Terminal forced sliding mode collaborative direct speed control method and system of SMPMSM driving system

Abstract

The application relates to a terminal forced sliding mode collaborative direct speed control method of an SMPMSM driving system, which comprises the following steps: in a synchronous speed rotating dq axis coordinate system, an SMPMSM driving system hyperlocal model of speed control is established; a macro variable containing a sliding surface is designed, and a dynamic evolution equation containing a non-singular terminal term is proposed; system voltage and current constraints are processed; finally, a terminal forced sliding mode collaborative direct speed control law is generated to realize high-performance speed control. The non-singular terminal dynamic evolution equation designed in the application can significantly improve the convergence speed of the macro variable approaching the flow field and improve the dynamic response of the system. Therefore, the terminal forced sliding mode collaborative direct speed control proposed in the application has a more superior speed fast dynamic response on the premise of guaranteeing the speed and current steady-state control performance.

Description

A method and system for forced sliding mode cooperative direct speed control of an SMPMSM drive system Technical Field

[0001] This invention relates to the field of motor control technology, and in particular to a terminal forced sliding mode cooperative direct speed control method and system for an SMPMSM drive system. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in industry due to their advantages such as high efficiency, high power density, high dynamic performance, and low maintenance. Traditional PI control is widely used in speed control of PMSM drive systems due to its simplicity and ease of implementation. However, in a PI-controlled PMSM dual-loop cascaded speed control system, the outer speed loop provides a reference current command to the inner current loop. This results in the speed loop control bandwidth being much smaller than the current loop control bandwidth, leading to insufficient dynamic performance in the PMSM drive system's speed control. Furthermore, the PMSM drive system is a multivariable, strongly coupled nonlinear system, with uncertainties in motor parameters, inverter nonlinearity, and unknown disturbances coexisting, making it difficult for the PI-controlled PMSM dual-loop cascaded speed control system to achieve satisfactory control performance.

[0003] PMSM drive systems with direct speed control can simplify controller design, achieve simultaneous control of speed and current at different time scales, and improve system control performance. Finite Control Set Model Predictive Direct Speed ​​Control (FCS-MPDSC) defines a single cost function to directly control speed and current, improving system dynamic response, but suffers from significant current and speed ripple.

[0004] Cooperative control leverages the system's inherent nonlinearity and the self-organizing ability of an open system far from equilibrium to stably converge to a manifold. The manifold in cooperative control is similar to the sliding surface in sliding mode control, but unlike sliding mode control which uses switching control to bring the system trajectory closer to the sliding surface, cooperative control defines a continuous dynamic process that approaches the manifold, ensuring the global asymptotic stability of the high-dimensional nonlinear system through the manifold. Therefore, cooperative control possesses the advantages of sliding mode control while avoiding its chattering problem. Comparative studies of cooperative control and sliding mode control confirm that cooperative control effectively eliminates the chattering problem of sliding mode control and is more suitable for digital control implementation. A forced sliding mode control proposed based on the intrinsic connection between cooperative control and sliding mode variable structure control not only achieves accelerated sliding towards the sliding surface but also avoids the chattering of sliding mode control. For PMSM drive systems, the influence of motor parameter uncertainties, unmodeled dynamics, and load torque disturbances leads to a decrease in the control performance of forced sliding mode cooperative direct speed control PMSM drive systems, and may even cause the system to become unstable. Summary of the Invention

[0005] To address the technical shortcomings of poor dynamic speed performance and low steady-state accuracy in SMPMSM drive systems with forced sliding mode cooperative control, the primary objective of this invention is to provide a terminal forced sliding mode cooperative direct speed control method for SMPMSM drive systems that can maintain a fast dynamic speed response with direct speed control while achieving better steady-state speed and current control performance.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a terminal forced sliding mode cooperative direct speed control method for an SMPMSM drive system, the method comprising the following sequential steps:

[0007] (1) Establish a hyperlocal model of speed control of the SMPMSM drive system in the dq axis coordinate system rotating at the same speed;

[0008] (2) Based on the hyperlocal model of speed control of the SMPMSM drive system, macro-variable design including sliding surface is carried out, and dynamic evolution equations including non-singular terminals are designed. System voltage and current constraints are handled, etc., and terminal forced sliding mode cooperative direct speed control law is generated. Terminal forced sliding mode cooperative direct speed control is proposed.

[0009] Step (1) specifically refers to:

[0010] Considering the uncertainties in motor parameters and unknown disturbances, the mathematical model of the SMPMSM drive system in the synchronous speed rotation dq axis coordinate system is as follows:

[0011]

[0012] Among them, i d and i q These are the d-axis and q-axis stator currents, respectively; u d and u q These are the stator voltages along the d and q axes, respectively; ω r T is the rotor's electrical angular velocity. e T L These are the electromagnetic torque and load torque of SMPMSM, respectively; R s It is the stator winding resistance; L d L q These are the d-axis and q-axis stator inductances, respectively; ψ f This represents the rotor permanent magnet flux linkage; J and B are the moment of inertia and coefficient of viscous friction, respectively; n p f is the extreme logarithm of SMPMSM; d f q and f ω These represent the parameter uncertainties and unknown disturbances in motor d / q current control and speed control, respectively;

[0013] According to model-free control, the first-order hyperlocal model of a single-input single-output system is expressed as:

[0014]

[0015] Where u and y represent the system input and output, respectively; α is the scaling factor of the system input; F includes the known and unknown parts of the system.

[0016] Define the input of the SMPMSM drive system as u d u q and i q The output is i d i q and ω r The hyperlocal model of speed control for the SMPMSM drive system is expressed as:

[0017]

[0018] In the formula, α d α q α ω Input u to the system d u q and i q For the SMPMSM drive system, the scaling factor is such that the stator inductances of the dq axes are equal, i.e., L d =L q Set α d =α q =α s ;

[0019] F d ,F q and F ω The known and unknown parts of the system are represented by the following expression:

[0020]

[0021] Using differential algebra to analyze F d F q and F ω Make an estimate and use Its estimated value is expressed as:

[0022]

[0023] Among them, T s For control period; T F =n F T s n is the length of the sliding window. F It is a constant and set to 10; it is considered to be within a shorter sampling interval. and It is a constant, and its differential is approximately 0.

[0024] Step (2) specifically refers to:

[0025] To achieve direct speed control of the SMPMSM drive system, the main control objective is:

[0026]

[0027] in, The reference value for electric angular velocity is ω. r Let Δω be the rotor's electric angular velocity. r This refers to the electrical angular velocity error.

[0028] To achieve maximum torque-to-current ratio operation of the SMPMSM drive system, a macro variable ψ1 is designed, and:

[0029] ψ1=|i d | (7)

[0030] To achieve speed tracking of its reference value Design a macro variable ψ2, and have:

[0031] ψ2=β|Δω r |+|s1| (8)

[0032] Where β is the speed error coefficient and s1 is the designed sliding surface;

[0033] s1=α ω i q +u2(9)

[0034] Where u2 is the undetermined internal control of the system;

[0035] For the designed macro variables ψ1 and ψ2, the non-singular terminal dynamic evolution equation is defined as follows:

[0036]

[0037] Where p and q are positive odd numbers, and 1 < p / q < 2, T1 and T2 are controller parameters, both of which are greater than 0 to ensure the stability of the closed-loop control system;

[0038] Substituting the designed macro variables ψ1 and ψ2 into equation (11), we obtain the terminal forced sliding mode cooperative direct velocity control law, and we have:

[0039]

[0040] In the formula, α s and α ω The scaling factor input to the system. and The F-estimates are the perturbation components of the current loop disturbance on the d-axis and q-axis.

[0041] The terminal-forced sliding mode cooperative direct velocity control law includes an equivalent control law and a switching control law, wherein the equivalent control law u deq and u qeq The expression is:

[0042]

[0043] Switching control law u dSMC and u qSMC The expression is:

[0044]

[0045] Under the action of the equivalent control law of equation (12) and the switching control law of equation (13), the system is made to move to manifolds ψ1=0 and ψ2=0 in any initial state, and remains on manifolds ψ1=0 and ψ2=0. Manifold ψ2=0 contains sliding surface s1, so it is forced to reach the sliding surface, then:

[0046] s1=α ω i q +u2=0 (14)

[0047] To determine the undefined internal control u2 of the system, a sliding surface s2 is designed, whose expression is:

[0048] s2=γΔω r ε +Δω r (15)

[0049] Where γ and ε are controller parameters, γ > 0, 1 < ε < 2;

[0050] For the designed sliding surface s2, its dynamic evolution equation is designed as follows:

[0051]

[0052] Where T3 is the controller parameter, and T3 is greater than 0;

[0053] Combining equations (15) and (16), and based on the hyperlocal model of speed control of the SMPMSM drive system, the undetermined internal control u2 of the system is obtained, and:

[0054]

[0055] In the formula, This is an estimate of the velocity loop disturbance component;

[0056] Within a shorter sampling interval Since is a constant, its differential is approximately 0. Taking the derivative of equation (17), we have:

[0057]

[0058] Substituting equations (17) and (18) into equation (11), we generate the inverter reference voltage vector, and we have:

[0059]

[0060] To prove the stability of the system, the Lyapunov function V is defined. i =0.5ψ i 2 For i = 1, 2, its differential is when When the time interval is negative, the asymptotic convergence condition is satisfied.

[0061] Differentials of macro variables ψ1 and ψ2 and Solving directly from the dynamic evolution equations, we have:

[0062]

[0063] In the formula, and Let p be the differential of the Lyapunov function. Since T1, T2, β, and γ are all greater than 0, p and q are positive odd numbers, and p+q is a positive even number, then... and All are negative, that is The defined Lyapunov function satisfies the asymptotic convergence condition, proving that the proposed sliding mode cooperative direct velocity control can achieve stable operation of the SMPMSM drive system;

[0064] Subsequently, based on the dynamic evolution equation of equation (10), the differentials of sliding surfaces s1 and s2 are obtained. and And there are:

[0065]

[0066] Because T2, T3, and γ are all greater than 0, and p+q is a positive even number, therefore The existence of the designed sliding surface has been proven;

[0067] To ensure that the generated inverter reference voltage simultaneously meets the current and voltage constraints of the SMPMSM drive system, constraint processing is necessary. The inverter q-axis reference voltage that satisfies the maximum current constraint is:

[0068]

[0069] Among them, I max It is the maximum stator current;

[0070] The inverter reference voltage that satisfies the current constraint is:

[0071]

[0072] Among them, u qlim This represents the maximum q-axis voltage component of the inverter.

[0073] To fully utilize the DC bus voltage of the inverter, the boundary equation of the inverter's hexagonal voltage vector is written as:

[0074]

[0075] Among them, h dn and h qn These are the proportionality coefficients for the d-axis voltage and the q-axis voltage, respectively, h cn For bus voltage, U dcIt is the DC bus voltage;

[0076] The inverter reference voltage is adjusted to obtain the optimal inverter reference voltage that simultaneously satisfies current and voltage constraints. and The expression is:

[0077]

[0078] To ensure that the inverter reference voltage generated by the terminal forced sliding mode cooperative direct speed control satisfies both current and voltage constraints, the stator current is predicted by the established SMPMSM drive system hyperlocal model based on the inverter reference voltage generated by equation (19). When the stator current exceeds the limit, the inverter reference voltage that satisfies the current constraint is obtained according to equation (23). Then, it is determined whether the inverter reference voltage exceeds the inverter voltage hexagon range. If it does, the optimal inverter reference voltage that satisfies both current and voltage constraints is calculated according to equation (25).

[0079] Another object of the present invention is to provide a terminal forced sliding mode cooperative direct speed control system for an SMPMSM drive system, comprising:

[0080] The surface-mounted permanent magnet synchronous motor SMPMSM, as the test object for speed control of the motor drive system, has a power of 900W and a rated speed of 500rpm.

[0081] The two-level three-phase inverter is responsible for providing drive voltage to the motor. The DC bus voltage of the two-level three-phase inverter is 48V and the dead time is 2us.

[0082] A rotary transformer is used to detect the rotor position of the motor under test.

[0083] Forced sliding mode coordinated control module, used to output the reference voltage vector of two-level three-phase inverter;

[0084] The limiting processing module is used to constrain the voltage vector output by the forced sliding mode cooperative control module to ensure the safe and stable operation of the motor.

[0085] The space vector pulse width modulation module is used to generate a frequency- and voltage-adjustable sine wave signal for motor drive.

[0086] As can be seen from the above technical solution, the beneficial effects of the present invention are as follows: First, the SMPMSM drive system terminal forced sliding mode cooperative direct speed control proposed in this invention can maintain the fast dynamic response of the speed of direct speed control, while achieving better speed and current steady-state control performance; Second, the present invention designs a non-singular terminal dynamic evolution equation, which accelerates the convergence speed of macrovariables approaching the manifold and improves the dynamic response speed of the controller; Third, the present invention is based on a hyperlocal model and considers known and unknown disturbances of the system, so the controller can obtain high-precision steady-state performance and has a certain robustness to disturbances. Attached Figure Description

[0087] Figure 1 shows the control structure diagram of the SMPMSM drive system for sliding mode cooperative speed control;

[0088] Figure 2 shows the steady-state experimental results of the two methods at a rotational speed of 500 rpm and a load torque of 10 Nm.

[0089] Figure 3 shows the steady-state experimental results of the two methods at a rotational speed of 300 rpm and a load torque of 10 Nm.

[0090] Figure 4 shows the steady-state experimental results of the two methods at a rotational speed of 100 rpm and a load torque of 10 Nm.

[0091] Figure 5 shows the dynamic experimental results of the two methods when the rotational speed jumps from 0 to 500 rpm.

[0092] Figure 6 shows the experimental results of the two methods with a load step when the rotation speed is 500 rpm and the load is 10 nm. Detailed Implementation

[0093] A terminal forced sliding mode cooperative direct speed control method for an SMPMSM drive system, the method comprising the following sequential steps:

[0094] (1) Establish a hyperlocal model of speed control of the SMPMSM drive system in the dq axis coordinate system rotating at the same speed;

[0095] (2) Based on the hyperlocal model of speed control of the SMPMSM drive system, macro-variable design including sliding surface is carried out, and dynamic evolution equations including non-singular terminals are designed. System voltage and current constraints are handled, etc., and terminal forced sliding mode cooperative direct speed control law is generated. Terminal forced sliding mode cooperative direct speed control is proposed.

[0096] Step (1) specifically refers to:

[0097] Considering the uncertainties in motor parameters and unknown disturbances, the mathematical model of the SMPMSM drive system in the synchronous speed rotation dq axis coordinate system is as follows:

[0098]

[0099] Among them, i d and i q These are the d-axis and q-axis stator currents, respectively; u d and u q These are the stator voltages along the d and q axes, respectively; ω r T is the rotor's electrical angular velocity. e T L These are the electromagnetic torque and load torque of SMPMSM, respectively; R s It is the stator winding resistance; L d L q These are the d-axis and q-axis stator inductances, respectively; ψ f This represents the rotor permanent magnet flux linkage; J and B are the moment of inertia and coefficient of viscous friction, respectively; n p f is the extreme logarithm of SMPMSM; d f q and f ω These represent the parameter uncertainties and unknown disturbances in motor d / q current control and speed control, respectively;

[0100] According to model-free control, the first-order hyperlocal model of a single-input single-output system is expressed as:

[0101]

[0102] Where u and y represent the system input and output, respectively; α is the scaling factor of the system input; F includes the known and unknown parts of the system.

[0103] Define the input of the SMPMSM drive system as u d u q and i q The output is i d i q and ω r The hyperlocal model of speed control for the SMPMSM drive system is expressed as:

[0104]

[0105] In the formula, α d α q α ω Input u to the system d u q and i q For the SMPMSM drive system, the scaling factor is such that the stator inductances of the dq axes are equal, i.e., L d =L q Set α d =αq =α s ;

[0106] F d ,F q and F ω The known and unknown parts of the system are represented by the following expression:

[0107]

[0108] Using differential algebra to analyze F d F q and F ω Make an estimate and use Its estimated value is expressed as:

[0109]

[0110] Among them, T s For control period; T F =n F T s n is the length of the sliding window. F It is a constant and set to 10; it is considered to be within a shorter sampling interval. and It is a constant, and its differential is approximately 0.

[0111] Step (2) specifically refers to:

[0112] To achieve direct speed control of the SMPMSM drive system, the main control objective is:

[0113]

[0114] in, The reference value for electric angular velocity is ω. r Let Δω be the rotor's electric angular velocity. r This refers to the electrical angular velocity error.

[0115] To achieve maximum torque-to-current ratio operation of the SMPMSM drive system, a macro variable ψ1 is designed, and:

[0116] ψ1=|i d | (7)

[0117] To achieve speed tracking of its reference value Design a macro variable ψ2, and have:

[0118] ψ2=β|Δω r |+|s1| (8)

[0119] Where β is the speed error coefficient and s1 is the designed sliding surface;

[0120] s1=α ω i q +u2(9)

[0121] Where u2 is the undetermined internal control of the system;

[0122] For the designed macro variables ψ1 and ψ2, the non-singular terminal dynamic evolution equation is defined as follows:

[0123]

[0124] Where p and q are positive odd numbers, and 1 < p / q < 2, T1 and T2 are controller parameters, both of which are greater than 0 to ensure the stability of the closed-loop control system;

[0125] Substituting the designed macro variables ψ1 and ψ2 into equation (11), we obtain the terminal forced sliding mode cooperative direct velocity control law, and we have:

[0126]

[0127] In the formula, α s and α ω The scaling factor input to the system. and The F-estimates are the perturbation components of the current loop disturbance on the d-axis and q-axis.

[0128] The terminal-forced sliding mode cooperative direct velocity control law includes an equivalent control law and a switching control law, wherein the equivalent control law u deq and u qeq The expression is:

[0129]

[0130] Switching control law u dSMC and u qSMC The expression is:

[0131]

[0132] Under the action of the equivalent control law of equation (12) and the switching control law of equation (13), the system is made to move to manifolds ψ1=0 and ψ2=0 in any initial state, and remains on manifolds ψ1=0 and ψ2=0. Manifold ψ2=0 contains sliding surface s1, so it is forced to reach the sliding surface, then:

[0133] s1=α ω iq +u2=0 (14)

[0134] To determine the undefined internal control u2 of the system, a sliding surface s2 is designed, whose expression is:

[0135] s2=γΔω r ε +Δω r (15)

[0136] Where γ and ε are controller parameters, γ > 0, 1 < ε < 2;

[0137] For the designed sliding surface s2, its dynamic evolution equation is designed as follows:

[0138]

[0139] Where T3 is the controller parameter, and T3 is greater than 0;

[0140] Combining equations (15) and (16), and based on the hyperlocal model of speed control of the SMPMSM drive system, the undetermined internal control u2 of the system is obtained, and:

[0141]

[0142] In the formula, This is an estimate of the velocity loop disturbance component;

[0143] Within a shorter sampling interval Since is a constant, its differential is approximately 0. Taking the derivative of equation (17), we have:

[0144]

[0145] Substituting equations (17) and (18) into equation (11), we generate the inverter reference voltage vector, and we have:

[0146]

[0147] To prove the stability of the system, the Lyapunov function V is defined. i =0.5ψ i 2 For i = 1, 2, its differential is when When the time interval is negative, the asymptotic convergence condition is satisfied.

[0148] Differentials of macro variables ψ1 and ψ2 and Solving directly from the dynamic evolution equations, we have:

[0149]

[0150] In the formula, and Let p be the differential of the Lyapunov function. Since T1, T2, β, and γ are all greater than 0, p and q are positive odd numbers, and p+q is a positive even number, then... and All are negative, that is The defined Lyapunov function satisfies the asymptotic convergence condition, proving that the proposed sliding mode cooperative direct velocity control can achieve stable operation of the SMPMSM drive system;

[0151] Subsequently, based on the dynamic evolution equation of equation (10), the differentials of sliding surfaces s1 and s2 are obtained. and And there are:

[0152]

[0153] Because T2, T3, and γ are all greater than 0, and p+q is a positive even number, therefore The existence of the designed sliding surface has been proven;

[0154] To ensure that the generated inverter reference voltage simultaneously meets the current and voltage constraints of the SMPMSM drive system, constraint processing is necessary. The inverter q-axis reference voltage that satisfies the maximum current constraint is:

[0155]

[0156] Among them, I max It is the maximum stator current;

[0157] The inverter reference voltage that satisfies the current constraint is:

[0158]

[0159] Among them, u qlim This represents the maximum q-axis voltage component of the inverter.

[0160] To fully utilize the DC bus voltage of the inverter, the boundary equation of the inverter's hexagonal voltage vector is written as:

[0161]

[0162] Among them, h dn and h qnThese are the proportionality coefficients for the d-axis voltage and the q-axis voltage, respectively, h cn For bus voltage, U dc It is the DC bus voltage;

[0163] The inverter reference voltage is adjusted to obtain the optimal inverter reference voltage that simultaneously satisfies current and voltage constraints. and The expression is:

[0164]

[0165] To ensure that the inverter reference voltage generated by the terminal forced sliding mode cooperative direct speed control satisfies both current and voltage constraints, the stator current is predicted by the established SMPMSM drive system hyperlocal model based on the inverter reference voltage generated by equation (19). When the stator current exceeds the limit, the inverter reference voltage that satisfies the current constraint is obtained according to equation (23). Then, it is determined whether the inverter reference voltage exceeds the inverter voltage hexagon range. If it does, the optimal inverter reference voltage that satisfies both current and voltage constraints is calculated according to equation (25).

[0166] As shown in Figure 1, this system includes:

[0167] The surface-mounted permanent magnet synchronous motor SMPMSM, as the test object for speed control of the motor drive system, has a power of 900W and a rated speed of 500rpm.

[0168] The two-level three-phase inverter, namely the Inverter in Figure 1, is responsible for providing drive voltage to the motor. The DC bus voltage of the two-level three-phase inverter is 48V and the dead time is 2us.

[0169] The rotary transformer, i.e. the sensor in Figure 1, is used to detect the rotor position of the motor under test.

[0170] The forced sliding mode cooperative control module, namely ULM-TSMSDSC in Figure 1, is used to output the reference voltage vector of the two-level three-phase inverter.

[0171] The limiting processing module, or constraint handling in Figure 1, is used to constrain the voltage vector output by the forced sliding mode cooperative control module to ensure the safe and stable operation of the motor.

[0172] The space vector pulse width modulation module, i.e. SVPWM in Figure 1, is used to generate a frequency- and voltage-adjustable sine wave signal for motor drive.

[0173] Example 1

[0174] To demonstrate the effectiveness of the proposed terminal forced sliding mode cooperative direct velocity control, an experimental platform for the SMPMSM drive system was built based on dSPACE / DS1007. All controller parameters were obtained through repeated trial and error, as shown in Table 1.

[0175] Table 1 Controller Parameters

[0176] ParametersValueT10.0002T20.005T30.005p9q7β300γ10ε1.28α s 1000α ω 1000 surface

[0177] The motor under test was a 900W SMPMSM, with nominal parameters shown in Table 2. The motor was powered by an inverter, which consisted of MOSFET integrated modules and used SVPWM to generate drive signals. The switching frequency was set to 10kHz, and the dead time was set to 2µs. A programmable DC power supply was used to power the inverter, with a DC bus voltage of 48V. A single-pole rotary transformer was used to detect the rotor position of the motor under test, and the motor phase current sensor was a LEMLA25-P. The three-phase asynchronous motor had a power of 2.2kW and served as the dynamometer for the motor under test, driven by an ABB ACS800 series frequency converter, capable of four-quadrant operation. During the experiment, the SMPMSM drive system operated in speed control mode, while the dynamometer operated in torque control mode.

[0178] Table 2 Measured SMM / SM parameters

[0179]

[0180]

[0181] This invention, hereinafter referred to as ULM-TFSMSDSC, was experimentally compared with Forced Sliding Model Synergetic Direct Speed ​​Control of SMPMSM Drives based on Extended model (EM-FSMSDSC). To ensure the fairness of the comparison, the SMPMSM system of EM-FSMSDSC was subjected to the same voltage and current constraints as described in this paper, and then the dynamic and steady-state control performance of the two control methods was experimentally compared under the same experimental conditions.

[0182] Steady-state experiments were conducted on ULM-TFSMSDSC and EM-FSMSDSC at different speeds when the load torque was 10 Nm. The steady-state waveforms of speed and current and the phase current THD of the two control methods at low speed (100 rpm), medium speed (300 rpm) and high speed (500 rpm) are compared as shown in Figures 2, 3 and 4.

[0183] When the system operates at low and high speeds, the speed ripple of ULM-TFSMSDSC is slightly smaller than that of EM-FSMSDSC. However, when the system operates at medium speed, the speed ripple of ULM-TFSMSDSC is significantly smaller than that of EM-FSMSDSC, only ±2.479 rpm, while the speed ripple of EM-FSMSDSC is ±4.567 rpm. The dq-axis current ripple and phase current THD of ULM-TFSMSDSC are both smaller than those of EM-FSMSDSC. The comparison of the steady-state performance indicators of the two control methods is shown in Table 3. The experimental study of the system confirms that the proposed control has better steady-state speed control performance and better steady-state current quality.

[0184] Table 3 Comparison of steady-state performance indices of the two methods

[0185]

[0186] Under the same experimental conditions, speed command step tests and load step tests were conducted using two different control methods. Under no-load conditions, a speed command step test was performed at 0.2s to reach the rated speed of 500 rpm, as shown in Figure 5. The experimental results confirmed that the ULM-TFSMSDSC has a faster speed response, with a rise time to the command value of 0.18s, while the rise time of the EM-FSMSDSC is 0.2s. Furthermore, the ULM-TFSMSDSC has a smaller overshoot and a faster settling time. Simultaneously, the ULM-TFSMSDSC exhibits better current steady-state performance in terms of q-axis current and three-phase current.

[0187] Figure 6 shows the experimental results of suddenly removing the 10Nm load at 0.3s when the system is running at a rated speed of 500rpm and a load torque of 10Nm in steady state. The experimental results show that the speed overshoot of ULM-TFSMSDSC and EM-FSMSDSC is similar during sudden unloading, but ULM-TFSMSDSC has a faster settling time and better steady-state performance in terms of d-axis and q-axis currents and motor phase currents. Table 4 shows a comparison of the dynamic performance indicators of the system under the two control methods.

[0188] Table 4 Comparison of dynamic performance indicators of the two methods

[0189]

[0190] In summary, the SMPMSM drive system terminal forced sliding mode cooperative direct speed control proposed in this invention can maintain the fast dynamic response of direct speed control while achieving better steady-state control performance for speed and current. This invention designs a non-singular terminal dynamic evolution equation, accelerating the convergence speed of macrovariables approaching the manifold and improving the dynamic response speed of the controller. Based on a hyperlocal model, this invention considers both known and unknown disturbances in the system; therefore, the controller can achieve high-precision steady-state performance and has a certain robustness to disturbances.

Claims

1. A terminal forced sliding mode cooperative direct speed control method for an SMPMSM drive system, comprising the following sequential steps: (1) establishing a hyperlocal model of the SMPMSM drive system for speed control in a synchronous speed rotation dq axis coordinate system; (2) based on the hyperlocal model of the SMPMSM drive system speed control, carrying out macrovariable design including sliding surfaces, designing dynamic evolution equations including non-singular terminals; processing system voltage and current constraints, generating a terminal forced sliding mode cooperative direct speed control law, and proposing a terminal forced sliding mode cooperative direct speed control; step (2) specifically refers to: to achieve direct speed control of the SMPMSM drive system, the main control objective is: ,in, This is the reference value for electric angular velocity. The rotor's electric angular velocity, To account for the electrical angular velocity error; to achieve maximum torque-to-current ratio operation of the SMPMSM drive system, a macrovariable is designed. And there are: In order to achieve speed tracking of its reference value Design macro variables And there are: ,in, It is the speed error coefficient. For the designed sliding surface; ,in, For the internal control of the system to be determined; for the designed macro variables and The dynamic evolution equation for a non-singular terminal is defined as follows: Where p and q are positive odd numbers, and 1 < p / q < 2, T1 and T2 are controller parameters, both of which are greater than 0 to ensure the stability of the closed-loop control system; the designed macro variables and Substituting into equation (11), we obtain the terminal forced sliding mode cooperative direct velocity control law, and we have: In the formula, and The scaling factor input to the system. and The F-estimates are the disturbance components of the current loop disturbance on the d-axis and q-axis; the terminal forced sliding mode cooperative direct velocity control law includes an equivalent control law and a switching control law, wherein the equivalent control law... and The expression is: Switching control laws and The expression is: Under the action of the equivalent control law of equation (12) and the switching control law of equation (13), the system moves to the manifold from any initial state. and And it has always remained in manifold and Above, manifold Includes sliding surface Therefore, if forced to reach the sliding surface, then: In order to obtain the internal control of the system to be determined Design of sliding surface Its expression is: ,in, and For controller parameters, ＞0，1＜ <2; For the designed sliding surface Its dynamic evolution equation is designed as follows: ,in, For controller parameters, Greater than 0; combining equations (15) and (16), and based on the hyperlocal model of speed control of the SMPMSM drive system, the undetermined internal control of the system is obtained. And there are: In the formula, This is an estimate of the velocity loop disturbance component; within a short sampling interval. It is a constant, and its differential is approximately 0. Taking the derivative of equation (17), we have: Substituting equations (17) and (18) into equation (11), the inverter reference voltage vector is generated, and we have: To prove the stability of the system, a Lyapunov function is defined. For i=1, 2, its differential is ,when Negative time, satisfying the asymptotic convergence condition; macro variables and Differential and Solving directly from the dynamic evolution equations, we have: In the formula, and The derivative of the Lyapunov function is given by T1, T2, and Since both are greater than 0, p and q are positive odd numbers, and p+q is a positive even number, therefore... and All are negative, that is ， The defined Lyapunov function satisfies the asymptotic convergence condition, proving that the proposed sliding mode cooperative direct velocity control can achieve stable operation of the SMPMSM drive system; subsequently, based on the dynamic evolution equation of equation (10), the sliding surface is obtained. and Differential and And there are: Because T2, T3 and Both are greater than 0, and p+q is a positive even number, so ， The existence of the designed sliding surface was proven. To ensure that the generated inverter reference voltage simultaneously satisfies the current and voltage constraints of the SMPMSM drive system, constraint processing is necessary. The inverter q-axis reference voltage that satisfies the maximum current constraint is: , among which, I max This is the maximum stator current; the inverter reference voltage that satisfies the current constraint is: ,in, Let be the maximum voltage component along the q-axis of the inverter; to fully utilize the DC bus voltage of the inverter, the boundary equation of the hexagonal voltage vector of the inverter is written as: ,in, and These are the proportionality coefficients for the d-axis voltage and the q-axis voltage, respectively. For bus voltage, ， ， U dc It is the DC bus voltage; the inverter reference voltage is adjusted to obtain the optimal inverter reference voltage that simultaneously satisfies current and voltage constraints. and The expression is: To ensure that the inverter reference voltage generated by the terminal forced sliding mode cooperative direct speed control satisfies both current and voltage constraints, the stator current is predicted by the established SMPMSM drive system hyperlocal model based on the inverter reference voltage generated according to equation (19). When the stator current exceeds the limit, the inverter reference voltage that satisfies the current constraint is obtained according to equation (23). Then, it is determined whether the inverter reference voltage exceeds the inverter voltage hexagon range. If it does, the optimal inverter reference voltage that satisfies both current and voltage constraints is calculated according to equation (25).

2. The terminal forced sliding mode cooperative direct speed control method for the SMPMSM drive system according to claim 1, characterized in that: The step (1) specifically refers to: considering the uncertainty of motor parameters and unknown disturbances, the mathematical model of the SMPMSM drive system in the synchronous speed rotation dq axis coordinate system is as follows: , where i d and i q These are the d-axis and q-axis stator currents, respectively; u d and u q These are the d-axis and q-axis stator voltages, respectively. r T is the rotor's electrical angular velocity. e T L These are the electromagnetic torque and load torque of SMPMSM, respectively; R s It is the stator winding resistance; L d L q These are the d-axis and q-axis stator inductances, respectively; ψ f This represents the rotor permanent magnet flux linkage; J and B are the moment of inertia and coefficient of viscous friction, respectively; n p f is the extreme logarithm of SMPMSM; d f q and f ω These represent the parameter uncertainties and unknown disturbances in the d / q current control and speed control of the motor, respectively; according to model-free control, the first-order hyperlocal model of the single-input single-output system is expressed as: Where u and y represent the system input and output, respectively; α is the scaling factor of the system input; F includes both known and unknown parts of the system; the input of the SMPMSM drive system is defined as... ， and The output is ， and The hyperlocal model of speed control for the SMPMSM drive system is expressed as: In the formula, ， ， Input to the system ， and For the SMPMSM drive system, the scaling factor is such that the stator inductances of the dq axes are equal, i.e., L d =L q ,set up ;F d , F q and F ω The known and unknown parts of the system are represented by the following expression: Using differential algebra to 、 and Make an estimate and use 、 、 Its estimated value is expressed as: , among which, T s For control period; T F =n F T s n is the length of the sliding window. F It is a constant and set to 10; it is considered to be within a shorter sampling interval. 、 and It is a constant, and its differential is approximately 0.

3. A system implementing the terminal forced sliding mode cooperative direct speed control method for the SMPMSM drive system according to any one of claims 1 to 2, characterized in that: include: The surface-mounted permanent magnet synchronous motor (SMPMSM), used as the test object for speed control of the motor drive system, has a power of 900W and a rated speed of 500rpm. A two-level three-phase inverter provides the drive voltage to the motor; its DC bus voltage is 48V and its dead time is 2µs. A rotary transformer is used to detect the rotor position of the tested motor. A forced sliding mode cooperative control module outputs the reference voltage vector of the two-level three-phase inverter. A limiting processing module constrains the voltage vector output by the forced sliding mode cooperative control module to ensure safe and stable motor operation. A space vector pulse width modulation module generates a frequency- and voltage-adjustable sine wave signal for motor drive.

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