CN105262379B - The controller design method of twin drive system - Google Patents

Abstract

The present invention provides a synchronous control scheme for a dual-motor drive system, which includes the following steps: first, a dual-motor synchronous drive experimental system is built, wherein the dual-motor drive experimental system includes two sets of permanent magnet synchronous motors and a synchronous belt. Two sets of permanent magnet synchronous motors jointly drive the synchronous belt to run; secondly, according to the principle of dynamics, a mathematical model of the dual-motor drive experimental system is established, which belongs to a system with the first nonlinear subsystem and the second nonlinear subsystem. The interconnection system of the system; finally, based on the above-mentioned mathematical model, a distributed robust full-closed-loop fuzzy segmental synchronous H _∞ controller is designed, and a simulation test platform of the system is given. The synchronous control scheme provided by the invention can improve the synchronous precision of the double motors, and enables the closed-loop control system to have _H∞ anti-interference ability.

Description

Controller Design Method for Dual Motor Drive System

technical field

The invention relates to a design scheme of a synchronous controller of a dual-motor drive system.

Background technique

As people's requirements for control are getting higher and higher, the control of a single system is difficult to meet the needs of social development, so the synchronous control or consistency control of multiple systems has been proposed. However, most real systems are nonlinear, and there are parameter uncertainties and input disturbances, and there may be physical coupling between subsystems in the multi-system, these factors make the synchronous control of multi-system very difficult.

In the existing double motor synchronous system, the system is driven by two sets of permanent magnet synchronous motors to run the same belt. However, since the two sets of synchronous motors cannot be fully synchronized, their asynchrony will pull each other through the belt, which makes the dual-motor synchronous system have disadvantages such as low synchronization accuracy and poor anti-interference ability.

Contents of the invention

In view of the above situation, it is necessary to provide a synchronous controller design scheme for the dual motor drive system, which can effectively solve the above problems.

The present invention provides a controller design scheme of a dual-motor drive system, comprising the following steps:

First set up the dual-motor synchronous drive experimental system, wherein the experimental system includes two sets of permanent magnet synchronous motors and a synchronous belt, and the two sets of permanent magnet synchronous motors jointly drive the synchronous belt to run;

Then according to the principle of dynamics, the mathematical model of the synchronous drive experimental system of the two motors is established, and this mathematical model belongs to an interconnected system with a nonlinear subsystem (10) and a nonlinear subsystem (20);

Finally, based on the mathematical model, a design scheme of a decentralized robust full-closed-loop fuzzy segmented synchronous H _∞ controller is established.

The controller obtained by the design method provided by the invention can improve the synchronous precision of the double motors, and enable the closed-loop control system to have _H∞ anti-interference ability.

Description of drawings

Figure 1 is a schematic diagram of the structure of the dual-motor synchronous drive experimental system.

Figure 2 is a schematic diagram of the structure of the dual-motor synchronous drive experimental system.

Fig. 3 is a block diagram of decentralized full-closed-loop fuzzy subsection synchronous control.

Figure 4 is a graph of the fuzzy membership function.

Figure 5 is the synchronous control experiment platform.

Detailed ways

Please refer to Fig. 1, an embodiment of the present invention provides a synchronous controller design scheme of a dual-motor drive system, including the following steps:

S1, please refer to Fig. 2, set up dual-motor synchronous drive experimental system 100, wherein, described dual-motor synchronous drive experimental system 100 comprises two sets of permanent magnet synchronous motors 11/21 and a synchronous belt 30, and the two sets of permanent magnet synchronous The motor 11/21 jointly drives the synchronous belt 30 to run;

S2, according to the principle of dynamics, set up the mathematical model of described dual-motor drive experimental system, this mathematical model belongs to an interconnected system with nonlinear subsystem (10) and nonlinear subsystem (20);

S3. Based on the mathematical model, a design scheme of a decentralized robust full-closed-loop fuzzy segmented synchronous H _∞ controller is established.

In step S1, the permanent magnet synchronous motor 11, the first reduction box 12 and the first synchronous wheel 13 form a sub-system 10; the permanent magnet synchronous motor 21, the second reduction box 22 and the second synchronous wheel 23 form a sub-system System 20.

In step S2, the mathematical model of the subsystem (10) is as formula (1):

in Be the angular velocity of the permanent magnet synchronous motor 11, P ₁ is the number of stages of the permanent magnet synchronous motor 11, is the q-axis current, R ₁ is the stator resistance, L ₁ is the stator inductance, is the q-axis voltage, is the moment of inertia of the permanent magnet synchronous motor 11, is the d-axis voltage, is the electromagnetic torque of the permanent magnet synchronous motor 11, is the moment of inertia of the first reduction box 12, Be the moment of inertia of the first synchronous wheel 13, k ₁ (s ₁ ), k ₂ (s ₁ ), k ₃ is the elastic coefficient of the synchronous belt 30, r is the radius of the first synchronous wheel 13, M is the load mass, Be the frictional force of the first synchronous wheel 13, F _f is the damping coefficient under load, is the d-axis current, is the load torque, Be the viscous damping coefficient of permanent magnet synchronous motor 11, λ ₁ is magnetic flux, is the rotational speed of the first synchronous wheel 13, B ₁ is the viscous damping coefficient of the linear guide rail, is the viscous damping coefficient of the first synchronous wheel 13, G ₁ is the reduction ratio of the first reduction box 12, s is the moving distance of the synchronous belt 30, and v is the moving speed of the synchronous belt 30.

The mathematical model of subsystem (20) is as formula (2):

in is the angular velocity of the synchronous motor 21, P ₂ is the number of stages of the synchronous motor 21, is the q-axis current, R ₂ is the stator resistance, L ₂ is the stator inductance, is the q-axis voltage, is the moment of inertia of the synchronous motor 21, is the d-axis voltage, is the electromagnetic torque of the synchronous motor 21, is the moment of inertia of the second reduction box 22, is the moment of inertia of the second synchronous wheel 23, Be the frictional force of the second synchronous wheel 23, F _f is the damping coefficient under load, is the d-axis current, is the load torque, Be the viscous damping coefficient of synchronous motor 21, λ ₂ is magnetic flux, is the rotational speed of the second synchronous wheel 23, is the viscous damping coefficient of the second synchronous wheel 23, and G ₂ is the reduction ratio of the second reduction box 22.

Further, define And after substituting it into (1), the following state space expression is obtained:

in And η ₁ represents the out-of-synchronization coefficient of the dual-motor speed, and

In addition, when the motor is working, the resistance value of its internal copper winding will satisfy the relationship as follows:

R _n ＝R ₀ +aR ₀ (T _n -T ₀ ) (4)

Among them, R ₀ is the resistance value at temperature T ₀ , R _n is the resistance value at temperature T _n , a is the temperature coefficient of copper resistance, and the parameter uncertainty of obtaining subsystem (10) is as follows:

Similarly, the system model of subsystem (20) is obtained as follows:

in And η ₂ represents the out-of-synchronization coefficient of the dual-motor speed, and

Further, referring to the fuzzy membership function shown in Fig. 4, the nonlinear interconnection system can be expressed as follows through the T-S fuzzy model:

In step S3, please refer to Fig. 3, the design scheme of described setting up decentralized robust full-closed-loop fuzzy subsection synchronous _H∞ controller, comprises the following steps:

S31, constructing a discrete model of the virtual principal axis:

Wherein, the virtual main shaft outputs the reference signal of the motor current and speed, and the position of the synchronous belt;

S32, segment the fuzzy antecedent variable space into a single linear space and fuzzy space, and design the following decentralized full-closed-loop fuzzy segmented synchronous controller:

u _i (t)=K _ij (y _i (t)-y _r (t)),j∈{1,2,…,27},i={1,2} (8)

The parameters of the decentralized full-closed-loop fuzzy segment synchronous controller are obtained by the following method:

First, based on the switching principle of fuzzy antecedent variable space, the discrete model (6) is rewritten as:

in,

Combining formulas (7)-(9), the following closed-loop fuzzy control system is obtained:

in

By means of augmentation, the closed-loop fuzzy control system (10) is expressed as the following generalized system model:

in

Consider the following piecewise Lyapunov functional:

in, and define

△V _i (t)=V _i (t+1)-V _i (t), and along the trajectory of the generalized system model (11), obtain:

definition We get the following inequality:

definition and matrix And with the generalized system model (11), we get:

Introduce scalar parameter 0<ρ _ij ≤ρ _i0 , and through (14) and (15), get:

Consider the following performance metrics function:

And after combining (13)-(17), get:

in

From the inequality (18), it can be concluded that in the case of zero initial, the closed-loop control system is asymptotically stable, and can ensure that the system has H _∞ performance index γ, when the following matrix inequality holds:

Among them, (j,s)∈{1,2,…,27}, i∈{1,2}.

By using Schur's lemma, formula (19) can be rewritten into the following form:

Next, in order to transform the inequality (20) into the case of linear matrix inequality, the matrix G _ij is limited to the following structure:

in, is a non-singular matrix.

undetermined parameter Written as follows:

in,

Substituting formulas (21) and (22) into (20), for all m∈Ι _i (j), i∈{1,2}, j={1,2,...,27}, the following matrix inequality holds Guarantee that formula (20) holds:

in

design method as claimed in claim 8, is characterized in that, by the LMI solving formula (23) of MATLAB, thereby obtains the design parameter of decentralized robust full-closed-loop fuzzy subsection synchronous H _∞ controller:

After step S3, please refer to FIG. 5, which may further include the step of building a DSPACE simulation test platform.

Note that the above are only preferred embodiments of the present invention and applied technical principles. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the protection scope of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and can also include more other equivalent embodiments without departing from the concept of the present invention, and the present invention The scope is determined by the scope of the appended claims.

Claims (7)

1. A controller design method for a dual-motor drive system, characterized in that, comprising the steps: Build a dual-motor synchronous drive experimental system, wherein the experimental system includes two sets of permanent magnet synchronous motors and a synchronous belt, and the two sets of permanent magnet synchronous motors jointly drive the synchronous belt to run; According to the principle of dynamics, a mathematical model of the dual-motor synchronous drive experimental system is established, which belongs to an interconnected system with a nonlinear subsystem 10 and a nonlinear subsystem 20; Based on the mathematical model, the design scheme of the decentralized robust full-closed-loop fuzzy subsection synchronous _H∞ controller is established, including the following steps: First, construct a discrete model of the virtual principal axis: Wherein, the virtual main shaft outputs the reference signal of the motor current and speed, and the position of the synchronous belt; Then, the fuzzy antecedent variable space is divided into a single linear space and a fuzzy space, and the following decentralized full-closed-loop fuzzy segmented synchronous controller is designed: u _i (t) = K _ij (y _i (t) - y _r (t)), j ∈ {1,2,...,27}, i = {1,2} (8); The mathematical model of the nonlinear subsystem 10 is as formula (1): in in, is the angular velocity of the motor, P ₁ is the number of stages of the motor, is the q-axis current, R ₁ is the stator resistance, L ₁ is the stator inductance, V ₁ ^(qs) is the q-axis voltage, is the moment of inertia of the motor, V ₁ ^(ds) is the d-axis voltage, is the electromagnetic torque of the motor, is the moment of inertia of the reduction gear, is the moment of inertia of the synchronous wheel, k ₁ (s), k ₂ (s), k ₃ is the elastic coefficient of the synchronous belt, r is the radius of the synchronous wheel, M is the load mass, T ₁ ^(w) is the friction force of the synchronous wheel, F _f is the damping coefficient under load, is the d-axis current, T ₁ ^(L) is the load torque, is the viscous damping coefficient of the motor, λ ₁ is the magnetic flux, is the speed of the driving wheel, B _l is the viscous damping coefficient of the linear guide, is the viscous damping coefficient of the drive wheel, G ₁ is the reduction ratio of the reduction device, s is the moving distance of the synchronous belt, and v is the moving speed of the synchronous belt; The mathematical model of nonlinear subsystem 20 is as formula (2): in, is the angular velocity of the motor, P ₂ is the number of stages of the motor, is the q-axis current, R ₂ is the stator resistance, L ₂ is the stator inductance, is the q-axis voltage, is the moment of inertia of the motor, is the d-axis voltage, is the electromagnetic torque of the motor, is the moment of inertia of the reduction gear, is the moment of inertia of the synchronous wheel, is the synchronous wheel friction, F _f is the damping coefficient under load, is the d-axis current, is the load torque, is the viscous damping coefficient of the motor, λ ₂ is the magnetic flux, is the driving wheel speed, is the viscous damping coefficient of the driving wheel, and _G2 is the reduction ratio of the reduction gear. 2. The design method according to claim 1, characterized in that the definition And substituting it into formula (1) to get the state space expression of the first drive system: in And η represents the asynchronous coefficient of the dual-motor speed, and In addition, when the motor is working, the resistance value of its internal copper winding will satisfy the relationship as follows: R _n =R ₀ +aR ₀ (T _n -T ₀ ), (4) Among them, R ₀ is the resistance value at temperature T ₀ , R _n is the resistance value at temperature T _n , a is the temperature coefficient of copper resistance, and the parameter uncertainty of obtaining the nonlinear subsystem 10 is as follows: 3. design method as claimed in claim 2, obtain the state-space expression of following second cover drive system: in And η represents the asynchronous coefficient of the dual-motor speed, and 4. the design method as claimed in claim 3, is characterized in that, described nonlinear interconnected system is represented as follows by T-S fuzzy model: 5. design method as claimed in claim 4, is characterized in that, the parameter of described decentralized full-closed-loop fuzzy subsection synchronous controller obtains by following method: First, based on the switching principle of fuzzy antecedent variable space, the discrete model (6) is rewritten as: in, Combining formulas (7)-(9), the following closed-loop fuzzy control system is obtained: in By means of augmentation, the closed-loop fuzzy control system (10) is expressed as the following generalized system model: in Consider the following piecewise Lyapunov functional: in, And define △V _i (t)=V _i (t+1)-V _i (t), and along the trajectory of the generalized system model (11), get: definition We get the following inequality: definition and matrix And with the generalized system model (11), we get: Introduce the scalar parameter 0<ρ _ij ≤ρ _i0 , and through (14) and (15), get: Consider the following performance metrics function: And after combining (13)-(17), get: in From the inequality (18), it can be concluded that in the case of zero initial, the closed-loop control system is asymptotically stable, and can ensure that the system has H _∞ performance index γ, when the following matrix inequality holds: where j∈{1,2,…,27}, i∈{1,2} By using Schur's lemma, formula (19) can be rewritten into the following form: Next, in order to transform the inequality (20) into the case of linear matrix inequality, the matrix G _ij is limited to the following structure: in, is a non-singular matrix, undetermined parameter Written as follows: in, Substituting formulas (21) and (22) into (20), for all m∈Ι _i (j), i∈{1,2}, j={1,2,…,27}, the following matrix inequalities hold Guarantee that formula (20) holds: in 6. design method as claimed in claim 5, it is characterized in that, by the LMI solving formula (23) of MATLAB, thereby obtain the design parameter of decentralized robust fully closed-loop fuzzy subsection synchronous H∞ controller: 7. The design method according to claim 1, further comprising setting up a simulation test platform of DSPACE.