CN111293949A - Control method of anti-interference electric six-degree-of-freedom parallel mechanism - Google Patents

Control method of anti-interference electric six-degree-of-freedom parallel mechanism Download PDF

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CN111293949A
CN111293949A CN202010207104.5A CN202010207104A CN111293949A CN 111293949 A CN111293949 A CN 111293949A CN 202010207104 A CN202010207104 A CN 202010207104A CN 111293949 A CN111293949 A CN 111293949A
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torque
control
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CN111293949B (en
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陈熙源
刘建国
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Southeast University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P23/0027—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using different modes of control depending on a parameter, e.g. the speed
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/12—Observer control, e.g. using Luenberger observers or Kalman filters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/14—Estimation or adaptation of motor parameters, e.g. rotor time constant, flux, speed, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/08—Arrangements for controlling the speed or torque of a single motor
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/34—Modelling or simulation for control purposes
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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Abstract

The invention discloses an anti-interference control method for an electric six-freedom-degree parallel mechanism, which comprises the steps of firstly establishing a mathematical model of the mechanism aiming at the characteristics of nonlinearity, strong coupling and the like of the electric six-freedom-degree parallel mechanism, designing a cascade control model based on a hinge space of a linear actuator and an attitude space of a motion platform, taking control based on a hinge point space as an inner ring and taking control based on the attitude space of the motion platform as an outer ring, and adopting PID controllers for the two. Aiming at the characteristics that the load torque of a single linear actuator of a six-degree-of-freedom parallel mechanism changes in real time and influences the control precision, the angular acceleration information of the actuator is acquired by adopting a state observer, and an anti-interference compensation controller is designed on the basis of the angular acceleration information so as to eliminate the influence of disturbance on the control precision. And finally, obtaining the optimal PID control parameter by using a Zieler-Nichols PID parameter setting method. The control effect of the method on the electric six-degree-of-freedom parallel mechanism is superior to that of the traditional PID method based on the hinge space.

Description

Control method of anti-interference electric six-degree-of-freedom parallel mechanism
Technical Field
The invention belongs to the field of automatic control of systems, and particularly relates to a control method of an anti-interference electric six-degree-of-freedom parallel mechanism.
Background
In recent years, a control algorithm of a six-degree-of-freedom parallel mechanism becomes one of research hotspots of scholars at home and abroad, and the six-degree-of-freedom parallel mechanism is taken as a large branch of an industrial robot, has the advantages of large bearing capacity, strong rigidity, high precision, simple design and the like, is widely applied to military and civil fields such as ships, aviation, electric power, vehicles and the like, and has extremely wide application prospect. The six-degree-of-freedom parallel mechanism is a complex system with the characteristics of nonlinearity, strong coupling and static instability, and has certain difficulty in realizing efficient and stable control. Meanwhile, due to the change of the load and the motion characteristic of the load, the load of each linear actuating mechanism is changed in real time, and the change characteristic is difficult to obtain, so that the control difficulty is further increased. Therefore, the control method for designing the high-performance six-degree-of-freedom parallel mechanism has very important application value.
The PID controller which controls according to the proportion (P), the integral (I) and the differential (D) of the deviation is the most widely applied six-freedom-degree parallel mechanism controller and has the characteristics of simplicity, stability and easy realization. However, as the complexity of the system is higher and higher, and the system parameters and the working environment are changed continuously, the conventional PID controller is difficult to meet the precise control requirement. New controllers need to be designed to meet the complex control requirements.
In the existing research results, the attitude control of the parallel mechanism is mostly designed based on an actuator hinge space model, the coupling effect between an attitude space and each actuator is not considered, and the control effect is difficult to guarantee when model uncertainty and external interference exist. The six-degree-of-freedom electric motion platform has the characteristic of serious nonlinearity, is a space multi-degree-of-freedom and multi-parameter cross coupling system, and the research on the control method mainly comprises a control strategy based on a hinge point space and a control strategy based on a mechanism dynamic model. The former is a traditional control mode, and six linear actuators of the motion platform are regarded as independent single-channel systems to be controlled. For each electric servo system, the load characteristic is changed at any time along with the pose change of the moving platform, in the process of designing the control system, the load characteristic is equivalent to equivalent interference force and equivalent mass, however, the moving platform of the six-degree-of-freedom parallel mechanism is in different poses, the equivalent mass change is large, and meanwhile, the equivalent interference force change is very large. On the basis of comprehensively considering the dynamic characteristics of the system and the dynamic performance of each channel, the controller is designed by adopting a control strategy based on a system dynamic model, the overall performance of the system can be improved, but when the load has a time-varying characteristic, the control effect is not obvious, the modeling is difficult, and the calculation amount is large.
Disclosure of Invention
In order to solve the problems, the invention discloses an anti-interference electric six-degree-of-freedom parallel mechanism control method, which aims at the six-degree-of-freedom parallel mechanism with strong interference, uncertain model and coupling of each channel and realizes accurate attitude control.
In order to achieve the purpose, the technical scheme of the invention is as follows:
an anti-interference electric six-degree-of-freedom parallel mechanism control method comprises the following steps:
step 1), the actuator researched by the invention is a linear guide rail type actuator driven by a permanent magnet synchronous servo motor, the transmission part of the actuator is a ball screw, the system simplifies the screw transmission part into an ideal model, and the screw transmission part is equivalent to a mathematical model mainly considering the rigidity, the damping and the rotational inertia of the screw transmission part:
step 1.1), obtaining a torque balance equation according to the transmission characteristics of the screw rod, wherein the torque balance equation is as follows:
Figure BDA0002421495800000021
wherein, JLFor the mechanical transmission part, calculating the total moment of inertia of the motor, BLCalculating the total viscous damping coefficient, T, to the motor for the mechanical transmission partL(T) is the load torque, Tm(t) is motor output torque, θLAnd (t) is the output rotation angle of the screw rod.
Step 1.2), according to a screw stiffness formula, a screw driving torque can be expressed as:
Tm＝KL[θe-θL]
wherein, TL(t) is the output torque of the motor, KLFor converting the mechanical transmission part into the total rotational stiffness, theta, of the output shaft of the linear actuatore(t) is the motor output rotation angle, θLAnd (t) is the output rotation angle of the screw rod.
Step 1.3), the relationship between the expansion amount of the linear actuator and the output displacement of the screw shaft is as follows:
Figure BDA0002421495800000022
wherein, thetaL(t) is the motor output rotation angle, PhFor transmission lead, XLIs the linear displacement of the screw rod.
And step 2), modeling the permanent magnet synchronous servo motor.
Step 2.1), a driving motor torque model is established, the model adopts a permanent magnet synchronous servo motor, and the torque equation process expression is as follows:
Figure BDA0002421495800000023
Te(t)＝Ktiq(t)
wherein, Te(T) is the electromagnetic torque of the machine, TL(t) load torque, J moment of inertia, KtIs a torque constant, iqAnd (t) is a q-axis stator current. B is the damping coefficient of the motor, thetaeAnd (t) is the output rotation angle of the motor.
And 2.2) establishing a driving motor control model. The servo motor of the system is a speed ring structure, the speed controller is a PI controller, and the current ring is used as an inner ring of the speed ring controller.
The closed loop transfer function of the current loop is equivalent to a first-order inertia link, omegacCurrent loop bandwidth:
Figure BDA0002421495800000024
the transfer function of the motor current to the electromagnetic torque is:
MI(s)＝Ktiq(t)
wherein, KtIs the motor torque constant, iq(t) is a q-axis current.
The electromagnetic torque to motor speed transfer function is:
Figure BDA0002421495800000031
wherein, J moment of inertia, B damping coefficient.
The digital low pass filter is designed to suppress high frequency noise in the velocity signal with a transfer function of, wherefFor the filter bandwidth:
Figure BDA0002421495800000032
and step 3), designing a cascade controller. And taking control based on a hinge point space as an inner ring and taking control based on a motion platform attitude space as an outer ring. The inner ring controller is a single-input single-output system loop formed by each supporting leg, a PID controller is adopted, and a feedback signal is measured by a linear displacement sensor. The outer ring is compensation control based on an attitude space, the actual measurement attitude is obtained through positive solution to realize the correction of the input attitude, and a PID control method is adopted. The system is positively solved, namely the space attitude of the moving platform is calculated through the length of the supporting leg, a Newton-Raphson iteration method is adopted, and the method comprises the following specific steps:
step 3.1), the distance formula between the hinge points of the linear actuator is as follows:
Figure BDA0002421495800000033
Δli＝li-l0
wherein liIs the i-th actuator length, gkiFor each point after the moving coordinate system is transformed into the static coordinate systemLabel, bkiAs a reference frame coordinate point,/0To the initial length of the actuator, Δ liCorresponding to the expansion amount of the actuator.
Step 3.2), solving the moving platform attitude by utilizing linearization processing and a Newton-Raphson iteration method, wherein the equation is as follows:
Figure BDA0002421495800000034
obtaining a nonlinear equation system containing six unknowns:
Figure BDA0002421495800000035
wherein q is [ q ]1,q2…q6]T＝[x,y,z,α,β,γ]TRepresenting six poses of the motion platform, respectively.
And 3.3) solving a nonlinear equation system. In the formula fi(q1,q2…q6) At point (q)10,q20…q60) Performing binary Taylor series expansion on the neighborhood, and obtaining the linear part of the binary Taylor series expansion:
Figure BDA0002421495800000041
in the formula (f)i(Q0)＝fi(q10,q20…q60) (i ═ 1,2 … 6). And obtaining a solution meeting the calculation precision through repeated approximation and iterative operation.
And 4), designing an anti-interference compensator.
Step 4.1), acquiring angular acceleration information of the actuator by adopting a state observer, and designing a strategy for compensating and controlling disturbance by observing the angular acceleration information on the basis of the angular acceleration information, wherein the design basis is a driving motor torque equation, and a specific expression of the driving motor torque equation is as follows:
Figure BDA0002421495800000042
angular velocity information
Figure BDA0002421495800000043
Measured by a motor encoder, the output torque T of the motore(T) is an input signal, which is sent to an execution motor by a control command, and the load torque TLAnd (t) is a disturbance signal and is a variable to be estimated.
Step 4.2), mixing
Figure BDA0002421495800000044
And
Figure BDA0002421495800000045
as state variables, the design state equations are as follows:
Figure BDA0002421495800000046
y(t)＝Cx(t)
state vector:
Figure BDA0002421495800000047
input quantity: u (T) ═ Te(t), outputting:
Figure BDA0002421495800000048
Figure BDA0002421495800000049
step 4.3), the system can be completely observed by the observability matrix, so the state observer is designed as follows:
Figure BDA00024214958000000410
wherein
Figure BDA00024214958000000411
Is an estimate of x (t), G is the state observer gain matrix, which will
Figure BDA00024214958000000412
Negative feedback loop
Figure BDA00024214958000000413
The purpose of the method is to configure the pole of the observer, improve the dynamic performance and enable the error vector of the estimated state and the real state
Figure BDA00024214958000000414
Approaching 0 as soon as possible.
Step 4.4), the dynamic behavior of the error is:
Figure BDA0002421495800000051
step 4.5), solving an error equation, wherein a specific expression of the error equation is as follows:
Figure BDA0002421495800000052
and 4.6) considering the A-GC as a second-order system, and calculating a gain matrix by referring to the optimal parameters of the second-order system.
And 5) based on the above, obtaining the optimal PID control parameter by using a Zieler-Nichols PID parameter diagnosis method.
The invention has the beneficial effects that:
1. the invention comprehensively uses cascade control, an anti-interference compensator and a Zieler-Nichols PID parameter setting method, overcomes the defects of dependence on an accurate mathematical model, complex operation process and the like of the traditional control method, and improves the control precision;
2. the invention uses the cascade control idea to improve the control precision. The invention designs the cascade controller of the inner ring controller based on the hinge space and the outer ring controller based on the hinge space, overcomes the attitude error caused by the coupling between linear actuators, and makes up the defects of the traditional method only applying the controller based on the hinge space;
3. the invention adopts the state observer to acquire the angular acceleration information of the actuator, designs the disturbance compensation control strategy based on the angular acceleration information on the basis, and overcomes the influence of load change on the control precision of the linear actuator.
Drawings
FIG. 1 is a schematic control flow diagram of the process of the present invention.
FIG. 2 is a diagram of the commanded pose for simulation according to the present invention. Where roll represents angle around the x-axis, pitch represents angle around the y-axis, and heave represents displacement along the z-axis.
Fig. 3 is a 6 linear actuator tracking error curve. 0-100s only use a traditional hinge space based PID controller; 100-200s, the cascade controller of the invention is used, but the anti-interference compensator is closed; 200s and 300s use the cascade controller and the anti-interference compensator of the invention.
Fig. 4 shows the motion platform attitude tracking error curves [ (1), (2), and (3) respectively correspond to roll, pitch, and heave tracking errors ]. 0-100s only use a traditional hinge space based PID controller; 100-200s, the cascade controller of the invention is used, but the anti-interference compensator is closed; 200s and 300s use the cascade controller and the anti-interference compensator of the invention.
FIG. 5 is a structure diagram of a six-degree-of-freedom parallel mechanism, which is composed of a moving platform, a static platform, a linear actuator and the like.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention.
As shown in fig. 1, the invention discloses an anti-interference electric six-degree-of-freedom parallel mechanism control method, which comprises the following steps:
step 1), the actuator studied in this paper is the linear guide rail type actuator driven by the permanent magnet synchronous servo motor, its transmission part is the ball screw, simplify the screw transmission part to the ideal model in this system, equate the screw transmission part to a mathematical model mainly considering its rigidity, damping and moment of inertia:
step 1.1), obtaining a torque balance equation according to the transmission characteristics of the screw rod, wherein the torque balance equation is as follows:
Figure BDA0002421495800000061
wherein, JLFor the mechanical transmission part, calculating the total moment of inertia of the motor, BLCalculating the total viscous damping coefficient, T, to the motor for the mechanical transmission partL(T) is the load torque, Tm(t) is motor output torque, θLAnd (t) is the output rotation angle of the screw rod.
Step 1.2), according to a screw stiffness formula, a screw driving torque can be expressed as:
Tm＝KL[θe-θL](2)
wherein, TL(t) is the output torque of the motor, KLFor converting the mechanical transmission part into the total rotational stiffness, theta, of the output shaft of the linear actuatore(t) is the motor output rotation angle, θLAnd (t) is the output rotation angle of the screw rod.
Step 1.3), the relationship between the expansion amount of the linear actuator and the output displacement of the screw shaft is as follows:
Figure BDA0002421495800000062
wherein, thetaL(t) is the motor output rotation angle, PhFor transmission lead, XLIs the linear displacement of the screw rod.
The parameters of the electric push rod of a certain model are as follows: b isL＝0.35，KL＝5364.98N·m/rad，Ph＝16mm。
And step 2), modeling the permanent magnet synchronous servo motor.
Step 2.1), a driving motor torque model is established, the model adopts a permanent magnet synchronous servo motor, and the torque equation process expression is as follows:
Figure BDA0002421495800000063
Te(t)＝Ktiq(t) (5)
wherein，Te(T) is the electromagnetic torque of the machine, TL(t) load torque, J moment of inertia, KtIs a torque constant, iqAnd (t) is a q-axis stator current. B is the damping coefficient of the motor, thetaeAnd (t) is the output rotation angle of the motor.
And 2.2), establishing a driving motor control model. The servo motor of the system is a speed ring structure, the speed controller is a PI controller, and the current ring is used as an inner ring of the speed ring controller.
The closed loop transfer function of the current loop is equivalent to a first-order inertia link, omegacCurrent loop bandwidth:
Figure BDA0002421495800000064
the transfer function of the motor current to the electromagnetic torque is:
MI(s)＝Ktiq(t) (7)
wherein, KtIs the motor torque constant, iq(t) is a q-axis current.
The electromagnetic torque to motor speed transfer function is:
Figure BDA0002421495800000071
wherein, J moment of inertia, B damping coefficient.
The digital low pass filter is designed to suppress high frequency noise in the velocity signal with a transfer function of, wherefFor the filter bandwidth:
Figure BDA0002421495800000072
the parameters of a motor of a certain model are as follows: j is 0.05kg cm2，Kt＝0.9Nm/A，B＝0.01Nm·s/rad，ωc＝0.02，ωf0.01. And step 3), designing a cascade controller. And taking control based on a hinge point space as an inner ring and taking control based on a motion platform attitude space as an outer ring. The inner ring controller is provided for each supporting legThe single input and single output system loop is formed by adopting a PID controller, and a feedback signal is measured by a linear displacement sensor. The outer ring is compensation control based on an attitude space, the actual measurement attitude is obtained through positive solution to realize the correction of the input attitude, and a PID control method is adopted. The system is positively solved, namely the space attitude of the moving platform is calculated through the length of the supporting leg, a Newton-Raphson iteration method is adopted, and the method comprises the following specific steps:
step 3.1), the distance formula between hinge points of the actuator is as follows:
Figure BDA0002421495800000073
Δli＝li-l0(11)
wherein liIs the i-th actuator length, gkiFor the coordinates of the points after the moving coordinate system has been transformed into the stationary coordinate system, bkiAs a reference frame coordinate point,/0To the initial length of the actuator, Δ liCorresponding to the expansion amount of the actuator.
And 3.2) solving the moving platform attitude by utilizing linearization processing and a Newton-Raphson iteration method. Obtained from the formulae (10), (11):
Figure BDA0002421495800000074
obtaining a nonlinear equation system containing six unknowns:
Figure BDA0002421495800000075
wherein q is [ q ]1,q2…q6]T＝[x,y,z,α,β,γ]TAnd respectively representing six postures of the motion platform.
Step 3.3), solving a nonlinear equation system (9). In the formula fi(q1,q2…q6) At point (q)10,q20…q60) Performing binary Taylor series expansion on the neighborhood, and obtaining the linear part of the binary Taylor series expansion:
Figure BDA0002421495800000081
in the formula (f)i(Q0)＝fi(q10,q20…q60) (i ═ 1,2 … 6). And obtaining a solution meeting the calculation precision through repeated approximation and iterative operation.
And 4), designing an anti-interference compensator.
Step 4.1), acquiring angular acceleration information of the actuator by adopting a state observer, and designing a strategy for compensating and controlling disturbance by observing the angular acceleration information on the basis of the angular acceleration information, wherein the design basis is a driving motor torque equation, and a specific expression of the driving motor torque equation is as follows:
Figure BDA0002421495800000082
angular velocity information
Figure BDA0002421495800000083
Measured by a motor encoder, the output torque T of the motore(T) is an input signal, which is sent to an execution motor by a control command, and the load torque TLAnd (t) is a disturbance signal and is a variable to be estimated.
Step 4.2), mixing
Figure BDA0002421495800000084
And
Figure BDA0002421495800000085
as state variables, the design state equations are as follows:
Figure BDA0002421495800000086
state vector:
Figure BDA0002421495800000087
input quantity: u. of0(t)＝Te(t), outputting:
Figure BDA0002421495800000088
Figure BDA0002421495800000089
step 4.3), the system can be completely observed by the observability matrix, so the state observer is designed as follows:
Figure BDA00024214958000000810
wherein
Figure BDA00024214958000000811
Is x0(t) estimation, G0For the state observer gain matrix, he will
Figure BDA00024214958000000812
Negative feedback loop
Figure BDA00024214958000000813
The purpose of the method is to configure the pole of the observer, improve the dynamic performance and enable the error vector of the estimated state and the real state
Figure BDA00024214958000000814
Approaching 0 as soon as possible.
Step 4.4), the dynamic behavior of the error is:
Figure BDA0002421495800000091
step 4.5), solving an error equation, wherein a specific expression of the error equation is as follows:
Figure BDA0002421495800000092
step 4.6), considering the A-GC as a second-order system, referring to the optimal parameters of the second-order system, and designing the bandwidth f by the observern112Hz, damping ratio ξ 0.707, and gain matrix G [959, 50%0000]T。
And 5) based on the above, obtaining the optimal PID control parameter by using a Zieler-Nichols PID parameter diagnosis method.
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features.

Claims (2)

1. An anti-interference electric six-degree-of-freedom parallel mechanism control method is characterized by comprising the following steps:
step 1), the actuator is a linear guide rail type actuator driven by a permanent magnet synchronous servo motor, the transmission part of the actuator is a ball screw, the screw transmission part is simplified into an ideal model, and the screw transmission part is equivalent to a mathematical model considering the rigidity, the damping and the rotational inertia of the screw transmission part:
step 1.1), obtaining a torque balance equation according to the transmission characteristics of the screw rod, wherein the torque balance equation is as follows:
Figure FDA0002421495790000011
wherein, JLFor the mechanical transmission part, calculating the total moment of inertia of the motor, BLCalculating the total viscous damping coefficient, T, to the motor for the mechanical transmission partL(T) is the load torque, Tm(t) is motor output torque, θL(t) is the screw output rotation angle;
step 1.2), according to a screw rod rigidity formula, a screw rod driving torque is expressed as follows:
Tm＝KL[θe-θL]
wherein, TL(t) is the output torque of the motor, KLFor converting the mechanical transmission part into the total rotational stiffness, theta, of the output shaft of the linear actuatore(t) is the motor output rotation angle, θL(t) is the screw output rotation angle;
step 1.3), the relationship between the expansion amount of the linear actuator and the output displacement of the screw shaft is as follows:
Figure FDA0002421495790000012
wherein, thetaL(t) is the motor output rotation angle, PhFor transmission lead, XLIs the linear displacement of the screw rod;
step 2), modeling a permanent magnet synchronous servo motor;
step 2.1), a driving motor torque model is established, the model adopts a permanent magnet synchronous servo motor, and the torque equation process expression is as follows:
Figure FDA0002421495790000013
Te(t)＝Ktiq(t)
wherein, Te(T) is the electromagnetic torque of the machine, TL(t) load torque, J moment of inertia, KtIs a torque constant, iq(t) is the q-axis stator current; b is the damping coefficient of the motor, thetae(t) is the motor output rotation angle;
step 2.2), establishing a driving motor control model; the servo motor of the system is a speed ring structure, the speed controller is a PI controller, and a current ring is used as an inner ring of the speed ring controller;
the closed loop transfer function of the current loop is equivalent to a first-order inertia link, omegacCurrent loop bandwidth:
Figure FDA0002421495790000021
the transfer function of the motor current to the electromagnetic torque is:
MI(s)＝Ktiq(t)
wherein, KtIs the motor torque constant, iq(t) is the q-axis current;
the electromagnetic torque to motor speed transfer function is:
Figure FDA0002421495790000022
j moment of inertia and B damping coefficient;
the digital low pass filter is designed to suppress high frequency noise in the velocity signal with a transfer function of, wherefFor the filter bandwidth:
Figure FDA0002421495790000023
step 3), designing a cascade controller; taking control based on a hinge point space as an inner ring and taking control based on a motion platform attitude space as an outer ring; the inner ring controller is a single-input single-output system loop formed by each supporting leg, a PID controller is adopted, and a feedback signal is measured by a linear displacement sensor; the outer ring is compensation control based on an attitude space, the actual measurement attitude is obtained through positive solution to realize the correction of the input attitude, and a PID control method is adopted; the system is positively solved, namely the space attitude of the moving platform is calculated through the length of the supporting leg, and the method adopts a Newton-Raphson iterative method for calculation;
step 4), designing a state observer based on the acceleration information of the actuator, and compensating the external disturbance;
and 5) based on the above, obtaining the optimal PID control parameter by using a Zieler-Nichols PID parameter diagnosis method.
2. The method for controlling the anti-interference electric six-degree-of-freedom parallel mechanism according to claim 1, wherein the detailed steps of the step 4) are as follows:
step 4.1), acquiring angular acceleration information of the actuator by adopting a state observer, and designing a strategy for compensating and controlling disturbance by observing the angular acceleration information on the basis of the angular acceleration information, wherein the design basis is a driving motor torque equation, and a specific expression of the driving motor torque equation is as follows:
Figure FDA0002421495790000024
angular velocity information
Figure FDA0002421495790000025
Measured by a motor encoder, the output torque T of the motore(T) is an input signal, which is sent to an execution motor by a control command, and the load torque TL(t) is a disturbance signal which is a variable to be estimated;
step 4.2), mixing
Figure FDA0002421495790000026
And
Figure FDA0002421495790000027
as state variables, the design state equations are as follows:
Figure FDA0002421495790000028
y(t)＝Cx(t)
state vector:
Figure FDA0002421495790000031
input quantity: u (T) ═ Te(t), outputting:
Figure FDA0002421495790000032
Figure FDA0002421495790000033
C＝[1 0]
step 4.3), the system can be completely observed by the observability matrix, so the state observer is designed as follows:
Figure FDA0002421495790000034
wherein
Figure FDA0002421495790000035
Is an estimate of x (t), G is the state observer gain matrix, which will
Figure FDA0002421495790000036
Negative feedback loop
Figure FDA0002421495790000037
The purpose of the method is to configure the pole of the observer, improve the dynamic performance and enable the error vector of the estimated state and the real state
Figure FDA0002421495790000038
Approaching 0 as soon as possible;
step 4.4), the dynamic behavior of the error is:
Figure FDA0002421495790000039
step 4.5), solving an error equation, wherein a specific expression of the error equation is as follows:
Figure FDA00024214957900000310
and 4.6) considering the A-GC as a second-order system, and calculating a gain matrix by referring to the optimal parameters of the second-order system.
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CN104142692A (en) * 2014-06-26 2014-11-12 陕西高华知本化工科技有限公司 Six-degree-of-freedom motion platform
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CN104142692A (en) * 2014-06-26 2014-11-12 陕西高华知本化工科技有限公司 Six-degree-of-freedom motion platform
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