CN113489385B - Method and system for synchronously controlling pitching axes of large optical telescope by double motors - Google Patents
Method and system for synchronously controlling pitching axes of large optical telescope by double motors Download PDFInfo
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- CN113489385B CN113489385B CN202110763724.1A CN202110763724A CN113489385B CN 113489385 B CN113489385 B CN 113489385B CN 202110763724 A CN202110763724 A CN 202110763724A CN 113489385 B CN113489385 B CN 113489385B
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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
- H02P5/00—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors
- H02P5/46—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors for speed regulation of two or more dynamo-electric motors in relation to one another
- H02P5/50—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors for speed regulation of two or more dynamo-electric motors in relation to one another by comparing electrical values representing the speeds
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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
- H02P5/00—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors
- H02P5/46—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors for speed regulation of two or more dynamo-electric motors in relation to one another
- H02P5/52—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors for speed regulation of two or more dynamo-electric motors in relation to one another additionally providing control of relative angular displacement
- H02P5/56—Speed and position comparison between the motors by electrical means
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Abstract
The invention discloses a method and a system for synchronously controlling double motors of a pitching axis of a large optical telescope, which are used for carrying out decoupling control on a double motor system based on an active disturbance rejection control method and realizing double motor synchronous control by combining a speed feedforward, an acceleration feedforward and a friction compensation control algorithm. The method can effectively control the synchronous error of the double-end motor, thereby reducing the deformation and shafting vibration of the middle frame of the pitching axis of the optical telescope, and being simpler and more convenient while considering more influencing factors compared with the prior art.
Description
Technical Field
The invention relates to the technical field of synchronous control of double motors, in particular to a method and a system for synchronously controlling double motors of a pitching axis of a large optical telescope.
Background
The large-scale optical telescope is a high-precision equipment for astronomical observation. The field of view of the telescope is usually smaller, and the optical telescope has higher requirements on the vibration, deformation and tracking precision of the system. The larger the aperture of the optical telescope is, the more distant, weaker, and weaker objects are observed. As the aperture of the optical telescope increases, the size of the intermediate frame of the telescope becomes larger, and the rigidity of the structure further decreases. This results in the telescope pitch axis decelerating during movement or, in the case of external disturbance moments (such as wind, friction, unbalanced moments, etc.), in vibrations and large structural deformations which can affect the imaging quality of the optical telescope.
In order to reduce deformation and shafting vibration of an intermediate frame of a pitching axis of the optical telescope, the pitching axis of the optical telescope is synchronously driven by adopting double motors, so that synchronism of the double-end motors is ensured. The existing double-motor synchronous control method comprises a cross-coupling control method, and the effect of reducing the synchronous error is achieved by adding a coupling compensator in the system, but the method adds coupling moment from the outside, so that the motors at two ends achieve the synchronization, flexible connection between loads is not considered, the characteristic of internal coupling of a controlled object is not considered, and forced coupling is only carried out from the outside. In order to solve the problem, an adaptive coupling compensator is adopted to realize synchronous control, but the complexity of a control algorithm is increased, and engineering implementation is inconvenient.
Disclosure of Invention
In order to solve the problems, the invention provides a method and a system for synchronously controlling a pitching axis of a large optical telescope by using a double-motor system as a MIMO system (multiple input multiple output system), and provides a method for performing decoupling control on the FFLADRC (friction compensation and feedforward self-disturbance rejection control) double-motor system by combining the excellent performances of an Active Disturbance Rejection Control (ADRC) technology in three aspects of uncertainty problem, synchronization problem and mechanical vibration problem, thereby realizing the synchronous control of the double motors.
The invention provides a method for synchronously controlling double motors of a pitching axis of a large optical telescope, which comprises the following steps:
step A, inputting expected positions of the double motors into a synchronous command generator for planning to obtain the planned expected positions, expected speeds and expected accelerations of the double motors;
step B, the linear expansion state observer obtains the observation position, the observation speed and the total disturbance of the double motors according to the existing inertia position output by the double motor encoder;
c, carrying out error evaluation on the expected position and the expected speed obtained in the step A and the observed position and the observed speed obtained in the step B respectively, and generating adjusted data and outputting the adjusted data to a controller;
d, carrying out summation calculation on the adjusted data output in the step C and the expected acceleration obtained in the step A, subtracting the total disturbance and the friction compensation term to obtain a virtual control quantity, and outputting the virtual control quantity to a static decoupling unit;
step E, the static decoupling unit decouples the virtual control quantity and then outputs the actual control quantity to the double motors;
step F, after the double motors are regulated according to the actual control quantity, the double motor encoder outputs the regulated existing inertia position to a linear expansion state observer, and the linear expansion state observer calculates according to the regulated existing inertia position and the observation position obtained in the step B to obtain a new observation position, an observation speed and total disturbance;
and G, repeating the step C, D, E, F, and performing control adjustment of the double motors for a new round until the double motors are adjusted to the optimal control quantity.
Wherein, the step A comprises the following steps:
inputting the expected position into a synchronous command generator, and obtaining a planned expected position value and an expected speed through a first nonlinear differentiator in the synchronous command generator; and inputting the obtained expected speed into a second nonlinear differentiator to obtain the expected speed and the expected acceleration after re-planning. The step inputs the expected position to a nonlinear differentiator for smoothing, and filters out signals with higher frequencies and exceeding the system capacity.
The step B specifically comprises the following steps:
obtaining an error value of an observed position value and an existing inertia position value according to the existing inertia positions of the two ends of the double motors output by the double motor encoder;
according to the error value, obtaining the total disturbance at the two ends of the double motors;
obtaining the observation speeds of the two ends of the double motors according to the obtained total disturbance;
obtaining the observation positions of the two ends of the double motors according to the observation speeds and the error values of the two ends of the double motors;
wherein, in the first operation calculation, the observation position is an initial test value and is zero; in the subsequent operation calculation, the observed position value is the observed position value calculated in the last operation.
Wherein, in the step D:
in performing the virtual control amount calculation, the total disturbance and the friction compensation term are excluded, which is obtained by:
wherein: c v1 And c v2 Respectively representing the coulomb friction coefficients of two ends of the double motor; j (J) M1 And J M2 Respectively representing the corresponding rotational inertia of the double motors; z is Z 12 And Z 22 Respectively representing the observation speeds at two ends of the double motors; c f1 And c f2 Respectively represent the viscous friction coefficients corresponding to the two ends of the double motors. In order to reduce the burden of the linear expansion state observer, the invention combines the known friction moment part in the telescope pitching axis model and adopts a coulomb friction model to compensate.
The invention also provides a double-motor synchronous control system of the pitching axis of the large optical telescope, which comprises the following components:
a dual motor system, a synchronous command generator and a linear active disturbance rejection controller;
the dual motor system comprises dual motors;
the synchronous command generator includes: the two nonlinear differentiators are connected in series and are used for planning the input expected positions of the double motors and outputting the planned expected positions, expected speeds and expected accelerations to the linear active disturbance rejection controller;
the linear active disturbance rejection controller includes: a linear extended state observer, a controller, and a static decoupling unit; the linear expansion state observer is used for obtaining the observation position, the observation speed and the total disturbance of the double motors; the controller adjusts based on the adjusted data, wherein the adjusted data is obtained after the expected position and the expected speed are respectively evaluated with the observed position and the observed speed error; the static decoupling unit is used for performing static decoupling on the virtual control quantity to obtain an actual control quantity and outputting the actual control quantity to the dual-motor system, and the virtual control quantity is obtained based on the adjusted data, the total disturbance and the friction compensation term.
The expected position of the double motors is passed through a first nonlinear differentiator in the synchronous command generator to obtain a planned expected position value and an expected speed; the obtained expected speed is input to a second nonlinear differentiator in the synchronous command generator to obtain the expected speed and the expected acceleration after re-planning.
Wherein, the linear active disturbance rejection controller includes: 2 controllers, 2 linear extended state observers, and 1 static decoupling unit.
According to the technical scheme, the invention provides a friction compensation feedforward linear active disturbance rejection control device and a method thereof. The synchronous error of the double-end motor can be effectively controlled through the device and the method, so that the deformation and shafting vibration of the middle frame of the pitching axis of the optical telescope are reduced, and compared with the prior art, the device and the method are simpler and more convenient while more influencing factors are considered.
Drawings
FIG. 1 is a diagram of a dual motor synchronous control system for the pitch axis of a large optical telescope according to the present invention;
fig. 2 is a flow chart of a method for synchronously controlling the pitching axes of a large optical telescope by using double motors.
Detailed Description
The foregoing of the invention will be described in further detail with reference to the following detailed description of the examples. It should not be understood that the scope of the above subject matter of the present invention is limited to the following examples only. Various substitutions and alterations are also possible, without departing from the spirit of the invention, and are intended to be within the scope of the invention.
As shown in FIG. 1, the pitch axis double-motor synchronous control system of the large optical telescope of the invention comprises the following steps:
the system comprises a double-motor system, a synchronous command generator and a linear active disturbance rejection controller;
the dual motor system comprises dual motors;
the synchronous command generator includes: the two nonlinear differentiators are connected in series and are used for planning the input expected positions of the double motors and outputting the planned expected positions, expected speeds and expected accelerations to the linear active disturbance rejection controller; seeFIG. 1, input of a given signal θ ref To a synchronous command controller comprising two nonlinear differentiators in series, where the signal θ is given ref I.e. the desired position of the double motor; for a given signal θ via a nonlinear differentiator ref After planning, outputting the planned expected positionDesired speed omega ref Desired acceleration a f Into a linear active disturbance rejection controller. The expected position of the double motors is passed through a first nonlinear differentiator in the synchronous command generator to obtain a planned expected position value and an expected speed; the obtained expected speed is input to a second nonlinear differentiator in the synchronous command generator to obtain the expected speed and the expected acceleration after re-planning.
The linear active disturbance rejection controller includes: a linear extended state observer, a controller, and a static decoupling unit; the linear expansion state observer is used for obtaining the observation position, the observation speed and the total disturbance of the double motors; the controller adjusts based on the adjusted data, wherein the adjusted data is obtained after the expected position and the expected speed are respectively evaluated with the observed position and the observed speed error; the static decoupling unit is used for performing static decoupling on the virtual control quantity to obtain an actual control quantity and outputting the actual control quantity to the dual-motor system, and the virtual control quantity is obtained based on the adjusted data, the total disturbance and the friction compensation term. Referring to fig. 1, the linear active disturbance rejection controller includes: 2 controllers, 2 linear extended state observers and 1 static decoupling unit; data Z of operation output in linear expansion state observer 11 、Z 12 (representing the observed position and observed speed of the 1 st end of the motor, respectively) and Z 21 、Z 22 (respectively representing the observation position and the observation speed of the 2 nd end of the double motor) and the data output by the synchronous command generator are respectively output to the controller after being calculated, the result is output after being calculated in the controller, and the friction force compensation term f is added on the basis 1 And f 2 Obtaining a virtualThe control quantity is decoupled from the virtual control quantity by the static decoupling unit B to obtain an actual control quantity which is output to the double-motor system; the linear expansion state observer carries out a new round of data output according to the feedback of the double-motor system.
As shown in a flow chart of a method for synchronously controlling the pitching axes of the large optical telescope by using the double motors in the invention shown in FIG. 2:
the method comprises the steps of A, obtaining a planned expected position, expected speed and expected acceleration according to the expected position:
inputting the expected position into a synchronous command generator, and obtaining a planned expected position value and an expected speed through a first nonlinear differentiator in the synchronous command generator; and inputting the obtained expected speed into a second nonlinear differentiator to obtain the expected speed and the expected acceleration after re-planning.
And B, obtaining the observation position, the observation speed and the total disturbance of the double motors through a linear expansion state observer:
the operation procedure of the two linear expansion state observers is the same, and only one of the linear expansion state observers is taken as an example for explanation;
B1. solving the error between the two inertia positions and the observation positions according to the existing inertia positions at the two ends of the double motors; the specific expression is:
e＝Z 11 -θ M1
wherein: e represents the error between the observed position and the existing inertia position actually measured by the double-motor encoder;
Z 11 representing an observed position, the observed position being an initial value and being equal to zero in a first round of calculation;
θ M1 representing the existing inertia position measured by the dual motor encoder.
B2. Obtaining total disturbance at two ends of the double motors according to the error value; the specific expression is:
wherein: z is Z 13 Representing the total disturbance;β 03 parameters indicating that the observer needs to be debugged.
B3. According to the obtained total disturbance, calculating the observation speeds at two ends of the double motors;
wherein: beta 02 Parameters indicating that the observer needs to be debugged; z is Z 12 Representing the observation speed;
B4. obtaining the observation positions of the two ends of the double motors according to the observation speeds and the error values of the two ends of the double motors; in the first round of calculation, the expression is:
wherein: z is Z 11 Representing the observation position; beta 01 Parameters indicating that the observer needs to be debugged.
In the following calculation, the specific expression is:
wherein U is (1) Representing the virtual control amount obtained in the previous round of calculation; z is Z (12) Representing the observed speed obtained in the previous round of calculation; c v1 Representing the coulomb friction coefficient of the motor; j (J) M1 Representing the moment of inertia of the motor; z is Z 12 Representing the observed speed of the motor; c f1 Viscous friction coefficient corresponding to the motor.
And C, carrying out error evaluation according to the data obtained in the step A and the step B:
c, carrying out error evaluation on the expected position and the expected speed obtained in the step A and the observed position and the observed speed obtained in the step B respectively, and outputting the error evaluation to a controller for further adjustment; the specific expression is:
wherein:representing the desired position obtained in step A; omega r Indicating a desired speed; k (K) p 、K D Representing the parameters of the controller, the parameters that need to be debugged.
And D, eliminating friction compensation items on the basis of the step C to obtain virtual control quantity:
and C, carrying out summation calculation according to the adjusted data output in the step C and the expected acceleration in the step A, and subtracting the total disturbance and the friction compensation term to obtain a virtual control quantity, wherein the specific expression is as follows:
wherein: a, a r Indicating a desired acceleration; f (f) 1 Representing a friction torque, i.e. a friction compensation term;
further, the expression of the friction compensation term is:
wherein: c v1 And c v2 Respectively representing the coulomb friction coefficients of two ends of the double motor; j (J) M1 And J M2 Respectively representing the corresponding rotational inertia of the double motors; z is Z 12 And Z 22 Respectively representing the observation speeds at two ends of the double motors; c f1 And c f2 Respectively represent the viscous friction coefficients corresponding to the two ends of the double motors.
And E, performing static decoupling on the virtual control quantity to obtain an actual control quantity, and outputting the actual control quantity to a dual-motor system for adjustment, wherein the specific expression is as follows:
wherein:wherein J M1 And J M2 Respectively correspond to the rotational inertia, k of the two motors T0 Representing the torque coefficient of the motor.
Step F, after the double motors are adjusted according to the actual control quantity, outputting the adjusted existing inertia position to a linear expansion state observer, and performing error calculation on the linear expansion state observer according to the existing inertia position and the observation position in the step B, and correcting according to the obtained error to obtain a new observation position, an observation speed and total disturbance;
and G, repeating the step C, D, E, F again according to the obtained new observation position, the obtained observation speed and the obtained total disturbance, and performing new control adjustment of the double motors until the double motors are adjusted to the optimal control amount.
The system and the method can effectively control the synchronous error of the double-end motor, thereby reducing the deformation and shafting vibration of the middle frame of the pitching axis of the optical telescope, and being simpler and more convenient while considering more influencing factors compared with the prior art.
The foregoing is merely a specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims and equivalents thereof. Various alternatives and modifications can be made by those skilled in the art without departing from the scope of the invention, and such alternatives and modifications are intended to fall within the scope of the invention.
Claims (6)
1. The method for synchronously controlling the pitching axes of the large optical telescope by using the double motors is characterized by comprising the following steps of:
step A, inputting expected positions of the double motors into a synchronous command generator for planning to obtain the planned expected positions, expected speeds and expected accelerations of the double motors;
step B, the linear expansion state observer obtains the observation position, the observation speed and the total disturbance of the double motors according to the existing inertia position output by the double motor encoder;
c, carrying out error evaluation on the expected position and the expected speed obtained in the step A and the observed position and the observed speed obtained in the step B respectively, and generating adjusted data and outputting the adjusted data to a controller;
step D, the adjusted data output in the step C and the expected acceleration obtained in the step A are summed and calculated, and then the total disturbance and the friction compensation term are subtracted to obtain a virtual control quantity, and the virtual control quantity is output to a static decoupling unit,
in the step D, the virtual control quantity is obtained by subtracting the total disturbance and the friction compensation term after the summation calculation is carried out on the adjusted data output in the step C and the expected acceleration in the step A, and the specific expression is as follows:
wherein: a, a r Representing a desired acceleration; f (f) 1 Represents the friction torque, i.e. the friction compensation term,representing the desired position obtained in step A; omega r Indicating the desired speed, K p 、K D Representing parameters of the controller, Z 11 Indicating the observation position, Z 12 Indicating the observation speed, Z 13 Representing the total disturbance;
step E, the static decoupling unit decouples the virtual control quantity and then outputs the actual control quantity to the double motors;
step F, after the double motors are regulated according to the actual control quantity, the double motor encoder outputs the regulated existing inertia position to a linear expansion state observer, and the linear expansion state observer calculates according to the regulated existing inertia position and the observation position obtained in the step B to obtain a new observation position, an observation speed and total disturbance;
step G, repeating the step C, D, E, F, and performing new control adjustment of the double motors until the double motors are adjusted to the optimal control amount;
in the step D:
in performing the virtual control amount calculation, the total disturbance and the friction compensation term are excluded, which is obtained by:
wherein: c v1 And c v2 Respectively representing the coulomb friction coefficients of two ends of the double motor; j (J) M1 And J M2 Respectively representing the corresponding rotational inertia of the double motors; z is Z 12 And Z 22 Respectively representing the observation speeds at two ends of the double motors; c f1 And c f2 Respectively represent the viscous friction coefficients corresponding to the two ends of the double motors.
2. The method for synchronously controlling the pitching axes of the large optical telescope according to claim 1, wherein the step a comprises:
inputting the expected position into a synchronous command generator, and obtaining a planned expected position value and an expected speed through a first nonlinear differentiator in the synchronous command generator; and inputting the obtained expected speed into a second nonlinear differentiator to obtain the expected speed and the expected acceleration after re-planning.
3. The method for synchronously controlling the pitching axes of the large optical telescope according to claim 1, wherein the step B specifically comprises:
obtaining an error value of an observed position value and an existing inertia position value according to the existing inertia positions of the two ends of the double motors output by the double motor encoder;
according to the error value, obtaining the total disturbance at the two ends of the double motors;
obtaining the observation speeds of the two ends of the double motors according to the obtained total disturbance;
obtaining the observation positions of the two ends of the double motors according to the observation speeds and the error values of the two ends of the double motors;
wherein, in the first running calculation, the observed position is an initial value and is zero; in the subsequent operation calculation, the observed position value is the observed position value calculated in the last operation.
4. A large optical telescope pitching axis double-motor synchronous control system is characterized by comprising:
a dual motor system, a synchronous command generator and a linear active disturbance rejection controller;
the dual motor system comprises dual motors;
the synchronous command generator includes: the two nonlinear differentiators are connected in series and are used for planning the input expected positions of the double motors and outputting the planned expected positions, expected speeds and expected accelerations to the linear active disturbance rejection controller;
the linear active disturbance rejection controller includes: a linear extended state observer, a controller, and a static decoupling unit; the linear expansion state observer is used for obtaining the observation position, the observation speed and the total disturbance of the double motors; the controller adjusts based on the adjusted data, wherein the adjusted data is obtained after the expected position and the expected speed are respectively evaluated with the observed position and the observed speed error; the static decoupling unit is used for performing static decoupling on the virtual control quantity to obtain an actual control quantity and outputting the actual control quantity to the dual-motor system, and the virtual control quantity is obtained based on the adjusted data, the total disturbance and the friction compensation item;
the virtual control quantity is obtained by subtracting the total disturbance and the friction compensation term after the summation calculation is carried out on the adjusted data and the expected acceleration, and the specific expression is as follows:
wherein: a, a r Representing a desired acceleration; f (f) 1 Represents the friction torque, i.e. the friction compensation term,representing the desired position obtained in step A; omega r Indicating the desired speed, K p 、K D Representing parameters of the controller, Z 11 Indicating the observation position, Z 12 Indicating the observation speed, Z 13 Representing the total disturbance;
wherein, when the virtual control amount calculation is performed, the total disturbance and the friction compensation term are excluded, and the friction compensation term is obtained by the following formula:
wherein: c v1 And c v2 Respectively representing the coulomb friction coefficients of two ends of the double motor; j (J) M1 And J M2 Respectively representing the corresponding rotational inertia of the double motors; z is Z 12 And Z 22 Respectively representing the observation speeds at two ends of the double motors; c f1 And c f2 Respectively represent the viscous friction coefficients corresponding to the two ends of the double motors.
5. The system of claim 4, wherein,
the expected position of the double motors is passed through a first nonlinear differentiator in the synchronous command generator to obtain a planned expected position value and an expected speed; the obtained expected speed is input to a second nonlinear differentiator in the synchronous command generator to obtain the expected speed and the expected acceleration after re-planning.
6. The system of claim 4, wherein,
the linear active disturbance rejection controller includes: 2 controllers, 2 linear extended state observers, and 1 static decoupling unit.
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