of the observer can be obtained as:

[0077] s 3 +L v2 s 2 +(λL v2 +L v1 )s+λL v2 =0 (18)

[0078] Let L v1 =2ξω n , L v2 =ω n 2 , then the observer characteristic equation is:

[0079]

[0080] Where ζ represents the damping ratio; ω n represents the observer bandwidth, and λ is the low-pass filter cutoff frequency.

[0081] In order to configure the parameters effectively, it is necessary to understand the impact of each CFO parameter on the interference and noise suppression performance. The damping ratio is represented by ζ, and based on experience, there is usually a value around 1.0. The low-pass filter cutoff frequency, represented by λ, is proportional to the convergence rate of the compensation disturbance function. Finally, the observer bandwidth is selected based on the maximum interference frequency and the minimum noise frequency, with ω n The meaning of these parameters can help you choose the appropriate parameter adjustment range.

[0082] When selecting parameters, if the characteristic equation is in the left half plane, the observer system is stable. After many experiments, the parameter L is set. v1 =84.84,L v2 =3600, λ=5, ζ=0.707, the root distribution of the characteristic equation under this set of parameters is as follows Figure 1 As shown in Figure 2, the three roots of the third-order characteristic equation are all distributed in the left half plane of the coordinate system, and the constructed enhanced disturbance observer can achieve stability.

[0083] According to formula (11) and formula (14), we can construct Figure 2 In order to verify the performance of the permanent magnet motor vector control system using cascaded auto-disturbance rejection speed control, a system simulation model was built in Matlab-Simulink. The simulation model structure is as follows: Figure 3 The motor parameters are shown below.

[0084]

[0085] After many experiments and calculations, the parameters of the super-helix enhanced active disturbance rejection controller are: L v1 =84.84,L v2 =3600, λ=5, ζ=0.707, k p =727, k i = 5. In order to verify the excellent anti-disturbance performance of the super-helical enhanced active disturbance rejection controller, the system performance based on the PI controller and the cascaded active disturbance rejection controller was compared and analyzed under the conditions of speed mutation and load mutation.

[0086] The PMSM initially runs at 1500rpm without load, then suddenly increases to 1000rpm at t=0.3s, and suddenly increases to 1500rpm at t=0.6s. Under this condition, the motor speed waveform based on the super-helical enhanced active disturbance rejection controller system and the PI system is shown in the figure below. Figure 4As shown in the figure. During deceleration, the motor under PI control has an overshoot of 90rpm, while the super-helical enhanced anti-disturbance control has no overshoot and the adjustment time is shortened by 61.8% compared with PI. During acceleration, the adjustment time of the super-helical enhanced anti-disturbance control is shortened by 57.4% compared with PI. Compared with PI, the super-helical enhanced anti-disturbance control has better dynamic performance.

[0087] The PMSM is given a speed of 1500 rpm, with an initial load of 100 Nm. At t=0.3s, the load is suddenly increased to 800 Nm, and at t=0.6s, the load is suddenly reduced to 600 Nm. Figure 5 For this purpose, a speed waveform comparison diagram based on the superhelical enhanced anti-disturbance control system and the PI system under sudden load increase / reduction conditions is shown. After the sudden load increase, the speed drops of the PI and superhelical enhanced anti-disturbance control are 492.3rpm and 108.2rpm respectively, and the adjustment time is 0.125s and 0.096s respectively. Compared with PI control, the speed drop of the superhelical enhanced anti-disturbance control is reduced by 78.0%, and the adjustment time is shortened by 23.2%; and after the sudden load reduction, compared with PI control, the speed rise of the superhelical enhanced anti-disturbance control is reduced by 94.6%, and the adjustment time is shortened by 82.6%. Therefore, the superhelical enhanced anti-disturbance control proposed in the present invention can effectively suppress system load disturbances and uncertain disturbances, and has strong anti-disturbance ability and good dynamic performance.

[0088] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. An enhanced active disturbance rejection control method for a permanent magnet synchronous motor based on a super-helical control law, characterized in that: The following steps are involved: Step 1, in the control of the permanent magnet synchronous motor, the influence of load disturbance, current sampling disturbance and flux parameter change disturbance in the actual motor operation is considered, and a mathematical model of the permanent magnet synchronous motor is established; Step 2, improve the algorithm of the extended state observer (ESO) in the active disturbance rejection control (ADRC), add a lumped disturbance compensation function, and use the compensation function to achieve accurate observation of the disturbance in the mathematical model of the permanent magnet synchronous motor in step 1; Step 3: Improve the linear state error feedback control law (LSEF) algorithm by introducing the super-twisting sliding mode (STSM) control law and using the hyperbolic tangent function to weaken the inherent jitter of the sliding mode. Based on the information such as the lumped disturbance observation value provided by the improved ESO in step 2, the disturbance in the mathematical modeling of step 1 is suppressed to achieve fast and accurate control of the system state.

2. The method for enhanced active disturbance rejection control of a permanent magnet synchronous motor based on a super-helical control law according to claim 1 is characterized in that: In step 1, the established permanent magnet synchronous motor mathematical model is converted into the permanent magnet synchronous motor motion equation: The motion equation of the interior PMSM (Interior Permanent Magnet Synchronous Motor, IPMSM) set under load disturbance is expressed as: Where, T L is the load torque converted to the motor spindle end, B is the PMSM damping coefficient, ω m is the mechanical angular velocity of the PMSM, J is the moment of inertia of the entire mechanical load converted to the motor spindle end, T e is the electromagnetic torque, and its expression is: Where P em is the electromagnetic power, n p is the number of PMSM pole pairs; ψ f Represents the permanent magnet flux of the motor, L d , L q Respectively represent the direct-axis and quadrature-axis inductances of the motor, i d 、i q They represent the direct-axis current and quadrature-axis current of the motor respectively. According to equations (1) and (2), considering the disturbance caused by current sampling and flux parameters, the motion equation is transformed into: Where, T A , T flux They are the disturbances caused by current sampling and flux parameters, b0=J, and f represents the total disturbance including current sampling disturbance, flux change disturbance, load disturbance and other disturbances.

3. The method for enhanced active disturbance rejection control of a permanent magnet synchronous motor based on a super-helical control law according to claim 1 is characterized in that: In step 2, the speed loop anti-disturbance controller adopts a compensation function observer and introduces the lumped disturbance compensation function into the state expansion observer, thereby improving the system's ability to observe load disturbances. Let x1 = θ m 、x2=ω m 、u=T e , then the state space equation of the system is: In the traditional LADRC, LESO is a non-derivative observer, and only uses the velocity feedback signal. The relationship between the position and velocity feedback signals is established. The observer is designed as follows: Where z1 and z2 are the positions θ m and the mechanical angular velocity ω m The observed value of is the lumped disturbance observation value of the control system, L v1 , L v2 is the observer gain, and e1 = x1-z1, e2 = x2-z2; Subtracting equation (5) from equation (4) yields the differential relation of the error: The problem of observation error accumulation is solved through the differential relationship; In addition, it can be seen from formula (6) that the estimation error is also affected by the lumped disturbance of the system. The compensation function of the lumped disturbance is introduced, and the observer equation is applied with the lumped disturbance compensation function as follows: In the formula, is the lumped disturbance compensation function. Subtracting equation (7) from equation (4) yields the observer error after adding the compensation function: According to formula (8), the closer the compensation function of the lumped disturbance is to the lumped disturbance, the smaller the observer error is. and the aggregate disturbance observation The goal is to approach the lumped disturbance. The two are connected through a low-pass filter, and the expression is: Where λ = 2πf c , f c is the cutoff frequency of the low-pass filter; therefore, the observer expression with compensation function can be changed to: Assume compensation function is z3, and formula (10) can be rearranged to obtain: In the formula, is the lumped disturbance observation value after compensation.

4. The method for enhanced active disturbance rejection control of a permanent magnet synchronous motor based on a super-helical control law according to claim 1 is characterized in that: In step 3, the speed loop ADRC adopts the super-helical sliding mode error feedback control law to weaken the chattering of the ADRC and enhance the dynamic response capability, thereby enhancing the anti-disturbance capability and dynamic performance of the ADRC. Design the super-helical sliding mode state error feedback control law and define the sliding surface function: Where s is the sliding surface function, is the mechanical angular velocity observation value, ω mref is the mechanical angular velocity reference value. According to the basic principle of the second-order sliding mode of the super spiral algorithm, we can get: In the formula, u0, u s represents the state variable, and tanh(s) is the hyperbolic tangent function. k p , k i is the parameter to be designed of the super-helical sliding mode controller and is greater than zero, and r is the coefficient to be designed. Then the super-helical sliding mode state error feedback control law is: Where u represents the PMSM control variable.

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