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

Abstract

The application discloses a PMSM angular velocity control method and device based on a target function online optimization, relates to the field of motor control, and comprises the following steps: constructing a discrete mechanical motion equation of a permanent magnet synchronous motor and determining a constraint condition of q-axis current; a robust control invariant set is constructed in combination with a performance constraint condition; a target function of a continuous set model predictive mechanical angular velocity control strategy at k time is constructed, the target function is converted into a least two norm problem based on the discrete mechanical motion equation of the permanent magnet synchronous motor and the robust control invariant set, constraint conditions of decision variables of the least two norm problem are determined, and the least two norm problem is converted into a least two norm problem with a constraint set invariant; a mechanical angular velocity of the permanent magnet synchronous motor at k time is acquired, the least two norm problem with the constraint set invariant is solved by using a projection active set method, a constraint optimal solution is obtained, and an optimal q-axis current at k time is calculated. The application solves the problems of heavy real-time calculation burden of a traditional active set method.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of motor control, in particular to a PMSM angular velocity control method and device based on online optimization of target function. BACKGROUND

[0002] The efficient control of new energy vehicle driving systems is a core challenge to improve energy utilization and driving performance. Permanent magnet synchronous motor (PMSM) has become the preferred actuator for new energy vehicle powertrain due to its high power density, excellent torque characteristics and low loss advantage. Traditional PMSM control mostly uses proportional integral (PI) regulator, but it has limitations in dynamic response speed, multi-variable coupling suppression and constraint processing capability. Especially under high-speed heavy load conditions, the motor state variables and control inputs are easily saturated in the saturation region due to physical limitations, and PI control is difficult to balance constraint satisfaction and tracking accuracy, resulting in a decrease in system robustness.

[0003] Model predictive control (MPC) provides a new idea for the above problems through rolling optimization and explicit constraint processing, but its real-time performance and computational complexity in PMSM application still face challenges. Traditional MPC needs to solve high-dimensional quadratic programming problems online, resulting in significant algorithm delay; at the same time, the weight matrix of the objective function and the system dynamics are closely coupled, and the parameter tuning complexity is high, which restricts the practical engineering application. Existing methods mostly rely on numerical iterative solvers, which are difficult to meet the stringent requirements of vehicle-mounted controllers for millisecond-level response.

[0004] Traditional aggressive set method has strong dependence on initial feasible solution, and if the initial solution is not properly selected, it will lead to slow convergence speed or even failure. In addition, the active constraint set needs to be dynamically adjusted every iteration, and the sub-problem needs to be reconstructed and solved to update the Karush-Kuhn-Tucker (KKT) matrix. The real-time calculation burden is heavy, and it is difficult to apply to motor servo driving. In addition, the convergence and calculation time of the traditional aggressive set method are heavily dependent on the quality of the initial feasible solution, and when the system is in complex conditions such as constraint boundary (such as q-axis current saturation, mechanical angular velocity over-limit), the algorithm may diverge due to invalid iteration direction. SUMMARY

[0005] The present application aims to solve the above-mentioned technical problems by providing a PMSM angular velocity control method and device based on online optimization of target function.

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

[0007] Discrete mechanical motion equations of a permanent magnet synchronous motor are constructed, and the constraint conditions of the q-axis current of the permanent magnet synchronous motor are determined by the maximum torque-current ratio control method. An observer-based augmented permanent magnet synchronous motor is introduced and its performance constraints are constructed. A robust control invariant set is constructed based on the q-axis current constraint and the performance constraint.

[0008] For the objective function of the continuous set model used to predict the mechanical angular velocity control strategy of the augmented permanent magnet synchronous motor at time k, the objective function is transformed into a least-norm 2 problem based on the discrete mechanical motion equations and robust control invariant set of the permanent magnet synchronous motor. The constraints of the decision variables of the least-norm 2 problem are determined, and then the least-norm 2 problem is transformed into a least-norm 2 problem with 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 norm problem with invariant constraint set is solved by the projected positive set method to obtain the constraint optimal solution. The optimal q-axis current at time k is calculated based on the constraint optimal solution.

[0010] As a preferred embodiment, the discrete mechanical motion equations of the permanent magnet synchronous motor are:

[0011] ;

[0012] Where k represents time k, The sampling period is For rotational inertia, The coefficient of friction, For q-axis current, It is a permanent magnet flux linkage. For extreme logarithms, For load torque, For mechanical angular velocity, This is the state matrix of the angular velocity loop of the permanent magnet synchronous motor. This is the input matrix for the angular velocity loop of the permanent magnet synchronous motor;

[0013] In a surface-mounted permanent magnet synchronous motor, the d-axis inductance is equal to the q-axis inductance. When the maximum torque-to-current ratio control method is used, i.e., the d-axis current... The control method and the constraint condition for the q-axis current of the permanent magnet synchronous motor are as follows:

[0014] ;

[0015] in, Let be the allowable set of the q-axis current. For the maximum allowable current, Rated current, It is the space of real numbers.

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

[0017] Under the premise of satisfying the constraint condition of q-axis current, the permanent magnet synchronous motor State variables of permanent magnet synchronous motor at time t Continuously track without bias with bounded error Reference state variables at time 1 That is, the tracking error of the state variables of the permanent magnet synchronous motor. The following performance constraints need to be met:

[0018] ;

[0019] in, Indicates the tracking error threshold; Indicates any, Represents positive integers;

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

[0021] ;

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

[0023] Considering external disturbances and parameter mismatch, lumped disturbance Defined as:

[0024] ;

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

[0026] Introducing an extended permanent magnet synchronous motor, its corresponding model is represented as:

[0027] ;

[0028] in, For the extended state matrix of permanent magnet synchronous motors, For the input matrix of the extended permanent magnet synchronous motor, For the output matrix of the extended permanent magnet synchronous motor; Let be the rate of change of the lumped disturbance. express The lumped disturbance at any given moment. express Lumped disturbance at any given moment; To extend the output of the permanent magnet synchronous motor, For the extended state variables of permanent magnet synchronous motors, For extended control inputs of permanent magnet synchronous motors;

[0029] State variables for extended permanent magnet synchronous motors Design the Luneburg observer, whose corresponding expression is:

[0030] ;

[0031] in, State variables for extended permanent magnet synchronous motors The estimated value, where T represents the transpose of the matrix. These are estimated values ​​for the state variables of the permanent magnet synchronous motor. This is an estimate of the lumped disturbance; Gain for the Romberg observer;

[0032] The estimation error of the state variables of the extended permanent magnet synchronous motor is defined as follows: Subtracting the expression for the extended permanent magnet synchronous motor model from the expression for the Romberg observer, we obtain the following equation:

[0033] ;

[0034] in, express The estimation error of the state variables of a permanent magnet synchronous motor over time extension. express Estimation error of state variables of permanent magnet synchronous motor with time extension;

[0035] Establish recursive dynamics and construct an augmented state variable by combining the state variables of the actual permanent magnet synchronous motor with those of the extended permanent magnet synchronous motor. The corresponding augmented permanent magnet synchronous motor model is described as follows:

[0036] ;

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

[0038] Based on Lyapunov stability theory, choose the gain Ensure that the closed-loop error system matrix satisfies the spectral radius condition. This leads to asymptotic convergence of the estimation error, thus implying that the Romberg observer is effective for any... Performance constraints for maintaining bounded estimation error:

[0039] ;

[0040] in, Indicates radius, Represents the closed-loop error system matrix; express The state variables of the permanent magnet synchronous motor at time t. express Estimates of the state variables of the permanent magnet synchronous motor at time t. This represents the state variables of the permanent magnet synchronous motor at time 0. State variables of permanent magnet synchronous motor The initial state set; Let the estimation error threshold of the Luneburg observer satisfy... ;

[0041] By combining the performance constraints of the tracking error of the state variables of the permanent magnet synchronous motor with the performance constraints of the estimation error of the Luneburg observer, the performance constraints are transformed into the following equation:

[0042] ;

[0043] in, Estimates of the state variables of a permanent magnet synchronous motor The tracking error threshold satisfies ;

[0044] Considering that the state variables, control input, and lumped disturbances of the augmented permanent magnet synchronous motor satisfy the following constraints:

[0045] ;

[0046] ;

[0047] ;

[0048] in, For the set of allowed state variables, To control the allowed set of inputs, To allow for aggregated disturbances. It is a three-dimensional real number space;

[0049] target set Robust Step-by-Step Set Indicates any possible disturbance Below, there exists permissible control input. Guided to a given set in one step The set of states, namely:

[0050] ;

[0051] For the model of the augmented permanent magnet synchronous motor The state variables of the augmented permanent magnet synchronous motor satisfy If there is an allowable control input that makes Then it is called a set. It is a robust control-invariant set, that is:

[0052] ;

[0053] in, Indicates implication, Indicates existence; Maximum robust control invariant set Includes All robust control invariant sets within; when At that time, it was called To control invariant sets;

[0054] For the model and state variables, control inputs, and lumped disturbances 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 It can always overcome lumped disturbances Make ,Right now:

[0055] ;

[0056] in, To augment the state variables of permanent magnet synchronous motors The allowed input set; if ,but ;if ,but ;

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

[0058] ;

[0059] in, This is the equivalent set of performance constraints.

[0060] Therefore, the performance constraint is equivalent to: ,if This ensures the next state Further research is needed to find robust control invariant sets. satisfy:

[0061] ;

[0062] in, The expression for the rate of change of the reference state variable is the reference state variable. The allowed reference input set;

[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 derived from the traditional inner approximation algorithm, and specifically includes:

[0067] Introducing a control invariant set during initialization The improved initial set is ;

[0068] The robust one-step set is improved as shown in the following equation:

[0069] ;

[0070] in, Let be the target set to which the state variables of the augmented permanent magnet synchronous motor belong in the m-th iteration. It is an adjustable parameter. for Improved robust one-step set;

[0071] The iteration termination condition is improved as follows: ;

[0072] in, Let m represent the improved target set in the m-th iteration. Let represent the improved target set in the (m+1)th iteration.

[0073] As a preferred option, the objective function of the continuous set model used at time k to predict the mechanical angular velocity control strategy is:

[0074] ;

[0075] in, Describe the objective function. for Time of the first The estimated values ​​of the state variables of the step-enhanced permanent magnet synchronous motor. , To predict the step size, for Time of the first The estimated values ​​of the state variables of the step-enhanced permanent magnet synchronous motor. for Time of the first The control input of the step-by-step extended permanent magnet synchronous motor, As a reference state variable, , and These are the first weighting coefficient, the second weighting coefficient, and the third weighting coefficient, respectively. To estimate the lumped disturbance, define .

[0076] As a preferred approach, the objective function is transformed into a least-norm 2 problem based on the discrete mechanical motion equations and robust control invariant sets of a permanent magnet synchronous motor. The constraints on the decision variables of the least-norm 2 problem are then determined, and the least-norm 2 problem is further transformed into a least-norm 2 problem with invariant constraint sets. Specifically, this includes:

[0077] make To augment the state variable vector of a permanent magnet synchronous motor, To enhance the control input vector of permanent magnet synchronous motors and To augment the reference state variable vector of the permanent magnet synchronous motor, the objective function is converted into matrix form, as shown in the following equation:

[0078] ;

[0079] in, For constant terms, A row vector consisting entirely of 1s. , and These are the first weight vector, the second weight vector, and the third weight vector, respectively, and their values ​​are as follows:

[0080] ;

[0081] ;

[0082] ;

[0083] in, It is an N-order identity matrix;

[0084] The state-space equation constraints are calculated based on the discrete mechanical motion equations of the permanent magnet synchronous motor, and their expression is as follows: ;

[0085] The state variable vector in the matrix form of the objective function is obtained based on the constraints of the state-space equation. and control input vector The matrix expression between them is shown in the following formula:

[0086] ;

[0087] in, Represents the state weights. The input weights are represented by the following expressions:

[0088] ;

[0089] ;

[0090] The state variable vector and control input vector Substituting the matrix expression between the two into the matrix form of the objective function, we obtain the simplified objective function, as shown in the following equation:

[0091] ;

[0092] in, The vector of unconstrained optimal state variables. For weighted matrices, For reference state variable vector and the state variables at time k The changing parameter, -T, indicates that the inverse is taken first and then the transpose is taken. The problem of solving the simplified objective function constitutes the least-norm 2 problem.

[0093] because , and Since all are positive semi-definite matrices, the weighted matrix retains the properties of a positive semi-definite matrix. The weighted matrix can be decomposed by Cholesky into... ,in Let be an upper triangular matrix; let the equivalent decision variables be... And the equivalent unconstrained optimal solution is The simplified objective function is expressed as follows: For the center of the ball A 3D sphere, that is:

[0094] ;

[0095] Robust control invariant set Preserving convexity and possessing linear properties, it can therefore be expressed in the form of a linear inequality:

[0096] ;

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

[0098] The final transformation yields the least-norm 2 problem for predicting mechanical angular velocity control using PMSM as follows:

[0099] ;

[0100] in, Represents Y when minimized. Indicates constraints;

[0101] In the above formula and The value of does not change with the operating conditions, therefore the decision variable The shape of the constraints remains unchanged and can be equivalent to a constraint set. Overall displacement Therefore, the problem of constructing the least 2 norm with invariant constraint set is:

[0102] ;

[0103] in, As the final decision variable, Represents the minimization process , This is the final unconstrained optimal solution.

[0104] As a preferred method, the projected positive set method is used to solve the least-norm problem with invariant constraint sets, obtaining the constraint-optimal solution. Based on the constraint-optimal solution, the optimal q-axis current at time k is calculated, specifically including:

[0105] S31, according to , , and Calculate the final unconstrained optimal solution The effective constraint set at the initial moment is determined based on the final unconstrained optimal solution, the least 2 norm problem with invariant constraint set, and the effective constraints. As shown in the following formula:

[0106] ;

[0107] in, Coefficient matrix The OK, constant vector The One element, To satisfy the inequality of The set that constitutes;

[0108] S32, project the final unconstrained optimal solution onto the effective constraint set at the initial time step. In the effective constraint set for the initial time period Each element The final unconstrained optimal solution is projected onto the solution using the following projection formulas. On the indexed hyperplane, the corresponding projection point is obtained. :

[0109] ;

[0110] in, Indicates will Projected onto by On the hyperplane of the index, For the reason The rows of the indexed matrix. For the reason constant vector of indices Multiple elements; Represents the effective constraint set at the initial time. Any element in the equation; determine the effective constraint set corresponding to each projection point based on the least-two norm problem with invariant constraint set and the effective constraints, as shown in the following equation:

[0111] ;

[0112] S33, determine each projection point Effective constraint set intersection Does it include the valid constraint set at the initial time? That is, to determine whether the condition is met. ;

[0113] If satisfied According to Calculate the final effective constraint set ,in, This represents the set of valid constraint indexes that appear most frequently. This function represents the frequency of occurrence. This indicates taking the maximum value;

[0114] The final unconstrained optimal solution is projected onto the final effective constraint set using the following projection common method. The constrained optimal solution is obtained at the intersection of multiple hyperplanes of the index. :

[0115] ;

[0116] in, Indicates will Projected onto by On the intersection of multiple hyperplanes of the index, For the reason Index matrix OK, For the reason constant vector of indices Multiple elements;

[0117] constrained optimal solution Perform an inverse transformation to obtain the optimal state variable vector. As shown in the following formula:

[0118] ;

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

[0120] ;

[0121] in, and These represent the optimal state variable vectors respectively. The first and second values, This represents the optimal q-axis current at time k;

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

[0123] ;

[0124] in, This indicates assignment. This indicates a new effective constraint;

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

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

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

[0128] The problem transformation module is configured to construct the objective function of the mechanical angular velocity control strategy for the augmented permanent magnet synchronous motor at time k using a continuous set model. Based on the discrete mechanical motion equations and robust control invariant set of the permanent magnet synchronous motor, the objective function is transformed into a least-norm 2 problem. The constraints of the decision variables of the least-norm problem are determined, and then the least-norm problem is transformed into a least-norm problem with 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. It uses the projected positive set method to solve the least-norm problem with invariant constraint set to obtain the constraint optimal solution. Based on the constraint optimal solution, it calculates the optimal q-axis current at time k.

[0130] Thirdly, the present invention provides an electronic device including one or more processors; and a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any implementation of the first aspect.

[0131] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method as described in any of the implementations of the first aspect.

[0132] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the method as described in any of the implementations in the first aspect.

[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 objective function proposed in this invention can eliminate the steady-state error of mechanical angular velocity tracking under disturbance by designing a continuous set model to predict the objective function of the mechanical angular velocity control strategy.

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

[0136] (3) The PMSM angular velocity control method based on online optimization of objective function proposed in this invention is equivalent to the least second norm problem, which is transformed into the projection of the unconstrained optimal solution onto the feasible region. This avoids the dependence on the initial feasible solution and the solution of the KKT matrix, and significantly reduces the amount of online computation.

[0137] (4) The PMSM angular velocity control method based on online optimization of objective function proposed in this invention avoids the dependence on the iterative process and the requirement for a specific initial feasible solution, ensuring that an optimal solution that strictly satisfies all linear constraints can be obtained under each working condition, and avoiding divergence due to invalid iteration directions under complex working conditions. Attached Figure Description

[0138] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0139] Figure 1 This is a flowchart illustrating the PMSM angular velocity control method based on online optimization of the objective function, as an embodiment of this application.

[0140] Figure 2 This is a block diagram illustrating the control principle of the PMSM angular velocity control method based on online optimization of the objective function, as an embodiment of this application.

[0141] Figure 3 A flowchart illustrating the improved internal approximation algorithm of the PMSM angular velocity control method based on online optimization of the objective function, as an embodiment of this application;

[0142] Figure 4 The flowchart is a representation of the PMSM angular velocity control method based on online optimization of the objective function, according to an embodiment of this application.

[0143] Figure 5 This is a schematic diagram of the feasible region of the PMSM angular velocity control method based on online optimization of the objective function, as an embodiment of this application.

[0144] Figure 6This serves as an experimental test platform for the PMSM angular velocity control method based on online optimization of the objective function, as described in the embodiments of this application.

[0145] Figure 7 This is a schematic diagram of the experimental platform for the PMSM angular velocity control method based on online optimization of the objective function, which is an embodiment of this application.

[0146] Figure 8 The rotational speed response curve is shown in the performance analysis results of the slope trajectory tracking of the PMSM angular velocity control method based on online optimization of objective function, which is an embodiment of this application.

[0147] Figure 9 The graph shows the speed tracking error in the slope trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of objective function, which is an embodiment of this application.

[0148] Figure 10 The image shows the tracking error of the estimated mechanical angular velocity in the slope trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of objective function, as described in an embodiment of this application.

[0149] Figure 11 The rotational speed response curve under no-load condition is shown in the performance analysis results of the sinusoidal trajectory tracking of the PMSM angular velocity control method based on online optimization of objective function, which is an embodiment of this application.

[0150] Figure 12 The graph shows 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 objective function, which is an embodiment of this application.

[0151] Figure 13 The figure shows the tracking error of the estimated 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 objective function in the embodiments of this application.

[0152] Figure 14 The rotational speed response curve under constant load is shown in the performance analysis results of the sinusoidal trajectory tracking of the PMSM angular velocity control method based on online optimization of objective function, which is an embodiment of this application.

[0153] Figure 15 The graph shows the speed tracking error under constant load conditions in the sinusoidal trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of objective function, which is an embodiment of this application.

[0154] Figure 16The figure shows the tracking error of the estimated mechanical angular velocity under constant load conditions in the sinusoidal trajectory tracking performance analysis results of the PMSM angular velocity control method based on online optimization of objective function in the embodiments of this application.

[0155] Figure 17 This is a schematic diagram of a PMSM angular velocity control device based on online optimization of an objective function, as an embodiment of this application.

[0156] Figure 18 A schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0157] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0158] Figure 1 This application illustrates an embodiment of 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 determine the constraint conditions of the q-axis current of the permanent magnet synchronous motor by using the maximum torque-current ratio control method. Introduce an observer-based augmented permanent magnet synchronous motor and construct performance constraints. 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 equations of the permanent magnet synchronous motor are:

[0161] ;

[0162] Where k represents time k, The sampling period is For rotational inertia, The coefficient of friction, For q-axis current, It is a permanent magnet flux linkage. For extreme logarithms, For load torque, For mechanical angular velocity, This is the state matrix of the angular velocity loop of the permanent magnet synchronous motor. This is the input matrix for the angular velocity loop of the permanent magnet synchronous motor;

[0163] In a surface-mounted permanent magnet synchronous motor, the d-axis inductance is equal to the q-axis inductance. When the maximum torque-to-current ratio control method is used, i.e., the d-axis current... The control method and the constraint condition for the q-axis current of the permanent magnet synchronous motor are as follows:

[0164] ;

[0165] in, Let be the allowable set of the q-axis current. For the maximum allowable current, Rated current, It is the space of real numbers.

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

[0167] Under the premise of satisfying the constraint condition of q-axis current, the permanent magnet synchronous motor State variables of permanent magnet synchronous motor at time t Continuously track without bias with bounded error Reference state variables at time 1 That is, the tracking error of the state variables of the permanent magnet synchronous motor. The following performance constraints need to be met:

[0168] ;

[0169] in, Indicates the tracking error threshold; Indicates any, Represents positive integers;

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

[0171] ;

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

[0173] Considering external disturbances and parameter mismatch, lumped disturbance Defined as:

[0174] ;

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

[0176] Introducing an extended permanent magnet synchronous motor, its corresponding model is represented as:

[0177] ;

[0178] in, For the extended state matrix of permanent magnet synchronous motors, For the input matrix of the extended permanent magnet synchronous motor, For the output matrix of the extended permanent magnet synchronous motor; Let be the rate of change of the lumped disturbance. express The lumped disturbance at any given moment. express Lumped disturbance at any given moment; To extend the output of the permanent magnet synchronous motor, For the extended state variables of permanent magnet synchronous motors, For extended control inputs of permanent magnet synchronous motors;

[0179] State variables for extended permanent magnet synchronous motors Design the Luneburg observer, whose corresponding expression is:

[0180] ;

[0181] in, State variables for extended permanent magnet synchronous motors The estimated value, where T represents the transpose of the matrix. These are estimated values ​​for the state variables of the permanent magnet synchronous motor. This is an estimate of the lumped disturbance; Gain for the Romberg observer;

[0182] The estimation error of the state variables of the extended permanent magnet synchronous motor is defined as follows: Subtracting the expression for the extended permanent magnet synchronous motor model from the expression for the Romberg observer, we obtain the following equation:

[0183] ;

[0184] in, express The estimation error of the state variables of a permanent magnet synchronous motor over time extension. express Estimation error of state variables of permanent magnet synchronous motor with time extension;

[0185] Establish recursive dynamics and construct an augmented state variable by combining the state variables of the actual permanent magnet synchronous motor with those of the extended permanent magnet synchronous motor. The corresponding augmented permanent magnet synchronous motor model is described as follows:

[0186] ;

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

[0188] Based on Lyapunov stability theory, choose the gain Ensure that the closed-loop error system matrix satisfies the spectral radius condition. This leads to asymptotic convergence of the estimation error, thus implying that the Romberg observer is effective for any... Performance constraints for maintaining bounded estimation error:

[0189] ;

[0190] in, Indicates radius, Represents the closed-loop error system matrix; express The state variables of the permanent magnet synchronous motor at time t. express Estimates of the state variables of the permanent magnet synchronous motor at time t. This represents the state variables of the permanent magnet synchronous motor at time 0. State variables of permanent magnet synchronous motor The initial state set; Let the estimation error threshold of the Luneburg observer satisfy... ;

[0191] By combining the performance constraints of the tracking error of the state variables of the permanent magnet synchronous motor with the performance constraints of the estimation error of the Luneburg observer, the performance constraints are transformed into the following equation:

[0192] ;

[0193] in, Estimates of the state variables of a permanent magnet synchronous motor The tracking error threshold satisfies ;

[0194] Considering that the state variables, control input, and lumped disturbances of the augmented permanent magnet synchronous motor satisfy the following constraints:

[0195] ;

[0196] ;

[0197] ;

[0198] in, For the set of allowed state variables, To control the allowed set of inputs, To allow for aggregated disturbances. It is a three-dimensional real number space;

[0199] target set Robust Step-by-Step Set Indicates any possible disturbance Below, there exists permissible control input. Guided to a given set in one step The set of states, namely:

[0200] ;

[0201] For the model of the augmented permanent magnet synchronous motor The state variables of the augmented permanent magnet synchronous motor satisfy If there is an allowable control input that makes Then it is called a set. It is a robust control-invariant set, that is:

[0202] ;

[0203] in, Indicates implication, Indicates existence; Maximum robust control invariant set Includes All robust control invariant sets within; when At that time, it was called To control invariant sets;

[0204] For the model and state variables, control inputs, and lumped disturbances 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 It can always overcome lumped disturbances Make ,Right now:

[0205] ;

[0206] in, To augment the state variables of permanent magnet synchronous motors The allowed input set; if ,but ;if ,but ;

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

[0208] ;

[0209] in, This is the equivalent set of performance constraints.

[0210] Therefore, the performance constraint is equivalent to: ,if This ensures the next state Further research is needed to find robust control invariant sets. satisfy:

[0211] ;

[0212] in, The expression for the rate of change of the reference state variable is the reference state variable. The allowed reference input set;

[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 derived from the traditional inner approximation algorithm, and specifically includes:

[0217] Introducing a control invariant set during initialization The improved initial set is ;

[0218] The robust one-step set is improved as shown in the following equation:

[0219] ;

[0220] in, Let be the target set to which the state variables of the augmented permanent magnet synchronous motor belong in the m-th iteration. It is an adjustable parameter. for Improved robust one-step set;

[0221] The iteration termination condition is improved as follows: ;

[0222] in, Let m represent the improved target set in the m-th iteration. Let represent the improved target set in the (m+1)th iteration.

[0223] For details, please refer to Figure 2 In the embodiments of this application, the input of the MPC controller is a reference state variable. And the mechanical angular velocity of the permanent magnet synchronous motor at time k. The 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. A continuous set model is used to predict the mechanical angular velocity, guiding the generation of the optimal q-axis current at time k+1. This application uses a surface-mounted permanent magnet synchronous motor (PMSM) as an example for illustration.

[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 embodiments of this application employ a maximum torque per ampere (MTPA) control method, i.e. The control method allows for the construction of constraints on the q-axis current.

[0225] The control objective of the embodiments of this application is to require the PMSM to achieve an actual mechanical angular velocity while satisfying the constraint condition of the q-axis current. To continuously and unbiasedly track time-varying reference state variables with bounded error. .

[0226] Because the mechanical angle and current of a surface-mounted PMSM are subject to rigid constraints, the reference state variables... and the rate of change of the reference state variable Constraints must be met:

[0227] ;

[0228] in, , These are the constraint sets for the reference state variables and the constraint sets for the rate of change of the reference state variables, respectively.

[0229] Furthermore, traditional MPC strategies are highly dependent on the parameters of the motor itself (friction coefficient, moment of inertia, and permanent magnet flux linkage, etc.). However, in practical engineering applications, it is difficult to know the precise values ​​of these parameters. Embodiments of this application introduce an extended permanent magnet synchronous motor model to simplify calculations. Since the extended permanent magnet synchronous motor model is fully observable, the state variables of the extended permanent magnet synchronous motor... A Luenberger observer (LO) can be designed. Recursive dynamics are established, and the state variables of an augmented permanent magnet synchronous motor (PMSM) are constructed by combining the estimated state variables of the actual PMSM with those of an extended PMSM. The corresponding model of the augmented PMSM is then obtained, and performance constraints are established. To expand the initial state set... Furthermore, since the augmented permanent magnet synchronous motor model contains bounded disturbances, the definitions of robust one-step sets are introduced, and robust control invariant sets are constructed based on the constraints of the q-axis current and performance constraints. Because of the set... Since iterative feasibility cannot be satisfied, it is necessary to further solve for the set of robust control invariant (RCI) conditions that satisfy the constraints. .

[0230] Solving for the RCI set usually requires the use of an iterative inner approximation algorithm: , The termination condition for the iteration is This will give you the RCI set. If the termination condition is met, then the RCI set... It is determined within a finite number of iterations. However, due to the strict termination condition... This makes the method highly dependent on the maximum number of iterations or numerically difficult to determine whether sets are equal. Therefore, the embodiments of this application improve the inner approximation algorithm, referring to... Figure 3 The robust one-step set and iteration termination condition in the internal approximation algorithm have been improved. Furthermore, it avoids the drawback of traditional algorithms that cannot explicitly terminate iterations, and introduces a control-invariant set during initialization. The initial set is improved.

[0231] S2, for the augmented permanent magnet synchronous motor, constructs the objective function of the continuous set model used at time k to predict the mechanical angular velocity control strategy. Based on the discrete mechanical motion equations and robust control invariant set of the permanent magnet synchronous motor, the objective function is transformed into a least-norm 2 problem. The constraints of the decision variables of the least-norm problem are determined, and then the least-norm problem is transformed into a least-norm problem with invariant constraint set.

[0232] In a specific embodiment, the objective function of the continuous set model used at time k to predict the mechanical angular velocity control strategy is:

[0233] ;

[0234] in, Describe the objective function. for Time of the first The estimated values ​​of the state variables of the step-enhanced permanent magnet synchronous motor. , To predict the step size, for Time of the first The estimated values ​​of the state variables of the step-enhanced permanent magnet synchronous motor. for Time of the first The control input of the step-by-step extended permanent magnet synchronous motor, As a reference state variable, , and These are the first weighting coefficient, the second weighting coefficient, and the third weighting coefficient, respectively. To estimate the lumped disturbance, define .

[0235] In a specific embodiment, the objective function is transformed into a least-norm 2 problem based on the discrete mechanical motion equations and robust control invariant sets of the permanent magnet synchronous motor. The constraints on the decision variables of the least-norm 2 problem are determined, and then the least-norm 2 problem is transformed into a least-norm 2 problem with invariant constraint sets. Specifically, this includes:

[0236] make To augment the state variable vector of a permanent magnet synchronous motor, To enhance the control input vector of permanent magnet synchronous motors and To augment the reference state variable vector of the permanent magnet synchronous motor, the objective function is converted into matrix form, as shown in the following equation:

[0237] ;

[0238] in, For constant terms, A row vector consisting entirely of 1s. , and These are the first weight vector, the second weight vector, and the third weight vector, respectively, and their values ​​are as follows:

[0239] ;

[0240] ;

[0241] ;

[0242] in, It is an N-order identity matrix;

[0243] The state-space equation constraints are calculated based on the discrete mechanical motion equations of the permanent magnet synchronous motor, and their expression is as follows: ;

[0244] The state variable vector in the matrix form of the objective function is obtained based on the constraints of the state-space equation. and control input vector The matrix expression between them is shown in the following formula:

[0245] ;

[0246] in, Represents the state weights. The input weights are represented by the following expressions:

[0247] ;

[0248] ;

[0249] The state variable vector and control input vector Substituting the matrix expression between the two into the matrix form of the objective function, we obtain the simplified objective function, as shown in the following equation:

[0250] ;

[0251] in, The vector of unconstrained optimal state variables. For weighted matrices, For reference state variable vector and the state variables at time k The changing parameter, -T, indicates that the inverse is taken first and then the transpose is taken. The problem of solving the simplified objective function constitutes the least-norm 2 problem.

[0252] because , and Since all are positive semi-definite matrices, the weighted matrix retains the properties of a positive semi-definite matrix. The weighted matrix can be decomposed by Cholesky into... ,in Let be an upper triangular matrix; let the equivalent decision variables be... And the equivalent unconstrained optimal solution is The simplified objective function is expressed as follows: For the center of the ball A 3D sphere, that is:

[0253] ;

[0254] Robust control invariant set Preserving convexity and possessing linear properties, it can therefore be expressed in the form of a linear inequality:

[0255] ;

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

[0257] The final transformation yields the least-norm 2 problem for predicting mechanical angular velocity control using PMSM as follows:

[0258] ;

[0259] in, Represents Y when minimized. Indicates constraints;

[0260] In the above formula and The value of does not change with the operating conditions, therefore the decision variable The shape of the constraints remains unchanged and can be equivalent to a constraint set. Overall displacement Therefore, the problem of constructing the least 2 norm with invariant constraint set is:

[0261] ;

[0262] in, As the final decision variable, Represents the minimization process , This is the final unconstrained optimal solution.

[0263] Specifically, in PMSM predictive mechanical angular velocity control, in order to realize the reference state variable Mechanical angular velocity Multi-objective optimization of harmonic suppression and disturbance compensation. Taking into account both dynamic performance and robustness requirements in the prediction time domain, a system is constructed for augmented permanent magnet synchronous motors. The objective function of the continuous set predictive mechanical angular velocity control strategy at each time step is given. This objective function is further expressed in matrix form, and a QP problem is constructed by combining the discrete mechanical motion equations of the permanent magnet synchronous motor and the robust control invariant set. This QP problem is then transformed into an equivalent QP problem, namely the least-norm 2 problem, and further equivalently, a least-norm 2 problem with invariant constraint sets is constructed. At this point, the predictive control problem is equivalent to the final unconstrained optimal solution. By projecting onto the polyhedral constraint set, the optimal solution of the constraints can be obtained. Then, by performing an inverse transformation, the optimal state variable vector can be obtained. .

[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 projection positive set method to solve the least 2 norm problem with invariant constraint set to obtain the constraint optimal solution. Calculate the optimal q-axis current at time k based on the constraint optimal solution.

[0265] In a specific embodiment, the projected positive set method is used to solve the least-norm problem with invariant constraint sets, obtaining the constraint-optimal solution. Based on the constraint-optimal solution, the optimal q-axis current at time k is calculated, specifically including:

[0266] S31, according to , , and Calculate the final unconstrained optimal solution The effective constraint set at the initial moment is determined based on the final unconstrained optimal solution, the least 2 norm problem with invariant constraint set, and the effective constraints. As shown in the following formula:

[0267] ;

[0268] in, Coefficient matrix The OK, constant vector The One element, To satisfy the inequality of The set that constitutes;

[0269] S32, project the final unconstrained optimal solution onto the effective constraint set at the initial time step. In the effective constraint set for the initial time period Each element The final unconstrained optimal solution is projected onto the solution using the following projection formulas. On the indexed hyperplane, the corresponding projection point is obtained. :

[0270] ;

[0271] in, Indicates will Projected onto by On the hyperplane of the index, For the reason The rows of the indexed matrix. For the reason constant vector of indices Multiple elements; Represents the effective constraint set at the initial time. Any element in the equation; determine the effective constraint set corresponding to each projection point based on the least-two norm problem with invariant constraint set and the effective constraints, as shown in the following equation:

[0272] ;

[0273] S33, determine each projection point Effective constraint set intersection Does it include the valid constraint set at the initial time? That is, to determine whether the condition is met. ;

[0274] If satisfied According to Calculate the final effective constraint set ,in, This represents the set of valid constraint indexes that appear most frequently. This function represents the frequency of occurrence. This indicates taking the maximum value;

[0275] The final unconstrained optimal solution is projected onto the final effective constraint set using the following projection common method. The constrained optimal solution is obtained at the intersection of multiple hyperplanes of the index. :

[0276] ;

[0277] in, Indicates will Projected onto by On the intersection of multiple hyperplanes of the index, For the reason Index matrix OK, For the reason constant vector of indices Multiple elements;

[0278] constrained optimal solution Perform an inverse transformation to obtain the optimal state variable vector. As shown in the following formula:

[0279] ;

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

[0281] ;

[0282] in, and These represent the optimal state variable vectors respectively. The first and second values, This represents the optimal q-axis current at time k;

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

[0284] ;

[0285] in, This indicates assignment. This indicates a new effective constraint;

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

[0287] For details, please refer to Figure 4 The effective set method proposed in the embodiments of this application avoids the calculation of the initial feasible solution and the multiple iterative solutions of the KKT equation system.

[0288] The following example illustrates this point.

[0289] Take the prediction step size For example, consider the constraints on the q-axis current and the mechanical angular velocity (state variables). The final decision variable under the one-step reachable set and Represented as As the x-axis, with Using the polygonal feasible region as the ordinate, plot the polygonal feasible region and the final unconstrained optimal solution under different conditions, such as... Figure 5 As shown.

[0290] exist Figure 5 middle, , and These represent the final unconstrained optimal solutions under different conditions; 1, 2, 3, 4, 5, and 6 are the labels for different feasible region boundary constraints; the black dashed line is the extension line of the feasible region boundary; the red solid line is the ray perpendicular to the feasible region boundary. Effective constraints and ineffective constraints are defined as follows:

[0291] Valid constraints mean that the constraints are satisfied. The j-th constraint; the effective constraint set To effectively constrain the set corresponding to index j, it is defined as follows: Invalid constraints indicate that the constraint is satisfied. The j-th constraint.

[0292] The embodiments of this application illustrate the methods proposed for unconstrained optimal solutions under different conditions:

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

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

[0295] in, Coefficient matrix The OK; constant vector The One element; To satisfy the inequality of The set that constitutes.

[0296] (b) will Projection to effective constraint set In the middle, the projection point is obtained. . Projected to The formula is:

[0297] ;

[0298] (c) According to the formula Calculate projection points Effective constraint set ;

[0299] (d) The constrained optimal solution is ;

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

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

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

[0303] (b) will Projection to effective constraint set In the middle, the projection point is obtained. , , as well as ;

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

[0305] ;

[0306] ;

[0307] ;

[0308] ;

[0309] (d) Effective constraint set Without introducing new effective constraints, the calculation The most frequently occurring valid constraint is selected as the final set of valid constraints. ;

[0310] (e) will Projected to In this process, the constrained optimal solution is obtained. The calculation formula is: ;

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

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

[0313] (a) According to the formula Calculate the initial time and put it into the effective constraint set. ;

[0314] (b) will Projection to effective constraints In the middle, the projection point is obtained. , as well as ;

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

[0316] ;

[0317] ;

[0318] ;

[0319] (d) Effective constraint set Without introducing new effective constraints, the calculation The most frequently occurring valid constraint is selected as the final set of valid constraints. ;

[0320] (e) will Projected to In this process, the constrained optimal solution is obtained. ;

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

[0322] The effects of this invention will be illustrated below through specific experiments.

[0323] (1) Experimental platform

[0324] Building such Figure 6 The experimental test platform shown verifies the proposed continuous set model predictive mechanical angular velocity control strategy (PE-CMPC). The main parameters of the surface-mount PMSM in the experimental platform constructed in the embodiments 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. was used to drive the load motor, applying load torque to the control motor. The surface-mount PMSM was equipped with a 2500-line incremental encoder, providing a rotor position resolution of 10,000 pulses / revolution. The experimental platform block diagram is shown below. Figure 7 As shown.

[0327] (2) Analysis of experimental results

[0328] In order to obtain the set disturbance allowance set First, different desired mechanical angular velocity trajectories are defined. Experiments are conducted based on these desired trajectories, and the range of values ​​for the lumped perturbation is approximated using a Romberg observer. The obtained values ​​are then... Adding 10% as a safety redundancy, the range of values ​​for the lumped disturbance is obtained as follows: r / min. The allowable mechanical angular velocity tracking error is set to 1% of the rated mechanical angular velocity, i.e. r / min. The mechanical angular velocity tracking error is estimated based on performance constraints and set to... r / min.

[0329] To verify the PE-CMPC's ability to track time-varying reference mechanical angular velocities, a ramp tracking test was conducted. The reference mechanical angular velocity was set to start from 0 r / min and increased to the rated mechanical angular velocity of 3000 r / min with constant acceleration. Figure 8 The mechanical angular velocity response curves for PI, traditional MPC, and PE-CMPC are shown.

[0330] like Figure 9 As shown, the mechanical angular velocity tracking error is evaluated for three control methods. The comparative tests were conducted, and the performance of the control strategies is listed in Table 2. The root mean square of the tracking error. This represents the maximum absolute value of the tracking error.

[0331]

[0332] It can be seen that neither PI nor traditional MPC can meet the control objective. The mechanical angular velocity tracking error of PE-CMPC meets the preset error boundary throughout the entire process. It also 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 Lundberg observer Strictly limited by the RCI set Within the range.

[0333] To further verify the dynamic tracking performance of PE-CMPC for periodic reference signals, the reference mechanical angular velocity was set as... . Figure 11 and Figure 14 They are respectively no-load and constant load. Mechanical angular velocity response curves for three control strategies under two operating conditions.

[0334] like Figure 12 and Figure 15 As shown, under no-load and load conditions, embodiments of this application address mechanical angular velocity tracking errors for three control strategies. The comparative tests were conducted, and the performance of the control strategies is listed in Table 3. It can be seen that the traditional MPC exhibits better tracking performance than PI, but it exceeds the preset error band near the peaks and troughs. Conversely, the tracking error of PE-CMPC remained within the error band throughout the entire process. Internally, under no-load conditions, the root mean square error of the traditional MPC is 13.46 r / min, and the root mean square error of the PE-CMPC is 11.09 r / min, a decrease of 17.61%. Under load conditions, the root mean square error of the traditional MPC is 18.92 r / min, and the root mean square error of the PE-CMPC is 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 loaded conditions, the tracking error of the estimated mechanical angular velocity based on the Romberg observer is... All can be strictly restricted by the RCI set constraints in MPC. Within the range.

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

[0338] This application provides a PMSM angular velocity control device based on online optimization of the objective function, including:

[0339] Motor model building module 1 is configured to construct the discrete mechanical motion equations of a permanent magnet synchronous motor, determine the constraints of the q-axis current of the permanent magnet synchronous motor using the maximum torque-to-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 constraints of the q-axis current and the performance constraints.

[0340] Problem transformation module 2 is configured to construct the objective function of the mechanical angular velocity control strategy for the augmented permanent magnet synchronous motor using a continuous set model at time k. Based on the discrete mechanical motion equations and robust control invariant set of the permanent magnet synchronous motor, the objective function is transformed into a least-norm 2 problem. The constraints of the decision variables of the least-norm problem are determined, and then the least-norm problem is transformed into a least-norm 2 problem with invariant constraint set.

[0341] 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. It uses the projected positive set method to solve the least-norm problem with invariant constraint set to obtain the constraint optimal solution. Based on the constraint optimal solution, it calculates the optimal q-axis current at time k.

[0342] Figure 18 This is a schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present invention. For example... Figure 18 As shown, the electronic device in this embodiment includes a processor 1801 and a memory 1802; wherein the memory 1802 is used to store computer execution instructions; and the processor 1801 is used to execute the computer execution instructions stored in the memory to implement the various steps performed by the electronic device in the above embodiment. For details, please refer to the relevant descriptions in the foregoing method embodiments.

[0343] Alternatively, the memory 1802 can be either standalone or integrated with the processor 1801.

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

[0345] This invention also provides a computer storage medium storing computer execution instructions, which, when executed by the processor 1801, implement the above method.

[0346] This invention also provides a computer program product, including a computer program that, when executed by a processor 1801, implements the above-described method.

[0347] In the embodiments provided by this invention, 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 instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0348] The modules described as separate components may or may not be physically separate. The 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 units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0349] Furthermore, the functional modules in the various embodiments of this invention can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit formed by the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0350] The integrated modules implemented as software functional modules described above can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor 1801 to execute certain steps of the methods of the various embodiments of this application.

[0351] It should be understood that the processor 1801 described above can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor, or the processor 1801 can be any conventional processor 1801. The steps of the method disclosed in this invention can be directly manifested as the hardware processor 1801 executing the steps, or as a combination of hardware and software modules within the processor 1801 executing the steps.

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

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

[0354] The aforementioned storage medium can be implemented from any type of volatile or non-volatile storage 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 can be any available medium accessible to general-purpose or special-purpose computers.

[0355] An exemplary storage medium is coupled to a processor 1801, enabling the processor 1801 to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor 1801. The processor 1801 and the storage medium can reside in an application-specific integrated circuit (ASIC). Alternatively, the processor 1801 and the storage medium can exist as discrete components in an electronic device or a host device.

[0356] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to 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; and 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, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions 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 the objective function, characterized in that, Includes the following steps: Discrete mechanical motion equations of a permanent magnet synchronous motor are constructed, and the constraint conditions of the q-axis current of the permanent magnet synchronous motor are determined by the 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 constraint and the performance constraint. For the objective function of the continuous set model used to predict the mechanical angular velocity control strategy of the augmented permanent magnet synchronous motor at time k, the objective function is transformed into a least-norm 2 problem based on the discrete mechanical motion equations and robust control invariant set of the permanent magnet synchronous motor. The constraints of the decision variables of the least-norm 2 problem are determined, and then the least-norm 2 problem is transformed into a least-norm 2 problem with 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 2 norm problem with invariant constraint set is solved by the projected positive set method to obtain the constraint optimal solution. The optimal q-axis current at time k is calculated based on the constraint optimal solution.

2. The PMSM angular velocity control method based on online optimization of the objective function according to claim 1, characterized in that, The discrete mechanical motion equations of the permanent magnet synchronous motor are as follows: Where k represents time k, T s Where J is the sampling period, J is the moment of inertia, and b is the sampling period. f Let i be the coefficient of friction. q Let ψ be the q-axis current. f For permanent magnet flux linkage, p is the number of pole pairs, T L ω is the load torque, G is the mechanical angular velocity, H is the state matrix of the permanent magnet synchronous motor angular velocity loop, and H is the input matrix of the permanent magnet synchronous motor angular velocity loop. In a surface-mounted permanent magnet synchronous motor, the d-axis inductance is equal to the q-axis inductance. When the maximum torque-to-current ratio control method is used, i.e., the d-axis current i d In the =0 control mode, the constraint condition for the q-axis current of the permanent magnet synchronous motor is: Among them, I c Let |I| be the allowable set of the q-axis current. max For the maximum allowable current, I N Rated current, It is the space of real numbers.

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 constructed. Based on the constraints of the q-axis current and performance constraints, a robust control invariant set is constructed, specifically including: Under the premise of satisfying the constraint condition of the q-axis current, the state variable ω(k) of the permanent magnet synchronous motor at time k continuously and unbiasedly tracks the reference state variable ω at time k with bounded error. r (k), which is the tracking error of the state variables of the permanent magnet synchronous motor |ω(k)-ω r (k)| The following performance constraints must be met: Where ε represents the tracking error threshold; Indicates any, Represents positive integers; The reference state variables satisfy the following equations: Where, ω r (k+1) represents the reference state variable at time k+1, ω r (k) represents the reference state variable at time k, and Δ is the rate of change of the reference state variable; Considering external disturbances and parameter mismatch, the lumped disturbance d ω Defined as: Where, ψ f0 This is the nominal value of the permanent magnet flux linkage. This is the reference value for the q-axis current; Introducing an extended permanent magnet synchronous motor, its corresponding model is represented as: Among them, A e For the extended state matrix of the permanent magnet synchronous motor, B e For the input matrix of the extended permanent magnet synchronous motor, C e For the output matrix of the extended permanent magnet synchronous motor; n d =(d ω (k+1)-d ω (k)) / T s Let d be the rate of change of the lumped disturbance. ω (k+1) represents the lumped disturbance at time k+1, d ω (k) represents the lumped disturbance at time k; y is the output of the extended permanent magnet synchronous motor. For the extended state variables of permanent magnet synchronous motors, For extended control inputs of permanent magnet synchronous motors; For the extended permanent magnet synchronous motor state variable x e Design the Luneburg observer, whose corresponding expression is: in, For the extended state variable x of the permanent magnet synchronous motor e The estimated value, where T represents the transpose of the matrix. These are estimated values ​​for the state variables of the permanent magnet synchronous motor. This is an estimate of the lumped disturbance; l o Gain for the Romberg observer; The estimation error of the state variables of the extended permanent magnet synchronous motor is defined as follows: Subtracting the expression for the extended permanent magnet synchronous motor model from the expression for the Luneburg observer, we obtain the following equation: in, The estimation error of the extended state variables of the permanent magnet synchronous motor at time k is represented. The estimation error of the extended state variables of the permanent magnet synchronous motor at time k+1 is represented. Establish recursive dynamics and construct an augmented state variable by combining the state variables of the actual permanent magnet synchronous motor with those of the extended permanent magnet synchronous motor. The corresponding augmented permanent magnet synchronous motor model is described as follows: Where A is the state matrix of the augmented permanent magnet synchronous motor, B is the input matrix of the augmented permanent magnet synchronous motor, F is the lumped disturbance gain matrix of the augmented permanent magnet synchronous motor, and C is the output matrix of the augmented permanent magnet synchronous motor. Based on Lyapunov's stability theory, the gain l is chosen. o Ensure that the closed-loop error system matrix satisfies the spectral radius condition ρ(A) e -l o C e The result is that the estimation error asymptotically converges, thus implying that the Romberg observer is effective for any... Performance constraints for maintaining bounded estimation error: Where ρ represents the radius, A e -l o C e Let represent the closed-loop error system matrix; ω(k) represent the state variables of the permanent magnet synchronous motor at time k. Let Ω represent the estimated state variables of the permanent magnet synchronous motor at time k, ω(0) represent the state variables of the permanent magnet synchronous motor at time 0, and Ω p Let ε be the initial state set of the state variable ω of the permanent magnet synchronous motor; p Let ε be the estimation error threshold of the Luneburg observer, satisfying ε p >0; By combining the performance constraints of the tracking error of the state variables of the permanent magnet synchronous motor with the performance constraints of the estimation error of the Luneburg observer, the performance constraint conditions are transformed into the following equation: Where, ε e Estimates of the state variables of a permanent magnet synchronous motor The tracking error threshold satisfies ε e =ε-ε p ; Considering that the state variables, control input, and lumped disturbances of the augmented permanent magnet synchronous motor satisfy the following constraints: in, For the set of allowed state variables, To control the input tolerance set, To allow for aggregated disturbances. It is a three-dimensional real number space; The robust one-step set P(Ω) of the target set Ω represents the set under any possible perturbation. Below, there exists permissible control input. The process leads to the state set of the given set x(k+1)∈Ω in one step, i.e.: For the augmented permanent magnet synchronous motor model, x(k+1)=Ax(k)+Bu(k)+Fd ω (k), the state variables of the augmented permanent magnet synchronous motor satisfy If there exists an admissible control input such that x(k+1)∈Ω RCI Then the set Ω is called RCI It is a robust control-invariant set, that is: in, Indicates implication, Indicates existence; Maximum robust control invariant set Includes All robust control invariant sets within; when When, it is called Ω CI To control invariant sets; For the model and state variables, control inputs, and lumped disturbances of the augmented permanent magnet synchronous motor, given the state variable x∈Ω of the augmented permanent magnet synchronous motor... RCI For the control input u∈Ω of the augmented permanent magnet synchronous motor u (x) can always overcome lumped disturbances. Make Ax + Bu + Fd ω ∈Ω, that is: Among them, Ω u (x) is the admissible input set of the state variable x of the augmented permanent magnet synchronous motor; if x∈Ω RCI ,but if but Considering the model of the augmented permanent magnet synchronous motor, the performance constraints are achieved by defining the following set: in, This is the equivalent set of performance constraints. Therefore, the performance constraint is equivalent to: if Able to ensure the next step status We need to find more robust control invariant sets. satisfy: in, In the expression for the rate of change of the reference state variable ω r The allowed reference input set; remember The above formula is equivalent to: The equivalent set of the performance constraints is input into the improved inner approximation algorithm to obtain the robust control invariant set Ω. RCI ; The improved inner approximation algorithm is derived from an improvement on the traditional inner approximation algorithm, specifically including: Introducing a control invariant set Ω during initialization CI The improved initial set is The robust one-step set is improved as shown in the following equation: Among them, Ω m Let be the target set of the state variables of the augmented permanent magnet synchronous motor in the m-th iteration, and δ≥1 be an adjustable parameter. Ω m Improved robust one-step set; The iteration termination condition is improved as follows: in, Let m represent the improved target set in the m-th iteration. Let represent the improved target set in the (m+1)th iteration.

4. The PMSM angular velocity control method based on online optimization of the objective function according to claim 3, characterized in that, The objective function for predicting the mechanical angular velocity control strategy using the continuous set model at time k is: Where V represents the objective function, x(i|k) is the estimated value of the state variables of the augmented permanent magnet synchronous motor at the i-th step at time k, i = 1, 2, ..., N, where N is the prediction step size, x(i+1|k) is the estimated value of the state variables of the augmented permanent magnet synchronous motor at the (i+1)-th step at time k, and u(i|k) = I q (i|k) is the control input of the augmented permanent magnet synchronous motor at time k and step i, ω r As the reference state variable, q, r, and s are the first weighting coefficient, the second weighting coefficient, and the third weighting coefficient, respectively. Let b be an estimate of the lumped disturbance. c =3pψ f T s / (2J).

5. The PMSM angular velocity control method based on online optimization of the objective function according to claim 4, characterized in that, Based on the discrete mechanical motion equations and robust control invariant set of the permanent magnet synchronous motor, the objective function is transformed into a least-two norm problem. The constraints of the decision variables in the least-two norm problem are determined, and then the least-two norm problem is transformed into a least-two norm problem with invariant constraint sets. Specifically, this includes: Let X = [x(1|k),...,x(N|k)] T For the augmented state variable vector of the permanent magnet synchronous motor, U = [u(0|k),...,u(N-1|k)] T To augment the control input vector of the permanent magnet synchronous motor and X ref =[ω r ,...,ω r ] T To augment the reference state variable vector of the permanent magnet synchronous motor, the objective function is converted into matrix form, as shown in the following equation: Where C0 is a constant term, 1 N Let Q be a row vector consisting entirely of 1s, and let Q, R, and M be the first, second, and third weight vectors, respectively, with values ​​as follows: Q=q·I N ; M=s·I N ; Among them, I N It is an N-order identity 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: x(i+1|k)=Ax(i|k)+Bu(i|k); Based on the constraints of the state-space equation, the matrix expression between the state variable vector X and the control input vector U in the matrix form of the objective function is obtained, as shown in the following equation: Y = CX = CΦx(0|k) + CΓU; Where Φ represents the state weight and Γ represents the input weight, and their expressions are as follows: Substituting the matrix expression between the state variable vector X and the control input vector U into the matrix form of the objective function, we obtain the simplified objective function, as shown in the following equation: V=(X-X r ) T Q′(X-X r ); Among them, X r =-Q′ -T E′ T The vector of unconstrained optimal state variables. Q′=Q+R+(CΓ) -T M(CΓ) -1 For weighted matrices, For the reference state variable vector X ref The parameters of the change of the state variable x(0|k) at time k, -T indicates taking the inverse and then transposing, the problem of solving the simplified objective function constitutes the least 2 norm problem; Due to Q, R, and (CΓ) -T M(CΓ) -1 All are positive semi-definite matrices, therefore the weighted matrix retains the properties of a positive semi-definite matrix. The weighted matrix is ​​decomposed by Cholesky into Q′=L T Let L be an upper triangular matrix; let the equivalent decision variable be Y = LX and the equivalent unconstrained optimal solution be Y. r =LX r The simplified objective function is expressed as Y r An N-dimensional sphere with center at its center, i.e.: V=(YY r ) T (YY r ); Robust control invariant set Ω RCI Preserving convexity and possessing linear properties, it can therefore be expressed in the form of a linear inequality: Oh RCI ={X|A in X≤b in }; Among them, A in b in These are the coefficient matrix and constant vector of the inequality constraints, respectively; The final transformation yields the least-norm 2 problem for predicting mechanical angular velocity control using PMSM as follows: Where, min Y Y represents the minimum value, and st represents the constraint condition; In the above formula, A in L -1 and b in The value of does not change with the operating conditions, therefore the shape of the constraints on the decision variable Y = LX remains unchanged, and it can be equivalent to the constraint set A. in L -1 Y≤b in The overall displacement is LCΦx(0|k), therefore the problem of constructing the least 2 norm with invariant constraint set is: Where Z = Y - LCΦx(0|k) is the final decision variable, min Z Z represents the minimized value. r =Y r -LCΦx(0|k) 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-norm problem with invariant constraint set is solved using the projected positive set method to obtain the constraint-optimal solution. Based on this constraint-optimal solution, the optimal q-axis current at time k is calculated, specifically including: S31, according to Z r =Y r -LCΦx(0|k),X r =-Q′ -T H′ T Q′=Q+R+Γ -T MΓ -1 and Calculate the final unconstrained optimal solution Z r The initial effective constraint set A0 is determined based on the final unconstrained optimal solution, the least-norm problem with invariant constraint set, and the effective constraints, as shown in the following equation: A0={j|(A in L -1 ) j Z r >(b in ) j }; Among them, (A) in L -1 )j is the coefficient matrix A in L -1 The j-th row, (b in ) j b is a constant vector in The j-th element, A0, satisfies the inequality (A in L -1 ) j Z r >(b in ) j The set consisting of j; S32, the final unconstrained optimal solution is projected onto the effective constraint set A0 at the initial time. For each element A0(j) = j in the effective constraint set A0 at the initial time, the final unconstrained optimal solution is projected onto the hyperplane indexed by A0(j) using the following projection formula to obtain the corresponding projection point. in, Indicates that Z r Project onto the hyperplane indexed by A0(j). For the rows of the matrix indexed by A0(j), Let b be a constant vector indexed by A0(j). in Multiple elements; l represents any element in the effective constraint set A0 at the initial moment; the effective constraint set corresponding to each projection point is determined based on each projection point, the least 2 norm problem with the constraint set remaining unchanged, and the effective constraints, as shown in the following formula: S33, determine each projection point Effective constraint set The intersection ∪ l A0 (l) Whether it is included in the valid constraint set A0 at the initial time, i.e., whether it is satisfied. If satisfied Then according to A * =max(count(A0) (l) )) Calculate the final effective constraint set A * , where max(count(A0) (l) )) represents the set of valid constraint indices that appear most frequently, count represents the frequency counting function, and max represents taking the maximum value; The final unconstrained optimal solution is projected onto the final effective constraint set A using the following projection formula. * The constrained optimal solution Z is obtained on the intersection of multiple hyperplanes of the index. * : in, Indicates that Z r Projected onto A * On the intersection of multiple hyperplanes of the index, For A * Index matrix A in L -1 OK, For A * The constant vector b of the index in Multiple elements; The optimal solution Z under the constraints * Perform an inverse transformation to obtain the optimal state variable vector X * As shown in the following formula: X * =L -1 Z * +Φx(0|k); The optimal q-axis current at time k is calculated based on the constraints of the state-space equations, as shown in the following equation: Among them, X * (1) and X * (2) Let X represent the optimal state variable vector respectively. * The first and second values, i q * This represents the optimal q-axis current at time k; If not satisfied Then, the new valid constraints are obtained according to the following formula: c←∪ l A0 (l) -A0; Where ← represents assignment, and c represents a new valid constraint; Update the effective constraint set A0 = A0∪{c} with the new effective 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 an objective function, characterized in that, include: The motor model building module is configured to construct the discrete mechanical motion equations of the permanent magnet synchronous motor, determine the constraint conditions of the q-axis current of the permanent magnet synchronous motor using the 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 constraint conditions and performance constraints. The problem transformation module is configured to predict the objective function of the mechanical angular velocity control strategy for the augmented permanent magnet synchronous motor using a continuous set model at time k. Based on the discrete mechanical motion equations and robust control invariant set of the permanent magnet synchronous motor, the objective function is transformed into a least-norm 2 problem. The constraints of the decision variables of the least-norm 2 problem are determined, and then the least-norm 2 problem is transformed into a least-norm 2 problem with 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. It then uses the projected positive set method to solve the least-norm problem with invariant constraint set to obtain the optimal constraint solution. Based on the optimal constraint solution, it calculates the optimal q-axis current at time k.

8. An electronic device, comprising: One or more processors; 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 as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-6.

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