Permanent magnet synchronous motor double-closed environmental protection performance control method based on sliding mode variable structure and self-coupling PI

Abstract

The invention discloses a permanent magnet synchronous motor double-closed environmental protection performance control method based on a sliding mode variable structure and a self-coupling PI, and the method comprises the steps: carrying out the equivalent mapping on a mathematical model of a permanent magnet synchronous motor in a synchronous rotating coordinate system to form a linear system, and designing a current loop controller based on the self-coupling PI; on the basis of error conversion, a speed environmental protection performance controller based on a sliding mode variable structure is designed. According to the invention, under the current loop controller based on the self-coupling PI, accurate current control is realized, the calculated amount is small, and the dynamic response speed is fast; the designed speed guaranteed performance controller has a good robust effect on load disturbance existing in the system, under the conditions of no-load starting and sudden load adding of the motor, no overshoot of the rotating speed and quick response are achieved, transient and steady state planning of the system can be achieved, and the dynamic and static characteristics and disturbance rejection performance of a speed outer ring are improved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of permanent magnet synchronous motor control, and particularly relates to a permanent magnet synchronous motor double-closed-loop performance control method based on a sliding mode variable structure and a self-coupling PI. BACKGROUND

[0002] The permanent magnet synchronous motor is widely applied to new energy and aerospace industries due to its advantages of high efficiency, high power factor and strong load capacity. However, with the wide application of the permanent magnet synchronous motor, its nonlinear and strong coupling characteristics become more obvious, thereby reducing the control precision and even causing instability. Therefore, the design of the current loop and speed loop controller of the motor becomes the key to solving the problem.

[0003] The traditional vector control scheme cannot solve the problem of poor motor control performance, and a simple and practical control method meeting the system performance requirements needs to be researched. Many control strategies are proposed by experts and scholars for the design of the current loop and speed loop, such as PID control, predictive control and adaptive control. These control strategies achieve good steady-state control precision, but cannot analyze the transient performance of the system.

[0004] In view of the characteristics of load disturbance and uncertain nonlinearity in motor control, it is urgent to design a method meeting the control requirements to improve the current dynamic response speed and weaken the influence of load change on the speed loop control performance. SUMMARY

[0005] The application aims to provide a permanent magnet synchronous motor double-closed-loop performance control method based on a sliding mode variable structure and a self-coupling PI, which solves the problems in the background technology.

[0006] To achieve the above object, the application provides the following technical scheme: a permanent magnet synchronous motor double-closed-loop performance control method based on a sliding mode variable structure and a self-coupling PI, comprising the following steps:

[0007] Step 1, a mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system is established, and is equivalent to a linear system, and a current controller is designed, and the process is as follows:

[0008]

[0009] Wherein K t = 3 / 2n p ψ f ;

[0010] 1.2, according to formula (1), respectively A virtual control quantity is introduced And the virtual gain c3 = 1.5n p ψ fJ is a constant, defined as the total disturbance of the current loop as follows

[0011]

[0012] 1.3, according to formula (2), formula (1) is equivalent to the following form

[0013]

[0014] Wherein, c1=c2=1 / L,

[0015] 1.4, the cross-axis current tracking error and its integral are Combined with formula (3) can be obtained Thus the cross-axis current error system is as follows

[0016]

[0017] Wherein, the composite total disturbance

[0018] 1.5, the cross-axis current loop self-coupling PI controller is designed as follows

[0019]

[0020] Wherein, the speed factor λ q =20α / T r , 1<α≤10, the larger α is, the faster the dynamic response of the system is, the stronger the anti-disturbance robustness is; otherwise, vice versa. T r Is the transition time from the dynamic stage to the steady state stage of the system, T r Is determined according to the time scale of the controlled system;

[0021] 1.6, using The direct-axis current tracking error and its integral are Combined with formula (3) can be obtained Thus the direct-axis current error system is as follows

[0022]

[0023] 1.7, the direct-axis current loop self-coupling PI controller is designed as follows

[0024]

[0025] Wherein, the speed factor λ d =20α / T r , 1<α≤10, the larger α is, the faster the dynamic response of the system is, the stronger the anti-disturbance robustness is; otherwise, vice versa. T ris the transition time from the dynamic phase to the steady phase, T r is determined according to the time scale of the controlled system.

[0026] Step 2, the speed performance preserving controller based on the sliding mode variable structure is designed, the process is as follows

[0027] 2.1, the motor speed tracking error is e = ω s -ω m , while meeting the performance preserving index requirements, the mathematical expression is as follows

[0028] -σ L P(t)<e(t)<σ R P(t) (8)

[0029] Where, σ L and σ R are overshoot suppression parameters, σ L ∈[0, 1], σ R ∈[0, 1], and the value should meet -σ L p0<e(0)<σ R p0, p0 is the initial value of the function P(t), p ∞ is the final value of the function P(t);

[0030] 2.2, P(t) in equation (8) is a performance function, the selected exponential function is as follows

[0031] P(t)=(p0-p ∞ )e -ll +p ∞ (9)

[0032] Where, ι is the decay rate parameter, ι>0;

[0033] 2.3, in order to realize the equivalent conversion from the performance constraint space to the unconstrained space, the tracking error e(t) needs to be converted to ensure that the system realizes performance preserving asymptotic stability, the conversion error function expression is as follows

[0034]

[0035] Where, Q(·) is a class of smooth decreasing function, with the following properties

[0036] Q: (-σ, 1)→(-∞, ∞), e(0)≥0 (11)

[0037] Q: (-1, σ)→(-∞, ∞), e(0)≤0 (12)

[0038] 2.4, on the basis of equation (8), the expression of conversion error function ε(t) is

[0039]

[0040] 2.5, derivative of formula (13) is obtained as follows

[0041]

[0042] Wherein, z = e(t) / P(t);

[0043] 2.6, in order to realize better tracking effect of speed, the sliding mode surface is selected as follows

[0044]

[0045] Wherein, c is the coefficient to be designed, c>0;

[0046] 2.7, in order to ensure that the system has better dynamic performance, the exponential approach law is selected, and the control law of permanent magnet synchronous motor can be designed as follows

[0047]

[0048] Wherein, m is the conditional coefficient, m>0, q is the exponential coefficient, q>0, D is the parameter to be designed, D>0; BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 It is the control schematic diagram of the application;

[0050] Figure 2 It is the motor system control strategy diagram of the application;

[0051] Figure 3 It is the motor speed response waveform diagram of the application;

[0052] Figure 4 It is the motor speed error schematic diagram of the application;

[0053] Figure 5 It is the cross axis current response waveform diagram of the application;

[0054] Figure 6 It is the motor stator winding three-phase current waveform diagram of the application;

[0055] Figure 7 It is the motor torque response waveform diagram of the application. DETAILED DESCRIPTION

[0056] The application will be further described below in combination with the drawings.

[0057] REFERENCE Figures 1-7A permanent magnet synchronous motor double closed loop energy-saving control method based on sliding mode variable structure and self-coupling PI, comprising the following steps:

[0058] Step 1, establish the mathematical model of permanent magnet synchronous motor under the coordinate system, and equivalent mapping into a linear system, and design current controller, the process is as follows:

[0059] 1.1, the current equation of permanent magnet synchronous motor under dq coordinate system is as follows

[0060]

[0061] Wherein K t = 3 / 2n p ψ f ;

[0062] 1.2, according to formula (1), respectively Introducing virtual control variable And virtual gain c3 = 1.5n p ψ f / J is a constant, the total disturbance of current loop is defined as follows

[0063]

[0064] 1.3, according to formula (2), formula (1) is equivalent to the following form

[0065]

[0066] Wherein, c1 = c2 = 1 / L,

[0067] 1.4, the tracking error of quadrature axis current and its integral are Combined with formula (3), we can get So the quadrature axis current error system is as follows

[0068]

[0069] Where, the complex total disturbance

[0070] 1.5, the self-coupling PI controller of quadrature axis current loop is designed as follows

[0071]

[0072] Wherein, the speed factor λ q = 20α / T r , 1 < α ≤ 10, the larger α is, the faster the dynamic response of the system is, and the stronger the anti-disturbance robustness is; otherwise, vice versa. T r is the transition time of the system from dynamic stage to steady stage, Tr is determined according to the time scale of the controlled system;

[0073] 1.6, adopt The direct-axis current tracking error and its integral are Combined with equation (3), we can get Thus the direct-axis current error system is as follows

[0074]

[0075] 1.7, the direct-axis current loop self-coupling PI controller is designed as follows

[0076]

[0077] where the speed factor λ d = 20α / T r , 1 < α ≤ 10, the larger α is, the faster the dynamic response of the system is, and the stronger the anti-disturbance robustness is; otherwise, the opposite. T r is the transition time from the dynamic stage to the steady state stage of the system, T r is determined according to the time scale of the controlled system.

[0078] Step 2, speed performance guarantee controller design based on sliding mode variable structure, the process is as follows

[0079] 2.1, the motor speed tracking error e = ω s - ω m , while meeting the performance guarantee index requirements, the mathematical expression is as follows

[0080] - σ L P(t) < e(t) < σ R P(t) (8)

[0081] where σ L and σ R are overshoot suppression parameters, σ L ∈ [0, 1], σ R ∈ [0, 1], and the values meet - σ L p0 < e(0) < σ R p0, p0 is the initial value of the function P(t), and p ∞ is the final value of the function P(t);

[0082] 2.2, P(t) in equation (8) is a performance function, and the selected exponential function is as follows

[0083] P(t) = (p0-p ∞ )e -ll + p ∞ (9)

[0084] where, i is the attenuation rate parameter, i > 0

[0085] 2.3, in order to realize the performance constraint space to the unconstrained space equivalence conversion, the tracking error e(t) is converted to ensure that the system realizes the guaranteed cost asymptotic stability, the conversion error function expression is as follows

[0086]

[0087] Wherein, Q(·) is a class of smooth decreasing function, has the following properties

[0088] Q: (-sigma, 1) → (-∞, ∞), e(0) ≥ 0 (11)

[0089] Q: (-1, sigma) → (-∞, ∞), e(0) ≤ 0 (12)

[0090] 2.4, on the basis of formula (8), the expression of conversion error function ε(t) is

[0091]

[0092] 2.5, the derivation of formula (13) is as follows

[0093]

[0094] Wherein, z=e(t) / P(t);

[0095] 2.6, in order to realize the better tracking effect of speed, the sliding mode surface is selected as follows

[0096]

[0097] Wherein, c is the coefficient to be designed, c > 0

[0098] 2.7, in order to ensure that the system has better dynamic performance, the exponential approach law is selected, and the control law of permanent magnet synchronous motor can be designed as follows

[0099]

[0100] Wherein, m is the conditional coefficient, m > 0, q is the exponential coefficient, q > 0, D is the parameter to be designed, D > 0

[0101] In order to verify the effectiveness of the method, the simulation experiment is carried out in Matlab / Simulink, and the initial conditions and part of the parameters of the simulation experiment are set, that is, the motor parameters inductance L=3.325mH, permanent magnet flux ψ f =0.269Wb, resistance R=0.92Ω, moment of inertia J=2.77×10-3 kg·m 2 , friction coefficient B = 8 x 10- 4 N / rad / s, the number of pole pairs n p = 4, reference speed ω s = 1000 rpm, the current loop sampling period is T s = 1 x 10- -4 s. The parameters of the speed preserving performance controller based on sliding mode variable structure are set as c = 30, m = 100, q = 9500, p ∞ = 40, τ = 250, σ L = σ R = 1, the parameters of the current controller based on self-coupling PI are set as α = 1.6, T r = 9.7; the parameters of the speed loop and current loop PID controllers are set as k p = 0.058814683, k1 = 3.532988462 and k p = 2.989210101, k i = 114.9696193. The simulation runs for 1s, and a sudden load torque of 5 N.m is added at 0.5s.

[0102] Figure 3 and Figure 4 respectively represent the speed tracking and speed error waveform diagrams under the controller (PPSMC+SCPI) and the PID controller (PI+PI) designed in the application, the method of the application realizes speed without overshoot and without steady-state error, has good reference tracking performance, and meets the requirements of the preserving performance control index, and has strong robustness.

[0103] Figure 5 represent the quatrature axis current waveform diagrams under the controller (PPSMC+SCPI) and the PID controller (PI+PI) designed in the application, the dynamic response speed of the quatrature axis current is faster under the method of the application, and the method has good stability and tracking precision.

[0104] Figure 6 and Figure 7 respectively represent the three-phase current and electromagnetic torque waveform diagrams under the controller designed in the application, and after the sudden load is added, the three-phase current and electromagnetic torque can quickly enter a new stable state.

[0105] The above illustrates the excellent effect of one example given by the present application, and obviously the present application is not limited to the above-mentioned embodiments, and various modifications can be made to the embodiments without departing from the basic spirit of the present application and beyond the scope involved by the essential content of the present application. The proposed scheme is effective in solving the problems of how to improve the current dynamic response speed of the surface-mounted permanent magnet synchronous motor and weaken the influence of load change on the speed loop control performance, and under the action of the proposed double closed-loop controller, the performance index is met, the speed overshoot is realized, the current is accurately regulated, the dynamic response is fast, and the anti-disturbance performance is good.

Claims

1. A method for controlling the dual-closed environmental performance of a permanent magnet synchronous motor based on a sliding mode variable structure and an auto-coupling PI, characterized in that the control method comprises the following steps: Step 1: Establish a mathematical model of the permanent magnet synchronous motor in the dq coordinate system, map it to a linear system, and design a current controller. The process is as follows: 1.1, the current equation of the permanent magnet synchronous motor in the dq coordinate system is as follows where K t =3 / 2n p ψ f ; 1.2, according to formula (1), let Introducing virtual control quantities And the virtual gain c3=1.5n p ψ f / J is a constant, and the total disturbance of the current loop is defined as follows 1.3, according to formula (2), formula (1) is equivalently mapped into the following form Where, c1=c2=1 / L, 1.4, the quadrature axis current tracking error and its integral are Combining formula (3) we can get So the quadrature-axis current error system is as follows Among them, the composite total disturbance 1.5, the quadrature axis current loop autocoupler PI controller is designed as follows Where, the speed factor λ q =20α / T r , 1<α≤10, when α is larger, the system's dynamic response is faster and its anti-disturbance robustness is stronger; otherwise, the opposite is true. r is the transition time of the system from the dynamic stage to the steady state stage, T r It is determined based on the time scale of the controlled system; 1.6, adopt The direct axis current tracking error and its integral are: Combining equation (3) gives The direct axis current error system is then given in the form 1.7, The direct-axis current loop self-coupling PI controller is designed as follows wherein Speed factor λ d = 20α / T r , 1 < α ≤ 10, the larger α is, the faster the dynamic response of the system is, and the stronger the anti-disturbance robustness is; otherwise, vice versa. r is the transition time from the dynamic phase to the steady phase of the system, T r is determined according to the time scale of the controlled system. Step 2, The speed preserving performance controller based on sliding mode variable structure is designed as follows 2.1, the motor speed tracking error is e = ω s -ω m while meeting the performance guarantee index requirements, the mathematical expression is as follows -σ L P(t) < e(t) < σ R P(t) (8) where σ L and σ R are overshoot suppression parameters, σ L ∈ [0, 1], σ R ∈ [0, 1], and the values satisfy -σ L p0 < e(0) < σ R p0, p0 is the initial value of the function P(t), and p ∞ is the final value of the function P(t); 2.2, P(t) in formula (8) is a performance function, and the selected exponential function is as follows Wherein, ι is the decay rate parameter, ι > 0; 2.3, In order to realize the equivalent conversion from the performance constraint space to the unconstrained space, the tracking error e(t) needs to be converted to preserve the system to realize the performance preserving asymptotic stability, and the conversion error function expression is as follows Wherein, Q(·) is a kind of smooth decreasing function, which has the following properties Q: (-σ, 1)→(-∞, ∞), e(0)≥0 (11) Q: (-1, σ)→(-∞, ∞), e(0)≤0 (12) 2.4, On the basis of formula (8), the expression of the conversion error function ε(t) is 2.5, Derivation of formula (13) is as follows wherein, z=e(t) / P(t); 2.6, In order to realize better tracking effect of speed, the sliding surface is selected as follows wherein, C is the coefficient to be designed, c > 0; 2.7, In order to ensure that the system has better dynamic performance, the exponential reaching law is selected, and the control law of the permanent magnet synchronous motor can be designed as follows Wherein, m is the conditional coefficient, m > 0, q is the exponential coefficient, q > 0, and D is the parameter to be designed, D > 0.

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