PMSM angular velocity control method and device based on objective function online optimization

Abstract

The invention discloses a PMSM angular velocity control method and device based on objective function online optimization, and relates to the field of motor control, and the method comprises the steps: constructing a discrete mechanical motion equation of a permanent magnet synchronous motor, and determining a constraint condition of a q-axis current; a robust control invariant set is constructed in combination with performance constraint conditions; constructing an objective function of a continuous set model prediction mechanical angular velocity control strategy at a k moment, converting the objective function into a least two norm problem based on a discrete mechanical motion equation and a robust control invariant set of the permanent magnet synchronous motor, and determining constraint conditions of decision variables of the least two norm problem; converting a least two norm problem into a least two norm problem with an invariable constraint set; and the mechanical angular speed of the permanent magnet synchronous motor at the moment k is obtained, the least two norm problem with the invariant constraint set is solved by adopting a projection positive set method, a constraint optimal solution is obtained, and the optimal q-axis current at the moment k is obtained through calculation. The problem that a traditional positive set method is heavy in real-time calculation burden is solved.

Description

Technical Field

[0001] The present invention relates to the field of motor control, and in particular to a PMSM angular velocity control method and device based on online optimization of an objective function. Background Art

[0002] Efficient control of new energy vehicle drive systems is a core challenge in improving energy efficiency and driving performance. Permanent magnet synchronous motors (PMSMs), with their high power density, excellent torque characteristics, and low losses, have become the preferred actuator for new energy vehicle powertrains. Traditional PMSM control often utilizes a proportional-integral (PI) regulator, but this controller is limited in terms of dynamic response speed, multivariable coupling suppression, and constraint handling capabilities. Especially under high-speed, high-load conditions, motor state variables and control inputs are prone to saturation due to physical limitations. PI control struggles to balance constraint satisfaction with tracking accuracy, resulting in reduced system robustness.

[0003] Model predictive control (MPC) offers a new approach to addressing these challenges through rolling optimization and explicit constraint handling. However, its real-time performance and computational complexity remain challenges in PMSM applications. Traditional MPC requires solving a high-dimensional quadratic programming problem online, resulting in significant algorithmic latency. Furthermore, the objective function's weight matrix is tightly coupled to the system dynamics, resulting in high parameter tuning complexity, which restricts practical engineering applications. Existing methods often rely on numerical iterative solvers, which struggle to meet the stringent millisecond-level response requirements of onboard controllers.

[0004] Traditional active set methods are highly dependent on the initial feasible solution. If the initial solution is not chosen properly, convergence will be slow or even fail. Furthermore, each iteration requires dynamic adjustment of the active constraint set, reconstruction of the subproblem solution, and updating of the Karush-Kuhn-Tucker (KKT) matrix. This imposes a heavy real-time computational burden, making it difficult to apply to motor servo drives. Furthermore, the convergence and computational time of traditional active set methods are heavily dependent on the quality of the initial feasible solution. When the system is operating under complex conditions, such as constraint boundary conditions (e.g., q-axis current saturation, mechanical angular velocity exceeding limits), the algorithm may diverge due to invalid iteration directions. Summary of the Invention

[0005] The purpose of this application is to propose a PMSM angular velocity control method and device based on online optimization of the objective function to address the above-mentioned technical problems.

[0006] In a first aspect, the present invention provides a PMSM angular velocity control method based on online optimization of an objective function, comprising the following steps:

[0007] The discrete mechanical motion equations of the permanent magnet synchronous motor are constructed, and the maximum torque-current ratio control method is used to determine the constraints on the q-axis current of the permanent magnet synchronous motor. An observer-based augmented permanent magnet synchronous motor is introduced and performance constraints are established. Based on the constraints on the q-axis current and performance constraints, a robust control invariant set is constructed.

[0008] For the augmented permanent magnet synchronous motor, a continuous set model is constructed to predict the objective function of the mechanical angular velocity control strategy at time k. Based on the discrete mechanical motion equations of the permanent magnet synchronous motor and the robust control invariant set, the objective function is converted into a least squares norm problem. The constraints of the decision variables of the least squares norm problem are determined, and then the least squares norm problem is converted into a least squares norm problem with an invariant constraint set.

[0009] The rotor position of the permanent magnet synchronous motor at time k is obtained and the mechanical angular velocity of the permanent magnet synchronous motor at time k is calculated. The least square norm problem with an invariant constraint set is solved using the projected positive set method to obtain the constrained optimal solution. The optimal q-axis current at time k is calculated based on the constrained optimal solution.

[0010] Preferably, the discrete mechanical motion equation of the permanent magnet synchronous motor is:

[0011] ;

[0012] Among them, k represents the kth moment, is the sampling period, is the moment of inertia, is the friction coefficient, is the q-axis current, is the permanent magnet flux, is the pole pair number, is the load torque, is the mechanical angular velocity, is the state matrix of the angular velocity loop of the permanent magnet synchronous motor, is the input matrix of the angular velocity loop of the permanent magnet synchronous motor;

[0013] In the surface-mount permanent magnet synchronous motor, the d-axis inductance is equal to the q-axis inductance. When the maximum torque current ratio control method is adopted, that is, the d-axis current Control mode, the constraints of the q-axis current of the permanent magnet synchronous motor are:

[0014] ;

[0015] in, is the admissible set of q-axis current, is the maximum allowable current, is the rated current, is the real number space.

[0016] As a preferred method, an observer-based augmented permanent magnet synchronous motor is introduced and performance constraints are constructed. A robust control invariant set is constructed based on the q-axis current constraints and performance constraints, specifically including:

[0017] The permanent magnet synchronous motor satisfies the constraints of the q-axis current. The state variables of the permanent magnet synchronous motor at time Continuous and unbiased tracking with bounded error Reference state variables at time , that is, the tracking error of the state variable of the permanent magnet synchronous motor The following performance constraints need to be met:

[0018] ;

[0019] in, represents the tracking error threshold; Indicates any represents a positive integer;

[0020] The reference state variables satisfy the following equation:

[0021] ;

[0022] in, express The reference state variable at time t, express The reference state variable at time t, is the rate of change of the reference state variable;

[0023] Taking into account external disturbances and parameter mismatch, the lumped disturbance Defined as:

[0024] ;

[0025] in, is the nominal value of permanent magnet flux linkage, is the reference value of q-axis current;

[0026] The extended permanent magnet synchronous motor is introduced, and its corresponding model is expressed as:

[0027] ;

[0028] in, is the state matrix of the extended permanent magnet synchronous motor, is the input matrix of the extended permanent magnet synchronous motor, is the output matrix of the extended permanent magnet synchronous motor; is the rate of change of the lumped disturbance, express The aggregate disturbance at time t, express The aggregate disturbance at time For the output of the extended permanent magnet synchronous motor, is the state variable of the extended permanent magnet synchronous motor, Control input for the extended permanent magnet synchronous motor;

[0029] State variables for extended permanent magnet synchronous motors , design the Lumberg observer, and its corresponding expression is:

[0030] ;

[0031] in, The state variables of the extended permanent magnet synchronous motor The estimated value of , T represents the transpose of the matrix, is the estimated value of the state variable of the permanent magnet synchronous motor, is the estimated value of the lumped disturbance; is the gain of the Romberg observer;

[0032] The estimation error of the state variables of the extended permanent magnet synchronous motor is defined as , subtract the expression of the model corresponding to the extended permanent magnet synchronous motor from the expression of the Romberg observer to obtain the following formula:

[0033] ;

[0034] in, express The estimation error of the state variables of the extended permanent magnet synchronous motor at time t, express The estimation error of the state variables of the extended permanent magnet synchronous motor at time t;

[0035] Establish recursive dynamics and combine the state variables of the actual permanent magnet synchronous motor with the state variables of the extended permanent magnet synchronous motor to construct the augmented state variables. , and the corresponding augmented permanent magnet synchronous motor model is described as follows:

[0036] ;

[0037] in, is the state matrix of the augmented permanent magnet synchronous motor, is the input matrix of the augmented permanent magnet synchronous motor, is the lumped disturbance gain matrix of the augmented permanent magnet synchronous motor, is the output matrix of the augmented permanent magnet synchronous motor;

[0038] According to Lyapunov stability theory, the gain is selected Ensure that the closed-loop error system matrix satisfies the spectral radius condition , so that the estimation error converges asymptotically, which means that the Lumberg observer is Performance constraints that maintain bounded estimation error:

[0039] ;

[0040] in, represents the radius, represents the closed-loop error system matrix; express The state variables of the permanent magnet synchronous motor at time , express The estimated value of the state variable of the permanent magnet synchronous motor at time , Represents the state variables of the permanent magnet synchronous motor at time 0, is the state variable of the permanent magnet synchronous motor The initial state set of is the estimation error threshold of the Lumberg observer, satisfying ;

[0041] The performance constraint of the tracking error of the permanent magnet synchronous motor state variable is combined with the performance constraint of the estimation error of the Romberg observer to obtain the performance constraint condition as shown in the following formula:

[0042] ;

[0043] in, is the estimated value of the state variable of the permanent magnet synchronous motor The tracking error threshold satisfies ;

[0044] Consider the state variables, control inputs and lumped disturbances of the augmented permanent magnet synchronous motor to meet the following constraints:

[0045] ;

[0046] ;

[0047] ;

[0048] in, is the admissible set of state variables, is the control input admissible set, is the lumped perturbation admissible set, is a three-dimensional real space;

[0049] Target Collection Robust one-step set Indicates that any possible disturbance Under the condition that there is an allowable control input One-step navigation to a given set The state set is:

[0050] ;

[0051] For the augmented permanent magnet synchronous motor model , the state variables of the augmented permanent magnet synchronous motor satisfy , if there is an admissible control input such that , then it is called a set is the robust control invariant set, namely:

[0052] ;

[0053] in, Indicates implication, Indicates the existence of a maximum robust control invariant set Contains All robust control invariant sets in When is the control invariant set;

[0054] For the model and state variables, control input and lumped disturbance of the augmented permanent magnet synchronous motor, given the state variables of the augmented permanent magnet synchronous motor , for the control input of the augmented permanent magnet synchronous motor , can always overcome the lumped disturbance Make ,Right now:

[0055] ;

[0056] in, is the state variable of the augmented permanent magnet synchronous motor The permissible input set of ,but ;if ,but ;

[0057] Considering the model of an augmented permanent magnet synchronous motor, the performance constraints are implemented by defining the following set:

[0058] ;

[0059] in, is an equivalent set of performance constraints;

[0060] Therefore, the performance constraint is equivalent to: ,if , can ensure the next state ; We need to further find the robust control invariant set satisfy:

[0061] ;

[0062] in, The reference state variable in the expression for the rate of change of the reference state variable The set of admissible reference inputs;

[0063] remember , the above formula is equivalent to:

[0064] ;

[0065] The equivalent set of performance constraints is input into the improved inner approximation algorithm to obtain the robust control invariant set ;

[0066] The improved inner approximation algorithm is obtained by improving the traditional inner approximation algorithm, specifically including:

[0067] Introducing control invariant sets at initialization , the improved initial set is ;

[0068] The robust one-step set is improved as shown below:

[0069] ;

[0070] in, is the target set to which the state variables of the permanent magnet synchronous motor augmented in the mth iteration belong, is an adjustable parameter, for The improved robust one-step set;

[0071] The iteration end condition is improved. The improved iteration end condition is: ;

[0072] in, represents the improved target set in the mth iteration, represents the improved target set in the m+1th iteration.

[0073] Preferably, the objective function of the continuum model prediction mechanical angular velocity control strategy adopted at time k is:

[0074] ;

[0075] in, represents the objective function, for Moment The estimated values of the state variables of the augmented permanent magnet synchronous motor are , is the prediction step length, for Moment The estimated values of the state variables of the augmented permanent magnet synchronous motor are for Moment The control input of the augmented permanent magnet synchronous motor is is the reference state variable, 、 and are the first weight coefficient, the second weight coefficient and the third weight coefficient respectively, is the estimated value of the lumped disturbance, and we define .

[0076] Preferably, the objective function is converted into a least squares norm problem based on the discrete mechanical motion equations of the permanent magnet synchronous motor and the robust control invariant set, the constraints of the decision variables of the least squares norm problem are determined, and then the least squares norm problem is converted into a least squares norm problem with an invariant constraint set, specifically including:

[0077] make is the state variable vector of the augmented permanent magnet synchronous motor, The control input vector of the augmented permanent magnet synchronous motor and For the reference state variable vector of the augmented permanent magnet synchronous motor, the objective function is converted into a matrix form as shown below:

[0078] ;

[0079] in, is a constant term, is a row vector of all 1s, 、 and are the first weight vector, the second weight vector and the third weight vector respectively, and their values are:

[0080] ;

[0081] ;

[0082] ;

[0083] in, is the N-order unit matrix;

[0084] The state space equation constraint is calculated based on the discrete mechanical motion equation of the permanent magnet synchronous motor, and its expression is: ;

[0085] Obtain the state variable vector in the objective function in matrix form based on the state space equation constraints and the control input vector The matrix expression between is as follows:

[0086] ;

[0087] in, represents the state weight, Represents the input weight, and its expressions are:

[0088] ;

[0089] ;

[0090] The state variable vector and the control input vector Substitute the matrix expression between into the matrix form of the objective function to obtain the simplified objective function, as shown below:

[0091] ;

[0092] in, is the unconstrained optimal state variable vector, is the weighting matrix, is the reference state variable vector and the state variables at time k The changing parameters, - T means taking the inverse first and then transposing, and the problem of solving the simplified objective function constitutes a least squares norm problem;

[0093] because 、 and are all semi-positive definite matrices, so the weighted matrix maintains the characteristics of the semi-positive definite matrix, and the weighted matrix Cholesky decomposition is ,in is an upper triangular matrix; let the equivalent decision variables be And the equivalent unconstrained optimal solution is , the simplified objective function is expressed as For the center of the ball dimensional sphere, that is:

[0094] ;

[0095] Robust Control Invariant Set It maintains convexity and has linear properties, so it can be expressed in the form of a linear inequality:

[0096] ;

[0097] in, 、 are the coefficient matrix and constant vector of the inequality constraints respectively;

[0098] The final conversion results in the minimum square norm problem of PMSM predictive mechanical angular velocity control:

[0099] ;

[0100] in, represents the minimized Y, Indicates constraints;

[0101] In the above formula and The value of does not change with the working conditions, so the decision variable The shape of the constraints remains unchanged and can be equivalent to the constraint set Overall displacement , so the least squares norm problem with an unchanged constraint set is constructed as:

[0102] ;

[0103] in, is the final decision variable, Indicates the minimized , is the final unconstrained optimal solution.

[0104] As a preferred method, the projected active set method is used to solve the least squares norm problem with an unchanged constraint set to obtain the constrained optimal solution. The optimal q-axis current at time k is calculated based on the constrained optimal solution, specifically including:

[0105] S31, according to 、 、 and Calculate the final unconstrained optimal solution ; Determine the effective constraint set at the initial moment based on the final unconstrained optimal solution, the least squares problem with an unchanged constraint set, and the effective constraints , as shown below:

[0106] ;

[0107] in, is the coefficient matrix No. OK, is a constant vector No. elements, To satisfy the inequality of The set formed;

[0108] S32, project the final unconstrained optimal solution to the effective constraint set at the initial moment In the effective constraint set at the initial moment, Every element of , the final unconstrained optimal solution is projected by the following projection formula On the hyperplane of the index, get the corresponding projection point :

[0109] ;

[0110] in, Indicates that Projected onto On the hyperplane of index, for the reason The rows of the matrix of indices.. for the reason constant vector of indices Multiple elements of represents the effective constraint set at the initial moment Any element in; According to each projection point, the least squares norm problem with the constraint set unchanged and the effective constraints, the effective constraint set corresponding to each projection point is determined as shown in the following formula:

[0111] ;

[0112] S33, determine each projection point The effective constraint set intersection of Whether it is included in the valid constraint set at the initial time , that is, to determine whether ;

[0113] If satisfied , then according to Calculate the final effective constraint set ,in, represents the set of valid constraint indexes that appear the most times, Represents the occurrence count function, Indicates taking the maximum value;

[0114] The final unconstrained optimal solution is projected onto the final effective constraint set using the following projection formula: Obtain the optimal solution to the constraints on the intersection of multiple hyperplanes of the index :

[0115] ;

[0116] in, Indicates that Projected onto On the intersection of multiple hyperplanes of index, for the reason Indexed matrix OK, for the reason constant vector of indices Multiple elements of

[0117] Constrain the optimal solution Perform inverse transformation to obtain the optimal state variable vector , as shown below:

[0118] ;

[0119] The optimal q-axis current at time k is calculated based on the state space equation constraints, as shown in the following formula:

[0120] ;

[0121] in, and Represent the optimal state variable vectors The first and second values of represents the optimal q-axis current at time k;

[0122] If not satisfied , then the new effective constraints are obtained according to the following formula:

[0123] ;

[0124] in, Indicates assignment, represents the new effective constraint;

[0125] Update the valid constraint set with the new valid constraints , and repeat steps S32-S33 until the optimal q-axis current at time k is calculated.

[0126] In a second aspect, the present invention provides a PMSM angular velocity control device based on online optimization of an objective function, comprising:

[0127] The motor model construction module is configured to construct the discrete mechanical motion equations of the permanent magnet synchronous motor, determine the q-axis current constraints of the permanent magnet synchronous motor using a maximum torque-current ratio control method, introduce an observer-based augmented permanent magnet synchronous motor and establish performance constraints, and construct a robust control invariant set based on the q-axis current constraints and performance constraints.

[0128] a problem conversion module configured to construct a continuous set model for predicting the objective function of the mechanical angular velocity control strategy at time k for the augmented permanent magnet synchronous motor, convert the objective function into a least squares norm problem based on the discrete mechanical motion equations of the permanent magnet synchronous motor and the robust control invariant set, determine the constraints of the decision variables of the least squares norm problem, and then convert the least squares norm problem into a least squares norm problem with an invariant constraint set;

[0129] The problem-solving module is configured to obtain the rotor position of the permanent magnet synchronous motor at time k and calculate the mechanical angular velocity of the permanent magnet synchronous motor at time k, use the projected positive set method to solve the least square norm problem with an unchanged constraint set, obtain the constrained optimal solution, and calculate the optimal q-axis current at time k based on the constrained optimal solution.

[0130] In a third aspect, the present invention provides an electronic device comprising one or more processors; a storage device for storing one or more programs, wherein when the one or more programs are executed by one or more processors, the one or more processors implement the method described in any implementation manner in the first aspect.

[0131] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in any implementation manner in the first aspect.

[0132] In a fifth aspect, the present invention provides a computer program product, comprising a computer program, which implements the method described in any implementation manner in the first aspect when the computer program is executed by a processor.

[0133] Compared with the prior art, the present invention has the following beneficial effects:

[0134] (1) The PMSM angular velocity control method based on online optimization of the objective function proposed in this paper performs disturbance compensation by designing a continuum model to predict the objective function of the mechanical angular velocity control strategy, which can eliminate the steady-state error of the mechanical angular velocity tracking under disturbance.

[0135] (2) The improved internal approximation algorithm proposed in the PMSM angular velocity control method based on online optimization of the objective function based on the augmented permanent magnet synchronous motor model can solve the RCI set within a limited number of iterations. The experimental results show that the continuous set model predicts the mechanical angular velocity control strategy under ramp tracking and sinusoidal trajectory tracking conditions, and the mechanical angular velocity tracking error can be strictly kept within the preset error boundary.

[0136] (3) The PMSM angular velocity control method based on online optimization of the objective function proposed in this invention equates the minimum square norm problem to a minimum square norm problem, and converts it into the projection of the unconstrained optimal solution on the feasible domain, avoiding the dependence on the initial feasible solution and the solution of the KKT matrix, and significantly reducing the amount of online calculation.

[0137] (4) The PMSM angular velocity control method based on online optimization of the objective function proposed in this invention avoids the dependence on the iterative process and the need for a specific initial feasible solution, ensuring that an optimal solution that strictly satisfies all linear constraints can be obtained under each operating condition, avoiding divergence caused by invalid iteration directions under complex operating conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0138] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0139] Figure 1 Schematic diagram of the flow of the PMSM angular velocity control method based on online optimization of the objective function according to an embodiment of the present application;

[0140] Figure 2 This is a control principle block diagram of a PMSM angular velocity control method based on online optimization of an objective function according to an embodiment of the present application;

[0141] Figure 3 A flowchart of an improved internal approximation algorithm of a PMSM angular velocity control method based on online optimization of an objective function according to an embodiment of the present application;

[0142] Figure 4 A flow chart of a PMSM angular velocity control method based on online optimization of an objective function according to an embodiment of the present application;

[0143] Figure 5 Schematic diagram of the feasible region of the PMSM angular velocity control method based on online optimization of the objective function according to an embodiment of the present application;

[0144] Figure 6It is an experimental test platform for the PMSM angular velocity control method based on online optimization of the objective function according to the embodiment of the present application;

[0145] Figure 7 This is a principle block diagram of an experimental platform for a PMSM angular velocity control method based on online optimization of an objective function according to an embodiment of the present application;

[0146] Figure 8 A speed response curve diagram of a ramp trajectory tracking performance analysis result of a PMSM angular velocity control method based on online optimization of an objective function according to an embodiment of the present application;

[0147] Figure 9 A result diagram of the speed tracking error in the ramp trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of the objective function according to an embodiment of the present application;

[0148] Figure 10 A result diagram of the tracking error of the estimated value of the mechanical angular velocity in the ramp trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of the objective function according to an embodiment of the present application;

[0149] Figure 11 A speed response curve diagram under no-load conditions from the sinusoidal trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of the objective function in an embodiment of the present application;

[0150] Figure 12 A result diagram of the speed tracking error under no-load conditions in the sinusoidal trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of the objective function according to an embodiment of the present application;

[0151] Figure 13 A result diagram of the tracking error of the estimated value of the mechanical angular velocity under no-load conditions in the sinusoidal trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of the objective function in an embodiment of the present application;

[0152] Figure 14 A speed response curve diagram under a constant load condition from the sinusoidal trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of the objective function according to an embodiment of the present application;

[0153] Figure 15 A result diagram of the speed tracking error under a constant load condition in the sinusoidal trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of the objective function according to an embodiment of the present application;

[0154] Figure 16A result diagram of the tracking error of the estimated value of the mechanical angular velocity under a constant load condition in the sinusoidal trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of the objective function according to an embodiment of the present application;

[0155] Figure 17 Schematic diagram of a PMSM angular velocity control device based on online optimization of an objective function according to an embodiment of the present application;

[0156] Figure 18 A schematic diagram of the hardware structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0157] To make the objectives, technical solutions, and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings. It is apparent that the embodiments described are only some, not all, of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0158] Figure 1 The embodiment of the present application provides a PMSM angular velocity control method based on online optimization of an objective function, comprising the following steps:

[0159] S1, construct the discrete mechanical motion equations of the permanent magnet synchronous motor, and use the maximum torque current ratio control method to determine the q-axis current constraints of the permanent magnet synchronous motor; introduce the observer-based augmented permanent magnet synchronous motor and construct performance constraints, and construct a robust control invariant set based on the q-axis current constraints and performance constraints.

[0160] In a specific embodiment, the discrete mechanical motion equation of the permanent magnet synchronous motor is:

[0161] ;

[0162] Among them, k represents the kth moment, is the sampling period, is the moment of inertia, is the friction coefficient, is the q-axis current, is the permanent magnet flux, is the pole pair number, is the load torque, is the mechanical angular velocity, is the state matrix of the angular velocity loop of the permanent magnet synchronous motor, is the input matrix of the angular velocity loop of the permanent magnet synchronous motor;

[0163] In the surface-mount permanent magnet synchronous motor, the d-axis inductance is equal to the q-axis inductance. When the maximum torque current ratio control method is adopted, that is, the d-axis current Control mode, the constraints of the q-axis current of the permanent magnet synchronous motor are:

[0164] ;

[0165] in, is the admissible set of q-axis current, is the maximum allowable current, is the rated current, is the real number space.

[0166] In a specific embodiment, an observer-based augmented permanent magnet synchronous motor is introduced and performance constraints are established. A robust control invariant set is constructed based on the q-axis current constraints and the performance constraints, specifically including:

[0167] The permanent magnet synchronous motor satisfies the constraints of the q-axis current. The state variables of the permanent magnet synchronous motor at time Continuous and unbiased tracking with bounded error Reference state variables at time , that is, the tracking error of the state variable of the permanent magnet synchronous motor The following performance constraints need to be met:

[0168] ;

[0169] in, represents the tracking error threshold; Indicates any represents a positive integer;

[0170] The reference state variables satisfy the following equation:

[0171] ;

[0172] in, express The reference state variable at time t, express The reference state variable at time t, is the rate of change of the reference state variable;

[0173] Taking into account external disturbances and parameter mismatch, the lumped disturbance Defined as:

[0174] ;

[0175] in, is the nominal value of permanent magnet flux linkage, is the reference value of q-axis current;

[0176] The extended permanent magnet synchronous motor is introduced, and its corresponding model is expressed as:

[0177] ;

[0178] in, is the state matrix of the extended permanent magnet synchronous motor, is the input matrix of the extended permanent magnet synchronous motor, is the output matrix of the extended permanent magnet synchronous motor; is the rate of change of the lumped disturbance, express The aggregate disturbance at time t, express The aggregate disturbance at time For the output of the extended permanent magnet synchronous motor, is the state variable of the extended permanent magnet synchronous motor, Control input for the extended permanent magnet synchronous motor;

[0179] State variables for extended permanent magnet synchronous motors , design the Lumberg observer, and its corresponding expression is:

[0180] ;

[0181] in, The state variables of the extended permanent magnet synchronous motor The estimated value of , T represents the transpose of the matrix, is the estimated value of the state variable of the permanent magnet synchronous motor, is the estimated value of the lumped disturbance; is the gain of the Lumberg observer;

[0182] The estimation error of the state variables of the extended permanent magnet synchronous motor is defined as , subtract the expression of the model corresponding to the extended permanent magnet synchronous motor from the expression of the Romberg observer to obtain the following formula:

[0183] ;

[0184] in, express The estimation error of the state variables of the extended permanent magnet synchronous motor at time t, express The estimation error of the state variables of the extended permanent magnet synchronous motor at time t;

[0185] Establish recursive dynamics and combine the state variables of the actual permanent magnet synchronous motor with the state variables of the extended permanent magnet synchronous motor to construct the augmented state variables. , and the corresponding augmented permanent magnet synchronous motor model is described as follows:

[0186] ;

[0187] in, is the state matrix of the augmented permanent magnet synchronous motor, is the input matrix of the augmented permanent magnet synchronous motor, is the lumped disturbance gain matrix of the augmented permanent magnet synchronous motor, is the output matrix of the augmented permanent magnet synchronous motor;

[0188] According to Lyapunov stability theory, the gain is selected Ensure that the closed-loop error system matrix satisfies the spectral radius condition , so that the estimation error converges asymptotically, which means that the Lumberg observer is Performance constraints that maintain bounded estimation error:

[0189] ;

[0190] in, represents the radius, represents the closed-loop error system matrix; express The state variables of the permanent magnet synchronous motor at time , express The estimated value of the state variable of the permanent magnet synchronous motor at time , Represents the state variable of the permanent magnet synchronous motor at time 0, is the state variable of the permanent magnet synchronous motor The initial state set of is the estimation error threshold of the Lumberg observer, satisfying ;

[0191] The performance constraint of the tracking error of the permanent magnet synchronous motor state variable is combined with the performance constraint of the estimation error of the Romberg observer to obtain the performance constraint condition as shown in the following formula:

[0192] ;

[0193] in, is the estimated value of the state variable of the permanent magnet synchronous motor The tracking error threshold satisfies ;

[0194] Consider the state variables, control inputs and lumped disturbances of the augmented permanent magnet synchronous motor to meet the following constraints:

[0195] ;

[0196] ;

[0197] ;

[0198] in, is the admissible set of state variables, is the control input admissible set, is the lumped perturbation admissible set, is a three-dimensional real space;

[0199] Target Collection Robust one-step set Indicates that any possible disturbance Under the condition that there is an allowable control input One-step navigation to a given set The state set is:

[0200] ;

[0201] For the augmented permanent magnet synchronous motor model , the state variables of the augmented permanent magnet synchronous motor satisfy , if there is an admissible control input such that , then it is called a set is the robust control invariant set, namely:

[0202] ;

[0203] in, Indicates implication, Indicates the existence of a maximum robust control invariant set Contains All robust control invariant sets in When is the control invariant set;

[0204] For the model and state variables, control input and lumped disturbance of the augmented permanent magnet synchronous motor, given the state variables of the augmented permanent magnet synchronous motor , for the control input of the augmented permanent magnet synchronous motor , can always overcome the lumped disturbance Make ,Right now:

[0205] ;

[0206] in, is the state variable of the augmented permanent magnet synchronous motor The permissible input set of ,but ;if ,but ;

[0207] Considering the model of an augmented permanent magnet synchronous motor, the performance constraints are implemented by defining the following set:

[0208] ;

[0209] in, is an equivalent set of performance constraints;

[0210] Therefore, the performance constraint is equivalent to: ,if , can ensure the next state ; We need to further find the robust control invariant set satisfy:

[0211] ;

[0212] in, The reference state variable in the expression for the rate of change of the reference state variable The set of admissible reference inputs;

[0213] remember , the above formula is equivalent to:

[0214] ;

[0215] The equivalent set of performance constraints is input into the improved inner approximation algorithm to obtain the robust control invariant set ;

[0216] The improved inner approximation algorithm is obtained by improving the traditional inner approximation algorithm, specifically including:

[0217] Introducing control invariant sets at initialization , the improved initial set is ;

[0218] The robust one-step set is improved as shown below:

[0219] ;

[0220] in, is the target set to which the state variables of the permanent magnet synchronous motor augmented in the mth iteration belong, is an adjustable parameter, for The improved robust one-step set;

[0221] The iteration end condition is improved. The improved iteration end condition is: ;

[0222] in, represents the improved target set in the mth iteration, represents the improved target set in the m+1th iteration.

[0223] Specifically, refer to Figure 2 , the input of the MPC controller of the embodiment of the present application is the reference state variable And the mechanical angular velocity of the permanent magnet synchronous motor at time k ; Output is the optimal q-axis current at time k The optimal q-axis current at time k is used to control the permanent magnet synchronous motor, obtaining the rotor position at time k+1. The mechanical angular velocity at time k+1 is then calculated and input into the MPC controller. The continuum set model is used to predict the mechanical angular velocity control strategy to guide the generation of the optimal q-axis current at time k+1. The embodiments of this application are described using a surface-mounted permanent magnet synchronous motor (PMSM) as an example.

[0224] First, a discrete mathematical model of the surface-mount PMSM is constructed, including discrete mechanical motion equations and constraints. In the surface-mount PMSM, the d-axis inductance is equal to the q-axis inductance. The embodiment of the present application adopts the maximum torque per ampere (MTPA) control method, that is, The control method can therefore construct the constraints of the q-axis current.

[0225] The control goal of the embodiment of the present application is to require the PMSM to have an actual mechanical angular velocity of Continuously and unbiasedly track a time-varying reference state variable with bounded error .

[0226] Since the mechanical angle and current of the surface-mount PMSM are subject to hard constraints, the reference state variable and the rate of change of the reference state variable Constraints must be met:

[0227] ;

[0228] in, 、 They are the constraint set of the reference state variable and the constraint set of the reference state variable change rate respectively.

[0229] Furthermore, the traditional MPC strategy is highly dependent on the parameters of the motor body (friction coefficient, moment of inertia and permanent magnet flux, etc.). However, in actual engineering applications, it is difficult to accurately know the values of these parameters. The embodiment of the present application introduces an extended permanent magnet synchronous motor model to simplify the calculation. Since the extended permanent magnet synchronous motor model is fully observable, the state variables of the extended permanent magnet synchronous motor are A Luenberger observer (LO) can be designed. Recursive dynamics is established to combine the actual state variables of the permanent magnet synchronous motor with the estimated values of the state variables of the extended permanent magnet synchronous motor to construct the state variables of the augmented permanent magnet synchronous motor, and the corresponding augmented permanent magnet synchronous motor model is obtained to construct performance constraints. In order to expand the initial state set At the same time, due to the existence of bounded disturbances in the augmented permanent magnet synchronous motor model, the definition of robust one-step set is introduced, and the robust control invariant set is constructed according to the constraints of q-axis current and performance constraints. It is not possible to satisfy the iterative feasibility, so it is necessary to further solve the robust control invariant (RCI) set that satisfies the constraints. .

[0230] The solution of RCI set is usually completed with the help of iterative inner approximation algorithm: , The end condition of the iteration is , you can get the RCI set If the termination condition is met, the RCI set is determined within a finite number of iterations. However, due to the strict end condition , which makes this method very dependent on the maximum number of iterations or difficult to determine whether the sets are equal in terms of value. Therefore, the embodiment of this application improves the inner approximation algorithm, referring to Figure 3 , which improves the robust step set and iteration end condition in the inner approximation algorithm. In addition, it avoids the disadvantage of the traditional algorithm that it cannot terminate the iteration clearly, and introduces the control invariant set during initialization. , improve the initial set.

[0231] S2, for the augmented permanent magnet synchronous motor, a continuous set model is constructed to predict the objective function of the mechanical angular velocity control strategy at time k. Based on the discrete mechanical motion equations of the permanent magnet synchronous motor and the robust control invariant set, the objective function is converted into a least squares norm problem, the constraints of the decision variables of the least squares norm problem are determined, and then the least squares norm problem is converted into a least squares norm problem with an invariant constraint set.

[0232] In a specific embodiment, the objective function of the continuum model prediction mechanical angular velocity control strategy adopted at time k is:

[0233] ;

[0234] in, represents the objective function, for Moment The estimated values of the state variables of the augmented permanent magnet synchronous motor are , is the prediction step length, for Moment The estimated values of the state variables of the augmented permanent magnet synchronous motor are for Moment The control input of the augmented permanent magnet synchronous motor is is the reference state variable, 、 and are the first weight coefficient, the second weight coefficient and the third weight coefficient respectively, is the estimated value of the lumped disturbance, and we define .

[0235] In a specific embodiment, the objective function is converted into a least squares norm problem based on the discrete mechanical motion equations of the permanent magnet synchronous motor and the robust control invariant set, the constraints of the decision variables of the least squares norm problem are determined, and then the least squares norm problem is converted into a least squares norm problem with an invariant constraint set, specifically including:

[0236] make is the state variable vector of the augmented permanent magnet synchronous motor, The control input vector of the augmented permanent magnet synchronous motor and For the reference state variable vector of the augmented permanent magnet synchronous motor, the objective function is converted into a matrix form as shown below:

[0237] ;

[0238] in, is a constant term, is a row vector of all 1s, 、 and are the first weight vector, the second weight vector and the third weight vector respectively, and their values are:

[0239] ;

[0240] ;

[0241] ;

[0242] in, is the N-order unit matrix;

[0243] The state space equation constraint is calculated based on the discrete mechanical motion equation of the permanent magnet synchronous motor, and its expression is: ;

[0244] Obtain the state variable vector in the objective function in matrix form based on the state space equation constraints and the control input vector The matrix expression between is as follows:

[0245] ;

[0246] in, represents the state weight, Represents the input weight, and its expressions are:

[0247] ;

[0248] ;

[0249] The state variable vector and the control input vector Substitute the matrix expression between into the matrix form of the objective function to obtain the simplified objective function, as shown below:

[0250] ;

[0251] in, is the unconstrained optimal state variable vector, is the weighting matrix, is the reference state variable vector and the state variables at time k The changing parameters, - T means taking the inverse first and then transposing, and the problem of solving the simplified objective function constitutes a least squares norm problem;

[0252] because 、 and are all semi-positive definite matrices, so the weighted matrix maintains the characteristics of the semi-positive definite matrix, and the weighted matrix Cholesky decomposition is ,in is an upper triangular matrix; let the equivalent decision variables be And the equivalent unconstrained optimal solution is , the simplified objective function is expressed as For the center of the ball dimensional sphere, that is:

[0253] ;

[0254] Robust Control Invariant Set It maintains convexity and has linear properties, so it can be expressed in the form of a linear inequality:

[0255] ;

[0256] in, 、 are the coefficient matrix and constant vector of the inequality constraints respectively;

[0257] The final conversion results in the minimum square norm problem of PMSM predictive mechanical angular velocity control:

[0258] ;

[0259] in, represents the minimized Y, Indicates constraints;

[0260] In the above formula and The value of does not change with the working conditions, so the decision variable The shape of the constraints remains unchanged and can be equivalent to the constraint set Overall displacement , so the least squares norm problem with an unchanged constraint set is constructed as:

[0261] ;

[0262] in, is the final decision variable, Indicates the minimized , is the final unconstrained optimal solution.

[0263] Specifically, in the PMSM predictive mechanical angular velocity control, in order to achieve the reference state variable , mechanical angular velocity Considering the dynamic performance and robustness requirements in the prediction time domain, a multi-objective optimization method for the augmented permanent magnet synchronous motor is constructed. The objective function of the mechanical angular velocity control strategy is predicted by the continuous set of moments. The objective function is further expressed in matrix form, and the QP problem is constructed by combining the discrete mechanical motion equations of the permanent magnet synchronous motor and the robust control invariant set. The QP problem is then transformed into an equivalent QP problem, that is, a least squares norm problem, and further equivalently constructed as a least squares norm problem with an invariant constraint set. At this point, the predictive control problem is equivalent to the final unconstrained optimal solution Projection on the polyhedron constraint set to find the optimal solution to the constraints Then, the optimal state variable vector can be obtained by performing the inverse transformation .

[0264] S3, obtain the rotor position of the permanent magnet synchronous motor at time k and calculate the mechanical angular velocity of the permanent magnet synchronous motor at time k, use the projected positive set method to solve the least squares norm problem with an invariant constraint set, obtain the constrained optimal solution, and calculate the optimal q-axis current at time k based on the constrained optimal solution.

[0265] In a specific embodiment, the projection active set method is used to solve the least squares norm problem with an unchanged constraint set to obtain a constrained optimal solution. The optimal q-axis current at time k is calculated based on the constrained optimal solution, specifically including:

[0266] S31, according to 、 、 and Calculate the final unconstrained optimal solution ; Determine the effective constraint set at the initial moment based on the final unconstrained optimal solution, the least squares problem with an unchanged constraint set, and the effective constraints , as shown below:

[0267] ;

[0268] in, is the coefficient matrix No. OK, is a constant vector No. elements, To satisfy the inequality of The set formed;

[0269] S32, project the final unconstrained optimal solution onto the effective constraint set at the initial moment In the effective constraint set at the initial moment, Every element of , the final unconstrained optimal solution is projected by the following projection formula On the hyperplane of the index, get the corresponding projection point :

[0270] ;

[0271] in, Indicates that Projected onto On the hyperplane of index, for the reason The rows of the matrix of indices.. for the reason constant vector of indices Multiple elements of represents the effective constraint set at the initial moment Any element in; According to each projection point, the least squares norm problem with the constraint set unchanged and the effective constraints, the effective constraint set corresponding to each projection point is determined as shown in the following formula:

[0272] ;

[0273] S33, determine each projection point The effective constraint set intersection of Whether it is included in the valid constraint set at the initial time , that is, to determine whether ;

[0274] If satisfied , then according to Calculate the final effective constraint set ,in, represents the set of valid constraint indexes that appear the most times, Represents the occurrence count function, Indicates taking the maximum value;

[0275] The final unconstrained optimal solution is projected onto the final effective constraint set using the following projection formula: Obtain the optimal solution to the constraints on the intersection of multiple hyperplanes of the index :

[0276] ;

[0277] in, Indicates that Projected onto On the intersection of multiple hyperplanes of index, for the reason Indexed matrix OK, for the reason constant vector of indices Multiple elements of

[0278] Constrain the optimal solution Perform inverse transformation to obtain the optimal state variable vector , as shown below:

[0279] ;

[0280] The optimal q-axis current at time k is calculated based on the state space equation constraints, as shown in the following formula:

[0281] ;

[0282] in, and Represent the optimal state variable vectors The first and second values of represents the optimal q-axis current at time k;

[0283] If not satisfied , then the new effective constraints are obtained according to the following formula:

[0284] ;

[0285] in, Indicates assignment, represents the new effective constraint;

[0286] Update the valid constraint set with the new valid constraints , and repeat steps S32-S33 until the optimal q-axis current at time k is calculated.

[0287] Specifically, refer to Figure 4 The active set method proposed in the embodiment of the present application avoids the calculation of the initial feasible solution and the multiple iterative solutions of the KKT equations.

[0288] The following is an example of this.

[0289] Take the prediction step size For example, the constraints of q-axis current and mechanical angular velocity (state variable The final decision variable under the one-step reachable set and Expressed as As the horizontal axis, The polygonal feasible domain is the vertical coordinate, and the polygonal feasible domain and the final unconstrained optimal solution under different conditions are drawn, such as Figure 5 shown.

[0290] exist Figure 5 middle, 、 and is the final unconstrained optimal solution under different circumstances; 1, 2, 3, 4, 5 and 6 are the labels of different feasible region boundary constraints; the black dotted line is the extension line of the feasible region boundary; the red solid line is the ray perpendicular to the feasible region boundary. The definitions of valid constraints and invalid constraints are as follows:

[0291] Valid constraints satisfy The jth constraint of is the set corresponding to the valid constraint index j, defined as ; Invalid constraints indicate satisfaction The jth constraint of .

[0292] The method proposed in the embodiments of this application is described for unconstrained optimal solutions in different situations:

[0293] 1) For the first final unconstrained optimal solution :

[0294] (a) According to the formula Compute the effective constraint set at the initial time ;

[0295] in, is the coefficient matrix No. OK; is a constant vector No. elements; To satisfy the inequality of The collection formed.

[0296] (b) Projection to the effective constraint set In the projected point . Projection to The formula is:

[0297] ;

[0298] (c) According to the formula Calculate the projection point The effective constraint set ;

[0299] (d) The optimal solution of the constraint is ;

[0300] (e) The optimal state variable vector obtained by inverse transformation is .

[0301] 2) For the second final unconstrained optimal solution :

[0302] (a) According to the formula Compute the effective constraint set at the initial time ;

[0303] (b) Projection to the effective constraint set In the projected point 、 、 as well as ;

[0304] (c) According to the formula Compute the effective constraint set for each projection point :

[0305] ;

[0306] ;

[0307] ;

[0308] ;

[0309] (d) Valid constraint set No new effective constraints are introduced, and the calculation The valid constraints that appear the most times are taken as the final valid constraint set ;

[0310] (e) Projection to In the constraint optimal solution , the calculation formula is: ;

[0311] (f) The optimal state variable vector obtained by inverse transformation is .

[0312] 3) For the third final unconstrained optimal solution :

[0313] (a) According to the formula Calculate the initial moment and put it into the valid constraint set ;

[0314] (b) Projection to valid constraints In the projected point 、 as well as ;

[0315] (c) According to the formula Compute the effective constraint set for each projection point :

[0316] ;

[0317] ;

[0318] ;

[0319] (d) Valid constraint set No new effective constraints are introduced, and the calculation The valid constraints that appear the most times are taken as the final valid constraint set ;

[0320] (e) Projection to In the constraint optimal solution ;

[0321] (g) The optimal state variable vector obtained by inverse transformation is .

[0322] The effects of the present invention are described below through specific experiments.

[0323] (1) Experimental platform

[0324] Build as Figure 6 The experimental test platform shown in the figure verifies the proposed continuum model predictive mechanical angular velocity control strategy (PE-CMPC). The main parameters of the surface-mounted PMSM in the experimental platform constructed in the embodiment of this application are shown in Table 1, and the control system sampling period is Set to 80 microseconds.

[0325]

[0326] In addition, a commercial inverter manufactured by Asea Brown Boveri Ltd is used to drive the load motor and apply load torque to the control motor. The surface-mount PMSM is equipped with a 2500-line incremental encoder with a rotor position resolution of 10,000 pulses / revolution. The experimental platform principle block diagram is shown below. Figure 7 shown.

[0327] (2) Analysis of experimental results

[0328] In order to obtain the admissible set of lumped perturbations First, we define different expected mechanical angular velocity trajectories. Based on these expected trajectories, we conduct experiments and approximate the range of the lumped disturbance using the Lumberg observer. Add 10% as safety redundancy, and the range of the total disturbance is r / min. Set the permissible mechanical angular velocity tracking error to 1% of the rated mechanical angular velocity, that is, r / min. According to the performance constraint, the mechanical angular velocity tracking error is estimated to be r / min.

[0329] To verify the PE-CMPC's ability to track a time-varying reference mechanical angular velocity, a ramp tracking test was performed. The reference mechanical angular velocity was set to start at 0 r / min and then increase to a rated mechanical angular velocity of 3000 r / min at a constant acceleration. Figure 8 Mechanical angular velocity response curves of PI, traditional MPC and PE-CMPC.

[0330] like Figure 9 As shown, the mechanical angular velocity tracking error is calculated for the three control methods. The comparative test of the control strategy is shown in Table 2. is the root mean square of the tracking error, is the maximum absolute value of the tracking error.

[0331]

[0332] It can be seen that both PI and traditional MPC cannot meet the control target. The mechanical angular velocity tracking error of PE-CMPC meets the preset error boundary throughout the process. , and has the smallest root mean square error. Further analysis Figure 10 It can be seen that the estimated mechanical angular velocity tracking error of the Lumberg observer is Strictly restricted by the RCI set within the range.

[0333] In order to further verify the dynamic tracking performance of PE-CMPC for periodic reference signals, the reference mechanical angular velocity is set to . Figure 11 and Figure 14 No load and constant load respectively Mechanical angular velocity response curves of three control strategies under two working conditions.

[0334] like Figure 12 and Figure 15 As shown, under no-load and load conditions, the embodiment of the present application performs mechanical angular velocity tracking error for three control strategies. The comparative test is conducted and the performance of the control strategy is listed in Table 3. It can be seen that the traditional MPC shows better tracking performance than PI, but exceeds the preset error band near the peak and trough. On the contrary, the tracking error of PE-CMPC is always within the error band. Under no-load conditions, the RMS error of the traditional MPC was 13.46 r / min, while that of the PE-CMPC was 11.09 r / min, a decrease of 17.61%. Under loaded conditions, the RMS error of the traditional MPC was 18.92 r / min, while that of the PE-CMPC was 10.70 r / min, a decrease of 43.45%.

[0335]

[0336] Further analysis Figure 13 and Figure 16 It can be seen that under no-load and load conditions, the estimated mechanical angular velocity tracking error based on the Lumberg observer is can be strictly limited by the RCI set constraints in MPC within the range.

[0337] Further references Figure 17 As an implementation of the methods shown in the above figures, the present application provides an embodiment of a PMSM angular velocity control device based on online optimization of an objective function. Figure 1 Corresponding to the method embodiment shown, the device can be specifically applied to various electronic devices.

[0338] The embodiment of the present application provides a PMSM angular velocity control device based on online optimization of an objective function, comprising:

[0339] The motor model construction module 1 is configured to construct the discrete mechanical motion equations of the permanent magnet synchronous motor, determine the q-axis current constraints of the permanent magnet synchronous motor using a maximum torque-current ratio control method, introduce an observer-based augmented permanent magnet synchronous motor and construct performance constraints, and construct a robust control invariant set based on the q-axis current constraints and performance constraints.

[0340] a problem conversion module 2 configured to construct a continuous set model for predicting the objective function of the mechanical angular velocity control strategy at time k for the augmented permanent magnet synchronous motor, convert the objective function into a least squares norm problem based on the discrete mechanical motion equations of the permanent magnet synchronous motor and the robust control invariant set, determine the constraints of the decision variables of the least squares norm problem, and then convert the least squares norm problem into a least squares norm problem with an invariant constraint set;

[0341] The problem-solving module 3 is configured to obtain the rotor position of the permanent magnet synchronous motor at time k and calculate the mechanical angular velocity of the permanent magnet synchronous motor at time k, use the projected positive set method to solve the least squares norm problem with an unchanged constraint set, obtain the constrained optimal solution, and calculate the optimal q-axis current at time k based on the constrained optimal solution.

[0342] Figure 18 Schematic diagram of the hardware structure of the electronic device provided by the embodiment of the present invention. Figure 18 As shown, the electronic device of this embodiment includes: a processor 1801 and a memory 1802; wherein the memory 1802 is configured to store computer-executable instructions; and the processor 1801 is configured to execute the computer-executable instructions stored in the memory to implement the various steps performed by the electronic device in the above-described embodiment. For details, please refer to the relevant description of the aforementioned method embodiment.

[0343] Optionally, the memory 1802 may be independent or integrated with the processor 1801 .

[0344] When the memory 1802 is independently provided, the electronic device further includes a bus 1803 for connecting the memory 1802 and the processor 1801 .

[0345] An embodiment of the present invention further provides a computer storage medium, in which computer execution instructions are stored. When the processor 1801 executes the computer execution instructions, the above method is implemented.

[0346] An embodiment of the present invention further provides a computer program product, including a computer program. When the computer program is executed by the processor 1801, the above method is implemented.

[0347] In the embodiments provided herein, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the module division is merely a logical functional division. In actual implementation, other division methods may be used. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not implemented. In addition, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interface, device or module, which may be electrical, mechanical or other forms.

[0348] Modules described as separate components may or may not be physically separate, and components shown as modules may or may not be physical units, that is, they may be located in one place or distributed across multiple network elements. Some or all of these modules may be selected to implement the solution of this embodiment based on actual needs.

[0349] In addition, the functional modules in various embodiments of the present invention may be integrated into a single processing unit, each module may exist physically separately, or two or more modules may be integrated into a single unit. The units formed by the above modules may be implemented in the form of hardware or hardware plus software functional units.

[0350] The above-mentioned integrated module implemented in the form of a software function module can be stored in a computer-readable storage medium. The above-mentioned software function module is stored in a storage medium and includes a number of instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) or processor 1801 to perform some steps of the methods of various embodiments of the present application.

[0351] It should be understood that the processor 1801 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), or application-specific integrated circuits (ASIC). A general-purpose processor may be a microprocessor, or the processor 1801 may be any conventional processor 1801. The steps of the method disclosed in the present invention may be directly implemented by the hardware processor 1801, or implemented by a combination of hardware and software modules in the processor 1801.

[0352] The memory 1802 may include a high-speed RAM memory, and may also include a non-volatile storage NVM, such as at least one disk memory, and may also be a USB flash drive, a mobile hard disk, a read-only memory, a magnetic disk, or an optical disk.

[0353] Bus 1803 can be an Industry Standard Architecture (ISA), a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus. Bus 1803 can be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, the bus 1803 in the drawings of this application is not limited to a single bus 1803 or a single type of bus 1803.

[0354] The storage medium may be implemented by any type of volatile or non-volatile memory device, or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium may be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0355] An exemplary storage medium is coupled to the processor 1801, so that the processor 1801 can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor 1801. The processor 1801 and the storage medium can be located in an application-specific integrated circuit (ASIC). Of course, the processor 1801 and the storage medium can also exist as discrete components in an electronic device or a main control device.

[0356] Those skilled in the art will appreciate that all or part of the steps in the above-described method embodiments can be implemented using hardware associated with program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0357] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A PMSM angular velocity control method based on online optimization of objective function, characterized in that: The following steps are involved: The discrete mechanical motion equations of the permanent magnet synchronous motor are constructed, and the q-axis current constraints of the permanent magnet synchronous motor are determined using a maximum torque-current ratio control method. An observer-based augmented permanent magnet synchronous motor is introduced and performance constraints are constructed. A robust control invariant set is constructed based on the q-axis current constraints and the performance constraints. Constructing a continuous set model for predicting the objective function of the mechanical angular velocity control strategy at time k for the augmented permanent magnet synchronous motor, converting the objective function into a least squares norm problem based on the discrete mechanical motion equations of the permanent magnet synchronous motor and a robust control invariant set, determining the constraints of the decision variables of the least squares norm problem, and then converting the least squares norm problem into a least squares norm problem with an invariant constraint set; The rotor position of the permanent magnet synchronous motor at time k is obtained and the mechanical angular velocity of the permanent magnet synchronous motor at time k is calculated. The least square norm problem with an unchanged constraint set is solved by using a projected positive set method to obtain a constrained optimal solution. The optimal q-axis current at time k is calculated based on the constrained optimal solution.

2. The PMSM angular velocity control method based on online optimization of the objective function according to claim 1 is characterized in that: The discrete mechanical motion equation of the permanent magnet synchronous motor is: ； Among them, k represents the kth moment, is the sampling period, is the moment of inertia, is the friction coefficient, is the q-axis current, is the permanent magnet flux, is the pole pair number, is the load torque, is the mechanical angular velocity, is the state matrix of the angular velocity loop of the permanent magnet synchronous motor, is the input matrix of the angular velocity loop of the permanent magnet synchronous motor; In the surface-mount permanent magnet synchronous motor, the d-axis inductance is equal to the q-axis inductance. When the maximum torque current ratio control method is adopted, that is, the d-axis current Control mode, the constraint condition of the q-axis current of the permanent magnet synchronous motor is: ； in, is the admissible set of q-axis current, is the maximum allowable current, is the rated current, is the real number space.

3. The PMSM angular velocity control method based on online optimization of the objective function according to claim 2, characterized in that: An observer-based augmented permanent magnet synchronous motor is introduced and performance constraints are established. A robust control invariant set is constructed based on the q-axis current constraints and performance constraints, specifically including: The permanent magnet synchronous motor satisfies the constraint condition of the q-axis current. The state variables of the permanent magnet synchronous motor at time Continuous and unbiased tracking with bounded error Reference state variables at time , that is, the tracking error of the state variable of the permanent magnet synchronous motor The following performance constraints need to be met: ； in, represents the tracking error threshold; Indicates any represents a positive integer; The reference state variables satisfy the following equation: ； in, express The reference state variable at time t, express The reference state variable at time t, is the rate of change of the reference state variable; Taking into account external disturbances and parameter mismatch, the lumped disturbance Defined as: ； in, is the nominal value of permanent magnet flux linkage, is the reference value of q-axis current; The extended permanent magnet synchronous motor is introduced, and its corresponding model is expressed as: ； in, is the state matrix of the extended permanent magnet synchronous motor, is the input matrix of the extended permanent magnet synchronous motor, is the output matrix of the extended permanent magnet synchronous motor; is the rate of change of the lumped disturbance, express The aggregate disturbance at time t, express The aggregate disturbance at time For the output of the extended permanent magnet synchronous motor, is the state variable of the extended permanent magnet synchronous motor, Control input for the extended permanent magnet synchronous motor; State variables for the extended permanent magnet synchronous motor , design the Lumberg observer, and its corresponding expression is: ； in, The state variables of the extended permanent magnet synchronous motor The estimated value of , T represents the transpose of the matrix, is the estimated value of the state variable of the permanent magnet synchronous motor, is the estimated value of the lumped disturbance; is the gain of the Lumberg observer; The estimation error of the state variables of the extended permanent magnet synchronous motor is defined as , subtract the expression of the model corresponding to the extended permanent magnet synchronous motor from the expression of the Romberg observer to obtain the following formula: ； in, express The estimation error of the state variables of the extended permanent magnet synchronous motor at time t, express The estimation error of the state variables of the extended permanent magnet synchronous motor at time t; Establish recursive dynamics and combine the state variables of the actual permanent magnet synchronous motor with the state variables of the extended permanent magnet synchronous motor to construct the augmented state variables. , and the corresponding augmented permanent magnet synchronous motor model is described as follows: ； in, is the state matrix of the augmented permanent magnet synchronous motor, is the input matrix of the augmented permanent magnet synchronous motor, is the lumped disturbance gain matrix of the augmented permanent magnet synchronous motor, is the output matrix of the augmented permanent magnet synchronous motor; According to Lyapunov stability theory, the gain is selected Ensure that the closed-loop error system matrix satisfies the spectral radius condition , so that the estimation error converges asymptotically, which means that the Lumberg observer is Performance constraints that maintain bounded estimation error: ； in, represents the radius, represents the closed-loop error system matrix; express The state variables of the permanent magnet synchronous motor at time , express The estimated value of the state variable of the permanent magnet synchronous motor at time , Represents the state variables of the permanent magnet synchronous motor at time 0, is the state variable of the permanent magnet synchronous motor The initial state set of is the estimation error threshold of the Lumberg observer, satisfying ; The performance constraint of the tracking error of the state variable of the permanent magnet synchronous motor is combined with the performance constraint of the estimation error of the Romberg observer to obtain a performance constraint condition, as shown in the following formula: ； in, is the estimated value of the state variable of the permanent magnet synchronous motor The tracking error threshold satisfies ; Consider the state variables, control inputs and lumped disturbances of the augmented permanent magnet synchronous motor to meet the following constraints: ； ； ； in, is the admissible set of state variables, is the control input admissible set, is the lumped perturbation admissible set, is a three-dimensional real space; Target Collection Robust one-step set Indicates that any possible disturbance Under the condition that there is an allowable control input One-step navigation to a given set The state set is: ； For the augmented permanent magnet synchronous motor model , the state variables of the augmented permanent magnet synchronous motor satisfy , if there is an admissible control input such that , then it is called a set is the robust control invariant set, namely: ； in, Indicates implication, Indicates the existence of a maximum robust control invariant set Contains All robust control invariant sets in When is the control invariant set; For the model and state variables, control input and lumped disturbance of the augmented permanent magnet synchronous motor, given the state variables of the augmented permanent magnet synchronous motor , for the control input of the augmented permanent magnet synchronous motor , can always overcome the lumped disturbance Make ,Right now: ； in, is the state variable of the augmented permanent magnet synchronous motor The permissible input set of ,but ;if ,but ; Considering the model of an augmented permanent magnet synchronous motor, the performance constraints are implemented by defining the following set: ； in, is an equivalent set of performance constraints; Therefore, the performance constraint is equivalent to: ,if , can ensure the next state ; We need to further find the robust control invariant set satisfy: ； in, The reference state variable in the expression for the rate of change of the reference state variable The set of admissible reference inputs; remember , the above formula is equivalent to: ； The equivalent set of performance constraints is input into the improved inner approximation algorithm to obtain the robust control invariant set ; The improved inner approximation algorithm is obtained by improving the traditional inner approximation algorithm, and specifically includes: Introducing control invariant sets at initialization , the improved initial set is ; The robust one-step set is improved as shown below: ； in, is the target set to which the state variables of the permanent magnet synchronous motor augmented in the mth iteration belong, is an adjustable parameter, for The improved robust one-step set; The iteration end condition is improved. The improved iteration end condition is: ; in, represents the improved target set in the mth iteration, represents the improved target set in the m+1th iteration.

4. The PMSM angular velocity control method based on online optimization of the objective function according to claim 3 is characterized in that: The objective function of the mechanical angular velocity control strategy predicted by the continuum model at time k is: ； in, represents the objective function, for Moment The estimated values of the state variables of the augmented permanent magnet synchronous motor are , is the prediction step length, for Moment The estimated values of the state variables of the augmented permanent magnet synchronous motor are for Moment The control input of the augmented permanent magnet synchronous motor is is the reference state variable, 、 and are the first weight coefficient, the second weight coefficient and the third weight coefficient respectively, is the estimated value of the lumped disturbance, and we define .

5. The PMSM angular velocity control method based on online optimization of the objective function according to claim 4 is characterized in that: The objective function is converted into a least squares norm problem based on the discrete mechanical motion equations of the permanent magnet synchronous motor and the robust control invariant set, the constraints of the decision variables of the least squares norm problem are determined, and then the least squares norm problem is converted into a least squares norm problem with an invariant constraint set, specifically including: make is the state variable vector of the augmented permanent magnet synchronous motor, is the control input vector of the augmented permanent magnet synchronous motor and For the reference state variable vector of the augmented permanent magnet synchronous motor, the objective function is converted into a matrix form as shown below: ； in, is a constant term, is a row vector of all 1s, 、 and are the first weight vector, the second weight vector and the third weight vector respectively, and their values are: ； ； ； in, is the N-order unit matrix; The state space equation constraint is calculated based on the discrete mechanical motion equation of the permanent magnet synchronous motor, and its expression is: ; The state variable vector in the matrix form of the objective function is obtained based on the state space equation constraint and the control input vector The matrix expression between is as follows: ； in, represents the state weight, Represents the input weight, and its expressions are: ； ； The state variable vector and the control input vector Substitute the matrix expression between into the matrix form of the objective function to obtain the simplified objective function, as shown in the following formula: ； in, is the unconstrained optimal state variable vector, is the weighting matrix, is the reference state variable vector and the state variables at time k The parameter of the change, - T means taking the inverse first and then transposing, and the problem of solving the simplified objective function constitutes a least squares norm problem; because 、 and are all positive semi-definite matrices, so the weighting matrix maintains the characteristics of the semi-positive semi-definite matrix, and the weighting matrix Cholesky decomposition is ,in is an upper triangular matrix; let the equivalent decision variables be And the equivalent unconstrained optimal solution is , the simplified objective function is expressed as For the center of the ball dimensional sphere, that is: ； Robust Control Invariant Set It maintains convexity and has linear properties, so it can be expressed in the form of a linear inequality: ； in, 、 are the coefficient matrix and constant vector of the inequality constraints respectively; The final conversion results in the minimum square norm problem of PMSM predictive mechanical angular velocity control: ； in, represents the minimized Y, Indicates constraints; In the above formula and The value of does not change with the working conditions, so the decision variable The shape of the constraints remains unchanged and can be equivalent to the constraint set Overall displacement , so the least squares norm problem with an unchanged constraint set is constructed as: ； in, is the final decision variable, Indicates the minimized , is the final unconstrained optimal solution.

6. The PMSM angular velocity control method based on online optimization of the objective function according to claim 5, characterized in that: The least squares norm problem with an unchanged constraint set is solved using a projected active set method to obtain a constrained optimal solution. The optimal q-axis current at time k is calculated based on the constrained optimal solution, specifically including: S31, according to 、 、 and Calculate the final unconstrained optimal solution ; Determine the effective constraint set at the initial moment based on the final unconstrained optimal solution, the least squares norm problem with an unchanged constraint set, and the effective constraints , as shown below: ； in, is the coefficient matrix No. OK, is a constant vector No. elements, To satisfy the inequality of The set formed; S32, projecting the final unconstrained optimal solution onto the effective constraint set at the initial moment In the effective constraint set at the initial moment, Every element of The final unconstrained optimal solution is projected on the On the hyperplane of the index, get the corresponding projection point : ； in, Indicates that Projected onto On the hyperplane of index, for the reason The rows of the matrix of indices.. for the reason constant vector of indices Multiple elements of represents the effective constraint set at the initial moment Any element in; According to each projection point, the least squares norm problem with the constraint set unchanged and the effective constraints, the effective constraint set corresponding to each projection point is determined as shown in the following formula: ； S33, determine each projection point The effective constraint set intersection of Whether it is included in the valid constraint set at the initial time , that is, to determine whether ; If satisfied , then according to Calculate the final effective constraint set ,in, represents the set of valid constraint indexes that appear the most times, Represents the occurrence count function, Indicates taking the maximum value; The final unconstrained optimal solution is projected onto the final effective constraint set using the following projection formula: Obtain the optimal solution to the constraints on the intersection of multiple hyperplanes of the index : ； in, Indicates that Projected onto On the intersection of multiple hyperplanes of index, for the reason Indexed matrix OK, for the reason constant vector of indices Multiple elements of The optimal solution of the constraint Perform inverse transformation to obtain the optimal state variable vector , as shown below: ； The optimal q-axis current at time k is calculated based on the state space equation constraints, as shown in the following formula: ； in, and Represent the optimal state variable vectors The first and second values of represents the optimal q-axis current at time k; If not satisfied , then the new effective constraints are obtained according to the following formula: ； in, Indicates assignment, represents the new effective constraint; Update the valid constraint set with the new valid constraints , and repeat steps S32-S33 until the optimal q-axis current at time k is calculated.

7. A PMSM angular velocity control device based on online optimization of objective function, characterized in that: include: a motor model construction module configured to construct discrete mechanical motion equations for the permanent magnet synchronous motor, determine q-axis current constraints for the permanent magnet synchronous motor using a maximum torque-current ratio control method, introduce an observer-based augmented permanent magnet synchronous motor and construct performance constraints, and construct a robust control invariant set based on the q-axis current constraints and the performance constraints; a problem conversion module configured to construct, for the augmented permanent magnet synchronous motor, a continuum set model used to predict the objective function of the mechanical angular velocity control strategy at time k, convert the objective function into a least squares norm problem based on the discrete mechanical motion equations of the permanent magnet synchronous motor and a robust control invariant set, determine constraints on decision variables of the least squares norm problem, and then convert the least squares norm problem into a least squares norm problem with an invariant constraint set; The problem-solving module is configured to obtain the rotor position of the permanent magnet synchronous motor at time k and calculate the mechanical angular velocity of the permanent magnet synchronous motor at time k, use the projected positive set method to solve the least square norm problem with an unchanged constraint set to obtain a constrained optimal solution, and calculate the optimal q-axis current at time k based on the constrained optimal solution.

8. An electronic device comprising: one or more processors; a storage device for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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