CN107992110B - Magnetic suspension control moment gyro frame angular rate servo system based on harmonic reducer - Google Patents
Magnetic suspension control moment gyro frame angular rate servo system based on harmonic reducer Download PDFInfo
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Abstract
The invention provides a magnetic suspension control moment gyro frame angular rate servo system based on a harmonic reducer, which comprises a controller, a power amplifier, a moment motor, a motor end linear Hall sensor, a harmonic reducer, a load end rotary transformer and a cascade expansion state observer. The controller controls the output and the load end angle position to serve as input signals of the cascade extended state observer, and additional control information is generated by the cascade extended state observer and is compensated into the controller; the method comprises the steps that a linear Hall sensor is installed at the end of a torque motor, accurate torque motor rotor position information is obtained through calculation, the torque motor is fixedly connected with the input end of a harmonic reducer, the output torque of the harmonic reducer acts on a load, and a rotary transformer is installed at the load end to measure the angular position of the load end. The magnetic suspension control moment gyro frame servo system provided by the invention can realize high-precision frame angular rate servo control.
Description
Technical Field
The invention belongs to the field of magnetic suspension control moment gyro angular rate servo control based on a harmonic reducer, and particularly relates to a magnetic suspension control moment gyro high-precision frame angular rate servo system adopting a composite control algorithm based on a cascade extended state observer, which is favorable for improving the angular rate servo control precision of the whole system.
Background
For a magnetic suspension control moment gyro frame servo system, if a direct driving mode is adopted, the volume and the weight of a moment motor can be correspondingly increased, and in order to reduce the volume and the weight of a frame system, a transmission mechanism is generally adopted to amplify the motor moment. The harmonic reducer has the advantages of large transmission ratio, high precision, small volume, light weight and the like, is one of the optimal choices for controlling the moment gyro frame transmission mechanism, but the nonlinear characteristics of the harmonic reducer, such as nonlinear torsional rigidity, nonlinear friction, return difference and the like, seriously influence the angular rate precision of the frame system.
In order to solve the problem that the angular rate precision of a frame system is reduced due to the nonlinear characteristic of a harmonic reducer, in a magnetic suspension control moment gyro frame system (patent No. ZL201310435526.8) based on the harmonic reducer, an output shaft of a torque motor is fixedly connected with an input end of the harmonic reducer, the harmonic reducer is used as a moment amplifying device, output moment acts on a load, the type and the installation position of a sensor generally adopt a structure that photoelectric code discs are installed at a torque motor end and a load end, and the angular rate of the motor end and the load end are respectively measured, an algorithm based on a torsional rigidity hysteresis model and compensation of the harmonic reducer is adopted on a control algorithm to inhibit the influence of the inherent hysteresis characteristic of the harmonic reducer in a magnetic suspension control moment gyro frame servo system on the system precision, but the environment adaptability and the service life of the whole frame system can be reduced by using the photoelectric code discs as the sensor, and the parameters of the lag model in the control algorithm are generally difficult to be accurately identified; in order to solve the problem that the angular rate precision of a frame system is reduced due to the nonlinear characteristic of a harmonic reducer, the type and the installation position of the conventional sensor generally adopt a structure of 'only installing a rotary transformer at a load end to measure the angular position of the load end and designing a controller algorithm', an extended state observer is adopted on a control algorithm to be combined with a controller to estimate and compensate the nonlinear transmission torque of the harmonic reducer, but the rotary transformer only installed at the load end cannot obtain the position information of a rotor of a torque motor, and the control algorithm has the problems that when the order of the system is higher, more parameters of the extended state observer are difficult to adjust.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the problem that the output rate precision of the existing magnetic suspension control moment gyro angular rate servo system based on a harmonic reducer is not high is solved, and a structural scheme and a control algorithm for improving the output angular rate precision of a frame system are provided.
The technical scheme adopted by the invention for solving the technical problems is as follows: a magnetic suspension control moment gyro frame angular rate servo system based on a harmonic reducer comprises a controller, a power amplifier, a torque motor, a linear Hall sensor, a rotor position resolving module, the harmonic reducer, a magnetic suspension control moment gyro frame system load, a rotary transformer, an angular position resolving module and a cascade expansion state observer; the controller generates a control signal by adopting a composite control algorithm based on the combination of state feedback and disturbance compensation, outputs actual control current to the torque motor through a power amplifier, a linear Hall sensor arranged at the end of the torque motor is used for measuring the related information of the position of the rotor of the torque motor, the position of the rotor of the torque motor is obtained through a rotor position calculating module, the output shaft of the torque motor is fixedly connected with the input end of a harmonic reducer, the harmonic reducer is used as a torque amplifying device, output torque acts on the load of a magnetic suspension control torque gyro frame system, a rotary transformer at the load end obtains the angular position of the load end through an angular position calculating module, the angular position of the load end and the control output of the controller are used as input information of a cascade expansion state observer, the cascade expansion state observer generates additional control quantity, and the additional control quantity is used for generating an angular rate instruction, a, The torque motor rotor position and the load end angular position together serve as input information to the controller.
Wherein, the composite control algorithm comprises the following steps:
step 1: constructing a mathematical model of a system
Taking the state variables of the system dynamic model based on the harmonic reducer as follows:
X＝[x1x2x3x4]T＝[θlωlΔθ ωm]Tthe control input is taken as u-TmThe state space equation is:
wherein, thetalIs the angular position of the load end, omegalIs the angular rate, omega, of the load end obtained after the angular position of the load end is differentiatedmIs the rotor position theta of the torque motormThe angular velocity of the end of the motor is obtained after differentiation, n is the reduction ratio of the harmonic reducer, and delta theta is thetam/n-θlIs the torsion angle of the harmonic reducer; t ismIs the electromagnetic torque, T, of the motorfIs a disturbance moment; j. the design is a squarem、JlThe rotational inertia of the motor and the load, respectively; b ism、BlDamping coefficients of the motor and the load are respectively; khIs the linear time-invariant part, Δ K, in the torsional stiffness of the harmonic reducerhIs a nonlinear time varying part of the torsional stiffness of the harmonic reducer.
The system mathematical model is subjected to coordinate transformation as follows:
the state space expression is:
wherein the content of the first and second substances,
step 2: cascaded extended state observer design
Defining a state variable of a cascaded extended state observer as z ═ z1,z2,z3,z4,z5,z6,z7,z8]TWherein z is1Estimating v1，z2Estimating v2，z4Estimating v3，z6Estimating v4，z8Estimate f', z3、z5、z7Is an intermediate variable of the cascaded extended state observer.
The state equation of the cascade extended state observer is as follows:
wherein the content of the first and second substances,
β1、β2two design parameters for the cascaded extended state observer. The cascade extended state observer generates additional control quantity through the state equation
Compensating into a control law in the controller (1).
The cascade form of four second-order extended state observers with the same parameters is adopted, and only two parameters need to be configured in the observer, namely β1And β2The problem that the parameters of the observer are difficult to configure can be well solved.
And step 3: composite control algorithm design
The controller (1) adopts the following control law:
wherein, ω islrefFor angular rate command, thetalrefFor reference rotor position information, v, obtained after integration of angular rate commands1＝θlIs the angular position of the load end, v2＝ωlFor loading end angular velocity, z4、z6、z8An additional control quantity generated for the cascaded extended state observer; k is a radical of1、k2、k3、k44 design parameters for the controller, b framework system parameters, and u controller control outputs.
And 4, step 4: parameter design of composite control algorithm
The whole control algorithm needs to be configured with six parameters, namely: controlSystem parameter k1、k2、k3、k4And two parameters β of a cascaded extended state observer1、β2. Wherein the controller parameter k1、k2、k3、k4According to a conventional pole arrangement, two parameters β of the extended state observer are cascaded1、β2Designing according to the disturbance condition of a specific system:
where, ζ is the system damping ratio, ωfThe rotation frequency of the magnetic suspension rotor of the magnetic suspension control moment gyroscope is obtained.
The basic principle of the invention is as follows: the invention installs the linear Hall sensor with small volume and light weight at the end of the torque motor, obtains the accurate position of the rotor of the torque motor through the rotor position calculating module, the torque motor is fixedly connected with the harmonic reducer, the output torque of the harmonic reducer acts on the load, the rotary transformer is installed at the load end, and the angular position of the load end is measured through the angular position calculating module; by adopting a compound control algorithm based on the cascaded extended state observer, the cascaded extended state observer estimates the system state and disturbance and generates additional control information to compensate the additional control information into the controller, so that the system disturbance is suppressed, and the high-precision frame angular rate output is realized.
Compared with the prior art, the invention has the advantages that:
1. compared with the existing magnetic suspension control moment gyro frame servo system, the invention adopts the linear Hall sensor with small volume and light weight to measure the angular position of the motor end, adopts the rotary transformer with high reliability to measure the angular position of the load end, can overcome the problem that the position information of the torque motor rotor and the angular position information of the load end in the existing system can not be simultaneously and accurately measured, and can also improve the environmental adaptability of the whole frame servo system.
2. Four second-order extended states with the same parameter are observed by adopting a compound control algorithm based on a cascade extended state observerThe observer has only two parameters to be configured in the cascade, namely β1And β2The method can well solve the problem that the existing controller design adopts methods of establishing a compensation model, combining a controller with an extended state observer and the like, so that more parameters are difficult to adjust. By designing the control parameters, the overall anti-interference capability of the system is improved, and the output angular rate precision of the system is improved.
Drawings
FIG. 1 is a control diagram of a frame angular rate servo control system;
FIG. 2 is a schematic diagram of a harmonic reducer-based frame system;
FIG. 3 is a linear Hall sensor output signal;
FIG. 4 is a rotor position calculation module based on a linear Hall sensor;
FIG. 5 is a diagram of a cascaded extended state observer.
The reference numbers in the figures mean: the system comprises a controller 1, a power amplifier 2, a torque motor 3, a linear Hall sensor 4, a rotor position calculating module 5, a harmonic reducer 6, a magnetic suspension control torque gyro frame system load 7, a rotary transformer 8, an angular position calculating module 9 and a cascade expansion state observer 10.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 1, a magnetic suspension control moment gyro frame angular rate servo system based on a harmonic reducer comprises a controller 1, a power amplifier 2, a torque motor 3, a linear hall sensor 4, a rotor position calculating module 5, a harmonic reducer 6, a magnetic suspension control moment gyro frame system load 7, a rotary transformer 8, an angular position calculating module 9 and a cascade expansion state observer 10; the controller 1 generates a control signal by adopting a composite control algorithm based on the combination of state feedback and disturbance compensation, outputs actual control current to a torque motor 3 through a power amplifier 2, a linear Hall sensor 4 arranged at the end of the torque motor is used for measuring the related information of the rotor position of the torque motor, the rotor position of the torque motor is obtained through a rotor position calculating module 5, an output shaft of the torque motor 3 is fixedly connected with the input end of a harmonic reducer 6, the harmonic reducer 6 is used as a torque amplifying device, the output torque acts on a load 7 of a magnetic suspension control torque gyro frame system, a rotary transformer 8 at the load end obtains the angular position of the load end through an angular position calculating module 9, the angular position of the load end and the control output of the controller are used as input information of a cascade expansion state observer 10, the cascade expansion state observer 10 generates additional control quantity, and the additional control quantity is used for generating an angular rate instruction, a control signal, The torque motor rotor position and the load end angle position together serve as input information for the controller 1.
Fig. 2 is a schematic diagram of mechanical connection of the torque motor 3, the linear hall sensor 4, the harmonic reducer 6, the magnetic suspension control torque gyro frame system load 7 and the rotary transformer 8 in fig. 1. The linear Hall sensor is installed at the end of a torque motor, the torque motor is fixedly connected with the input end of a harmonic reducer, the harmonic reducer is connected with a load of a magnetic suspension control torque gyro frame system, and a rotary transformer is installed at the load end.
The torque motor rotor position in fig. 1 is obtained as follows:
step 1: and the linear Hall sensor acquires a position related signal of the rotor of the torque motor. 2 linear Hall sensors (a linear Hall sensor A and a linear Hall sensor B) with 90-degree electrical angle difference are arranged at one end of the motor, and when the motor rotates, the output signals of the two linear Hall sensors are theoretically two sinusoidal signals V with 90-degree rotor position electrical angle differencesinAnd cosine signal VcosAs shown in fig. 3.
Step 2: the position of the rotor of the torque motor is obtained by a rotor position resolving module 5 of the torque motor
As shown in fig. 4, the signals of the linear hall sensor a and the linear hall sensor B pass through the signal conditioning circuit, undergo AD conversion (digital/analog conversion), and then undergo calculation to obtain the current rotor position of the torque motor
(electrical angle). Current torque motor rotor position
The formula of the calculation (in electrical degrees) can be expressed as:
the steps of the adopted composite control algorithm are as follows:
step 1: constructing a mathematical model of a system
Taking the state variables of the system dynamic model based on the harmonic reducer as follows:
X＝[x1x2x3x4]T＝[θlωlΔθ ωm]T，
the control input is taken as u-TmThe state space equation is:
wherein, thetalIs the angular position of the load end, omegalIs the angular rate, omega, of the load end obtained after the angular position of the load end is differentiatedmIs the rotor position theta of the torque motormThe angular velocity of the end of the motor is obtained after differentiation, n is the reduction ratio of the harmonic reducer, and delta theta is thetam/n-θlIs the torsion angle of the harmonic reducer; t ismIs the electromagnetic torque, T, of the motorfIs a disturbance moment; j. the design is a squarem、JlThe rotational inertia of the motor and the load, respectively; b ism、BlDamping coefficients of the motor and the load are respectively;
is the linear time-invariant part, Δ K, in the torsional stiffness of the harmonic reducerhIs a nonlinear time varying part of the torsional stiffness of the harmonic reducer.
The system mathematical model is subjected to coordinate transformation as follows:
the state space expression is:
wherein the content of the first and second substances,
step 2: cascaded extended state observer design
Defining a state variable of a cascaded extended state observer as z ═ z1,z2,z3,z4,z5,z6,z7,z8]TWherein z is1Estimating v1，z2Estimating v2，z4Estimating v3，z6Estimating v4，z8Estimate f', z3、z5、z7Is an intermediate variable of the cascaded extended state observer.
The state equation of the cascade extended state observer is as follows:
wherein the content of the first and second substances,
β1、β2two design parameters for the cascaded extended state observer. The structure of the cascaded extended state observer is shown in FIG. 5, and the cascaded extended state observer generates additional control quantity through the above state equation
Compensating the control into the controller (1)In law.
The cascade form of four second-order extended state observers with the same parameters is adopted, and only two parameters need to be configured in the observer, namely β1And β2The problem that the parameters of the observer are difficult to configure can be well solved.
And step 3: composite control algorithm design
The controller (1) adopts the following control law:
wherein, ω islrefFor angular rate command, thetalrefFor reference rotor position information, v, obtained after integration of angular rate commands1＝θlIs the angular position of the load end, v2＝ωlFor loading end angular velocity, z4、z6、z8An additional control quantity generated for the cascaded extended state observer; k is a radical of1、k2、k3、k44 design parameters for the controller, b framework system parameters, and u controller control outputs.
And 4, step 4: parameter design of composite control algorithm
The whole control algorithm needs to be configured with six parameters, namely: controller parameter k1、k2、k3、k4And two parameters β of a cascaded extended state observer1、β2. Wherein the controller parameter k1、k2、k3、k4According to a conventional pole arrangement, two parameters β of the extended state observer are cascaded1、β2Designing according to the disturbance condition of a specific system:
where, ζ is the system damping ratio, ωfThe rotation frequency of the magnetic suspension rotor of the magnetic suspension control moment gyroscope is obtained.
By adopting the control algorithm, the speed servo precision of the frame system can be improved.
Taking the magnetic suspension control moment gyro frame angular rate servo system based on the harmonic reducer with the angular momentum of 200Nms as an example, the angular rate bandwidth is 10 Hz. The system parameters are shown in table 1.
TABLE 1 System parameters
Controller parameter k1、k2、k3、k4In a conventional pole arrangement:
k1＝1.56×107，k2＝9.92×105，k3＝2.37×104，k4＝251.33。
the rotation frequency of the magnetic suspension rotor of the magnetic suspension control moment gyroscope is 200Hz, namely omegaf2 × pi × 200(rad/s), the system damping ratio is ζ 0.707, thus two parameters β of the cascaded extended state observer1、β2Is configured to:
simulation verification proves that when the angular rate instruction is 5 degrees/s, the fluctuation of the system output angular rate is only 0.01 degrees/s, and compared with a double-frame control moment gyro frame servo system (patent number: ZL201310435526.8) based on a harmonic reducer in Chinese patent, the precision of the system output angular rate is improved by 11.3%.
Claims (1)
1. The utility model provides a magnetic suspension control moment gyro frame angular rate servo based on harmonic speed reducer ware which characterized in that: the device comprises a controller (1), a power amplifier (2), a torque motor (3), a linear Hall sensor (4), a rotor position calculating module (5), a harmonic reducer (6), a magnetic suspension control moment gyro frame system load (7), a rotary transformer (8), an angular position calculating module (9) and a cascade expansion state observer (10); wherein, the controller (1) adopts a composite control algorithm based on the combination of state feedback and disturbance compensation to generate a control signal, actual control current is output to a torque motor (3) through a power amplifier (2), a linear Hall sensor (4) arranged at the end of the torque motor is used for measuring the related information of the position of a rotor of the torque motor, the position of the rotor of the torque motor is obtained through a rotor position calculating module (5), an output shaft of the torque motor (3) is fixedly connected with an input end of a harmonic reducer (6), the harmonic reducer (6) is used as a torque amplifying device, output torque acts on a load (7) of a magnetic suspension control torque gyro frame system, a rotary transformer (8) at the load end obtains the angular position of the load end through an angular position calculating module (9), and the angular position of the load end and the control output of the controller are used as input information of a cascade, the cascade extended state observer (10) generates an additional control quantity, and the additional control quantity and an angular rate instruction of a magnetic suspension control moment gyro frame angular rate servo system, a torque motor rotor position and a load end angular position given by an attitude control computer are used as input information of the controller (1);
the composite control algorithm comprises the following steps:
step 1: constructing a mathematical model of a system
Taking the state variables of the system dynamic model based on the harmonic reducer as follows:
X＝[x1x2x3x4]T＝[θlωlΔθ ωm]Tthe control input is taken as u-TmThe state space equation is:
wherein, thetalIs the angular position of the load end, omegalIs the angular rate, omega, of the load end obtained after the angular position of the load end is differentiatedmIs the rotor position theta of the torque motormThe angular rate of the motor end obtained after differentiation, n being the harmonic reductionReduction ratio of speed variator, Δ θ ═ θm/n-θlIs the torsion angle of the harmonic reducer; t ismIs the electromagnetic torque, T, of the motorfIs a disturbance moment; j. the design is a squarem、JlThe rotational inertia of the motor and the load, respectively; b ism、BlDamping coefficients of the motor and the load are respectively;
is the linear time-invariant part, Δ K, in the torsional stiffness of the harmonic reducerhIs a nonlinear time varying part in the torsional stiffness of the harmonic reducer;
the system mathematical model is subjected to coordinate transformation as follows:
v1＝x1，v2＝x2，
the state space expression is:
wherein the content of the first and second substances,
step 2: cascaded extended state observer design
Defining a state variable of a cascaded extended state observer as z ═ z1,z2,z3,z4,z5,z6,z7,z8]TWherein z is1Estimating v1，z2Estimating v2，z4Estimating v3，z6Estimating v4，z8Estimate f', z3、z5、z7Is an intermediate variable of the cascaded extended state observer;
the state equation of the cascade extended state observer is as follows:
wherein the content of the first and second substances,
β1、β2for two design parameters of the cascaded extended state observer, the cascaded extended state observer generates additional control quantity through the above state equation
Compensating into a control law in the controller (1);
the cascade form of four second-order extended state observers with the same parameters is adopted, and only two parameters need to be configured in the observer, namely β1And β2The problem that parameters of the observer are difficult to configure can be well solved;
and step 3: composite control algorithm design
The controller (1) adopts the following control law:
wherein, ω islrefFor angular rate command, thetalrefFor reference rotor position information, v, obtained after integration of angular rate commands1＝θlIs the angular position of the load end, v2＝ωlFor loading end angular velocity, z4、z6、z8An additional control quantity generated for the cascaded extended state observer; k is a radical of1、k2、k3、k44 design parameters of the controller, b is a frame system parameter, and u is a controller control output;
and 4, step 4: parameter design of composite control algorithm
The whole control algorithm needs to be configured with six parameters, namely: controller parameter k1、k2、k3、k4And two parameters β of a cascaded extended state observer1、β2Wherein the controller parameter k1、k2、k3、k4According to a conventional pole arrangement, two parameters β of the extended state observer are cascaded1、β2Designing according to the disturbance condition of a specific system:
where, ζ is the system damping ratio, ωfThe rotation frequency of the magnetic suspension rotor of the magnetic suspension control moment gyroscope is obtained.
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| CN110657809A (en) * | 2019-09-12 | 2020-01-07 | 中国人民解放军战略支援部队航天工程大学 | Hall sensor installation method for magnetically suspended control sensitive gyroscope |
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| CN112859613B (en) * | 2021-01-22 | 2022-05-13 | 北京航空航天大学 | High-precision control method of control moment gyro frame system based on harmonic reducer |
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