Method for analyzing stability of discrete domain of vehicle-motor system with introduced dynamics model

Abstract

The application discloses a kind of vehicle-motor system discrete domain stability analysis methods of introducing kinetics model, based on the digital control system of permanent magnet motor vector control method, establish discrete system mathematical model;After model is determined, the model is analyzed using discretization D segmentation method, based on unknown speed ring PI parameter, establish equation group containing unknown parameter, obtain the relationship between PI parameter and system frequency, and the relationship between PI parameters characterized by system frequency;Based on this relationship, the stable domain boundary of system PI parameter value can be drawn;A simplified two-degree-of-freedom vehicle dynamics discrete model is established, and the critical vehicle speed that can maintain the stability of vehicle motion during steering is analyzed. The above two analysis results are combined, and the theoretical design scheme of the permanent magnet motor vector control system of electric vehicle is obtained, which ensures the stability of the permanent magnet motor system operation and ensures the stability of the vehicle steering motion.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electric machines, and particularly relates to a discrete domain stability analysis method for a vehicle-motor system. BACKGROUND

[0002] For the control parameter design of the permanent magnet motor power system of an electric vehicle, the trial-and-error method is most commonly used, but the method requires high engineering experience and needs to refine the system mathematical model for analysis. With the development of motor control technology, digital processors have been applied to the power system of an electric vehicle, so it is necessary to analyze the relationship between the control parameters and the stability of the digitalized discrete system, and obtain the theoretical control parameter stability range through the relationship between the control parameters and the system frequency. This can greatly reduce the dependence on experience for parameter debugging and provide a theoretical guidance for the parameter setting of the electric control system. Meanwhile, the electric control system also needs to consider the stability of the vehicle motion. Vehicles with insufficient steering characteristics have a critical speed during steering, and exceeding the critical speed will cause the vehicle motion to be unstable. Therefore, the analysis of the discretized vehicle dynamics model can provide design constraints for the permanent magnet motor control system from the vehicle aspect, so that the entire system can meet the stability of the motor system operation and the stability of the vehicle motion. SUMMARY

[0003] In order to overcome the shortcomings of the prior art, the application provides a vehicle-motor system discrete domain stability analysis method introducing a dynamics model, which is based on a digital control system of a permanent magnet motor vector control method, and establishes a discrete system mathematical model. After the model is determined, the model is analyzed by using a discretization D partition method, an equation group containing unknown parameters is established based on unknown speed loop PI parameters, the relationship between the PI parameters and the system frequency is obtained, and the relationship between the PI parameters represented by the system frequency is obtained. Based on this relationship, the stable domain boundary of the system PI parameter values can be drawn. A simplified two-degree-of-freedom vehicle dynamics discrete model is established, and the critical vehicle speed at which the vehicle motion can be maintained stable during steering is analyzed. The above two analysis results are combined to obtain a theoretical design scheme of the permanent magnet motor vector control system of an electric vehicle, which ensures the stability of the permanent magnet motor system operation and the stability of the vehicle steering motion.

[0004] The technical solution adopted by the application to solve the technical problems comprises the following steps:

[0005] Step 1: establishing a mathematical model of the current loop of the motor vector control system considering a zero-order holder and discretizing the mathematical model to obtain a discrete closed-loop transfer function and a system characteristic equation of the mathematical model;

[0006] Step 1-1: the frequency domain voltage differential equation of a permanent magnet synchronous motor in a rotating dq coordinate system:

[0007]

[0008] The current loop adopts a PI controller:

[0009]

[0010] The zero-order holder element (1-e -sT ) of the digital system replaces the equivalent switching delay element in the system with a sampling delay element, and the closed-loop transfer function of the current loop in the q-axis is obtained as:

[0011]

[0012] Where T represents the switching frequency of the control system, u d and u q represent the components of the stator voltage of the permanent magnet synchronous motor in the rotating dq coordinate system, i d and i q represent the components of the stator current of the permanent magnet synchronous motor in the rotating dq coordinate system; ψ f represents the magnetic flux of the motor permanent magnet; ω e represents the electrical angular velocity of the rotor; k pi and k ii are the proportional coefficient and integral coefficient of the current loop controller, respectively; R s represents the stator resistance of the permanent magnet motor, L d represents the direct-axis inductance of the permanent magnet motor, and L q represents the quadrature-axis inductance of the permanent magnet motor; s represents the complex frequency variable in Laplace transform.

[0013] Step 1-2: Adopting bilinear transformation: Let the sampling frequency of the system be equal to the switching frequency, and substitute it into the closed-loop continuous transfer function of the current loop to obtain the pulse transfer function of the discrete system as:

[0014]

[0015] Step 1-3: For the speed-current double closed-loop permanent magnet motor vector control system, the speed loop adopts a PI controller:

[0016]

[0017] First, discretize the speed loop controller, and also adopt bilinear transformation to obtain:

[0018]

[0019] Ignoring the friction and viscous coefficient of the motor itself, the open-loop discrete transfer function of the system is obtained as:

[0020]

[0021] The system closed-loop discrete characteristic equation is:

[0022]

[0023] where k ps and k is are the proportional and integral coefficients of the speed loop controller, respectively;

[0024] Step 2: The system stability is analyzed by using the discrete domain D partition method, the relationship between the system controller parameters and the system frequency is obtained, and then the parameter stability domain is obtained;

[0025] For the characteristic equation of the control system, when the system is critically stable, there is:

[0026]

[0027] Substitute z into and regard ω as a constant, then a binary linear equation group with k ps and k is as unknowns is obtained, and the relationship between the parameter set k and the system frequency ω is obtained by solving the equation group:

[0028]

[0029] where:

[0030]

[0031] Divide the expression of k ps by k is , then the discrete system stability domain based on the relationship between the system frequency ω and the parameters k ps and k is is obtained; by changing the system frequency ω, the boundary curve of the discrete system stability domain is drawn;

[0032] Step 3: A two-degree-of-freedom dynamics model of an electric vehicle is established, considering the zero-order holder and discretizing it; the constraints of vehicle motion stability in the discrete domain are obtained by analyzing the discretized dynamics model of the electric vehicle;

[0033] Since the vehicle motion only considers the lateral and yaw, only a two-degree-of-freedom two-wheel dynamics model needs to be established;

[0034] Let X and Y be the relative coordinates fixed at the vehicle center of mass, a be the distance from the vehicle center of mass to the front axle, b be the distance from the vehicle center of mass to the rear axle, l be the wheelbase, and have l=a+b; V be the vehicle speed, δ be the front wheel steering angle, β be the vehicle center of mass steering angle; Ψ be the angle between the absolute coordinates and the relative coordinates, be the steering angle of the center of mass in the absolute coordinates;

[0035] Combining Newton's second law, the force and torque balance equations of the vehicle in longitudinal and yaw directions are listed as follows:

[0036]

[0037] where m is the mass of the vehicle, F yf and F yr are the y components of the front and rear tire forces, I z is the moment of inertia of the vehicle, and r is the yaw rate of the vehicle; the tire force expression is as follows:

[0038]

[0039] where K1 and K2 are the side stiffness coefficients of the front and rear tires, respectively.

[0040] Substituting the tire force expression into the force and torque balance equations, the following equations are obtained:

[0041]

[0042] Taking Laplace transform, the following equations are obtained:

[0043]

[0044] Solving the two equations, the transfer functions of r and β to δ are obtained, and they are arranged into the standard second-order system form as follows:

[0045]

[0046] The symbols in the equations are as follows:

[0047]

[0048] Discretizing the model, the discrete model is as follows:

[0049]

[0050] According to the model characteristic equation and the Jury criterion, the condition for maintaining the stability of the vehicle steering motion in the discrete domain is as follows:

[0051]

[0052] Step 4: The comprehensive constraint conditions of the electric motor vector control system of the electric vehicle based on the vehicle dynamics model in the discrete domain are as follows:

[0053] ① k ps and k isX and Y are the horizontal and vertical coordinates, respectively, and the control parameter point is taken, and when the point is located in the stable region determined by the mapping relationship between the parameter set k and omega derived in step 2, the motor control system can be guaranteed to be stable.

[0054] In order to guarantee that the vehicle steering does not cause side slip, the speed signal given by the motor control system needs to be limited, and the boundary value of the saturation link is less than the critical vehicle speed V c .

[0055] Preferably, the value of the η is 1.

[0056] The beneficial effects of the present application are as follows:

[0057] The present application proposes a comprehensive stability analysis method by analyzing the stability of the overall motor-vehicle discrete system from the perspectives of the motor and the vehicle. Based on the analysis of the continuous domain system model, the method considers the property that the discretization of the continuous system will cause the order of the system to increase, and based on the consideration of the zero-order holder, the discrete domain D partition method is used to analyze the stability of the motor control system, and the Zhu Li criterion is used to analyze the stability condition of the vehicle dynamics discrete model, which not only provides theoretical guidance for the speed loop control parameter design of the permanent magnet motor driving system, but also can apply the vehicle motion constraint to the permanent magnet motor control system, so that the permanent magnet motor system designed based on the above two conditions can not only ensure the convergence of the speed response, but also can guarantee that the vehicle does not produce motion instability during turning. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 The figure is a schematic diagram of the discrete permanent magnet motor vector control system of the present application.

[0059] Figure 2 The figure is a two-degree-of-freedom model of the vehicle dynamics of the present application. DETAILED DESCRIPTION

[0060] The present application will be further described below in combination with the drawings and examples.

[0061] The purpose of the present application is to propose a method that can be used to analyze whether the vehicle-machine system parameter design of the electric vehicle can guarantee the stability of the vehicle steering motion and the motor control system.

[0062] A vehicle-motor system discrete domain stability analysis method introducing a dynamics model, the scheme is as follows:

[0063] Step 1: Establish the mathematical model of the current loop of the motor vector control system considering the zero-order holder and discretize it to obtain the discrete closed-loop transfer function and the system characteristic equation;

[0064] Step 2: The system stability is analyzed by using the discrete domain D segmentation method, the relationship between the system controller parameters and the system frequency is obtained, and then the parameter stability domain is obtained;

[0065] Step 3: A two-degree-of-freedom dynamic model of the electric vehicle is established, considering the zero-order holder and discretizing it; the vehicle motion stability constraint condition in the discrete domain is obtained by analyzing the discretized model of the electric vehicle dynamics;

[0066] Step 4: All the conditions obtained in the above steps are integrated to obtain the constraint condition for the stability of the vehicle-motor motion control system in the discrete domain.

[0067] In the implementation process, the specific implementation of each step is as follows.

[0068] Step 1 is as follows:

[0069] Step 1-1: According to the frequency domain voltage differential equation of the permanent magnet synchronous motor in the rotating dq coordinate system:

[0070]

[0071] and the PI controller in the current loop:

[0072]

[0073] The zero-order holder element (1-e -sT ) / s of the digital system is considered, and since the switching time is less than for simplification, the sampling delay element is used to replace the equivalent switching delay element in the system. Taking the q-axis of the current loop as an example, the closed-loop transfer function of the q-axis current loop can be obtained as:

[0074]

[0075] where T represents the switching frequency of the control system, u d and u q represent the components of the stator voltage of the permanent magnet synchronous motor in the rotating dq coordinate system, i d and i q represent the components of the stator current of the permanent magnet synchronous motor in the rotating dq coordinate system; ψ f represents the magnetic flux of the motor permanent magnet; ω e represents the electrical angular velocity of the rotor; k pi and k ii are the proportional and integral coefficients of the current loop controller, respectively.

[0076] According to the sampling and switching positions shown in Figure 1 , in order to avoid frequency aliasing in the continuous domain to discrete domain mapping process, a bilinear transformation is used:

[0077] For simplifying analysis, the system sampling frequency can be equal to the switching frequency. Substituting the continuous transfer function of the current loop closed-loop into the discrete system, the pulse transfer function of the discrete system is:

[0078]

[0079] For the typical speed-current double closed-loop permanent magnet motor vector control system, the speed loop also uses a PI controller:

[0080]

[0081] According to the sampling switch position shown in Figure 1 , the speed loop controller needs to be discretized first. Similarly, using the bilinear transformation, we can get:

[0082]

[0083] Ignoring the friction and viscous coefficient of the motor itself, the open-loop discrete transfer function of the system is:

[0084]

[0085] Further, the closed-loop discrete characteristic equation of the system is:

[0086]

[0087] where k ps and k is are the proportional and integral coefficients of the speed loop controller, respectively.

[0088] Step 1 is complete.

[0089] Step 2: For the characteristic equation of the control system, when the system is critically stable, we have:

[0090]

[0091] Substitute z into it and consider ω as a constant. Then we can get a binary linear equation group with k ps and k is as unknowns. Solving the equation group can get the relationship between the parameter set k and the system frequency ω as:

[0092]

[0093] where:

[0094]

[0095] Divide the expression of k ps by k is , then we can get the parameter k ps based on the system frequency ω.The relationship between k is constitutes a discrete system stability domain. By changing the system frequency ω, the discrete system stability domain boundary curve can be plotted.

[0096] The step 2 ends.

[0097] Step 3: The vehicle motion involved in the present application only considers the lateral and yaw, so only a two-degree-of-freedom two-wheel dynamics model needs to be established. The simplified model is shown in Figure 1 .

[0098] Figure 1 In the formula, X and Y are relative coordinates fixed at the vehicle center of mass, a is the distance from the vehicle center of mass to the front axle, b is the distance from the vehicle center of mass to the rear axle, l is the wheelbase, and l=a+b. V is the vehicle speed, δ is the front wheel steering angle, β is the vehicle center of mass steering angle. Ψ is the angle between the absolute coordinates and the relative coordinates, is the steering angle of the center of mass in the absolute coordinates.

[0099] According to the geometric relationship between the physical quantities of Figure 1 , combined with Newton's second law, the force and torque balance equations of the vehicle in the longitudinal and yaw two degrees of freedom are listed:

[0100]

[0101] Where m is the vehicle mass, F yf and F yr are the y-direction components of the front and rear tire forces, I z is the moment of inertia of the vehicle, and r is the yaw angular velocity of the vehicle when turning. The tire force expression is:

[0102]

[0103] Where K1 and K2 are the lateral stiffness coefficients of the front and rear tires, respectively.

[0104] Substitute the tire force expression into the force and torque balance equations to get:

[0105]

[0106] Laplace transform can be obtained:

[0107]

[0108] Solve the two equations simultaneously to get the transfer functions of r to δ and β to δ, and arrange them into the standard form of a second-order system:

[0109]

[0110] The symbols in the formula are as follows:

[0111]

[0112] Here, η can usually be taken as 1.

[0113] Discretizing the model, the discrete model is:

[0114]

[0115] Based on the model's characteristic equation and the Julius criterion, the condition for maintaining stable vehicle steering motion in the discrete domain can be obtained as follows:

[0116]

[0117] This concludes step 3.

[0118] Step 4: Based on steps 1 to 3, the comprehensive constraint conditions of the electric vehicle motor vector control system based on the vehicle dynamics model in the discrete domain can be obtained as follows:

[0119] ①With k ps and k is The horizontal and vertical coordinates are respectively. The control parameter point is taken. When the point is located within the stability region determined by the mapping relationship between the parameter set k and ω obtained in step 2, the stability of the motor control system can be guaranteed.

[0120] ② To ensure that the vehicle does not skid during steering, the speed signal setpoint of the motor control system must be limited, and the boundary value of its saturation stage must be less than the critical vehicle speed V. c .

Claims

1. A method of introducing a dynamics model for a discrete domain stability analysis of a vehicle-motor system, characterized by, Comprising the following steps: Step 1: Establish the mathematical model of the current loop of the motor vector control system considering the zero-order holder and discretize it to obtain its discrete closed-loop transfer function and system characteristic equation; Step 1-1: The frequency-domain voltage differential equation of the permanent magnet synchronous motor in the rotating dq coordinate system is as follows: The current loop adopts a PI controller: Zero-order hold element (1-e -sT / s, the equivalent switching delay element in the system is replaced by a sampling delay element, and the closed-loop transfer function of the current loop of the q-axis is obtained as where T represents the switching frequency of the control system, u d , u q represent the components of the stator voltage of the permanent magnet synchronous motor in the rotating dq coordinate system, i d , i q represent the components of the stator current of the permanent magnet synchronous motor in the rotating dq coordinate system; ψ f represents the magnetic flux of the motor permanent magnet; ω e represents the electrical angular velocity of the rotor; k pi , k ii are the proportional coefficient and the integral coefficient of the current loop controller respectively; R s represents the stator resistance of the permanent magnet motor, L d represents the direct-axis inductance of the permanent magnet motor, L q represents the quadrature-axis inductance of the permanent magnet motor, and s represents the complex frequency variable in the Laplace transform. Steps 1-2: Use the bilinear transformation: Let the system sampling frequency equal to the switching frequency, substitute the current loop closed-loop continuous transfer function, and get the discrete system pulse transfer function as: Step 1-3: For the conventional speed-current double-closed-loop permanent magnet motor vector control system, the speed loop adopts a PI controller: First, discretize the speed loop controller, also using the bilinear transformation, to obtain: Ignoring the friction and viscous coefficient of the motor itself, the open-loop discrete transfer function of the system is as follows: Further, the closed-loop discrete characteristic equation of the system is as follows: where k ps , k is are the proportional and integral coefficients of the speed loop controller, respectively. Step 2: Analyze the stability of the system by using the discrete domain D-partition method to obtain the relationship between the controller parameters of the system and the system frequency, and then obtain the parameter stability domain; For the characteristic equation of the control system, when the system is critically stable, there is: Substitute z into, and take ω as a constant, then get the equation with k ps , k is as unknowns, and the solution of the equation set is the relationship between the parameter set k and the system frequency ω: Wherein: k ps and k is dividing the expressions, we get the discrete system stability domain based on the system frequency ω with the parameter k ps and k is The relationship constitutes a discrete system stability domain; by changing the system frequency ω, the boundary curve of the discrete system stability domain is drawn. Step 3: Establish a two-degree-of-freedom dynamics model of the electric vehicle, consider the zero-order holder, and discretize it; analyze the discretized model of the electric vehicle dynamics to obtain the constraint condition for the stability of the vehicle motion in the discrete domain; The vehicle motion only considers the lateral and yaw directions, so only a two-degree-of-freedom two-wheel dynamics model needs to be established; Let X, Y be the relative coordinates fixed to the vehicle's center of mass, a be the distance from the vehicle's center of mass to the front axle, b be the distance from the vehicle's center of mass to the rear axle, 1 be the wheelbase, and have 1 = a + b; V be the vehicle speed, δ be the front wheel steering angle, β be the vehicle's center of mass steering angle; Ψ be the angle between the absolute coordinates and the relative coordinates, be the center of mass steering angle in absolute coordinates; According to Newton's second law, the force and torque balance equations of the vehicle in the longitudinal and yaw directions are as follows: where m is the vehicle mass, F yf , F yr are the components of the front and rear tire forces in the y direction, I z is the moment of inertia of the vehicle, and r is the yaw rate of the vehicle during a turn; the tire force expression is: Fy = -Cf * (1 + 1 / (1 + (Cf / Cα)2)1 / 2) * (1 + (Cf / Cα)2)1 / 2 Wherein, K1 and K2 are the side stiffness coefficients of the front and rear tires, respectively; Substitute the tire force expression into the force and torque balance equations to obtain: After Laplace transformation, we obtain: By solving the two equations, the transfer functions of r to δ and β to δ can be obtained, and they can be arranged into the standard form of a second-order system as follows: The symbols in the formula are as follows: Discretize the model, and the discrete model is as follows: According to the model characteristic equation and the Jury criterion, the condition for maintaining the stability of the vehicle steering motion in the discrete domain is as follows: Step 4: Obtain the comprehensive constraint condition of the electric vehicle motor vector control system based on the vehicle dynamics model in the discrete domain as follows: ps and k is are the horizontal and vertical coordinates, respectively, and take the control parameter point. When the point is located in the stable region determined by the mapping relationship between the parameter set k and ω derived in step 2, the motor control system is guaranteed to be stable.​ ②In order to ensure that the vehicle steering will not produce side slip, the speed signal given by the motor control system shall be limited in amplitude, and the boundary value of the saturation link is less than the critical vehicle speed V c .

2. The method of claim 1, wherein, The η is taken as 1.

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