A method and system for controlling the speed of a permanent magnet synchronous motor

Abstract

This invention provides a method and system for controlling the speed of a permanent magnet synchronous motor, belonging to the field of motor control technology. The method first constructs a discrete-time mathematical model of the motor and an external system including lumped reference signals and lumped disturbances, and establishes a composite system model accordingly. Then, a dimension-reduced observer is constructed to estimate the external signals, and state and input transformations are performed in conjunction with regulator equations. Next, a constraint set for the transformed system is constructed, and the state variables are decomposed into nominal components, deterministic error components, and uncertain error components. Furthermore, a time-varying constraint compression set is dynamically constructed based on the errors, and an online model predictive control optimization problem with dynamically tightened constraints is solved to obtain the nominal control quantity. Finally, the nominal control quantity and the estimated external signals are combined to synthesize the actual control voltage. This invention effectively suppresses disturbances, strictly ensures system safety constraints, guarantees the recursive feasibility and closed-loop stability of the control, and improves the dynamic response speed.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, and in particular relates to a method and system for controlling the speed of a permanent magnet synchronous motor. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) have been widely used in high-end manufacturing, electric vehicles, and other fields due to their high power density and high efficiency. In these high-dynamic and high-precision applications, the control system not only needs to achieve accurate speed tracking but also must strictly meet safety constraints such as current and voltage to prevent equipment damage. However, in actual operation, motors are inevitably affected by complex disturbances such as model parameter uncertainties, unmodeled dynamics, and sudden load changes. This makes achieving high-precision and robust speed control while ensuring system safety a crucial research area.

[0003] To address the aforementioned challenges, advanced control methods such as model predictive control have been introduced into the control of permanent magnet synchronous motors (PMSMs). This generally involves the following steps: First, establishing a motor system model that includes uncertainties; second, decomposing the system state into a nominal component determined by the optimization variables and an error component representing the uncertainty; then, by designing a fixed, conservative constraint compression set, the influence of the uncertainty error component is "subtracted" from the system constraints, thereby constructing an optimization problem based on the nominal system; finally, solving this optimization problem yields the control variables. This method aims to ensure, through offline computation, that constraints are not violated under all possible uncertainty scenarios.

[0004] However, starting from the step of "decomposing the system state into two components," since it only contains one deterministic component, the characterization of uncertainty is rather coarse, leading to an overly conservative constraint compression set. This directly results in technical problems such as slow dynamic response and reduced anti-interference capability. More importantly, from the perspective of "designing a fixed constraint compression set" and the subsequent optimization problem construction steps, this scheme cannot theoretically guarantee the recursive feasibility of the controller in long-term operation, and also lacks rigorous proof of the asymptotic stability of the closed-loop system. In practical applications, the controller may be unsolvable in some situations, leading to system runaway, or it may not be able to guarantee that the tracking error eventually converges to zero. Therefore, how to design a speed control method that can strictly guarantee system safety constraints in the presence of disturbances, ensure recursive feasibility and closed-loop stability, and possess fast dynamic response capability is a technical problem that urgently needs to be solved. Summary of the Invention

[0005] This invention provides a speed control method and system for permanent magnet synchronous motors, which can strictly ensure system safety constraints and ensure recursive feasibility and closed-loop stability when there is interference in the permanent magnet synchronous motor, while also having a fast dynamic response capability for speed control.

[0006] In a first aspect, the present invention provides a method for controlling the speed of a permanent magnet synchronous motor, comprising:

[0007] Construct a discrete-time mathematical model for a permanent magnet synchronous motor;

[0008] An external system containing lumped reference signal and lumped interference is constructed based on the discrete-time mathematical model of the permanent magnet synchronous motor.

[0009] A system model in composite state-space form is constructed based on the discrete-time mathematical model, the external system, and the velocity tracking error.

[0010] A dimension-reduced observer is constructed to estimate the signal of the external system based on the measurable system state and tracking error, and combined with the preset regulator equation, the system model is transformed in terms of state and input to obtain the transformed system.

[0011] Construct a constraint set for the state variables and control inputs of the transformation system;

[0012] The state variables of the transformed system are decomposed into nominal state components, deterministic error components, and uncertain error components;

[0013] Based on the dynamic characteristics of deterministic and uncertain error components, a time-varying constrained compaction set is constructed.

[0014] Based on the nominal state components, constraint set, and constraint tightening set at each sampling time, a model predictive control optimization problem with dynamic tightening constraints is constructed and solved to obtain the nominal control quantity at the current time.

[0015] Based on the nominal control quantity at the current moment and the estimated external signal, a control voltage is constructed to act on the permanent magnet synchronous motor to control the speed of the permanent magnet synchronous motor.

[0016] Optionally, the construction of the discrete-time mathematical model of the permanent magnet synchronous motor includes:

[0017] Constructing a continuous-time mathematical model for a permanent magnet synchronous motor:

[0018] ;

[0019] in, J is the derivative of the mechanical angular velocity; r n is the rotor's moment of inertia. p It is the extreme logarithm; For rotor flux linkage; i q B is the q-axis stator current. f ω is the coefficient of friction; ω is the mechanical angular velocity; d ω This refers to the interference term in the velocity loop; L is the derivative of the q-axis stator current; s For stator inductance; u q R is the q-axis stator voltage; s d is the stator resistance; q This refers to the interference term in the current loop;

[0020] Based on the continuous-time mathematical model of the permanent magnet synchronous motor, a discrete-time mathematical model of the permanent magnet synchronous motor is constructed:

[0021] ;

[0022] Where, ω k+1 t represents the mechanical angular velocity of the permanent magnet synchronous motor at the (k+1)th sampling time. s ω is the sampling period; k Let i be the mechanical angular velocity of the permanent magnet synchronous motor at the k-th sampling time; q,k d is the q-axis stator current at the k-th sampling time; ω,k The discrete-time lumped interference of the speed loop of the permanent magnet synchronous motor at the k-th sampling time; i q,k+1 u is the q-axis stator current at the (k+1)th sampling time; q,k d is the q-axis stator voltage at the k-th sampling time; q,k This represents the discrete-time lumped disturbance of the q-axis current loop of the permanent magnet synchronous motor at the k-th sampling time.

[0023] Optionally, the construction of an external system containing lumped reference signals and lumped interference based on the discrete-time mathematical model of the permanent magnet synchronous motor includes:

[0024] Construct a high-order discrete-time disturbance vector δ for the velocity loop ω,k and the q-axis current loop discrete-time higher-order disturbance vector δ q,k The expression:

[0025] ;

[0026] Where, d ω,k The discrete-time lumped interference of the speed loop of the permanent magnet synchronous motor at the k-th sampling time; h i,k Let be the i-th discrete-time difference term of the velocity loop disturbance; i = 1, 2, ..., n; n is the total order of higher-order disturbance modeling; T represents the transpose of the matrix; d q,k The discrete-time lumped interference of the q-axis current loop of the permanent magnet synchronous motor at the kth sampling time; This is the i-th discrete-time difference term of the current loop disturbance;

[0027] Construct the lumped interference vector δ of the permanent magnet synchronous motor at the k-th sampling time. k The expression:

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] Where, δ k+1 Sk+1 represents the lumped interference vector of the permanent magnet synchronous motor at the (k+1)th sampling time; S1 is the discrete-time state transition matrix of the interference vector; 0 represents the zero matrix; Sk+1 ω S is the discrete-time state transition matrix for the higher-order disturbance vector of the velocity loop; q The discrete-time state transition matrix is ​​the higher-order disturbance vector of the q-axis current loop; t s The sampling period;

[0033] Construct the lumped reference signal α of the permanent magnet synchronous motor at the k-th sampling time. k The expression:

[0034] ;

[0035] Where, r k α is the reference speed of the permanent magnet synchronous motor at the k-th sampling time; k+1 S1 is the lumped reference signal of the permanent magnet synchronous motor at the (k+1)th sampling time; S2 is the discrete-time state transition matrix of the reference signal vector;

[0036] Construct an expression for the external system S that includes the lumped reference signal and the lumped interference:

[0037] .

[0038] Optionally, the construction of a system model in composite state-space form based on the discrete-time mathematical model, the external system, and the velocity tracking error includes:

[0039] The expression for constructing a system model in composite state-space form:

[0040] ;

[0041] ;

[0042] ;

[0043] C = [0, 1];

[0044] D=[-1,0];

[0045] ;

[0046] Where, x k+1 Let x be the state vector of the permanent magnet synchronous motor system at the (k+1)th sampling time; A is the discrete-time state matrix of the permanent magnet synchronous motor system; k Let B be the state vector of the permanent magnet synchronous motor system at the k-th sampling time; let B be the control input matrix of the discrete-time permanent magnet synchronous motor system; u k =u q,k ;u k u is the input variable for the q-axis control voltage of the permanent magnet synchronous motor at the k-th sampling time. q,k B is the q-axis stator voltage at the k-th sampling time; d v is the disturbance input matrix for the discrete-time system of a permanent magnet synchronous motor. k Let K be the vector of the external signal at the k-th sampling time. ;α k δ is the lumped reference signal of the permanent magnet synchronous motor at the k-th sampling time; k Let y be the lumped interference vector of the permanent magnet synchronous motor at the k-th sampling time; k Let v be the output variable of the permanent magnet synchronous motor system at the k-th sampling time; C is the output matrix of the discrete-time permanent magnet synchronous motor system; v k+1 Let S be the external signal vector at the (k+1)th sampling time; S is the external system containing the lumped reference signal and lumped interference; e k ω represents the speed tracking error of the permanent magnet synchronous motor at the k-th sampling time; D is the feedforward output matrix of the discrete-time system of the permanent magnet synchronous motor; k Let r be the mechanical angular velocity of the permanent magnet synchronous motor at the k-th sampling time; k i is the reference speed of the permanent magnet synchronous motor at the k-th sampling time; q,k θ1 represents the q-axis stator current at the k-th sampling time; 0 represents the zero matrix; T represents the transpose of the matrix; θ1 is the standard basis vector, with the first element of θ1 being 1 and the remaining elements being 0; n is the total order of higher-order disturbance modeling.

[0047] Optionally, the construction of the dimensionality-reduced observer to estimate the signal of the external system based on the measurable system state and tracking error, and the combination of a preset regulator equation to perform state and input transformation on the system model to obtain the transformed system, includes:

[0048] The expression for the augmented model is constructed based on the state vector of the permanent magnet synchronous motor system and the external signal vector at the k-th sampling time:

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] Among them, z k+1 Let A be the state vector of the augmented permanent magnet synchronous motor system at the (k+1)th sampling time; z z is the state transition matrix of the augmented model of the permanent magnet synchronous motor; k Let be the state vector of the augmented permanent magnet synchronous motor system at the k-th sampling time. ;x k v is the state vector of the permanent magnet synchronous motor system at the k-th sampling time; k Let T be the external signal vector at the k-th sampling time; T represents the transpose of the matrix; A is the state matrix of the discrete-time system of the permanent magnet synchronous motor; S is the external system including the lumped reference signal and lumped interference; B d B represents the disturbance input matrix of the discrete-time system of a permanent magnet synchronous motor; 0 represents the zero matrix; z B is the control input matrix of the augmented model of the permanent magnet synchronous motor; U is the control input matrix of the discrete-time system of the permanent magnet synchronous motor; k β is the input variable for the q-axis control voltage of the permanent magnet synchronous motor at the k-th sampling time. k The augmented model's measurable output vector at the k-th sampling time; C z I is the output matrix of the augmented model of the permanent magnet synchronous motor; C is the output matrix of the discrete-time system of the permanent magnet synchronous motor; D is the feedforward output matrix of the discrete-time system of the permanent magnet synchronous motor.

[0054] Construct v based on the augmented model k The expression for the dimension reduction observer:

[0055] ;

[0056] ;

[0057] ;

[0058] Where, ξ k+1 Let ξ be the internal state vector of the reduced-dimensional observer at the (k+1)th sampling time; H is the internal state transition matrix of the reduced-dimensional observer; ξ k Let F be the internal state vector of the dimension-reduced observer at the k-th sampling time; F is the measurable input feedback matrix of the dimension-reduced observer; and Ψ is the control input feedforward matrix of the dimension-reduced observer. For v k The estimated value; L is the gain matrix of the dimension-reduced observer; M is the coupling matrix of the dimension-reduced observer design; Output the state-state correlation matrix for the augmented model;

[0059] The estimation error of the external system signal is calculated based on the augmented model and the dimension-reduced observer:

[0060] ;

[0061] in, The estimation error of the external system signal at the (k+1)th sampling time; v is the estimated value of the external system signal at the (k+1)th sampling time; k+1 The vector of the external signal at the (k+1)th sampling time; The estimation error of the external system signal at the k-th sampling time is denoted as .

[0062] Construct the expression for the regulator equation:

[0063] ;

[0064] Where Π is the state feedforward mapping matrix; Γ is the control input feedforward mapping matrix;

[0065] Construct the expression for the transform system based on the estimated value of the external system signal and the regulator equation:

[0066] ;

[0067] in, The state vector of the system is transformed at the (k+1)th sampling time; x k+1 Let be the state vector of the permanent magnet synchronous motor system at the (k+1)th sampling time. Transform the system's state vector at the k-th sampling time; The control variables of the system are transformed at the k-th sampling time. Λ represents the interference term of the transform system at the k-th sampling time; Λ is the equivalent interference gain matrix of the transform system.

[0068] Optionally, the constraint set for constructing the state variables and control inputs of the transformation system includes:

[0069] Construct the constraint set expression for the state variables and control inputs of the transformed system:

[0070] ;

[0071] in, The state vector of the system is transformed at the k-th sampling time; X k X represents the set of constraints that transform the system state variables at the k-th sampling time; X is the allowable region of the state space. Π represents the Pontryagin difference; Π is the state feedforward mapping matrix. Y is the control variable of the system at the k-th sampling time. kΓ represents the set of constraints that transform the system control variables at the k-th sampling time; U is the allowable region of the control input space; Γ is the control input feedforward mapping matrix. This is the set of estimated values ​​of the external signal at the k-th sampling time. X is the set of estimated values ​​of the external signal at the (k+1)th sampling time; k+1 Y is the set of constraints that transform the system state variables at the (k+1)th sampling time. k+1 The set of constraints for changing the system control variables at the (k+1)th sampling time.

[0072] Optionally, constructing a time-varying constrained compaction set based on the dynamic characteristics of the deterministic error component and the uncertain error component includes:

[0073] Construct the dynamic equation expressions for the deterministic error components and the uncertain error components:

[0074] ;

[0075] in, This is the deterministic error component at the (k+1)th sampling time. A represents the deterministic error component at the k-th sampling time. K The state matrix of the closed-loop nominal system; This represents the uncertainty error component at the (k+1)th sampling time. This represents the uncertainty error component at the k-th sampling time. Let A be the disturbance term of the transformed system at the k-th sampling time; let A be the state matrix of the discrete-time system of the permanent magnet synchronous motor; let B be the control input matrix of the discrete-time system of the permanent magnet synchronous motor; let K be the feedback gain matrix; ρ(A K )<1;ρ(A K ) is A K spectral radius; This represents the initial deterministic error component; The state of the system is changed at the initial moment; The initial state of the nominal system; This represents the initial uncertainty error component;

[0076] Construct the recursive relation satisfied by the constraint-compressed set based on the state matrix of the closed-loop nominal system:

[0077] ;

[0078] Among them, S k+1 For the uncertainty error component at the (k+1)th sampling time Set; S k The uncertainty error component at the k-th sampling time The set in which it belongs; Minkowski addition; for The set it belongs to.

[0079] Optionally, the step of constructing and solving a model predictive control optimization problem with dynamic tightening constraints based on the nominal state components, constraint set, and constraint tightening set at each sampling time to obtain the nominal control quantity at the current time includes:

[0080] Expressions for constructing nominal state components:

[0081] ;

[0082] Where A is the state matrix of the discrete-time system of the permanent magnet synchronous motor; B is the control input matrix of the discrete-time system of the permanent magnet synchronous motor. The state of the system is defined at the (k+1)th sampling time. The state of the system is defined at the k-th sampling time. The nominal system control input is defined at the k-th sampling time.

[0083] Construct a model-predictive control optimization problem expression based on nominal state components:

[0084] ;

[0085] in, This represents the optimal value function for the optimization problem at the k-th sampling time. Let N be the state vector of the transformed system at the k-th sampling time; N is the prediction time domain. The predicted value of the nominal system state at the k+i' time step is the value of the k-th sampling time step. The predicted value of the nominal system control input at the k-th sampling time for the (k+i')-th future time is given by the k-th sampling time. Represents the terminal cost function; It represents the predicted value of the nominal system state at the k+Nth time from the kth sampling time. Represents the stage cost function; Q is the first positive definite matrix; R is the second positive definite matrix; P f A is the third positive definite matrix; K Let be the state matrix of the closed-loop nominal system; T represents the transpose of the matrix; K is the feedback gain matrix; Denotes the Euclidean norm;

[0086] Constructing constraints for the model predictive control optimization problem:

[0087] ;

[0088] in, It is the predicted value of the nominal system state at the k+i'+1 time point in the future, based on the k-th sampling time. The nominal initial value of the system state is defined at the k-th sampling time. The state vector of the system is transformed at the k-th sampling time; X f For the terminal constraint set; For A K i raised to the power of i'; This represents the set of constraints that will transform the system state variables at the (k+i)th time in the future; For the i'th uncertainty error component The set in which it belongs; This represents the set of constraints that will transform the system control variables at the (k+i)th time in the future. For A K S to the power of N; N For the Nth uncertainty error component The set in which it belongs;

[0089] Constructing the optimal solution to the model predictive control optimization problem:

[0090] ;

[0091] in, This is the sequence of optimal solutions for the nominal control quantity at the k-th sampling time. The optimal solution for the initial nominal control quantity at the k-th sampling time; The optimal solution for the nominal control quantity at the next k+N-1 time steps; This is the nominal system optimal state sequence at the k-th sampling time. This represents the initial nominal system optimal state at the k-th sampling time. This represents the nominal optimal state of the system at the (k+N)th time step.

[0092] Construct the nominal control quantity of the transformed system at the current moment based on the optimal solution:

[0093] .

[0094] Optionally, the step of constructing a control voltage for the permanent magnet synchronous motor based on the nominal control quantity at the current moment and the estimated external signal to control the speed of the permanent magnet synchronous motor includes:

[0095] Construct the expression for the control voltage acting on the permanent magnet synchronous motor:

[0096] ;

[0097] in, The control voltage applied to the permanent magnet synchronous motor at the kth sampling time; Let Γ be the nominal control quantity at the k-th sampling time; Γ is the control input feedforward mapping matrix. This is the estimated value of the external system signal at the k-th sampling time.

[0098] In a second aspect, the present invention provides a permanent magnet synchronous motor speed control system, comprising:

[0099] The first building module is used to build the discrete-time mathematical model of the permanent magnet synchronous motor;

[0100] The second construction module is used to construct an external system containing lumped reference signals and lumped interference based on the discrete-time mathematical model of the permanent magnet synchronous motor.

[0101] The third building module is used to construct a system model in composite state-space form based on the discrete-time mathematical model, the external system, and the velocity tracking error.

[0102] The fourth construction module is used to construct a dimension-reduced observer to estimate the signal of the external system based on the measurable system state and tracking error, and to perform state and input transformation on the system model in combination with the preset regulator equation to obtain the transformed system.

[0103] The fifth construction module is used to construct the constraint set of state variables and control inputs of the transformation system;

[0104] The variable decomposition module is used to decompose the state variables of the transformed system into nominal state components, deterministic error components, and uncertain error components.

[0105] The sixth construction module is used to construct a time-varying constrained compaction set based on the dynamic characteristics of deterministic and uncertain error components.

[0106] The seventh construction module is used to construct and solve a model predictive control optimization problem with dynamic tightening constraints based on the nominal state components, constraint set, and constraint tightening set at each sampling time, and to obtain the nominal control quantity at the current time.

[0107] The eighth construction module is used to construct the control voltage applied to the permanent magnet synchronous motor based on the nominal control quantity at the current moment and the estimated external signal, so as to control the speed of the permanent magnet synchronous motor.

[0108] This invention provides a method and system for speed control of a permanent magnet synchronous motor. The method constructs an external system comprising a lumped reference signal and lumped interference, unifying speed tracking and interference suppression within an output regulation framework. By combining a dimension-reduced observer to perform real-time estimation of the external system signal, effective observation and feedforward compensation of unknown interference and the dynamics of the reference signal can be achieved. This enables the controller to actively counteract interference effects and accurately follow the reference signal, thereby significantly improving the system's robustness and speed tracking accuracy under complex interference environments.

[0109] By constructing a constraint set of state variables and control inputs for the transformed system, and within the framework of Model Predictive Control (MPC), combining a time-varying constraint compression set to handle the influence of error components after state decomposition, this invention can rigorously consider and ensure that actual safety constraints such as current and voltage are always satisfied during the design phase. This constraint processing method based on set operations provides a theoretical guarantee for the safe operation of the system.

[0110] A three-component decomposition strategy is adopted, which decomposes the state variables of a changing system into nominal state components, deterministic error components, and uncertain error components. Compared with the traditional two-component decomposition, this strategy can more finely describe the system dynamics and effectively reduce the conservatism of the uncertainty description. Based on this, a "model predictive control optimization problem with dynamically tightened constraints" is constructed and solved, whose constraint set can be adjusted in real time according to the dynamic characteristics of the error components. This not only endows the controller with the ability to handle time-varying uncertainties and improves the dynamic response speed, but also rigorously proves the "recursive feasibility" of the control strategy and the "asymptotic stability" of the closed-loop system in theory, avoiding the risk of no solution or instability that may occur with traditional methods, and ensuring the long-term reliable operation of the control system. Attached Figure Description

[0111] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0112] Figure 1 A flowchart illustrating a method for controlling the speed of a permanent magnet synchronous motor, provided in an embodiment of the present invention;

[0113] Figure 2 A comparison chart of the overall dynamic response and anti-interference performance of the system provided in this embodiment of the invention;

[0114] Figure 3 This is a comparison chart of dynamic response characteristics during the startup phase provided in an embodiment of the present invention;

[0115] Figure 4Comparison chart of time-varying load disturbance suppression performance provided in embodiments of the present invention

[0116] Figure 5 The diagram shows the verification results of the overcurrent protection mechanism provided in the embodiments of the present invention.

[0117] Figure 6 This is a schematic diagram of a permanent magnet synchronous motor speed control system provided in an embodiment of the present invention. Detailed Implementation

[0118] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0119] Example 1

[0120] like Figure 1 As shown, an embodiment of the present invention provides a method for controlling the speed of a permanent magnet synchronous motor, comprising:

[0121] Step 101: Construct the discrete-time mathematical model of the permanent magnet synchronous motor.

[0122] In this embodiment, a non-cascaded control structure for a permanent magnet synchronous motor is adopted, and the d-axis current loop uses a PI controller with a d-axis current reference value. Setting it to zero, we construct a continuous-time mathematical model for the surface-mounted permanent magnet synchronous motor:

[0123] (1.1)

[0124] in, J is the derivative of the mechanical angular velocity; r n is the rotor's moment of inertia. p It is the extreme logarithm; For rotor flux linkage; i q B is the q-axis stator current. f ω is the coefficient of friction; ω is the mechanical angular velocity; d ω This refers to the interference term in the velocity loop; L is the derivative of the q-axis stator current; s For stator inductance; u q R is the q-axis stator voltage; s d is the stator resistance; q This is the interference term in the current loop.

[0125] The continuous model is transformed into a discrete-time model using the forward Euler discretization method:

[0126] (1.2)

[0127] Where, ω k+1 t represents the mechanical angular velocity of the permanent magnet synchronous motor at the (k+1)th sampling time. s ω is the sampling period; k Let i be the mechanical angular velocity of the permanent magnet synchronous motor at the k-th sampling time; q,k d is the q-axis stator current at the k-th sampling time; ω,k The discrete-time lumped interference of the speed loop of the permanent magnet synchronous motor at the k-th sampling time; i q,k+1 u is the q-axis stator current at the (k+1)th sampling time; q,k d is the q-axis stator voltage at the k-th sampling time; q,k This represents the discrete-time lumped disturbance of the q-axis current loop of the permanent magnet synchronous motor at the k-th sampling time.

[0128] Step 102: Construct an external system containing lumped reference signal and lumped interference based on the discrete-time mathematical model of the permanent magnet synchronous motor.

[0129] During the operation of a permanent magnet synchronous motor servo system, the system may be affected by various disturbances, including model parameter uncertainties, unmodeled dynamic characteristics, and external load interference. Explicitly establishing an accurate mathematical model for all disturbances is often difficult. Therefore, this embodiment employs a high-order polynomial model to uniformly approximate different types of disturbances. Based on the above high-order disturbance modeling method, a discrete-time high-order disturbance vector δ for the speed loop is constructed. ω,k and the q-axis current loop discrete-time higher-order disturbance vector δ q,k The expression:

[0130] (1.3)

[0131] Where, d ω,k The discrete-time lumped interference of the speed loop of the permanent magnet synchronous motor at the k-th sampling time; h i,k Let be the i-th discrete-time difference term of the velocity loop disturbance; i = 1, 2, ..., n; n is the total order of higher-order disturbance modeling; T represents the transpose of the matrix; d q,k The discrete-time lumped interference of the q-axis current loop of the permanent magnet synchronous motor at the kth sampling time; This is the i-th discrete-time difference term of the current loop disturbance.

[0132] Assumption That is, the highest-order difference term remains constant. The higher-order difference terms satisfy the following dynamic relationship:

[0133] (1.4)

[0134] Construct the lumped interference vector δ of the permanent magnet synchronous motor at the k-th sampling time. k The expression:

[0135] ;

[0136] ;

[0137] (1.5)

[0138] Where, δ k+1 Sk+1 represents the lumped interference vector of the permanent magnet synchronous motor at the (k+1)th sampling time; S1 is the discrete-time state transition matrix of the interference vector; 0 represents the zero matrix; Sk+1 ω S is the discrete-time state transition matrix for the higher-order disturbance vector of the velocity loop; q The discrete-time state transition matrix is ​​the higher-order disturbance vector of the q-axis current loop; t s The sampling period.

[0139] Construct the lumped reference signal α of the permanent magnet synchronous motor at the k-th sampling time. k The expression:

[0140] (1.6)

[0141] Where, r k α is the reference speed of the permanent magnet synchronous motor at the k-th sampling time; k+1 S1 is the lumped reference signal of the permanent magnet synchronous motor at the (k+1)th sampling time; S2 is the discrete-time state transition matrix of the reference signal vector.

[0142] Construct an expression for the external system S that includes the lumped reference signal and the lumped interference:

[0143] (1.7)

[0144] Among them, v k Let be the external signal vector at the k-th sampling time.

[0145] In this step, the reference signal and interference are modeled as a unified external system (1.7), which can uniformly handle the speed tracking and interference suppression problems of permanent magnet synchronous motors under the output regulation framework, providing a theoretical basis for achieving high-performance control.

[0146] Step 103: Construct a system model in composite state-space form based on the discrete-time mathematical model, the external system, and the velocity tracking error.

[0147] For example, the expression for constructing a system model in composite state-space form is as follows:

[0148] (1.8)

[0149] ;

[0150] ;

[0151] C = [0, 1];

[0152] D=[-1,0];

[0153] ;

[0154] Where, x k+1 Let x be the state vector of the permanent magnet synchronous motor system at the (k+1)th sampling time; A is the discrete-time state matrix of the permanent magnet synchronous motor system; k Let B be the state vector of the permanent magnet synchronous motor system at the k-th sampling time; let B be the control input matrix of the discrete-time permanent magnet synchronous motor system; u k =u q,k ;u k u is the input variable for the q-axis control voltage of the permanent magnet synchronous motor at the k-th sampling time. q,k B is the q-axis stator voltage at the k-th sampling time; d v is the disturbance input matrix for the discrete-time system of a permanent magnet synchronous motor. k Let K be the vector of the external signal at the k-th sampling time. ;α k δ is the lumped reference signal of the permanent magnet synchronous motor at the k-th sampling time; k Let y be the lumped interference vector of the permanent magnet synchronous motor at the k-th sampling time; k Let v be the output variable of the permanent magnet synchronous motor system at the k-th sampling time; C is the output matrix of the discrete-time permanent magnet synchronous motor system; v k+1 Let S be the external signal vector at the (k+1)th sampling time; S is the external system containing the lumped reference signal and lumped interference; e k ω represents the speed tracking error of the permanent magnet synchronous motor at the k-th sampling time; D is the feedforward output matrix of the discrete-time system of the permanent magnet synchronous motor; k Let r be the mechanical angular velocity of the permanent magnet synchronous motor at the k-th sampling time; k i is the reference speed of the permanent magnet synchronous motor at the k-th sampling time; q,k Let θk be the q-axis stator current at the k-th sampling time; 0 denotes the zero matrix; T denotes the transpose of the matrix; θ1 is the standard basis vector. , Let θ1 represent an n+1 dimensional real space; the first element of θ1 is 1, and the rest are 0; n is the total order of higher-order disturbance modeling.

[0155] To ensure the safety and reliability of the permanent magnet synchronous motor servo system during operation, the controller needs to strictly enforce safe operating limits for current and voltage. Specifically, the q-axis current must meet overcurrent protection constraints: |i k |≤i q,max At the same time, the q-axis voltage must meet the overvoltage protection constraint: |u k |≤u q,max , where i q,max This indicates the maximum permissible q-axis current value of the motor; u q,max This represents the maximum q-axis voltage value that the inverter can provide. For ease of subsequent controller design and stability analysis, the above safety constraints are uniformly expressed as a set: system state variables. Must meet Control input quantity u k Must meet ,in U is defined as the permissible region of the state space, and U is defined as the permissible region of the control input space.

[0156] Based on the aforementioned established composite system model of permanent magnet synchronous motor, the dynamic characteristics of external signals, and the system's safe operation requirements, the following formal definition is given for the safe speed regulation and control problem of permanent magnet synchronous motor under interference environment:

[0157] Question 1: For the safety-constrained permanent magnet synchronous motor composite system shown in equation (1.8), design a controller with interference suppression capability so that the closed-loop control system simultaneously meets the following three core performance indicators:

[0158] (1) Asymptotic tracking performance: under lumped disturbance δ k Despite the influence of the reference signal, the system output speed can still asymptotically track the reference signal, i.e., satisfy the requirement that... .

[0159] (2) State and control input constraints are satisfied: During system operation, the state variables and control input variables are always within the safe region, that is, they satisfy the condition. , .

[0160] (3) Recursive feasibility and stability guarantee: The controller has a feasible solution at any time, and the closed-loop system is asymptotically stable in the Lyapunov sense.

[0161] The technical problem to be solved in this embodiment is to design a controller that meets the above requirements, and to achieve high-precision speed tracking control and strong interference suppression capability while ensuring the safe and stable operation of the system.

[0162] Step 104: Construct a dimension-reduced observer to estimate the signal of the external system based on the measurable system state and tracking error, and combine it with the preset regulator equation to perform state and input transformation on the system model to obtain the transformed system.

[0163] Due to the external signal v k Since the state cannot be directly measured, this embodiment first designs a dimension-reduced observer to estimate it. Because the state is measurable, the dimension-reduced observer can save computational resources. This is achieved by estimating the system state x. k With external signal v k Augmentation is performed. For example, the augmented model expression is constructed based on the permanent magnet synchronous motor system state vector and the external signal vector at the k-th sampling time:

[0164] (2.1)

[0165] ;

[0166] ;

[0167] .

[0168] Among them, z k+1 Let A be the state vector of the augmented permanent magnet synchronous motor system at the (k+1)th sampling time; z z is the state transition matrix of the augmented model of the permanent magnet synchronous motor; k Let be the state vector of the augmented permanent magnet synchronous motor system at the k-th sampling time. ;x k v is the state vector of the permanent magnet synchronous motor system at the k-th sampling time; k Let T be the external signal vector at the k-th sampling time; T represents the transpose of the matrix; A is the state matrix of the discrete-time system of the permanent magnet synchronous motor; S is the external system including the lumped reference signal and lumped interference; B d B represents the disturbance input matrix of the discrete-time system of a permanent magnet synchronous motor; 0 represents the zero matrix; z B is the control input matrix of the augmented model of the permanent magnet synchronous motor; U is the control input matrix of the discrete-time system of the permanent magnet synchronous motor; k β is the input variable for the q-axis control voltage of the permanent magnet synchronous motor at the k-th sampling time. k The augmented model's measurable output vector at the k-th sampling time; C z I is the output matrix of the augmented model of the permanent magnet synchronous motor; C is the output matrix of the discrete-time system of the permanent magnet synchronous motor; and D is the feedforward output matrix of the discrete-time system of the permanent magnet synchronous motor.

[0169] Construct v based on the augmented model k The expression for the dimension reduction observer:

[0170] (2.2)

[0171] ;

[0172] .

[0173] Where, ξ k+1 Let ξ be the internal state vector of the reduced-dimensional observer at the (k+1)th sampling time; H is the internal state transition matrix of the reduced-dimensional observer; ξ k Let F be the internal state vector of the dimension-reduced observer at the k-th sampling time; F is the measurable input feedback matrix of the dimension-reduced observer; and Ψ is the control input feedforward matrix of the dimension-reduced observer. For v k The estimated value; L is the gain matrix of the dimension-reduced observer; M is the coupling matrix of the dimension-reduced observer design; Output the state-state correlation matrix for the augmented model;

[0174] The estimation error of the external system signal is calculated based on the augmented model and the dimension-reduced observer:

[0175] (2.3)

[0176] in, The estimation error of the external system signal at the (k+1)th sampling time; v is the estimated value of the external system signal at the (k+1)th sampling time; k+1 The vector of the external signal at the (k+1)th sampling time; The estimation error of the external system signal at the k-th sampling time is denoted as .

[0177] By selecting an appropriate observer gain matrix L such that the spectral radius of matrix H satisfies ρ(H) < 1, the dynamic system of the estimation error is asymptotically stable, i.e., the estimation error... It gradually converges to zero over time.

[0178] To further analyze the boundary characteristics of the estimation error, a set recursion relation is introduced. , where the initial set It contains the origin and is a positive invariant set for the error system (2.3). This construction produces a sequence of sets { },satisfy This provides a boundary for estimating the error trajectory (2.3), that is, it always ensures... Considering v k ∈V, we can obtain the estimated value. Located in set Inside. The resulting set sequence { } inherits { The nesting property of} satisfies This characteristic provides an important theoretical basis for the subsequent design of safety constraints.

[0179] Based on output regulation theory, the following standard assumptions are proposed, which are easy to satisfy and verifiable:

[0180] Assumption 1: The spectral radius of matrix S is equal to 1; the matrix pair (A, B) is stabilizable; for each eigenvalue λ of S, the matrix... All are in full rank.

[0181] Under the premise that the above assumptions hold, the expression for the regulator equation is constructed as follows:

[0182] (2.4)

[0183] Where Π is the state feedforward mapping matrix; Γ is the control input feedforward mapping matrix.

[0184] Estimated value based on external signal And the regulator equation (2.4), the transformed state variables and control inputs are defined as follows:

[0185] (2.5)

[0186] Construct the expression for the transform system based on the estimated value of the external system signal and the regulator equation:

[0187] (2.6)

[0188] in, The state vector of the system is transformed at the (k+1)th sampling time; x k+1 Let be the state vector of the permanent magnet synchronous motor system at the (k+1)th sampling time. Transform the system's state vector at the k-th sampling time; The control variables of the system are transformed at the k-th sampling time. Λ represents the interference term of the transform system at the k-th sampling time; Λ is the equivalent interference gain matrix of the transform system.

[0189] Due to estimation error Asymptotically converges to zero, interference term It also exhibits asymptotic stability.

[0190] Step 105: Construct the constraint set of state variables and control inputs of the transformation system.

[0191] Since the system has already undergone transformation in step 104, the constraints need to be redesigned for the transformed system (2.6), and it must be ensured that when and At that time, it can be ensured that the original system satisfies x. k ∈X and u k ∈U. Based on this requirement, construct the constraint set expression for the state variables and control inputs of the transformation system:

[0192] (2.7)

[0193] in, The state vector of the system is transformed at the k-th sampling time; X k X represents the set of constraints that transform the system state variables at the k-th sampling time; X is the allowable region of the state space. Π represents the Pontryagin difference; Π is the state feedforward mapping matrix. Y is the control variable of the system at the k-th sampling time. k Γ represents the set of constraints that transform the system control variables at the k-th sampling time; U is the allowable region of the control input space; Γ is the control input feedforward mapping matrix. This is the set of estimated values ​​of the external signal at the k-th sampling time. X is the set of estimated values ​​of the external signal at the (k+1)th sampling time; k+1 Y is the set of constraints that transform the system state variables at the (k+1)th sampling time. k+1 The set of constraints for changing the system control variables at the (k+1)th sampling time.

[0194] Equation (2.7) shows that the constraint set exhibits the characteristic of gradual relaxation, which effectively reduces the conservatism brought about by constraint tightening.

[0195] Based on the above transformation system (2.6) and reconstruction constraints (2.7), the problem of safe speed regulation of permanent magnet synchronous motor (Problem 1) is reformulated as the stabilization problem of the transformed system, which is summarized as follows:

[0196] Question 2: Based on the permanent magnet synchronous motor composite system (1.8), considering the transformation system (2.6) and reconfiguration constraints (2.7), design a controller such that the system satisfies the following condition: the state asymptotically converges to zero after the transformation. Furthermore, the transformed state and control input always satisfy the constraint conditions, i.e. , .

[0197] Step 106: Decompose the state variables of the transformed system into nominal state components, deterministic error components, and uncertain error components.

[0198] To address problem 2, this embodiment employs a robust model predictive control strategy. First, the nominal dynamics of the transformed system (2.6) are decomposed, and the transformed states are... Decomposed into three independent components:

[0199] (3.1)

[0200] in, This represents the nominal state component at the k-th sampling time. This represents the deterministic error component at the k-th sampling time. Let be the uncertainty error component at the k-th sampling time.

[0201] Step 107: Construct a time-varying constrained compaction set based on the dynamic characteristics of the deterministic error component and the uncertain error component.

[0202] In order to effectively suppress uncertain components The impact on system performance is illustrated by constructing dynamic equations for deterministic and uncertain error components:

[0203] (3.2)

[0204] in, This is the deterministic error component at the (k+1)th sampling time. A represents the deterministic error component at the k-th sampling time. K The state matrix of the closed-loop nominal system; This represents the uncertainty error component at the (k+1)th sampling time. This represents the uncertainty error component at the k-th sampling time. Let A be the disturbance term of the transformed system at the k-th sampling time; let A be the state matrix of the discrete-time system of the permanent magnet synchronous motor; let B be the control input matrix of the discrete-time system of the permanent magnet synchronous motor; let K be the feedback gain matrix; ρ(A K )<1;ρ(A K ) is A K spectral radius; This represents the initial deterministic error component; The state of the system is changed at the initial moment; The initial state of the nominal system; This represents the initial uncertainty error component.

[0205] Construct the recursive relation satisfied by the constraint-compressed set based on the state matrix of the closed-loop nominal system:

[0206] (3.3)

[0207] Among them, S k+1 For the uncertainty error component at the (k+1)th sampling time Set; S k The uncertainty error component at the k-th sampling time The set in which it belongs; Minkowski addition; for The set it belongs to.

[0208] Step 108: Based on the nominal state components, constraint set, and constraint tightening set at each sampling time, construct and solve a model predictive control optimization problem with dynamic tightening constraints to obtain the nominal control quantity at the current time.

[0209] For example, construct the expression for the nominal state component:

[0210] (3.4)

[0211] Where A is the state matrix of the discrete-time system of the permanent magnet synchronous motor; B is the control input matrix of the discrete-time system of the permanent magnet synchronous motor. The state of the system is defined at the (k+1)th sampling time. The state of the system is defined at the k-th sampling time. The nominal system control input is defined at the k-th sampling time.

[0212] The phase cost function and the terminal penalty function are defined as follows:

[0213] (3.5)

[0214] Among them, Q, R and P f All are positive definite matrices, and their selection satisfies Lyapunov's inequality:

[0215] (3.6)

[0216] Construct a model-predictive control optimization problem expression based on nominal state components:

[0217] (3.7a)

[0218] in, This represents the optimal value function for the optimization problem at the k-th sampling time. Let N be the state vector of the transformed system at the k-th sampling time; N is the prediction time domain. The predicted value of the nominal system state at the k+i' time step is the value of the k-th sampling time step. The predicted value of the nominal system control input at the k-th sampling time for the (k+i')-th future time is given by the k-th sampling time. Represents the terminal cost function; It represents the predicted value of the nominal system state at the k+Nth time from the kth sampling time. Represents the stage cost function; Q is the first positive definite matrix; R is the second positive definite matrix; P f A is the third positive definite matrix; K Let be the state matrix of the closed-loop nominal system; T represents the transpose of the matrix; K is the feedback gain matrix; This represents the Euclidean norm.

[0219] Constructing constraints for the model predictive control optimization problem:

[0220] (3.7b)

[0221] (3.7c)

[0222] (3.7d)

[0223] (3.7e)

[0224] (3.7f)

[0225] in, It is the predicted value of the nominal system state at the k+i'+1 time point in the future, based on the k-th sampling time. The nominal initial value of the system state is defined at the k-th sampling time. The state vector of the system is transformed at the k-th sampling time; X f For the terminal constraint set; For A K i raised to the power of i'; This represents the set of constraints that will transform the system state variables at the (k+i)th time in the future; For the i'th uncertainty error component The set in which it belongs; This represents the set of constraints that will transform the system control variables at the (k+i)th time in the future. For A K S to the power of N; N For the Nth uncertainty error component The set it belongs to.

[0226] Terminal set X f The system (3.2) is constructed under the constraints. , and The largest robust positive invariant set is found below. This set is calculated using the standard set iteration algorithm, the iterative process of which is defined as follows:

[0227] (3.8)

[0228] (3.9)

[0229] in, This is the (k+1)th intermediate operation set; For uncertainty error state components; This is the initial intermediate operation set; Y is the set of constraints for the Nth transformed system state variables; N Let N be the set of constraints for the control variables of the Nth transformation system.

[0230] Thus, X is obtained. f = In this embodiment, it is assumed that It is a non-empty set and converges in a finite number of steps.

[0231] Constructing the optimal solution to the model predictive control optimization problem:

[0232] (3.10)

[0233] Construct the nominal control quantity of the transformed system at the current moment based on the optimal solution:

[0234] (3.11)

[0235] Accordingly, the dynamic equations of the closed-loop system are:

[0236] (3.12)

[0237] in, This is the sequence of optimal solutions for the nominal control quantity at the k-th sampling time. The optimal solution for the initial nominal control quantity at the k-th sampling time; The optimal solution for the nominal control quantity at the (k+N-1)th time step in the future; This is the nominal system optimal state sequence at the k-th sampling time. This represents the initial nominal system optimal state at the k-th sampling time. This represents the nominal optimal state of the system at the (k+N)th time step.

[0238] Step 109: Based on the nominal control quantity at the current moment and the estimated external signal, construct the control voltage acting on the permanent magnet synchronous motor to control the speed of the permanent magnet synchronous motor.

[0239] For example, the expression for the control voltage (i.e., the control law) acting on a permanent magnet synchronous motor is constructed as follows:

[0240] (3.13)

[0241] in, The control voltage applied to the permanent magnet synchronous motor at the kth sampling time; Let Γ be the nominal control quantity at the k-th sampling time; Γ is the control input feedforward mapping matrix. This is the estimated value of the external system signal at the k-th sampling time.

[0242] Innovation in System Decomposition Method: This embodiment proposes an innovative design for system decomposition, decomposing the system state into three independent components, as shown in the decomposed system (3.1), which includes two deterministic components. Compared with the traditional robust model predictive control method, which typically decomposes the system into two components (containing only one deterministic component), the three-component decomposition structure adopted in this embodiment can more effectively reduce system uncertainty, significantly reduce conservatism in the design process of the compact set (3.3), and improve control performance.

[0243] The innovativeness of the optimization problem construction: The construction of the model predictive control optimization problem (3.7) constitutes the core innovation of this invention. Compared with existing permanent magnet synchronous motor speed control schemes, traditional methods have not involved the dynamic tightening constraint design used in the optimization problem (3.7) of this embodiment. This innovative design ensures that the controller has a feasible solution (recursive feasibility) at any time through the recursive update of the time-varying constraint set, while guaranteeing the asymptotic stability of the closed-loop system. In contrast, existing permanent magnet synchronous motor model predictive control schemes cannot theoretically guarantee the recursive feasibility of the controller and the stability of the closed-loop system.

[0244] The two innovative designs mentioned above complement each other and together constitute the technical advantages of this embodiment in high-performance control of permanent magnet synchronous motors, providing a solid technical guarantee for achieving safe and reliable speed regulation.

[0245] This embodiment also provides a recursive feasibility analysis, which aims to study whether the optimization problem (3.7, i.e., 3.7a-3.7f) remains feasible at any given time, thereby ensuring that the control law can continuously act on the motor system. However, existing methods typically do not rigorously verify this property, and therefore cannot ensure that the optimization problem remains solvable throughout the entire operation. A key innovation of this embodiment is that it can rigorously guarantee the recursive feasibility of the optimization problem (3.7). The relevant conclusions are as follows:

[0246] Conclusion 1: Assuming that the first assumption holds and that the optimization problem (3.7) has a feasible solution at the initial time, it can be ensured that the MPC optimization problem (3.7) remains recursively feasible at all subsequent time steps.

[0247] Proof 1: Assume that the optimization problem (3.7) is feasible at time k, and its optimal solution is shown in equation (3.10). Then, at time k+1, the following candidate solution can be constructed:

[0248] (4.1)

[0249] The following will verify that the candidate solution (4.1) satisfies all the constraints of the optimization problem (3.7) at time k+1.

[0250] Verify that the candidate solution (4.1) satisfies constraint (3.7c):

[0251] From equations (3.11), (3.12), and candidate solution (4.1), we can obtain:

[0252] (4.2)

[0253] For all Both are true. Because And set X f As a robust positive invariant set, the above relation ensures that constraint (3.7c) is satisfied at time k+1.

[0254] Verify that the candidate solution (4.1) satisfies constraints (3.7d) and (3.7e).

[0255] For all ,in Let the set of integer indices from 0 to N-1 be represented by equations (4.1) and (4.2):

[0256] (4.3)

[0257] Since at time k, there is already And for any and All have ,therefore

[0258] (4.4)

[0259] Therefore, for all ,get:

[0260] (4.5)

[0261] This ensures that the state constraint (3.7d) is satisfied at time k+1. Similarly, it can be deduced that the input constraint (3.7e) is satisfied for all... It is also true.

[0262] for =N-1, from the candidate solution (4.1) we can obtain:

[0263] (4.6)

[0264] because ,and Can be launched

[0265] (4.7)

[0266] Furthermore, due to X f X N X k+N Then there is

[0267] (4.8)

[0268] This ensures that the state constraint (3.7d) is in This holds true when the value is N-1.

[0269] Similarly, it can be verified Input constraints (3.7e) are satisfied. In summary, for all... Both constraints (3.7d) and (3.7e) are satisfied.

[0270] Verify that the candidate solution (4.1) satisfies constraint (3.7f).

[0271] for =N, because Combining equations (4.1) and (4.2), we can obtain

[0272] (4.9)

[0273] According to the terminal constraint (3.7f) at time k, we have

[0274] (4.10)

[0275] And because X f The system (3.2) is a robust positive invariant set, therefore

[0276] (4.11)

[0277] From equation (4.9), we can further obtain

[0278] (4.12)

[0279] This indicates that the terminal constraint (3.7f) is satisfied at time k+1.

[0280] In summary, the candidate solution (4.1) satisfies constraint (3.7c) – (3.7f) at time k+1, thus completing the proof.

[0281] Stability analysis of closed-loop system:

[0282] Conclusion 2: Under the condition that Assumption 1 holds, the closed-loop system (3.12) has exponential stability at the origin.

[0283] Proof 2: Approach: First, prove that the closed-loop system (3.12) is in set X f It possesses exponential stability, which will be further explained later.

[0284] The exponential stability of the system at the origin. Let C be... k For the feasible set of optimization problem (3.7) at time k, select... As a candidate Lyapunov function, the goal is to find two positive constants η1>0 and η2>0 such that for all... ,have

[0285] (5.1)

[0286] And the descent condition is met.

[0287] (5.2)

[0288] in, .

[0289] Proof: Based on candidate solution (4.1), we can obtain

[0290] (5.3)

[0291] The final step utilizes Lyapunov's inequality (5.3). Since there exists a constant η1 > 0, ... Therefore, the descent condition (5.2) is verified.

[0292] For all There exists a constant η3 > 0 such that

[0293] (5.4)

[0294] in, .

[0295] Since (3.7) is a multi-parameter quadratic programming problem, it is known that right It is Lipschitz continuous. Therefore, for any , ∈C k ,have

[0296] (5.5)

[0297] Among them, L ξ >0 represents the Lipschitz constant.

[0298] It is worth noting that when ∈X f At that time, the optimal solution to optimization problem (3.7) satisfies

[0299] , , , (5.6)

[0300] Therefore, for the terminal set X f The state within the closed-loop system, the evolution of the system can be represented as follows:

[0301] (5.7)

[0302] Pick From (5.6), we can know Therefore, there is .

[0303] Combining with (5.4), we can take Thus, we obtain (5.1), thereby proving the set X. f The exponential stability.

[0304] Finally, due to set X f The system (3.12) is exponentially stable, and for any The dynamics of the closed-loop system satisfy (5.7). Furthermore, because... The exponential convergence to zero, according to the input-state stability theory, The exponent converges to the origin of the system, thus completing the proof.

[0305] Solvability analysis of Problem 1:

[0306] Under the proposed control scheme, the solvability of problem 2 guarantees the solvability of problem 1, while all state and input constraints are satisfied.

[0307] According to Conclusion 1, the optimization problem (3.7) is recursively feasible, thus ensuring... and By appointment

[0308] According to the constraint condition (2.7), the combined system (1.8) satisfies

[0309] (6.1)

[0310] Similarly, the control input satisfies

[0311] (6.2)

[0312] Therefore, the state and input constraints of Problem 1 are satisfied throughout the entire process.

[0313] According to conclusion 2, The exponent converges to zero, which means

[0314] (6.3)

[0315] Furthermore, since the estimated value of the external signal converges to the true value... , can be obtained

[0316] (6.4)

[0317] Using regulator equation (2.4), the tracking error satisfies

[0318] (6.5)

[0319] This demonstrates that the core performance indicators for question 1 have all been achieved.

[0320] This embodiment verifies its effectiveness through a physical experimental platform and compares the proposed method with the closest existing technology. The experimental platform consists of three core parts: a hardware drive circuit, a host computer running MATLAB / Simulink, and a motor testing unit. The motor testing unit employs a driven motor and a load motor in a coupled structure. The drive motor operates in speed control mode under the control of the test algorithm, while the load motor operates in torque control mode to simulate a programmable external load. The drive hardware system is built on a DSP motion control board (TMS320F280039C) and a three-phase motor driver (TI DRV8305). The motion control board integrates an ADC acquisition module, a PWM output module, and an encoder interface unit. After the control algorithm is developed in the MATLAB / Simulink environment on the host computer, it is deployed to the DSP control board for execution using automatic code generation technology. The DSP and the host computer exchange data in real time via a UART interface at a 12 MHz baud rate. The experimental setup consisted of three phases: no-load speed tracking test from 0 to 0.6 s; a step load disturbance applied at 0.6 s and removed at 1.6 s; and a time-varying load disturbance applied at 2.1 s to verify dynamic disturbance rejection performance. The reference speed was set to 1250 r / min, and the system sampling period was 0.1 ms.

[0321] This embodiment adopts a three-component system state decomposition structure (such as system (3.1)). Based on the traditional two-component decomposition framework, a deterministic compensation component is introduced, which effectively reduces the impact of system uncertainty propagation and significantly improves the conservatism of controller design. The controller only needs to focus on processing the remaining uncertain components, thereby simultaneously improving the dynamic response speed and interference suppression capability of the system.

[0322] Running effect: such as Figure 2 As shown, in the comparison of the overall dynamic response speed and interference suppression capability of the system, the method proposed in this embodiment exhibits superior comprehensive performance. Specifically, as... Figure 3 As shown, experimental results demonstrate that, during the 0-0.2s startup phase, the method provided in this embodiment exhibits superior dynamic performance and a shorter rise time. Figure 4 As shown, under time-varying load disturbance conditions after 2.1 seconds, the method provided in this embodiment exhibits stronger disturbance suppression capability and maintains more stable speed tracking accuracy. Compared with the traditional two-component structure, the method provided in this embodiment achieves significant improvements in both dynamic response speed and steady-state control accuracy, effectively solving the technical problems of conservative compact set design, dynamic response hysteresis, and insufficient disturbance rejection performance in the prior art. Meanwhile, as... Figure 5 As shown, the method provided in this embodiment implements an effective overcurrent protection mechanism, thereby ensuring the safe operation of the motor system.

[0323] Example 2

[0324] Based on the same inventive concept as Embodiment 1, this embodiment provides a permanent magnet synchronous motor speed control system. Since the principle of solving the problem in this system is similar to the permanent magnet synchronous motor speed control method described in Embodiment 1, the implementation of this system can refer to the implementation of the permanent magnet synchronous motor speed control method.

[0325] like Figure 6 As shown, this embodiment provides a permanent magnet synchronous motor speed control system, including:

[0326] The first building module 10 is used to build a discrete-time mathematical model of a permanent magnet synchronous motor.

[0327] The second construction module 20 is used to construct an external system containing lumped reference signals and lumped interference based on the discrete-time mathematical model of the permanent magnet synchronous motor.

[0328] The third building module 30 is used to construct a system model in composite state-space form based on the discrete-time mathematical model, the external system, and the velocity tracking error.

[0329] The fourth construction module 40 is used to construct a dimension-reduced observer to estimate the signal of the external system based on the measurable system state and tracking error, and to perform state and input transformation on the system model in combination with the preset regulator equation to obtain the transformed system.

[0330] The fifth construction module 50 is used to construct the constraint set of state variables and control inputs of the transformation system.

[0331] The variable decomposition module 60 is used to decompose the state variables of the transformed system into nominal state components, deterministic error components, and uncertain error components.

[0332] The sixth construction module 70 is used to construct a time-varying constrained compaction set based on the dynamic characteristics of deterministic error components and uncertain error components.

[0333] The seventh construction module 80 is used to construct and solve a model predictive control optimization problem with dynamic tightening constraints based on the nominal state components, constraint set, and constraint tightening set at each sampling time, and to obtain the nominal control quantity at the current time.

[0334] The eighth construction module 90 is used to construct a control voltage for the permanent magnet synchronous motor based on the nominal control quantity at the current moment and the estimated external signal, so as to control the speed of the permanent magnet synchronous motor.

[0335] For more detailed information on the working process of each of the above modules, please refer to the relevant content disclosed in Example 1, which will not be repeated here.

[0336] Example 3

[0337] This embodiment provides a computer device, including a processor and a memory; wherein, when the processor executes the computer program stored in the memory, it implements the steps of the permanent magnet synchronous motor speed control method described in Embodiment 1.

[0338] For a more detailed explanation of the above method, please refer to the relevant content disclosed in Example 1, which will not be repeated here.

[0339] Example 4

[0340] This embodiment provides a computer-readable storage medium for storing a computer program; when the computer program is executed by a processor, it implements the steps of the permanent magnet synchronous motor speed control method described in Embodiment 1.

[0341] For a more detailed explanation of the above method, please refer to the relevant content disclosed in Example 1, which will not be repeated here.

[0342] Example 5

[0343] This embodiment provides a computer program product, including computer-executable instructions or a computer program. When the computer-executable instructions or the computer program are executed by a processor, they implement the steps of the permanent magnet synchronous motor speed control method described in Embodiment 1.

[0344] For a more detailed explanation of the above method, please refer to the relevant content disclosed in Example 1, which will not be repeated here.

[0345] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems, devices, storage media, and computer program products disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0346] Those skilled in the art will clearly understand that the techniques in the embodiments of the present invention can be implemented using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of the present invention.

[0347] In some embodiments, computer-executable instructions may take the form of programs, software, software modules, scripts, or code, written in any form of programming language (including compiled or interpreted languages, or declarative or procedural languages), and may be deployed in any form, including as stand-alone programs or as modules, components, subroutines, or other units suitable for use in a computing environment.

[0348] As an example, computer-executable instructions may, but do not necessarily, correspond to files in a file system. They may be stored as part of a file that holds other programs or data, for example, in one or more scripts in a Hyper Text Markup Language (HTML) document, in a single file dedicated to the program in question, or in multiple co-located files (e.g., files that store one or more modules, subroutines, or code sections).

[0349] As an example, computer-executable instructions can be deployed to execute on a single electronic device, or on multiple electronic devices located at one location, or on multiple electronic devices distributed across multiple locations and interconnected via a communication network.

[0350] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

Claims

1. A method for controlling the speed of a permanent magnet synchronous motor, characterized in that, include: Construct a discrete-time mathematical model for a permanent magnet synchronous motor; An external system containing lumped reference signal and lumped interference is constructed based on the discrete-time mathematical model of the permanent magnet synchronous motor. A system model in composite state-space form is constructed based on the discrete-time mathematical model, the external system, and the velocity tracking error. A dimension-reduced observer is constructed to estimate the signal of the external system based on the measurable system state and tracking error, and combined with the preset regulator equation, the system model is transformed in terms of state and input to obtain the transformed system. Construct a constraint set for the state variables and control inputs of the transformation system; The state variables of the transformed system are decomposed into nominal state components, deterministic error components, and uncertain error components; Based on the dynamic characteristics of deterministic and uncertain error components, a time-varying constrained compaction set is constructed. Based on the nominal state components, constraint set, and constraint tightening set at each sampling time, a model predictive control optimization problem with dynamic tightening constraints is constructed and solved to obtain the nominal control quantity at the current time. Based on the nominal control quantity at the current moment and the estimated external signal, a control voltage is constructed to act on the permanent magnet synchronous motor to control the speed of the permanent magnet synchronous motor.

2. The method for controlling the speed of a permanent magnet synchronous motor according to claim 1, characterized in that, The discrete-time mathematical model for constructing the permanent magnet synchronous motor includes: Constructing a continuous-time mathematical model for a permanent magnet synchronous motor: ； in, J is the derivative of the mechanical angular velocity; r n is the rotor's moment of inertia. p It is the extreme logarithm; For rotor flux linkage; i q B is the q-axis stator current. f ω is the coefficient of friction; ω is the mechanical angular velocity; d ω This refers to the interference term in the velocity loop; L is the derivative of the q-axis stator current; s For stator inductance; u q R is the q-axis stator voltage; s d is the stator resistance; q This refers to the interference term in the current loop; Based on the continuous-time mathematical model of the permanent magnet synchronous motor, a discrete-time mathematical model of the permanent magnet synchronous motor is constructed: ； Where, ω k+1 t represents the mechanical angular velocity of the permanent magnet synchronous motor at the (k+1)th sampling time. s ω is the sampling period; k Let i be the mechanical angular velocity of the permanent magnet synchronous motor at the k-th sampling time; q,k d is the q-axis stator current at the k-th sampling time; ω,k The discrete-time lumped interference of the speed loop of the permanent magnet synchronous motor at the k-th sampling time; i q,k+1 u is the q-axis stator current at the (k+1)th sampling time; q,k d is the q-axis stator voltage at the k-th sampling time; q,k This represents the discrete-time lumped disturbance of the q-axis current loop of the permanent magnet synchronous motor at the k-th sampling time.

3. The speed control method for a permanent magnet synchronous motor according to claim 2, characterized in that, The external system constructed based on the discrete-time mathematical model of the permanent magnet synchronous motor, including lumped reference signal and lumped interference, includes: Construct a high-order discrete-time disturbance vector δ for the velocity loop ω,k and the q-axis current loop discrete-time higher-order disturbance vector δ q,k The expression: ； Among them, h i,k Let be the i-th discrete-time difference term of the velocity loop disturbance; i = 1, 2, ..., n; n is the total order of higher-order disturbance modeling; T represents the transpose of the matrix; This is the i-th discrete-time difference term of the current loop disturbance; Construct the lumped interference vector δ of the permanent magnet synchronous motor at the k-th sampling time. k The expression: ； ； ； ； Where, δ k+1 Sk+1 represents the lumped interference vector of the permanent magnet synchronous motor at the (k+1)th sampling time; S1 is the discrete-time state transition matrix of the interference vector; 0 represents the zero matrix; Sk+1 ω S is the discrete-time state transition matrix for the higher-order disturbance vector of the velocity loop; q The discrete-time state transition matrix is ​​the higher-order disturbance vector of the q-axis current loop. Construct the lumped reference signal α of the permanent magnet synchronous motor at the k-th sampling time. k The expression: ； Where, r k α is the reference speed of the permanent magnet synchronous motor at the k-th sampling time; k+1 S1 is the lumped reference signal of the permanent magnet synchronous motor at the (k+1)th sampling time; S2 is the discrete-time state transition matrix of the reference signal vector; Construct an expression for the external system S that includes the lumped reference signal and the lumped interference: 。 4. The speed control method for a permanent magnet synchronous motor according to claim 3, characterized in that, The system model, constructed based on the discrete-time mathematical model, the external system, and the velocity tracking error, includes: The expression for constructing a system model in composite state-space form: ； ； ； C=[0,1]； D=[-1,0]； ； Where, x k+1 Let x be the state vector of the permanent magnet synchronous motor system at the (k+1)th sampling time; A is the discrete-time state matrix of the permanent magnet synchronous motor system; k Let B be the state vector of the permanent magnet synchronous motor system at the k-th sampling time; let B be the control input matrix of the discrete-time permanent magnet synchronous motor system; u k =u q,k ;u k B is the input variable for the q-axis control voltage of the permanent magnet synchronous motor at the k-th sampling time. d v is the disturbance input matrix for the discrete-time system of a permanent magnet synchronous motor. k Let K be the vector of the external signal at the k-th sampling time. ;y k Let v be the output variable of the permanent magnet synchronous motor system at the k-th sampling time; C is the output matrix of the discrete-time permanent magnet synchronous motor system; v k+1 e is the vector of the external signal at the (k+1)th sampling time; k θ1 represents the speed tracking error of the permanent magnet synchronous motor at the k-th sampling time; D is the feedforward output matrix of the discrete-time system of the permanent magnet synchronous motor; θ1 is the standard basis vector, with the first element of θ1 being 1 and the remaining elements being 0.

5. The method for controlling the speed of a permanent magnet synchronous motor according to claim 4, characterized in that, The construction of a dimensionality-reduced observer estimates the signal of the external system based on the measurable system state and tracking error, and, in conjunction with a pre-defined regulator equation, performs state and input transformations on the system model to obtain a transformed system, including: The expression for the augmented model is constructed based on the state vector of the permanent magnet synchronous motor system and the external signal vector at the k-th sampling time: ； ； ； ； Among them, z k+1 Let A be the state vector of the augmented permanent magnet synchronous motor system at the (k+1)th sampling time; z z is the state transition matrix of the augmented model of the permanent magnet synchronous motor; k Let be the state vector of the augmented permanent magnet synchronous motor system at the k-th sampling time. B z β is the control input matrix for the augmented model of the permanent magnet synchronous motor. k The augmented model's measurable output vector at the k-th sampling time; C z I represents the output matrix of the augmented model of the permanent magnet synchronous motor; I is the identity matrix. Construct v based on the augmented model k The expression for the dimension reduction observer: ； ； ； Where, ξ k+1 Let ξ be the internal state vector of the reduced-dimensional observer at the (k+1)th sampling time; H is the internal state transition matrix of the reduced-dimensional observer; ξ k Let F be the internal state vector of the dimension-reduced observer at the k-th sampling time; F is the measurable input feedback matrix of the dimension-reduced observer; and Ψ is the control input feedforward matrix of the dimension-reduced observer. For v k The estimated value; L is the gain matrix of the dimension-reduced observer; M is the coupling matrix of the dimension-reduced observer design; Output the state-state correlation matrix for the augmented model; The estimation error of the external system signal is calculated based on the augmented model and the dimension-reduced observer: ； in, The estimation error of the external system signal at the (k+1)th sampling time; This is the estimated value of the external system signal at the (k+1)th sampling time; The estimation error of the external system signal at the k-th sampling time is denoted as . Construct the expression for the regulator equation: ； Where Π is the state feedforward mapping matrix; Γ is the control input feedforward mapping matrix; Construct the expression for the transform system based on the estimated value of the external system signal and the regulator equation: ； in, Transform the system's state vector at the (k+1)th sampling time. Transform the system's state vector at the k-th sampling time; The control variables of the system are transformed at the k-th sampling time. Λ represents the interference term of the transform system at the k-th sampling time; Λ is the equivalent interference gain matrix of the transform system.

6. The method for controlling the speed of a permanent magnet synchronous motor according to claim 5, characterized in that, The constraint set for constructing the state variables and control inputs of the transformation system includes: Construct the constraint set expression for the state variables and control inputs of the transformed system: ； Among them, X k X represents the set of constraints that transform the system state variables at the k-th sampling time; X is the allowable region of the state space. For Pontryagin difference; Y k U represents the set of constraints that transform the system control variables at the k-th sampling time; U is the allowable region of the control input space. This is the set of estimated values ​​of the external signal at the k-th sampling time. X is the set of estimated values ​​of the external signal at the (k+1)th sampling time; k+1 Y is the set of constraints that transform the system state variables at the (k+1)th sampling time. k+1 The set of constraints for changing the system control variables at the (k+1)th sampling time.

7. The method for controlling the speed of a permanent magnet synchronous motor according to claim 6, characterized in that, The construction of a time-varying constrained compaction set based on the dynamic characteristics of deterministic and uncertain error components includes: Construct the dynamic equation expressions for the deterministic error components and the uncertain error components: ； in, This is the deterministic error component at the (k+1)th sampling time. A represents the deterministic error component at the k-th sampling time. K The state matrix of the closed-loop nominal system; This represents the uncertainty error component at the (k+1)th sampling time. Let ρ(A) be the uncertainty error component at the k-th sampling time; K is the feedback gain matrix; ρ(A) K )<1;ρ(A K ) is A K spectral radius; This represents the initial deterministic error component; The state of the system is changed at the initial moment; The initial state of the nominal system; This represents the initial uncertainty error component; Construct the recursive relation satisfied by the constraint-compressed set based on the state matrix of the closed-loop nominal system: ； Among them, S k+1 For the uncertainty error component at the (k+1)th sampling time Set; S k The uncertainty error component at the k-th sampling time The set in which it belongs; Minkowski addition; for The set it belongs to.

8. The method for controlling the speed of a permanent magnet synchronous motor according to claim 7, characterized in that, The process involves constructing and solving a model predictive control optimization problem with dynamic tightening constraints based on the nominal state components, constraint set, and constraint tightening set at each sampling time, to obtain the nominal control quantity at the current time, including: Expressions for constructing nominal state components: ； in, The state of the system is defined at the (k+1)th sampling time. The state of the system is defined at the k-th sampling time. The nominal system control input is defined at the k-th sampling time. Construct a model-predictive control optimization problem expression based on nominal state components: ； in, Let N represent the optimal value function of the optimization problem at the k-th sampling time; N is the prediction time domain. The predicted value of the nominal system state at the k+i' time step is the value of the k-th sampling time step. The predicted value of the nominal system control input at the k-th sampling time for the (k+i')-th future time is given by the k-th sampling time. Represents the terminal cost function; It represents the predicted value of the nominal system state at the k+Nth time from the kth sampling time. Represents the stage cost function; Q is the first positive definite matrix; R is the second positive definite matrix; P f It is the third positive definite matrix; Denotes the Euclidean norm; Constructing constraints for the model predictive control optimization problem: ； in, It is the predicted value of the nominal system state at the k+i'+1 time point in the future, based on the k-th sampling time. Let X be the initial value of the nominal system state at the k-th sampling time; f For the terminal constraint set; For A K i raised to the power of i'; This represents the set of constraints that will transform the system state variables at the (k+i)th time in the future; For the i'th uncertainty error component The set in which it belongs; This represents the set of constraints that will transform the system control variables at the (k+i)th time in the future. For A K S to the power of N; N For the Nth uncertainty error component The set in which it belongs; Constructing the optimal solution to the model predictive control optimization problem: ； in, This is the sequence of optimal solutions for the nominal control quantity at the k-th sampling time. The optimal solution for the initial nominal control quantity at the k-th sampling time; The optimal solution for the nominal control quantity at the (k+N-1)th time step in the future; This is the nominal system optimal state sequence at the k-th sampling time. This represents the initial nominal system optimal state at the k-th sampling time. This represents the nominal optimal state of the system at the (k+N)th time step. Construct the nominal control quantity of the transformed system at the current moment based on the optimal solution: 。 9. The method for controlling the speed of a permanent magnet synchronous motor according to claim 8, characterized in that, The step of constructing a control voltage for the permanent magnet synchronous motor based on the nominal control quantity at the current moment and the estimated external signal to control the speed of the permanent magnet synchronous motor includes: Construct the expression for the control voltage acting on the permanent magnet synchronous motor: ； in, The control voltage applied to the permanent magnet synchronous motor at the kth sampling time; This is the nominal control quantity at the k-th sampling time.

10. A speed control system for a permanent magnet synchronous motor, characterized in that, include: The first building module is used to build the discrete-time mathematical model of the permanent magnet synchronous motor; The second construction module is used to construct an external system containing lumped reference signals and lumped interference based on the discrete-time mathematical model of the permanent magnet synchronous motor. The third building module is used to construct a system model in composite state-space form based on the discrete-time mathematical model, the external system, and the velocity tracking error. The fourth construction module is used to construct a dimension-reduced observer to estimate the signal of the external system based on the measurable system state and tracking error, and to perform state and input transformation on the system model in combination with the preset regulator equation to obtain the transformed system. The fifth construction module is used to construct the constraint set of state variables and control inputs of the transformation system; The variable decomposition module is used to decompose the state variables of the transformed system into nominal state components, deterministic error components, and uncertain error components. The sixth construction module is used to construct a time-varying constrained compaction set based on the dynamic characteristics of deterministic and uncertain error components. The seventh construction module is used to construct and solve a model predictive control optimization problem with dynamic tightening constraints based on the nominal state components, constraint set, and constraint tightening set at each sampling time, and to obtain the nominal control quantity at the current time. The eighth construction module is used to construct the control voltage applied to the permanent magnet synchronous motor based on the nominal control quantity at the current moment and the estimated external signal, so as to control the speed of the permanent magnet synchronous motor.

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