CN117879419A - Improved sensorless control method for permanent magnet synchronous motor - Google Patents
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Abstract
The invention discloses an improved position-sensor-free control method of a permanent magnet synchronous motor. By utilizing Lagrange extremum method, a group of optimal values is found out in electromagnetic torque formula of permanent magnet synchronous motorAndand combining to realize the control of the maximum torque current ratio. And feeding back the observed value of the back electromotive force to an observation link of the current, establishing a full-order sliding mode observer, and copying an s-type function in the full-order sliding mode observer by adopting a recursive probability wavelet fuzzy neural network. Finally, based on the phase-locked loop, rotor position information is obtained from the back electromotive force. The invention improves the disturbance rejection and control precision of rotation speed regulation by utilizing a sliding mode variable structure in the rotation speed ring, reduces copper loss by MTPA control, improves the efficiency of the permanent magnet synchronous motor, avoids phase lag caused by low-pass filtering by using a new full-order sliding mode observer, and simultaneously, minimizes observation errors and buffeting under the condition of condition change by adopting a designed self-adaptive law.
Description
Technical Field
The invention relates to the field of motor control, in particular to an improved position-sensor-free control method of a permanent magnet synchronous motor.
Background
The permanent magnet synchronous motor has the advantages of high efficiency, high power density, high torque density, good dynamic response and the like. Is widely applied to the fields of industrial automation and renewable energy sources. Particularly in electric vehicles, it has become a common type of driving motor due to its low energy consumption, high acceleration performance and ability to provide longer distances. The permanent magnet synchronous motor control system needs to have a fast and accurate speed control capability and good dynamic response characteristics. The control strategy is adjusted by comparing the desired rotational speed with the actual rotational speed so that the motor operates stably within a predetermined rotational speed range. The rotational speed is an important parameter in the control system of the permanent magnet synchronous motor. In conventional control systems, position or speed sensors are used to accurately obtain position and speed information of the motor rotor. However, the installation and calibration of the sensor requires additional costs and effort and is also affected by environmental conditions and sensor lifetime. In contrast, sensorless control of permanent magnet synchronous motors may reduce system cost and complexity. In addition, it avoids sensor failures, thereby improving the reliability and robustness of the system.
The sensorless control technology of the permanent magnet synchronous motor can be divided into two basic types, namely a method based on high-frequency injection and a method based on observation. The high-frequency injection method is to inject a high-frequency voltage or a high-frequency current and superimpose a high-frequency signal on the base excitation. By detecting the high frequency response, the position of the motor can be estimated even at low speed or stationary. However, this method relies on the accuracy of high frequency signal detection. In addition, injection of high frequency excitation tends to generate high frequency noise, thereby degrading system performance. The observation-based approach is mainly used for medium-high speed applications. It takes motor current as input to an observer designed to estimate the position of the rotor. The observation methods include Extended Kalman Filtering (EKF), model Reference Adaptive Control (MRAC), and Sliding Mode Observer (SMO). Among other things, EKF and MRAC methods rely on mathematical models of the motor, the accuracy of which directly affects the accuracy of rotor position estimation. In contrast, the SMO method has low dependence on a motor model, has robustness on motor parameter change and external interference, and has wide application prospect. However, the conventional SMO method uses a current error as an input signal to an observer and generates a pulse signal as an estimated back electromotive force (EMF). This requires the design of filtering techniques to process the pulse signal, placing high demands on the sampling frequency and filtering characteristics of the system. In addition, the filtering process introduces delays and compensators need to be designed to alleviate this problem, thereby increasing the complexity of the system.
Disclosure of Invention
The invention aims to: in order to solve the problems in the prior art, the invention provides an improved position-sensor-free control method of a permanent magnet synchronous motor, which improves the disturbance resistance and control precision of rotation speed adjustment, enhances the description of dynamic behavior and control requirements of a system, and can obtain high-precision rotor speed and position information with less buffeting under the condition of speed or load change.
The technical scheme is as follows: the invention discloses an improved position-sensor-free control method of a permanent magnet synchronous motor, which comprises the following steps:
step 1: establishing an electric angular velocity error e, designing a sliding die surface s, and controlling the electric angular velocity omega in a rotating speed ring by adopting a sliding die e With electromagnetic torque T e Linking;
step 2: the electromagnetic torque T in the step 1 is set e Inputting the obtained values to an MTPA control module, and searching a group of optimal i by using a Lagrange extremum method d And i q Combined such that the electromagnetic torque T e Maximum stator current i s Minimum, reduce copper loss;
step 3: establishing a full-order state equation of the permanent magnet synchronous motor under a two-phase static coordinate system;
step 4: on the full-order state equation established in the step 3, a full-order sliding mode observer is constructed, and the voltage u of the permanent magnet synchronous motor under a two-phase static coordinate system is established s After being observed by a full-order sliding mode observer, the stator current is outputWith the stator current observations +.>With stator current i s Is the difference of (2) as the current observation error->
Step 5: error of current observation in step 4After passing through an s function module simulated by a recursive probability wavelet fuzzy neural network RPWFNN, the sliding mode control rate V(s) of the permanent magnet synchronous motor under a two-phase static coordinate system is output i )；
Step 6: the sliding mode function control rate V(s) i ) The feedback gain matrix G is fed back to the full-order sliding mode observer as input, and the back electromotive force observed value is output after the full-order sliding mode observer
Step 7: observed value of back electromotive force in step 6The back electromotive force observed value is processed by a phase-locked loop module and then is output to the rotor position observed value of the permanent magnet synchronous motorAnd electric angular velocity observations->Said rotor position observations +.>Feedback to the phase-locked loop module as its input, said electric angular velocity observation +.>And also fed back to the full-order sliding mode observer as its input.
Further, in the step 1, the rotating speed ring based on sliding mode control is designed as follows:
the electrical angular velocity error e is as follows:
e＝ω e * -ω e
wherein: omega e * To set the electrical angular velocity omega e Is the electrical angular velocity;
the slip plane s is as follows:
wherein:c is a positive constant, which is the first order conduction of the electrical angular velocity;
the slip-form control law is as follows:
wherein: alpha, beta are the normal numbers of the two,j is moment of inertia, n p Is of polar logarithm-> Is the first order derivative of electromagnetic torque.
Further, in the step 2, the MTPA control module is designed to:
wherein: l (L) d 、L q I is the equivalent inductance of the permanent magnet synchronous motor in the d axis and the q axis d For d-axis stator current, i q For q-axis stator current, ψ f Is a permanent magnet flux linkage.
Further, the full-order state equation in the step 3 is:
the model of the permanent magnet synchronous motor in the two-phase static coordinate system is as follows:
wherein: u (u) α For the alpha-axis stator voltage, u β For beta-axis stator voltage, i α For alpha-axis stator current, i β Is fixed by beta axisSub-current, θ e E is the rotor position of the permanent magnet synchronous motor α For alpha-axis back EMF, e β Is beta-axis back electromotive force R s The resistance value of the stator of the permanent magnet synchronous motor is;
the extended back emf and its rate of change satisfy the following relationship:
the full-order state equation of the permanent magnet synchronous motor is as follows:
wherein:A 12 ＝diag(-1/L d ,-1/L d )，/>B 1 ＝diag(1/L d ,1/L d )，u s ＝[u α u β ] T is the stator voltage in a two-phase stationary coordinate system, e= [ e ] α e β ] T Is the back electromotive force, i s ＝[i α i β ] T Is the stator current;
stator current i s The formula is as follows:
wherein: i.e a 、i b And i c Is the three-phase stator current of the permanent magnet synchronous motor.
Further, the full-order sliding mode observer in the step 4 is:
wherein:A 12 ＝diag(-1/L d ,-1/L d )，B 1 ＝diag(1/L d ,1/L d )，/>is the slip form control rate,/->Is a feedback gain matrix, < >>Is the slip form surface, k of the alpha-axis and beta-axis stator current i 、k e Is the switching gain of the sliding mode observer, +.>For stator current observations, +.>For the alpha-axis stator current observation, +.>Is the beta-axis stator current observation value,for the back EMF observations, +.>Is an alpha-axis back electromotive force observation value,/>Is an observed value of the beta-axis electromotive force.
Further, in the step 5, the sliding mode control rate V(s) output by the recursive probability wavelet fuzzy neural network RPWFNN i ) The method comprises the following steps:
wherein: n is the total number of rules and,indicate output->Represents the first output of the rule layer, +.>Representing adjustable weights between the rule layer and the output layer;
the adaptive law design of RPWFNN parameters is as follows:
wherein:is the wavelet weight of wavelet layer, m ij And c ij The ith input, the jth gaussian function to the center point and width of the layer node, respectively.
Further, the phase-locked loop in the step 7 has the following working procedures:
the rotor position error is obtained according to the formula of the extended back electromotive force:
when the steady state is reached, the actual angle of the motor is less error from the estimated angle, and therefore, the above equation is equivalent to:
wherein E is ex In order to extend the back emf amplitude,
the rotor position error signal epsilon is subjected to proportional amplification and integration links to obtain an electric angular velocity observation value of the permanent magnet synchronous motorObservation of the electrical angular velocity of a motor>Integrating link processing to obtain rotor position observation value +.>With rotor position observations +.>And the feedback signals of the phase-locked loop module are sequentially reciprocated to form a complete phase-locked loop position tracking structure.
The beneficial effects are that:
the invention utilizes the characteristics of no need of accurate mathematical model and strong robustness of the sliding mode variable structure in the rotating speed ring, improves the disturbance resistance and control precision of rotating speed adjustment, and ensures that the stator current i is controlled by MTPA s The amplitude is minimum, thereby reducing copper loss and improving permanent magnetSynchronous motor efficiency. Full-order SMO (FSMO) is an improvement over traditional SMO methods by introducing extended back electromotive force (EMF) state variables that enhance the description of system dynamics and control requirements. FSMO also has an inherent second order filter characteristic, eliminating the need for an additional filtering stage. The Recursive Probabilistic Wavelet Fuzzy Neural Network (RPWFNN) can be used to model s-type functions used in FSMO taking into account its ability to approximate, learn and infer arbitrary smooth functions. In combination with the adaptive law of network parameters, in the fuzzy neural network, the sliding surface is an input variable, and the output of the fuzzy neural network is an equivalent control law. The designed RPWFNN can adaptively update network parameters according to the actual running state of the permanent magnet synchronous motor system. Therefore, even in the case of a change in speed or load, high-accuracy rotor speed and position information with less buffeting can be obtained. Therefore, the invention has the following advantages:
1. the robustness is strong. When internal parameters change or are disturbed by the outside world, a well-defined sinusoidal waveform is generated for the estimated back emf, with lower harmonic disturbance over a wider speed range. The influence of current errors on back electromotive force is reduced, and the anti-interference capability is improved.
2. The precision is high. The designed Recursive Probability Wavelet Fuzzy Neural Network (RPWFNN) can adaptively update network parameters according to the actual running state of the permanent magnet synchronous motor system. Therefore, even in the case of a change in speed or load, high-accuracy rotor speed and position information with less buffeting can be obtained.
3. Is widely applicable. The designed full-order sliding mode observer is suitable for permanent magnet synchronous motors with different powers in different fields, can obviously reduce overshoot and static errors of various performance indexes of the motors, and effectively reduces buffeting of the system.
4. Is simple and practical. Sliding mode control is a commonly used nonlinear control method. The system does not need an accurate system model, but only needs to design a sliding mode controller to realize stable control of the system according to actual control requirements.
Drawings
FIG. 1 is a simplified control structure schematic diagram of a permanent magnet synchronous motor;
FIG. 2 is a schematic diagram of an improved full-order sliding mode observer based on RPWFNN;
FIG. 3 is a schematic diagram of a quadrature phase locked loop position tracker;
FIG. 4 is a schematic diagram of a neural network of RPWFNN;
FIG. 5 is a comparison of rotational speed observation errors under a conventional algorithm and a simulation algorithm of the present invention when the load rotational speed is suddenly changed;
FIG. 6 is a comparison of rotor position observation errors under a conventional algorithm and a simulation algorithm of the present invention when the load rotation speed is suddenly changed;
FIG. 7 is a comparison of rotational speed observation errors under a conventional algorithm and a simulation algorithm of the present invention at a sudden change of a fixed rotational speed load;
fig. 8 is a comparison of rotor position observation errors under a conventional algorithm and a simulation algorithm of the present invention at a sudden load change at a fixed rotational speed.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention.
The invention discloses an improved position-sensor-free control method of a permanent magnet synchronous motor, which comprises the following steps:
step 1. Design of sliding mode regulator of vector system of permanent magnet synchronous motor
Let e be the rotational speed error, then e=ω e * -ω e Then:
wherein:for the rate of change of the speed error +.>As a result of speed errorSecond derivative, T L Is the load torque.
Order theJ is moment of inertia, n p Is of polar logarithm->The above formula (1) can be arranged as:
design the sliding die surface asWhere c must satisfy the Hurwitz condition, i.e., c > 0. Definition of the Liapunov function as +.>Then:
according to the lispro stability criterion, V is stable when it is positive and has a continuous first partial derivative, while the first partial derivative of V is semi-negative. To ensure thatThe design sliding mode control law is as follows:
then:
the analysis shows that the designed control law can ensure that the system gradually and stably approaches to the sliding mode.
Step 2 design of MTPA control Module
Inductance (L) on permanent magnet synchronous motor straight shaft d ) And inductance (L) on the intersecting axis q ) Are not equal to each other. The additional torque generated by the structure of such motors can be well utilized by maximum torque to current ratio control (MTPA). Will i in the electromagnetic torque formula of the PMSM d And i q Taken as a variable, a group of optimal i is found d And i q Combining to obtain electromagnetic torque T e Maximum. The method of obtaining the extremum by using Lagrangian can be used for obtaining the i corresponding to the maximum electromagnetic torque d And i q Combining to achieve MTPA control.
The extremum calculation process using lagrangian is as follows: the expression formula of the motor stator current is shown as the following formula:
let the electromagnetic torque formula be zero as the limiting condition lambda of Lagrange extremum method, the form is shown as the formula:
wherein L is d 、L q I is the equivalent inductance of the permanent magnet synchronous motor in the d axis and the q axis d For d-axis stator current, i q For q-axis stator current, ψ f For permanent magnet flux linkage, under condition i s T is calculated at fixed time e According to the lagrangian extremum method, the following formula can be listed:
i is respectively carried out on the new functions H d 、i q And lambda bias can be obtained:
according to the Lagrangian extremum method, let the above three formulas be 0, namelyThe final result can be obtained:
bringing the above equation (10) into the electromagnetic torque equation (11) yields:
9n p 2 (L d -L q ) 2 i q 4 +6T e ψ f n p i q -4T e 2 ＝0
taking n p =4 can be obtained:
through i d And i q Calculating i d And i q MTPA control can be achieved.
Step 3, establishing a model of the permanent magnet synchronous motor in a two-phase static coordinate system:
wherein: u (u) α For the alpha-axis stator voltage, u β For beta-axis stator voltage, i α For alpha-axis stator current, i β For beta-axis stator current, e α For alpha-axis back EMF, e β Beta isThe shaft back emf. R is R s Is the resistance value of the stator of the permanent magnet synchronous motor, L d 、L q Equivalent inductance omega of permanent magnet synchronous motor in d axis and q axis e Is the electric angular velocity, theta e Is the rotor position of the permanent magnet synchronous motor.
In general, the mechanical time constant of the system is much greater than the electromagnetic time constant thereof, and the angular velocity can be considered to be a constant value during the PWM control period, i.eAt this time, the extended back electromotive force and the change rate thereof satisfy the following relationship:
the full-order state equation of the permanent magnet synchronous motor is obtained by the comprehensive formulas (13) and (14):
wherein:A 12 ＝diag(-1/L d ,-1/L d )，/>B 1 ＝diag(1/L d ,1/L d )，u s ＝[u α u β ] T is the stator voltage in a two-phase stationary coordinate system, e= [ e ] α e β ] T Is the back electromotive force, i s ＝[i α i β ] T Is the stator current.
Stator current i s The formula is as follows:
wherein: i.e a 、i b And i c Is the three-phase stator current of the permanent magnet synchronous motor.
Step 4. Design of full-order sliding mode observer
As can be seen from the full-order state equation in the equation (15), the positional information of the rotor exists only in the electromotive force. Thus, we can observe the position of the rotor using the expanded electromotive force (EMF). In the state equation, the stator current is the only measurable physical quantity. Thus, the sliding surface can be defined as:
wherein: for the alpha-axis stator current observation, +.>Is the beta-axis stator current observation.
According to the IPMSM full-order state equation, a full-order sliding mode observer using the stator current and the extended back emf as state variables is established, as shown in equation (18):
wherein:A 12 ＝diag(-1/L d ,-1/L d )，B 1 ＝diag(1/L d ,1/L d )，/>is the slip form control rate,/->Is a feedback gain matrix, k i 、k e Is the switching gain of the sliding mode observer, +.>For stator current observations, +.>For the back EMF observations, +.>Is an alpha-axis back electromotive force observation value,/>Is an observed value of the beta-axis electromotive force.
The observed vector of EMF (e) in equation (18) can be expressed as:
wherein: s is the laplace operator.
When equation (18) minus equation (15), and in general, the slip mode occurs, the rotational speed is observedCan converge to the actual rotation speed omega e I.e. +.>A dynamic equation of the observed error can be obtained as shown in equation (20):
wherein:as an observed error of the back emf,
when the system reaches the slip mode state, the observer value of the stator current converges to the actual value, i.e The electromotive force observer error is obtained from the dynamic equation of the current observation error in equation (20):
substituting equation (21) into equation (20) allows the dynamics equation of the electromotive force observation error to be rewritten as:
step 5. Full order sliding mode observer stability demonstration
Consider a direct Lyapunov candidate functionSubstituting (20) and (22) into V 1 Derivative over time, resulting in:
if the feedback gain k is selected i Satisfy k i ＞max(|e α |,|e β I). Thus can ensureIs a negative semi-definite function, which means +.>Is a bounded function, and the designed sliding mode curved surface converges to zero at the time of t & gtto & gtinfinity according to Lyapunov stability theory and Barbaat's quotients. Thus, a sliding movement of the entire observation process can be ensured, and the designed FSMO has stability even in the case of uncertainty in the system.
As can be seen from (19), the FSMO constructed based on the full-order model of the permanent magnet synchronous motor includes both current observation and electromotive force, and the observed value of the electromotive force is fed back to the current observation loop. In addition, the observed value of EMF inherently has a second-order low-pass filter characteristic known from (22), and high-frequency noise can be effectively filtered out. Compared with the traditional sliding mode observer, the sliding mode observer does not need an additional low-pass filter, so that the problem of phase lag in rotor position observation is avoided, and the observation precision is improved. And (3) rearranging the equation (22), so that a kinetic equation of the electromotive force observation error can be obtained to be a second-order system, and the variables between the two axes are mutually independent and have the same transient response process. The kinetic equation can be written as:
wherein:if FSMO (k) is designed i and k e ) The gain selection of (23) leads the eigenvalue of the corresponding eigenvalue to be strictly positioned at the left half plane of the complex plane, and obtains the optimal damping ratio +.>This ensures the expected convergence speed of the observer.
Step 6, designing a simulation s function based on a Recursive Probability Wavelet Fuzzy Neural Network (RPWFNN):
the 6-layer RPWFNN is shown in FIG. 4, and comprises an input layer, a membership layer, a probability layer, a wavelet layer, a rule layer and an output layer, which are used for realizing the design of the RPWFNN.
(1) The network and output of the neuron input layer are:
wherein:and->The input and output of the ith neuron, respectively, and N is the rule total.
The input of the proposed RPWFNN is the stator current observation errorAnd its derivative
(2) The membership layer adopts a Gaussian function to realize the fuzzy operation of RPWFNN, and the input and output of the nodes of the layer are expressed as follows:
wherein:and->The ith input, the jth gaussian function to the center point and width of the layer node, respectively.Representing the output of the j-th neuron of the membership layer.
(3) The probability layer also selects a gaussian function as the acceptance field function for this layer, expressed as:
wherein:and->The jth input, the p-th gaussian function to the center point and width of the layer node, respectively.Is the output of the j-th neuron of the probability layer.
(4) The wavelet layer includes k wavelet functions as follows:
wherein:the wavelet weight is the wavelet weight of the wavelet layer; />Wavelet, ψ, output to wavelet and layer node for the ith and kth item k (N) is the output of the kth wavelet layer node.
(5) In the rule layer, each node is represented by addition, and product operation is carried out to obtain a Mamdani reasoning set. The probability information is processed using bayesian theorem, taking the fuzzy class group as an argument, as shown in (33). Further, to achieve the cycle characteristics, the output of each rule node is fed back to itself as an input. Thus, the previous value can be memorized by the feedback structure shown in (34). The wavelet output is also processed in (34). The node output for this layer is expressed as:
wherein:the connection weight between the rule layer and the probability layer is set to be 1; />The connection weight of the node is used for realizing recursion; />Is the output of the rule layer.
(6) Each node of the output layer is the sum of the output of the rule layer and the product of the adjustable weights between the rule layer and the output layer, and the output of the network of the layer is:
wherein:is the output of RPWFNN, namely the slip form control rate V(s) of the permanent magnet synchronous motor under a two-phase static coordinate system i )，/>Is the connection weight between the rule layer and the output layer.
Based on the weight and parameters of the recursive probability wavelet fuzzy neural network of the gradient descent method, the objective function E (N) can be defined as:
the main objective is to minimize the error function E (N) to obtain online learning parameters. The online learning algorithm is described in detail as follows:
1) Layer 6 the propagation error term is expressed as:
the update amount of the connection weight in this layer is described as:
in eta 1 Is the learning rate. Accordingly, the connection rights are updated according to equation (40)
2) Layer 5: the two error terms propagated by this layer are:
/>
3) Layer 4 the error term that layer 4 needs to propagate is expressed as follows:
according to the chain rule, the updating rule of the layer 4 connection weight is calculated as follows:
in eta 2 Is the learning rate. Thereby obtaining updated connection weightThe method comprises the following steps:
4) Layer 2 the propagation error term for layer 2 is calculated as:
the updating amounts of the mean value and the standard deviation of the second-layer membership function are respectively obtained by a chain rule in the following formula:
wherein eta 3 And eta 4 Is the learning rate. Thus, the center point and width of the layer 2 membership function is updated according to the following formula:
because of the uncertainty of the storage system, the jacobian matrix of the storage system cannot be accurately calculatedTherefore, to solve this problem, to increase the online learning speed of network parameters, the following incremental adaptation law is adopted:
step 7, phase-locked loop design:
the method adopts the orthogonal phase-locked loop to process and expand the information of the back electromotive force observation value so as to obtain the rotor position angle observation value, and normalizes the rotor position angle error signal to simplify the phase-locked loop parameter design. As shown in fig. 3.
The rotor position error is obtained according to the formula of the extended back electromotive force:
when steady state is reached, the actual angle of the motor is less error from the estimated angle. Therefore, the above equation can be equivalent to:
wherein E is ex In order to extend the back emf amplitude,
it can be seen from the equation that the rotor position error obtained by the phase detector contains the amplitude of the extended back emf, and when the rotational speed changes, the extended back emf of the motor will correspondingly change, thereby causing the amplitude of the extended back emf to also change. But instead of extending the magnitude of the back emf, it is necessary to pass the angle error to the loop filter (PI element in fig. 3) and the voltage controlled oscillator (integration element in fig. 3) when extracting the rotor position information. Therefore, the amplitude of the extended back emf needs to be cancelled, which removes the effect of the rotational speed, thereby improving the accuracy of rotor position extraction.
The position error after the influence of the rotating speed is eliminated is as follows:
after the rotation factor is eliminated, the phase-locked loop transfer function irrelevant to the motor rotation speed is obtained as follows:
the rotor position error signal epsilon is subjected to proportional amplification and integration links to obtain the permanent magnet synchronous motor electricityAngular velocity observationsObservation of the electrical angular velocity of a motor>Integrating link processing to obtain rotor position observation value +.>With rotor position observations +.>And the feedback signals of the phase-locked loop module are sequentially reciprocated to form a complete phase-locked loop position tracking structure.
The experimental simulation is performed on the control method of the present invention, referring to fig. 5, which is a comparison of the rotation speed observation error under the conventional algorithm and the simulation algorithm of the present invention when the rotation speed of the fixed load is suddenly changed, and fig. 6 is a comparison of the rotor position observation error under the conventional algorithm and the simulation algorithm of the present invention when the rotation speed of the fixed load is suddenly changed. The algorithm is controlled by a full-order sliding-mode observer FSMO, and under the control of the recursive probability wavelet fuzzy neural network RPWFNN-full-order sliding-mode observer FSMO, as can be seen from the figure, when the fixed load rotation speed is suddenly changed, compared with the full-order sliding-mode observer FSMO, the recursive probability wavelet fuzzy neural network RPWFNN-full-order sliding-mode observer FSMO has smaller rotation speed observation errors and rotor position observation errors.
Fig. 7 is a comparison of the rotation speed observation error under the conventional algorithm and the simulation algorithm of the present invention when the rotation speed load suddenly changes, and fig. 8 is a comparison of the rotor position observation error under the conventional algorithm and the simulation algorithm of the present invention when the rotation speed load suddenly changes. The algorithm is controlled by a full-order sliding mode observer FSMO, and under the control of the recursive probability wavelet fuzzy neural network RPWFNN-full-order sliding mode observer FSMO, as can be seen from the figure, when the load is suddenly changed at a fixed rotating speed, the recursive probability wavelet fuzzy neural network RPWFNN-full-order sliding mode observer FSMO is more stable in rotating speed observation error and rotor position observation error compared with the full-order sliding mode observer FSMO, and is smaller in rotating speed observation error and rotor position observation error.
The foregoing embodiments are merely illustrative of the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the present invention and to implement the same, not to limit the scope of the present invention. All equivalent changes or modifications made according to the spirit of the present invention should be included in the scope of the present invention.
Claims (7)
1. The improved position-sensor-free control method of the permanent magnet synchronous motor is characterized by comprising the following steps of:
step 1: establishing an electric angular velocity error e, designing a sliding die surface s, and controlling the electric angular velocity omega in a rotating speed ring by adopting a sliding die e With electromagnetic torque T e Linking;
step 2: the electromagnetic torque T in the step 1 is set e Inputting the obtained values to an MTPA control module, and searching a group of optimal i by using a Lagrange extremum method d And i q Combined such that the electromagnetic torque T e Maximum stator current i s Minimum, reduce copper loss;
step 3: establishing a full-order state equation of the permanent magnet synchronous motor under a two-phase static coordinate system;
step 4: on the full-order state equation established in the step 3, a full-order sliding mode observer is constructed, and the voltage u of the permanent magnet synchronous motor under a two-phase static coordinate system is established s After being observed by a full-order sliding mode observer, the stator current is outputWith the stator current observationsWith stator current i s Is the difference of (2) as the current observation error->
Step 5: error of current observation in step 4After passing through an s function module simulated by a recursive probability wavelet fuzzy neural network RPWFNN, the sliding mode control rate V(s) of the permanent magnet synchronous motor under a two-phase static coordinate system is output i )；
Step 6: the sliding mode function control rate V(s) i ) The feedback gain matrix G is fed back to the full-order sliding mode observer as input, and the back electromotive force observed value is output after the full-order sliding mode observer
Step 7: observed value of back electromotive force in step 6The back electromotive force observed value is processed by a phase-locked loop module and then is output into a rotor position observed value of the permanent magnet synchronous motor>And electric angular velocity observations->Said rotor position observations +.>Feedback to the phase-locked loop module as its input, said electric angular velocity observation +.>And also fed back to the full-order sliding mode observer as its input.
2. The improved sensorless control method of permanent magnet synchronous motor according to claim 1, wherein in step 1, the slip-mode control-based rotation speed ring is designed as follows:
the electrical angular velocity error e is as follows:
e＝ω e * -ω e
wherein: omega e * To set the electrical angular velocity omega e Is the electrical angular velocity;
the slip plane s is as follows:
wherein:is the first order conduction of the electric angular velocity, namely c is more than 0;
the slip-form control law is as follows:
wherein: alpha, beta are the normal numbers of the two,j is moment of inertia, n p Is of polar logarithm-> Is the first order derivative of electromagnetic torque.
3. The improved sensorless control method of permanent magnet synchronous motor according to claim 1, wherein in step 2, the MTPA control module is designed to:
9n p 2 (L d -L q ) 2 i q 4 +6T e ψ f n p i q -4T e 2 ＝0
wherein: l (L) d 、L q I is the equivalent inductance of the permanent magnet synchronous motor in the d axis and the q axis d For d-axis stator current, i q For q-axis stator current, ψ f Is a permanent magnet flux linkage, n p Is the polar logarithm, n p ＝4。
4. The improved sensorless control method of permanent magnet synchronous motor of claim 1, wherein the full-order state equation in step 3 is:
the model of the permanent magnet synchronous motor in the two-phase static coordinate system is as follows:
wherein: u (u) α For the alpha-axis stator voltage, u β For beta-axis stator voltage, i α For alpha-axis stator current, i β Is beta-axis stator current, theta e E is the rotor position of the permanent magnet synchronous motor α For alpha-axis back EMF, e β Is beta-axis back electromotive force R s The resistance value of the stator of the permanent magnet synchronous motor is; l (L) d 、L q I is the equivalent inductance of the permanent magnet synchronous motor in the d axis and the q axis d For d-axis stator current, i q For q-axis stator current, ψ f Is permanent magnet flux linkage omega e Is the electric angular velocity, theta e The rotor position of the permanent magnet synchronous motor;
the extended back emf and its rate of change satisfy the following relationship:
the full-order state equation of the permanent magnet synchronous motor is as follows:
wherein:A 12 ＝diag(-1/L d ,-1/L d )，/>B 1 ＝diag(1/L d ,1/L d )，u s ＝[u α u β ] T is the stator voltage in a two-phase stationary coordinate system, e= [ e ] α e β ] T Is the back electromotive force, i s ＝[i α i β ] T Is the stator current;
stator current i s The formula is as follows:
wherein: i.e a 、i b And i c Is the three-phase stator current of the permanent magnet synchronous motor.
5. The improved sensorless control method of permanent magnet synchronous motor of claim 4, wherein the full-order sliding mode observer in step 4 is:
wherein:A 12 ＝diag(-1/L d ,-1/L d )，B 1 ＝diag(1/L d ,1/L d )，/>is the slip form control rate,/->Is a feedback gain matrix, < >>Is the slip form surface, k of the alpha-axis and beta-axis stator current i 、k e Is the switching gain of the sliding mode observer, +.>For stator current observations, +.>For the alpha-axis stator current observation, +.>Is the beta-axis stator current observation value,for the back EMF observations, +.>Is an alpha-axis back electromotive force observation value,/>Is an observed value of the beta-axis electromotive force.
6. The improved sensorless control method of a permanent magnet synchronous motor according to claim 1, wherein the sliding mode control ratio V (s i ) The method comprises the following steps:
wherein: n is the total number of rules and,indicate output->Represents the first output of the rule layer, +.>Representing adjustable weights between the rule layer and the output layer;
the adaptive law design of RPWFNN parameters is as follows:
wherein:is the wavelet weight of wavelet layer, m ij And c ij The ith input, the jth gaussian function to the center point and width of the layer node, respectively.
7. The improved sensorless control method of permanent magnet synchronous motor according to claim 1, wherein the phase-locked loop in step 7 comprises the following steps:
the rotor position error is obtained according to the formula of the extended back electromotive force:
when the steady state is reached, the actual angle of the motor is less error from the estimated angle, and therefore, the above equation is equivalent to:
wherein E is ex In order to extend the back emf amplitude,
the rotor position error signal epsilon is subjected to proportional amplification and integration links to obtain an electric angular velocity observation value of the permanent magnet synchronous motorObservation of the electrical angular velocity of a motor>Integrating link processing to obtain rotor position observation value +.>With rotor position observations +.>And the feedback signals of the phase-locked loop module are sequentially reciprocated to form a complete phase-locked loop position tracking structure.
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