CN116638544A - Joint module cooperative control method based on super local model - Google Patents
Joint module cooperative control method based on super local model Download PDFInfo
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Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J17/00—Joints
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P70/00—Climate change mitigation technologies in the production process for final industrial or consumer products
- Y02P70/10—Greenhouse gas [GHG] capture, material saving, heat recovery or other energy efficient measures, e.g. motor control, characterised by manufacturing processes, e.g. for rolling metal or metal working
Abstract
Compared with the prior art, the invention solves the problems that the control performance of the joint module is reduced and the control robustness of the joint module is poor because the control performance of the joint module cannot be effectively influenced by uncertainty factors only by completing high-performance control of the joint module by highly depending on a plurality of parameters of the joint module. The invention comprises the following steps: acquiring operation data of the joint module; establishing a dynamic equation of the joint module; building a super-local model of the joint module; designing a cooperative controller; and realizing cooperative control of the joint modules. The invention carries out cooperative controller design based on the super local model of the joint module, has the characteristic of not depending on a system model, and can effectively solve the problems of control performance reduction and poor robustness caused by uncertainty factors in the joint module.
Description
Technical Field
The invention relates to the technical field of joint module control of mechanical arms, in particular to a joint module cooperative control method based on a super local model.
Background
With the rapid development of information technology, control technology and mechanical technology, robotics have grown. As one of the most popular technologies in robotics, robotic arms have received increasing attention in recent years. With the wide application of mechanical arms in production and life, the mechanical arms are developing towards modularization and man-machine cooperation. The joint module is taken as a basic unit of the modularized mechanical arm, is a typical motor-gear system, mainly comprises a servo system controller, a permanent magnet synchronous motor, a transmission device and a sensor, and has the advantages of light weight, high load-to-weight ratio, low power and low power consumption. Therefore, the servo driving performance of the joint module largely determines the overall performance of the mechanical arm.
However, the joint model is a complex, nonlinear and uncertainty-sensitive system. There are various uncertainty factors in the joint model set, including: uncertainty of system structure, uncertainty of modeling, such as: uncertainty of moment of inertia, change of system parameters such as viscosity friction coefficient and the like caused by temperature change; unstructured uncertainties, such as: load torque disturbances, electromagnetic disturbances, control target variations, etc., which can greatly degrade the control performance of the joint module. In this case, the control of the joint module by the conventional control method cannot achieve a satisfactory control effect. Therefore, it is a challenging task how to achieve high performance control of the multi-variable, strongly coupled, time-varying nonlinear system of joint modules.
In order to overcome the influence of various uncertainty factors on the control performance of the mechanical arm joint module, some scholars begin to introduce a nonlinear control method into a control system of the mechanical arm joint module. The literature (Liu Rongyao. Design and drive control research of joint module system of cooperative robot. Joint module university of joint industry, 2020) adopts an adaptive robust control method aiming at the problem of control performance degradation caused by various uncertainty factors in joint modules, but the method needs real-time parameter estimation and adjustment of the system, and needs a large amount of calculation and storage resources, so that the complexity of the controller is high. Literature (Cui Yalei. Research on driving and controlling of joint modules of a collaborative robot based on a DSP. University of the joint industry, 2021) designs a robust control algorithm based on a model to solve the problem of control performance degradation caused by uncertainty factors in the joint modules, but the method needs to construct a system model, and a plurality of physical parameters of the system are required to construct the system model, and are often difficult to accurately acquire and are easily influenced by a plurality of difficult-to-quantify factors, so that control performance and robustness are degraded. Literature (Xue. Fuzzy backstepping control of PMSM driven joint robot. Qingdao university, 2020) adopts fuzzy control, and although a mathematical model of a system is not required to be established, the anti-jamming capability is strong, the capability of eliminating steady-state errors is poor, and high-precision control of a mechanical arm joint module is difficult to realize. Literature (Lu Zhiyuan. Industrial robot joint servo load disturbance rejection strategy research Anhui engineering university, 2022) uses nonlinear disturbance rejection controllers to improve the disturbance rejection capability of joint module servo control systems, but nonlinear disturbance rejection controllers generally require real-time parameter estimation and calculation of the system, are higher in computational complexity than conventional controllers, are higher in hardware requirements, and require controllers with stronger computational resources and real-time performance. Literature (Tang Bo. High response and high precision position control study of permanent magnet synchronous motors for integrated joints of cooperative robots. Zhejiang university of technology, 2022) adopts sliding mode variable structure control to improve response speed and anti-interference capability, but a sliding mode variable structure controller realizes control by introducing a sliding mode surface, and control signals are frequently switched on the sliding mode surface, so that buffeting phenomenon of a system can occur.
In summary, based on the defects of high dependence on an accurate mathematical model of a system and poor control performance of the existing mechanical arm joint module control method, designing a controller capable of getting rid of the dependence on parameters of the mechanical arm joint module and effectively aiming at uncertainty factors to cause the control performance to be reduced and effectively improving the control performance of the controller becomes a problem to be solved urgently.
Disclosure of Invention
The invention aims to solve the defects that in the prior art, high performance control on a joint module can be completed only by highly depending on a plurality of parameters of the joint module, the problem of control performance reduction caused by uncertainty factors cannot be effectively solved, and the robustness of joint module control is poor.
In order to achieve the above object, the technical scheme of the present invention is as follows:
a joint module cooperative control method based on a super local model comprises the following steps:
acquiring operation data of a joint module: measuring by an absolute value encoder on an output shaft of the joint module to obtain the angular displacement of the joint module, and differentiating the angular displacement to obtain the angular velocity of the joint module;
establishing a dynamic equation of the joint module;
building a super-local model of the joint module: according to a dynamics equation of the joint module, a super-local model of the joint module is established;
and (3) designing a cooperative controller: based on the super local model of the joint module, designing a cooperative controller according to a cooperative control theory;
realizing cooperative control of the joint modules: based on the obtained angular displacement and angular velocity information of the joint module, the output electromagnetic torque of the permanent magnet synchronous motor in the joint module is obtained through the cooperative controller, so that the joint module is driven to operate to reach the expected angular displacement.
The dynamic equation for establishing the joint module comprises the following steps:
based on dynamics analysis, the joint module is equivalent to be composed of a permanent magnet synchronous motor and a harmonic reducer, and then the mathematical model of the permanent magnet synchronous motor is set as follows:
wherein ,id 、i q 、u d 、u q 、L d 、L q Respectively represent the same permanent magnetStator current, stator voltage and stator inductance of d-axis and q-axis of step motor, n p Represents the pole pair number, q,Angular displacement, angular velocity and angular acceleration of the rotor, respectively, R is the stator resistance, ψ f Is a permanent magnet flux linkage, J, B, τ and T lp Respectively representing the rotational inertia, viscous friction coefficient, electromagnetic torque and load torque of the permanent magnet synchronous motor, wherein t is the running time of the joint module, and +.>Is the derivative operation of time t;
the electromagnetic torque output by the permanent magnet synchronous motor is as follows:
wherein ,id 、i q 、u d 、u q 、L d 、L q Stator current and stator inductance respectively representing d axis and q axis of permanent magnet synchronous motor, n p Represents the pole pair number, ψ f Representing the flux linkage of a permanent magnet, and tau represents the electromagnetic torque of the permanent magnet synchronous motor;
according to the magnetic field orientation control technology principle, aiming at the surface-mounted permanent magnet synchronous motor used by the joint module, the three-phase stator current synthesis vector is controlled on the q axis to ensure that i is d Zero, i.e. i d =0, realizing maximum torque control per ampere current, so that the torque control has better dynamic steady state performance;
l exists for surface-mounted permanent magnet synchronous motor used for joint module d ＝L q ＝L S Thus, the mathematical model of the surface-mounted permanent magnet synchronous motor is as follows:
wherein ,id 、i q 、u d 、u q 、L d 、L q Respectively representing the stator current, the stator voltage and the stator inductance of the d axis and the q axis of the permanent magnet synchronous motor, L S Represents the inductance of the stator, n p Represents the pole pair number, q,Angular displacement, angular velocity and angular acceleration of the rotor, respectively, R is the stator resistance, ψ f Is a permanent magnet flux linkage, J, B, τ and T lp Respectively representing the rotational inertia, viscous friction coefficient, electromagnetic torque and load torque of the permanent magnet synchronous motor, wherein t is the running time of the joint module, and +.>Is the derivative operation of time t;
according to the dynamics of the harmonic reducer, when the flexibility of the harmonic reducer is ignored, the following linear relationship exists at the input end and the output end of the harmonic reducer:
wherein eta is the transmission efficiency of the harmonic gear reducer, lambda is the transmission ratio and T l Representing the load torque on the output shaft of the joint module, T lp The load torque of the permanent magnet synchronous motor end in the joint module is represented, q is the angular displacement of the rotor of the permanent magnet synchronous motor, and x represents the angular displacement of the joint module;
based on the above formula (3) and formula (4), the kinetic equation of the joint module is deduced as follows:
wherein ,x、/> and />Respectively representing the angular displacement, the angular velocity and the angular acceleration of the joint module, J, B and tau respectively representing the moment of inertia, the viscous friction coefficient and the electromagnetic torque of the permanent magnet synchronous motor, and T l Representing the load torque on the output shaft of the joint module, T f The friction force in the harmonic reducer is represented, eta is the transmission efficiency of the harmonic reducer, lambda is the transmission ratio, and t is the running time of the joint module.
The building of the super local model of the joint module comprises the following steps:
defining a super local model:
x (v) (t)＝F+αu(t)，
where x (t) and u (t) represent the system output and system control input, respectively, and F is the sum of the nonlinearity and uncertainty of the system; alpha is the control channel gain, t is the system run time; v represents the highest order of the system, taking 1 or 2;
taking v=2 here, the super local model of the joint model is obtained as:
wherein ,the angular acceleration of the joint module is represented, F is the sum of nonlinearity and uncertainty of the joint module, tau represents electromagnetic torque of a permanent magnet synchronous motor in the joint module, and alpha is control channel gain;
the super-local model of the joint module is rewritten into the following form
wherein ,x1 Represents the angular displacement of the joint module, x 2 Represents the angular velocity of the joint module, F is the sum of the nonlinearity and uncertainty of the joint module, τ represents the electromagnetic torque of the permanent magnet synchronous motor in the joint module, α is the control channel gain, t is the running time of the joint module,is the derivative operation of time t;
the estimated value of the sum F of the nonlinearity and uncertainty of the joint module is obtained by using an algebraic estimation method, and comprises the following steps:
wherein ,TF Representing the size of the sliding window, is n of the sampling step size F Multiple, n F Setting according to the system condition; delta represents the sampling step size, alpha is the control channel gain,for time interval [0, T F ]An integral operation within.
The design cooperative controller comprises the following steps:
defining the angular displacement error e of the joint module 1 (t)＝x(t)-x d (t) angular velocity error of the Joint ModuleAngular acceleration error of a joint module>
wherein ,e1 (t) is the error of the desired angular displacement from the actual angular displacement, x (t) is the actual angular displacement of the joint module, x d (t) is the desired angular displacement of the joint module, e 2 (t) is the error of the desired angular velocity and the actual angular velocity,for the actual angular velocity of the joint module, +.>E is the desired angular velocity of the joint module 3 (t) is the error of the desired angular acceleration from the actual angular acceleration,for the actual angular acceleration of the joint module, +.>The desired angular acceleration for the joint module;
constructing a macro variable psi, and designing the macro variable in cooperative control into a proportional differential form:
ψ＝λ 1 e 1 (t)+λ 2 e 2 (t) (9)
wherein ψ is a macro variable, λ 1 ,λ 2 Is two normal numbers to be designed, e 1 (t) is the error of the desired angular displacement from the actual angular displacement, e 2 (t) is the error of the desired angular velocity and the actual angular velocity;
in order to ensure that the joint module system converges to the control manifold under the action of cooperative control, a dynamic evolution equation of macro-variable convergence is defined as follows:
wherein, psi is the macro variable of the above structure, T is the designed time constant, which represents the time of the state variable converging to the control manifold through the dynamic process, it has great influence on the convergence time of the system state, theoretically, the smaller the value of T, the faster the dynamic response speed of the system, but the value is limited by the requirement of the system stability;
bringing equation (9) into equation (10) yields:
T(λ 1 e 2 (t)+λ 2 e 3 (t))+(λ 1 e 1 (t)+λ 2 e 2 (t))＝0 (11)
wherein ,λ1 ,λ 2 Is two normal numbers to be designed, T is the time constant of the design, e 1 (t) is the error of the desired angular displacement from the actual angular displacement, e 2 (t) is the error between the desired angular velocity and the actual angular velocity, e 3 (t) is the error of the desired angular acceleration from the actual angular acceleration;
deriving a cooperative control law of the joint module based on the super-local model (7) of the joint module and the formula (11), and generating an electromagnetic torque reference value of the permanent magnet synchronous motor:
wherein ,represents an estimate of the sum of system nonlinearities and uncertainties, lambda 1 ,λ 2 Is two normal numbers to be designed, T is the time constant of the design, e 1 (t) is the error of the desired angular displacement from the actual angular displacement, e 2 (t) is the error of the desired angular velocity and the actual angular velocity, < >>For the desired angular acceleration of the joint module, α is the control channel gain, τ * Is the generated electromagnetic torque reference value of the permanent magnet synchronous motor.
Advantageous effects
Compared with the prior art, the joint module cooperative control method based on the super local model has the characteristics of being independent of a system model, and can effectively solve the problem of control performance reduction caused by uncertainty factors in the joint module. The invention is based on the establishment of the super local model of the joint module, and designs the cooperative controller, so that the control structure is simple, the dynamic and steady control performance of the joint module is effectively improved, and the system has strong robustness against the internal and external interference of the system.
Drawings
FIG. 1 is a process sequence diagram of the present invention;
FIG. 2 is a block diagram of a control method of the present invention;
FIG. 3 is a graph showing the comparison of the step response simulation effect of the joint module according to the embodiment of the present invention.
Fig. 4 is a graph comparing sinusoidal tracking simulation effects of a joint module provided by an embodiment of the present invention.
Detailed Description
For a further understanding and appreciation of the structural features and advantages achieved by the present invention, the following description is provided in connection with the accompanying drawings, which are presently preferred embodiments and are incorporated in the accompanying drawings, in which:
as shown in FIG. 1, the joint module cooperative control method based on the super local model provided by the invention comprises the following steps:
step one, acquiring operation data of a joint module: and measuring by an absolute value encoder on an output shaft of the joint module to obtain the angular displacement of the joint module, and differentiating the angular displacement to obtain the angular velocity of the joint module.
And secondly, establishing a dynamic equation of the joint module.
The joint module can be equivalent to the combination of a harmonic reducer and a permanent magnet synchronous motor, and the driving control performance of the permanent magnet synchronous motor can greatly influence the control performance of the joint module, so that the model of the permanent magnet synchronous motor is necessary to be taken into consideration. By linking the mathematical models of the permanent magnet synchronous motor and the harmonic reducer, a unified joint module dynamics equation is established.
The dynamic equation for establishing the joint module comprises the following steps:
(1) Based on dynamics analysis, the joint module is equivalent to be composed of a permanent magnet synchronous motor and a harmonic reducer, and then the mathematical model of the permanent magnet synchronous motor is set as follows:
wherein ,id 、i q 、u d 、u q 、L d 、L q Stator current, stator voltage and stator inductance respectively representing d axis and q axis of permanent magnet synchronous motor, n p Represents the pole pair number, q,Angular displacement, angular velocity and angular acceleration of the rotor, respectively, R is the stator resistance, ψ f Is a permanent magnet flux linkage, J, B, τ and T lp Respectively representing the rotational inertia, viscous friction coefficient, electromagnetic torque and load torque of the permanent magnet synchronous motor, wherein t is the running time of the joint module, and +.>Is a derivative operation of time t.
(2) The electromagnetic torque output by the permanent magnet synchronous motor is as follows:
wherein ,id 、i q 、u d 、u q 、L d 、L q Stator current and stator inductance respectively representing d axis and q axis of permanent magnet synchronous motor, n p Represents the pole pair number, ψ f Representing the permanent magnet flux linkage, τ represents the electromagnetic torque of the permanent magnet synchronous motor.
(3) According to the magnetic field orientation control technology principle, aiming at the surface-mounted permanent magnet synchronous motor used by the joint module, the three-phase stator current synthesis vector is controlled on the q axis to ensure that i is d Zero, i.e. i d =0, realizing maximum torque control per ampere current, so that the torque control has better dynamic steady state performance;
l exists for surface-mounted permanent magnet synchronous motor used for joint module d ＝L q ＝L S Thus, the mathematical model of the surface-mounted permanent magnet synchronous motor is as follows:
wherein ,id 、i q 、u d 、u q 、L d 、L q Respectively representing the stator current, the stator voltage and the stator inductance of the d axis and the q axis of the permanent magnet synchronous motor, L S Represents the inductance of the stator, n p Represents the pole pair number, q,Angular displacement, angular velocity and angular acceleration of the rotor, respectively, R is the stator resistance, ψ f Is a permanent magnet flux linkage, J, B, τ and T lp Respectively representing the rotational inertia, viscous friction coefficient, electromagnetic torque and load torque of the permanent magnet synchronous motor, wherein t is the running time of the joint module, and +.>Is a derivative operation of time t.
(4) According to the dynamics of the harmonic reducer, when the flexibility of the harmonic reducer is ignored, the following linear relationship exists at the input end and the output end of the harmonic reducer:
wherein eta is the transmission efficiency of the harmonic gear reducer, lambda is the transmission ratio and T l Representing the load torque on the output shaft of the joint module, T lp The load torque of the permanent magnet synchronous motor end in the joint module is represented, q is the angular displacement of the rotor of the permanent magnet synchronous motor, and x is the angular displacement of the joint module.
(5) Based on the above formula (3) and formula (4), the kinetic equation of the joint module is deduced as follows:
wherein ,x、/> and />Respectively representing the angular displacement, the angular velocity and the angular acceleration of the joint module, J, B and tau respectively representing the moment of inertia, the viscous friction coefficient and the electromagnetic torque of the permanent magnet synchronous motor, and T l Representing the load torque on the output shaft of the joint module, T f The friction force in the harmonic reducer is represented, eta is the transmission efficiency of the harmonic reducer, lambda is the transmission ratio, and t is the running time of the joint module.
Thirdly, building a super local model of the joint module: and establishing a super-local model of the joint module according to a dynamic equation of the joint module.
Based on the design of the controller by the joint module dynamics equation in the second step, it can be found that to complete the high-performance control of the joint module, a plurality of high-precision parameters of the joint module are required, and the control performance is deteriorated and even the system is unstable due to insufficient precision of the parameters; meanwhile, the design of the controller is carried out based on the dynamic equation of the joint module, and the influence of the control accuracy reduction caused by the parameter change in the operation process of the joint module cannot be effectively influenced. Therefore, it is extremely important to establish the super-local model of the joint module based on the joint module dynamics equation in the second step, dependence on various parameters of the joint module can be eliminated by depending on the super-local model of the joint module, and meanwhile, the condition of parameter change in operation of the joint module can be well processed, so that the robustness of joint module control is greatly improved.
The building of the super local model of the joint module comprises the following steps:
(1) Defining a super local model:
x (v) (t)＝F+αu(t)，
where x (t) and u (t) represent the system output and system control input, respectively, and F is the sum of the nonlinearity and uncertainty of the system; alpha is the control channel gain, t is the system run time; v represents the highest order of the system, taking 1 or 2;
taking v=2 here, the super local model of the joint model is obtained as:
wherein ,the angular acceleration of the joint module is represented, F is the sum of nonlinearity and uncertainty of the joint module, tau represents electromagnetic torque of a permanent magnet synchronous motor in the joint module, and alpha is control channel gain.
(2) The super-local model of the joint module is rewritten into the following form
wherein ,x1 Represents the angular displacement of the joint module, x 2 Represents the angular velocity of the joint module, F is the sum of the nonlinearity and uncertainty of the joint module, τ represents the electromagnetic torque of the permanent magnet synchronous motor in the joint module, α is the control channel gain, t is the running time of the joint module,is the derivative operation of time t;
the estimated value of the sum F of the nonlinearity and uncertainty of the joint module is obtained by using an algebraic estimation method, and comprises the following steps:
wherein ,TF Representing the size of the sliding window, is n of the sampling step size F Multiple, n F Setting according to the system condition; delta represents the sampling step size and alpha isThe gain of the channel is controlled and,for time interval [0, T F ]An integral operation within.
Fourth, designing a cooperative controller: based on the super local model of the joint module, the design of the cooperative controller is carried out according to the cooperative control theory.
The basic idea of cooperative control is to use self-organizing capability and nonlinear characteristics of the system to realize cooperative control of the system by designing a proper control manifold. The core is to realize control by utilizing the nonlinear characteristic of the system. The cooperative controller has low design difficulty, can generate smooth control signals, has good quick response performance, and can effectively strengthen the robustness of joint module control.
The design cooperative controller comprises the following steps:
(1) Defining the angular displacement error e of the joint module 1 (t)＝x(t)-x d (t) angular velocity error of the Joint ModuleAngular acceleration error of a joint module>
wherein ,e1 (t) is the error of the desired angular displacement from the actual angular displacement, x (t) is the actual angular displacement of the joint module, x d (t) is the desired angular displacement of the joint module, e 2 (t) is the error of the desired angular velocity and the actual angular velocity,for the actual angular velocity of the joint module, +.>E is the desired angular velocity of the joint module 3 (t) is the error of the desired angular acceleration from the actual angular acceleration, < >>For the actual angular acceleration of the joint module, +.>Is the desired angular acceleration of the joint module.
(2) Constructing a macro variable psi, and designing the macro variable in cooperative control into a proportional differential form:
ψ＝λ 1 e 1 (t)+λ 2 e 2 (t) (21)
wherein ψ is a macro variable, λ 1 ,λ 2 Is two normal numbers to be designed, e 1 (t) is the error of the desired angular displacement from the actual angular displacement, e 2 (t) is the error of the desired angular velocity and the actual angular velocity;
(3) In order to ensure that the joint module system converges to the control manifold under the action of cooperative control, a dynamic evolution equation of macro-variable convergence is defined as follows:
wherein, psi is the macro variable of the above structure, T is the designed time constant, which represents the time of the state variable converging to the control manifold through the dynamic process, it has great influence on the convergence time of the system state, theoretically, the smaller the value of T, the faster the dynamic response speed of the system, but the value is limited by the requirement of the system stability;
bringing equation (9) into equation (10) yields:
T(λ 1 e 2 (t)+λ 2 e 3 (t))+(λ 1 e 1 (t)+λ 2 e 2 (t))＝0 (23)
wherein ,λ1 ,λ 2 Is two normal numbers to be designed, T is the time constant of the design, e 1 (t) is the error of the desired angular displacement from the actual angular displacement, e 2 (t) is the error between the desired angular velocity and the actual angular velocity, e 3 (t) is the error of the desired angular acceleration from the actual angular acceleration。
(4) Deriving a cooperative control law of the joint module based on the super-local model (7) of the joint module and the formula (11), and generating an electromagnetic torque reference value of the permanent magnet synchronous motor:
wherein ,represents an estimate of the sum of system nonlinearities and uncertainties, lambda 1 ,λ 2 Is two normal numbers to be designed, T is the time constant of the design, e 1 (t) is the error of the desired angular displacement from the actual angular displacement, e 2 (t) is the error of the desired angular velocity and the actual angular velocity, < >>For the desired angular acceleration of the joint module, α is the control channel gain, τ * Is the generated electromagnetic torque reference value of the permanent magnet synchronous motor.
Fifthly, realizing cooperative control of the joint modules: based on the obtained angular displacement and angular velocity information of the joint module, the output electromagnetic torque of the permanent magnet synchronous motor in the joint module is obtained through the cooperative controller, so that the joint module is driven to operate to reach the expected angular displacement.
In order to verify the effectiveness of the joint module cooperative control method based on the super local model, matlab/Simulink simulation is carried out, and the specific process of the Matlab/Simulink simulation is as follows: the simulation model based on the superlocal model cooperative control joint module shown in figure 2 is established through Matlab/Simulink software, and parameters related to the joint module in the simulation are shown in the following table 1.
TABLE 1 model parameters table for joint model
| Parameter name | Symbolic representation | Numerical value | Unit (B) |
| Joint module displacement | x | - | rad |
| Moment of inertia of joint module | J | 1.65×10 -3 | kg·m 2 |
| PMSM viscous friction coefficient | B | 8×10 -3 | Nm/rad/sec |
| PMSM rotor flux linkage | ψ f | 0.025 | volts/rad/sec |
| PMSM pole pair number | n p | 6 | - |
| Speed reduction ratio of harmonic speed reducer | λ | 101 | - |
| Transmission efficiency of harmonic speed reducer | η | 0.95 | - |
As shown in FIG. 3, given the expected step signal in the simulation, compared with the control effect of the traditional PID and the super local model-based cooperative control two different controllers on the joint module, the super local model-based cooperative control joint module has higher response speed on the step signal without overshoot, and the steady-state precision is obviously improved compared with the PID control.
As shown in fig. 4, the input reference signal is a sinusoidal signal, and when the simulation starts, the influence of the two controllers on the joint module is consistent with the step signal, and when the system is stable, the cooperative control based on the super local model has smaller steady-state error than the PID control. Simulation results show that the designed controller has good dynamic performance, can realize rapid tracking, and meanwhile, greatly improves steady-state precision.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made therein without departing from the spirit and scope of the invention, which is defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (4)
1. The joint module cooperative control method based on the super local model is characterized by comprising the following steps of:
11 Acquisition of joint module operation data: measuring by an absolute value encoder on an output shaft of the joint module to obtain the angular displacement of the joint module, and differentiating the angular displacement to obtain the angular velocity of the joint module;
12 Establishing a dynamic equation of the joint module;
13 Building a super-local model of the joint module: according to a dynamics equation of the joint module, a super-local model of the joint module is established;
14 Design a cooperative controller: based on the super local model of the joint module, designing a cooperative controller according to a cooperative control theory;
15 Joint module cooperative control realization: based on the obtained angular displacement and angular velocity information of the joint module, the electromagnetic torque of the permanent magnet synchronous motor in the joint module is obtained through the cooperative controller, so that the joint module is driven to operate to reach the expected angular displacement.
2. The joint module cooperative control method based on the super local model according to claim 1, wherein the establishing a dynamic equation of the joint module comprises the following steps:
21 Based on dynamics analysis, the joint module is equivalent to be composed of a permanent magnet synchronous motor and a harmonic reducer, and then the mathematical model of the permanent magnet synchronous motor is as follows:
wherein ,id 、i q 、u d 、u q 、L d 、L q Stator current, stator voltage and stator inductance respectively representing d axis and q axis of permanent magnet synchronous motor, n p Represents the pole pair number, q,Angular displacement, angular velocity and angular acceleration of the rotor, respectively, R is the stator resistance, ψ f Is a permanent magnet flux linkage, J, B, τ and T lp Respectively representing the rotational inertia, viscous friction coefficient, electromagnetic torque and load torque of the permanent magnet synchronous motor, wherein t is the running time of the joint module, and +.>Is the derivative operation of time t;
22 For the electromagnetic torque of the permanent magnet synchronous motor, there are:
wherein ,id 、i q 、u d 、u q 、L d 、L q Stator current and stator inductance respectively representing d axis and q axis of permanent magnet synchronous motor, n p Represents the pole pair number, ψ f Representing the flux linkage of the permanent magnet, and tau represents the electromagnetic torque of the permanent magnet synchronous motor;
23 According to the magnetic field orientation control technology principle, the three-phase stator current synthesis vector is controlled on the q-axis aiming at the surface-mounted permanent magnet synchronous motor used by the joint module to ensure that i d Zero, i.e. i d =0, realizing maximum torque control per ampere current, so that the torque control has better dynamic steady state performance;
l exists for surface-mounted permanent magnet synchronous motor used for joint module d ＝L q ＝L S Thus, the mathematical model of the surface-mounted permanent magnet synchronous motor is as follows:
wherein ,id 、i q 、u d 、u q 、L d 、L q Respectively representing the stator current, the stator voltage and the stator inductance of the d axis and the q axis of the permanent magnet synchronous motor, L S Represents the inductance of the stator, n p Represents the pole pair number, q,Angular displacement, angular velocity and angular acceleration of the rotor, respectively, R is the stator resistance, ψ f Is a permanent magnet flux linkage, J, B, τ and T lp Respectively representing the rotational inertia, viscous friction coefficient, electromagnetic torque and load torque of the permanent magnet synchronous motor, wherein t is the running time of the joint module, and +.>Is the derivative operation of time t;
24 According to the dynamics of the harmonic reducer, when the flexibility of the harmonic reducer is ignored, the following linear relationship exists at the input end and the output end of the harmonic reducer:
wherein eta is the transmission efficiency of the harmonic gear reducer, lambda is the transmission ratio and T l Representing the load torque on the output shaft of the joint module, T lp The load torque of the permanent magnet synchronous motor end in the joint module is represented, q is the angular displacement of the rotor of the permanent magnet synchronous motor, and x represents the angular displacement of the joint module;
25 Based on the above formula (3) and formula (4), deriving the kinetic equation of the joint module in step 12) as:
wherein H (x, t) =λJ,x、/> and />Respectively representing the angular displacement, the angular velocity and the angular acceleration of the joint module, J, B and tau respectively representing the moment of inertia, the viscous friction coefficient and the electromagnetic torque of the permanent magnet synchronous motor, and T l Representing the load torque on the output shaft of the joint module, T f The friction force in the harmonic reducer is represented, eta is the transmission efficiency of the harmonic reducer, lambda is the transmission ratio, and t is the running time of the joint module.
3. The joint module cooperative control method based on the super-local model according to claim 1, wherein the building of the joint module super-local model comprises the following steps:
31 Defining a super local model:
x (v) (t)＝F+αu(t)，
where x (t) and u (t) represent the system output and system control input, respectively, and F is the sum of the nonlinearity and uncertainty of the system; alpha is the control channel gain, t is the system run time; v represents the highest order of the system, taking 1 or 2;
taking v=2 here, the super local model of the joint model is obtained as:
wherein ,the angular acceleration of the joint module is represented, F is the sum of nonlinearity and uncertainty of the joint module, tau represents electromagnetic torque of a permanent magnet synchronous motor in the joint module, and alpha is control channel gain;
32 The super-local model of the joint module is rewritten into the following form, namely:
wherein ,x1 Represents the angular displacement of the joint module, x 2 Represents the angular velocity of the joint module, F is the sum of the nonlinearity and uncertainty of the joint module, τ represents the electromagnetic torque of the permanent magnet synchronous motor in the joint module, α is the control channel gain, t is the running time of the joint module,is the derivative operation of time t;
the estimated value of the sum F of the nonlinearity and uncertainty of the joint module is obtained by using an algebraic estimation method, and comprises the following steps:
wherein ,TF Representing the size of the sliding window, is n of the sampling step size F Multiple, n F Setting according to the system condition; delta represents the sampling step size, alpha is the control channel gain,for time interval [0, T F ]An integral operation within.
4. The joint module cooperative control method based on the super local model as claimed in claim 1, wherein the design cooperative controller comprises the following steps:
41 Defining the angular displacement error e of the joint module 1 (t)＝x(t)-x d (t) angular velocity error of the Joint ModuleAngular acceleration error of a joint module>
wherein ,e1 (t) is the error between the desired and actual angular displacements, x (t) is the joint modelIs x d (t) is the desired angular displacement of the joint module, e 2 (t) is the error of the desired angular velocity and the actual angular velocity,for the actual angular velocity of the joint module, +.>E is the desired angular velocity of the joint module 3 (t) is the error of the desired angular acceleration from the actual angular acceleration,for the actual angular acceleration of the joint module, +.>The desired angular acceleration for the joint module;
42 Constructing a macro variable psi, and designing the macro variable in cooperative control into a proportional differential form:
ψ＝λ 1 e 1 (t)+λ 2 e 2 (t) (9)
wherein ψ is a macro variable, λ 1 ,λ 2 Is two normal numbers to be designed, e 1 (t) is the error of the desired angular displacement from the actual angular displacement, e 2 (t) is the error of the desired angular velocity and the actual angular velocity;
43 To ensure that the joint module converges to the control manifold under the action of cooperative control, a dynamic evolution equation of macro-variable convergence is defined as follows:
wherein, psi is the macro variable of the above structure, T is the designed time constant, which represents the time of the state variable converging to the control manifold through the dynamic process, it has great influence on the convergence time of the system state, theoretically, the smaller the value of T, the faster the dynamic response speed of the system, but the value is limited by the requirement of the system stability;
bringing equation (9) into equation (10) yields:
T(λ 1 e 2 (t)+λ 2 e 3 (t))+(λ 1 e 1 (t)+λ 2 e 2 (t))＝0 (11)
wherein ,λ1 ,λ 2 Is two normal numbers to be designed, T is the time constant of the design, e 1 (t) is the error of the desired angular displacement from the actual angular displacement, e 2 (t) is the error between the desired angular velocity and the actual angular velocity, e 3 (t) is the error of the desired angular acceleration from the actual angular acceleration;
44 Based on the super local model (7) of the joint module and the formula (11), deducing a cooperative control law of the joint module, and generating an electromagnetic torque reference value of the permanent magnet synchronous motor:
wherein ,represents an estimate of the sum of system nonlinearities and uncertainties, lambda 1 ,λ 2 Is two normal numbers to be designed, T is the time constant of the design, e 1 (t) is the error of the desired angular displacement from the actual angular displacement, e 2 (t) is the error of the desired angular velocity and the actual angular velocity, < >>For the desired angular acceleration of the joint module, α is the control channel gain, τ * Is the generated electromagnetic torque reference value of the permanent magnet synchronous motor.
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