CN114955011A - Fixed angle control method for frame system under DGVSCMG flywheel mode - Google Patents
Fixed angle control method for frame system under DGVSCMG flywheel mode Download PDFInfo
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Abstract
The invention relates to a fixed angle control method of a DGVSCMG flywheel mode lower frame system, aiming at realizing high-precision locking of a DGVSCMG frame servo system by designing an anti-interference control method. Firstly, establishing a mathematical model of a DGVSCMG frame servo system containing multi-source interference and dividing the interference into low-frequency interference and high-frequency interference; secondly, designing an interference observer to estimate and feed-forward compensate the low-frequency interference; then, a proportional-integral resonance controller is improved to inhibit dynamic unbalance high-frequency interference with the frequency and the amplitude changing simultaneously; and finally, combining the interference observer and the improved proportional-integral resonant controller to realize the accurate locking of the frame servo system. The invention has the advantages of simple structure, full utilization of interference information and strong engineering practice.
Description
Technical Field
The invention belongs to the field of servo system control, and particularly relates to a fixed angle control method of a DGVSCMG flywheel mode lower frame system, which is used for enhancing the anti-interference capability of inner and outer frame servo systems and realizing the accurate locking of the inner and outer frames.
Background
As a novel actuating mechanism, the double-frame variable-speed control moment gyro has two main working modes: a control moment gyro mode and a flywheel mode. In the flywheel mode, it can output a fine torque by accelerating or decelerating the gyro-house rotor. The moment can be used for singularity avoidance, attitude stabilization of the spacecraft and energy storage. In order to realize the high-precision attitude stabilization of the spacecraft, the frame angle of the double-frame variable-speed control moment gyro is not changed any more. However, the locking precision of the frame rotating speed is severely limited by the multi-source interference existing in the frame system. Multi-source interference mainly includes two major categories: (1) dynamic unbalance interference: due to production and assembly errors, high-frequency jitter is generated in the frame rotating speed. The frequency and the amplitude of the rotor are changed along with the speed change of the rotor, and the rotor is high-frequency and high-amplitude interference and is main disturbance influencing the frame locking precision; (2) rotor variable speed disturbance torque, friction torque and coupling torque between frames: the speed change of the rotor can affect the control precision of the rotating speed of the outer frame, further the rotating speed of the inner frame fluctuates due to the coupling of the inner frame and the outer frame, and the friction torque can bring the influences of tracking static difference and low-speed crawling to the rotating speeds of the inner frame and the outer frame. These three disturbances are a type of low frequency, low amplitude disturbance due to the low frame rotation speed. Therefore, the method has important research value in fully utilizing the interference information and realizing the high-precision locking of the frame servo system by designing the anti-interference control method.
Aiming at the problem that multi-source interference restricts the improvement of the frame locking precision under a flywheel mode, experts and scholars at home and abroad propose some control methods. A state feedback Composite Control method based on a Disturbance Observer is provided in Composite Decoupling Control of a Gimbal Servo System in Double-Gimbal Variable Speed CMG Via Disturbance Observer (Composite Decoupling Control of a Double-frame Variable Speed Control moment gyro frame Servo System based on the Disturbance Observer), and Decoupling Control of inner and outer frame Servo systems is realized. The document 'DGVSCMG double-frame servo system mismatch disturbance suppression based on ESO' aims at the problem that inner and outer frame systems have mismatch interference under two working modes of a double-frame variable speed control moment gyro, interference estimation is carried out through an extended state observer, and the influence of the mismatch interference on the frame servo system is effectively reduced by combining coordinate transformation and state feedback control. However, neither of the above two approaches considers the influence of dynamic unbalance interference.
For harmonic interference with unknown variable frequency and unknown amplitude, a Refined Disturbance Observer (RDO) is proposed in the literature, "reject of time-varying frequency-dependent sinusoidal Disturbance using for a class of uncertain systems based on the Refined Disturbance Observer", and can estimate and compensate the Disturbance in real time, but the method only aims at one class of harmonic interference, and the suppression capability of the method on multi-source interference needs to be enhanced. In order to improve the rotating speed tracking precision and stability of a frame servo system under a control moment gyro mode, the chinese application CN202110804350.3 provides a composite control method, which effectively inhibits the influence of multi-source interference, but the method is not suitable for the requirement of high-precision frame locking under a flywheel mode.
In summary, in the flywheel mode, the existing control method cannot effectively reduce the influence of multi-source interference in the dual-frame variable-speed control moment gyro frame servo system, and the realization of high-precision locking of the frame servo system is a difficult problem to be solved urgently.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a fixed angle control method of a frame system under a DGVSCMG flywheel mode, wherein the DGVSCMG refers to a double-frame variable speed control moment gyro. The double-frame variable-speed control moment gyro frame servo system is used as a research object, the anti-interference capability of the system is improved aiming at multi-source interference with the frequency and the amplitude changing simultaneously, the high-precision locking of the frame servo system is realized, and the double-frame variable-speed control moment gyro frame servo system has the advantages of simple structure, full utilization of interference information and strong engineering practice.
The technical scheme adopted by the invention for solving the technical problems is as follows: establishing a mathematical model of a double-frame variable speed control moment gyro frame servo system containing multi-source interference according to an Euler kinetic equation, and dividing the multi-source interference into low-frequency interference and high-frequency interference; secondly, designing an interference observer to estimate and feed-forward compensate the low-frequency interference; then, according to the known rotor rotating speed information, the traditional proportional-integral resonance controller is improved to inhibit high-frequency interference of simultaneous change of frequency and amplitude, and therefore accurate locking of a frame servo system in a flywheel mode is achieved.
The invention discloses a fixed angle control method of a frame system under a DGVSCMG flywheel mode, which comprises the following steps:
the method comprises the steps of firstly, considering the influence of dynamic unbalance interference, establishing a mathematical model of a DGVSCMG frame servo system, and dividing multi-source interference into low-frequency interference and high-frequency interference according to the frequency characteristics of the interference;
secondly, designing a disturbance observer according to the mathematical model in the first step, and aiming at the low-frequency moment d l1 ,d l2 Estimating in real time to obtain an estimated value of low-frequency interference;
thirdly, designing an improved proportional-integral resonance controller to inhibit high-frequency interference d with frequency and amplitude changing simultaneously according to the mathematical model in the first step and by utilizing the known rotor rotating speed information h1 ,d h2 ；
And fourthly, combining the interference observer in the second step with the improved proportional-integral resonance controller in the third step, and improving the anti-interference capability and the locking precision of the frame servo system.
In the first step, a mathematical model of the controlled object is determined. In the dynamic analysis process, the influence of dynamic unbalance interference is considered, and multi-source interference is divided into low-frequency interference and high-frequency interference. A mathematical model of a double-frame variable speed control moment gyro frame servo system is established as follows:
wherein d is 1 ＝d h1 +d l1 ，d 2 ＝d h2 +d l2 ，
θ gx 、
And
the angular position, angular velocity and angular acceleration of the rotation of the inner frame coordinate system relative to the outer frame coordinate system; theta jy 、
And
the angular position, the angular velocity and the angular acceleration of the rotation of the outer frame coordinate system relative to the inertial coordinate system; u. of qgx ,u qjy Q-axis components of the stator voltages of the driving motor of the inner frame and the outer frame respectively; j is a unit of rx ,J ry ,J rz For the moment of inertia of the high-speed rotor of the spinning top room about three axes of the rotor coordinate system, and J rx ＝J ry ＝J rr ；J gx ,J gy ,J gz The moment of inertia of the inner frame system around the three axes of the inner frame coordinate system; j. the design is a square x ,J y Equivalent rotational inertia of the inner frame system and the outer frame system around the frame shaft; l is qgx ,L qjy Q-axis inductance components of the inner and outer frame drive motors respectively; r gx ,R jy Stator resistors of the driving motor of the inner frame and the outer frame respectively; k tgx ,K tjy The electromagnetic torque coefficients of the driving motors of the inner frame and the outer frame are respectively; i.e. i qgx ,i qjy Q-axis components of stator currents of the driving motor of the inner frame and the outer frame are respectively; k egx ,K ejy Back electromotive force coefficients of the inner and outer frame driving motors, respectively, and K tgx ＝1.5·K egx ，K tjy ＝1.5·K ejy ；d 1 ,d 2 For multi-source interference acting on the inner and outer frames, wherein d h1 ,d h2 For high frequency interference, d l1 ,d l2 Low frequency interference;
the coupling moment of the inner frame servo system is acted on by the outer frame;
the coupling moment of the inner frame acting on the outer frame servo system; t is fgx ,T fjy Friction torque in the inner frame servo system and the outer frame servo system respectively;
the variable speed disturbance is carried out on the gyro room rotor; t is dx ,T dy The dynamic unbalance of the rotor of the gyro room interferes with the components of the inner ring system on the x and y axes; u shape d The dynamic unbalance amount of the gyro room rotor is obtained; omega is the rotating speed of the gyro chamber rotor;
is the phase angle of the dynamically unbalanced mass at the initial instant.
In the second step, the estimation of the low frequency interference is implemented as follows:
to compensate for low frequency disturbances d l1 ,d l2 Designing a frequency domain interference observer to carry out real-time estimation on the low-frequency interference observer to obtain an estimated value of the low-frequency interference:
wherein s is a Laplace transform complex variable operator;
is a low frequency interference estimation value;
angular velocity of the frame servo system;
a composite control quantity of a speed loop of a frame servo system; q(s) is a filter in a frequency domain disturbance observer; g 0 (s) is a nominal model of the frame servo system.
In order to avoid that the compensation effect of the low-frequency interference is limited by the bandwidth of the current loop, in the nominal model G 0 The dynamics of the current loop are taken into account in(s). Also, in order to effectively estimate the low frequency interference and reduce the introduction of detection noise, q(s) should be taken as a low pass filter. G 0 (s) and Q(s) are represented by:
wherein, ω is n And ξ are the cut-off frequency and the damping ratio of Q(s), respectively; k is t And K e Respectively is a moment coefficient and a counter potential coefficient; c i (s) a controller for the current loop; g i (s)＝1/(L q +R)，L q And R is the q-axis inductance component and the stator resistance of the driving motor respectively; g(s) ═ 1/(Js), and J is the moment of inertia in the axial direction of the drive motor.
The third step is to improve the traditional proportional-integral resonance controller to inhibit the high-frequency interference d with the frequency and the amplitude changing simultaneously h1 ,d h2 . The conventional proportional-integral resonant controller is:
wherein s is a Laplace transform complex variable operator; u. of PIR (s) is a proportional-integral resonant controller; k is a radical of sp ,k si Proportional and integral control coefficients, respectively;
is the resonant gain;
adjusting the angle for the phase; e.g. of the type ω (s) is the angular velocity tracking error;
is the resonant frequency.
1) Firstly, in order to make up for the defect that the traditional proportional-integral resonance controller can not deal with the harmonic interference of the variable frequency, the resonant frequency is enabled
Simultaneous phase angle pair
Real-time adjustment is performed. When the speed loop adopts PI control and ensures the stability of the system, the closed loop transfer function G of the speed loop cl (s) performing identification.
Wherein, C sPI (s) is a PI controller for the speed loop. Then, after the resonant controller is added, according to the open-loop transfer function G open The emergence angle of the root track at the(s) multiple pole point is in the range of (90 DEG, 270 DEG), and the phase angle is obtained
The range of stabilizing the system at different rotor speeds,
wherein G is cl0 (s)＝G cl (s)/C sPI (s)，G cl0 (s) is a transfer function of the speed loop control quantity to the frame rotational speed due to the desired rotational speed under PI control; open loop transfer function
ε Ω Is the resonant gain;
∠G cl0 (j Ω) is G cl0 (s) the phase angle at the frequency Ω, j being the unit length of the imaginary axis.
Due to the fact that
And
affected by motor parameters, considering the identification error of the motor parameters, and taking phase angle
The law of variation with time t is:
2) secondly, to further stabilize the system after the addition of the resonance controller, G is used open (s) selecting a certain number of rotation speed points (such as 10-20) in the known rotor rotation speed variation range to obtain the resonance gain epsilon for stabilizing the system critical under different rotor rotation speeds SΩ The value is obtained. For the obtained epsilon SΩ Fitting the value with the selected rotation speed point to obtain the resonance gain epsilon Ω Law of variation with time t:
ε Ω (t)＝ε SΩ (Ω)/N
wherein N is a constant greater than 1.
In the fourth step, the composite controller is:
wherein s is a Laplace transform complex variable operator; u. of IPIR (s) is the output of the improved proportional-integral resonant controller; e.g. of the type ω (s) is the angular velocity tracking error;
is an estimate of low frequency interference;
is a composite control quantity of the speed loop.
Compared with the prior art, the invention has the advantages that: aiming at the problem of disturbance suppression of a double-frame variable speed control moment gyro frame servo system in a flywheel mode, the prior art reduces the influence of coupling moment between frames, realizes decoupling of an inner frame servo system and an outer frame servo system, but does not consider dynamic unbalance interference. Compared with the prior art, the invention has the advantages of simple structure, full utilization of interference information and strong engineering practice. Firstly, the influence of dynamic unbalance interference is considered in the dynamic analysis process, so that the mathematical model of the double-frame variable speed control moment gyro frame servo system is more in line with the engineering practice. Secondly, a disturbance observer is designed to estimate and compensate three low-frequency disturbances including rotor variable-speed disturbance, friction torque and coupling torque between frames in real time, and a traditional proportional-integral resonance controller is improved to inhibit dynamic unbalance disturbance in a flywheel mode. And finally, the interference observer is combined with the improved proportional-integral resonance controller, so that the anti-interference capability of the frame servo system is enhanced, and the high-precision locking of the frame servo system in the flywheel mode is realized.
Drawings
FIG. 1 is a flow chart of a fixed angle control method of a frame servo system under a DGVSCMG flywheel mode of the invention;
FIG. 2 is a schematic block diagram of a frequency domain disturbance observer of a frame servo system speed loop adopted in the present invention;
FIG. 3 is an open loop transfer function G of the present invention open (s) root trajectory;
FIG. 4 is an open loop transfer function G of the present invention open (s) a partial enlargement of the root trajectory;
FIG. 5 is a block diagram of an anti-interference control structure of the inner and outer frame servo system according to the present invention;
FIG. 6 is a diagram of low-frequency interference estimation and estimation error of the outer frame servo system in the flywheel mode according to the present invention; the method comprises the following steps of obtaining a first sub-graph, a second sub-graph and a third sub-graph, wherein the first sub-graph is a low-frequency interference real value, the second sub-graph is an estimation quantity of an interference observer, and the third sub-graph is a compensation error of low-frequency interference;
FIG. 7 is a graph of the variation of phase and resonant gain parameters of an improved proportional-integral resonant controller in accordance with the present invention; wherein, the left graph is a phase change curve, and the right graph is a resonance gain change curve;
FIG. 8 is a graph showing the effect of locking the rotational speed of the inner frame servo system in the flywheel mode according to the present invention and the comparative method;
FIG. 9 is a graph showing the effect of locking the rotational speed of the outer frame servo system in the flywheel mode according to the present invention and the comparative method.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the method for controlling the angle of the frame system under the DGVSCMG flywheel mode according to the present invention comprises the following steps:
first, a mathematical model of the controlled object is established. Improving a mathematical model of an existing double-frame variable-speed control moment gyro frame servo system by utilizing an Euler kinetic equation, and identifying relevant parameters of a driving motor through experiments and a least square algorithm; secondly, designing a disturbance observer to estimate the variable speed disturbance of the rotor, the coupling torque between frames and the friction torque in real time; then, an improved proportional-integral resonance controller is adopted to suppress dynamic unbalance interference of simultaneous change of frequency and amplitude; and finally, combining the interference observer and the improved proportional-integral resonance controller to realize the estimation, feedforward compensation and inhibition of multi-source interference in a flywheel mode and improve the locking precision of the double-frame servo system.
The specific implementation steps are as follows:
firstly, a mathematical model of a controlled object is established. In the dynamic analysis process, the influence of dynamic unbalance interference is considered, multi-source interference is divided into low-frequency interference and high-frequency interference according to the frequency distribution characteristics of the interference, and a mathematical model of a double-frame variable-speed control moment gyro frame servo system directly driven by a permanent magnet synchronous motor is established as follows:
wherein d is 1 ＝d h1 +d l1 ，d 2 ＝d h2 +d l2 ，
θ gx 、
And
the angular position, angular velocity and angular acceleration of the rotation of the inner frame coordinate system relative to the outer frame coordinate system; theta.theta. jy 、
And
the angular position, the angular velocity and the angular acceleration of the rotation of the outer frame coordinate system relative to the inertial coordinate system; u. of qgx ,u qjy Q-axis components of the stator voltages of the driving motor of the inner frame and the outer frame respectively; j. the design is a square rx ,J ry ,J rz Moment of inertia about three axes of a rotor coordinate system for a high-speed rotor of a gyro-house, and J rx ＝J ry ＝J rr ；J gx ,J gy ,J gz The moment of inertia of the inner frame system around the three axes of the inner frame coordinate system; j. the design is a square x ,J y Equivalent rotational inertia of the inner frame system and the outer frame system around the frame shaft respectively; l is a radical of an alcohol qgx ,L qjy Q-axis inductance components of the inner and outer frame drive motors respectively; r gx ,R jy Stator resistors of the driving motor of the inner frame and the outer frame respectively; k tgx ,K tjy The electromagnetic torque coefficients of the driving motors of the inner frame and the outer frame are respectively; i.e. i qgx ,i qjy The q-axis component of the stator current of the driving motor of the inner frame and the outer frame respectively; k egx ,K ejy Back electromotive force coefficients of the inner and outer frame driving motors, respectively, and K tgx ＝1.5·K egx ，K tjy ＝1.5·K ejy ；d 1 ,d 2 For multi-source interference acting on the inner and outer frames, wherein d h1 ,d h2 For high frequency interference, d l1 ,d l2 Low frequency interference; .
The coupling moment of the inner frame servo system is acted on by the outer frame;
the coupling moment of the inner frame acting on the outer frame servo system; t is fgx ,T fjy Friction torque in the inner frame servo system and the outer frame servo system respectively;
the variable speed disturbance is carried out on the gyro room rotor; t is dx ,T dy The dynamic unbalance interference of the rotor of the gyro room is a component of an x axis and a y axis of an inner ring system; u shape d The dynamic unbalance amount of the gyro room rotor is obtained; omega is the rotating speed of the gyro chamber rotor;
is the phase angle of the dynamically unbalanced mass at the initial instant.
The parameters of the inner and outer frame servo systems and the dynamic unbalance interference parameters are shown in table 1.
TABLE 1 inner and outer frame servo system and dynamic unbalance interference parameters
In order to fully embody the characteristics of the friction torque, a LuGre friction model is adopted to represent the friction torque T in the inner frame servo system and the outer frame servo system fgx ,T fjy ：
Wherein σ 0 Is the coefficient of friction rigidity, σ 0 ＝1.00Nm/rad；σ 1 Is the coefficient of friction damping, σ 1 ＝0.50Nm/(rad/s)；σ 2 Is a viscous friction coefficient, σ 2 ＝0.60Nm/(rad/s)；T cf Is the Coulomb friction torque, T cf ＝0.0080Nm；T sf Is the static friction moment, T sf ＝0.10Nm；ω s Is the characteristic angular velocity, ω, of Stribeck s 0.10 rad/s; z is a state variable characterizing the immeasurable dynamic behavior of the frictional contact surface; g (ω) is a bounded function greater than 0; ω is the frame rotation speed.
Second step, in order to compensate for low frequency disturbances d l1 ,d l2 Designing a frequency domain interference observer to carry out real-time estimation on the low-frequency interference observer to obtain an estimated value of the low-frequency interference:
wherein s is a Laplace transform complex variable operator;
is a low frequency interference estimation value;
angular velocity of the frame servo system;
a composite control quantity of a speed loop of a frame servo system; q(s) is a filter in a frequency domain disturbance observer; g 0 (s) is a nominal model of the frame servo system.
A block diagram of the structure of the frequency domain disturbance observer is shown in fig. 2. In order to avoid that the compensation effect of the low-frequency interference is limited by the bandwidth of the current loop, in the nominal model G 0 The dynamics of the current loop are taken into account in(s). Also, in order to effectively estimate the low frequency interference and reduce the introduction of detection noise, q(s) should be taken as a low pass filter. G 0 (s) and Q(s) are represented by:
wherein, ω is n And ξ are the cut-off frequency and the damping ratio of Q(s), respectively; k t And K e Respectively is a moment coefficient and a counter potential coefficient; c i (s) a controller for the current loop; g i (s)＝1/(L q +R)，L q And R is the q-axis inductance component and the stator resistance of the driving motor respectively; g(s) ═ 1/(Js), and J is the moment of inertia in the axial direction of the drive motor.
Because the low-frequency interference amplitude in the inner frame servo system is low and the variable-speed disturbance of the rotor mainly acts on the outer frame, the interference observer is only added in the outer frame servo system. After multiple times of simulation debugging, the parameters of the disturbance observer are as follows: xi is 0.71, omega n ＝250.00rad/s。
Thirdly, designing an improved proportional-integral resonance controller to inhibit dynamic unbalance interference d with simultaneously changed frequency and amplitude according to the mathematical model established in the first step h1 ,d h2 . The conventional proportional-integral resonant controller is:
wherein s is a Laplace transform complex variable operator; u. of PIR (s) is a proportional-integral resonant controller; k is a radical of sp ,k si Proportional and integral control coefficients, respectively;
is the resonant gain;
adjusting the angle for the phase; e.g. of the type ω (s) is the angular velocity tracking error;
is the resonant frequency. The PI control parameters for system stabilization were selected before resonance control was added as shown in table 2.
1) Firstly, in order to make up for the defect that the traditional proportional-integral resonance controller can not deal with the harmonic interference of the variable frequency, the resonant frequency is enabled
Simultaneous phase angle pair
And performing real-time adjustment. When the speed loop adopts PI control and ensures the stability of the system, the closed loop transfer function G of the speed loop cl (s) performing identification. Wherein the content of the first and second substances,
wherein, C sPI (s) is a PI controller for the speed loop. Next, after the resonant controller is added, according to the open-loop transfer function G open (s) the emergence angle of the root locus at the repolarization point should be in the range of (90 deg., 270 deg.) (as shown in FIG. 3), resulting in a phase angle
The range in which the system is stable at different rotor speeds, namely:
wherein G is cl0 (s)＝G cl (s)/C sPI (s)，G cl0 (s) is a transfer function of a speed loop control quantity to a frame rotational speed due to a desired rotational speed under PI control; open loop transfer function
ε Ω Is the resonant gain;
∠G cl0 (j Ω) is G cl0 (s) the phase angle at the frequency Ω, j being the unit length of the imaginary axis.
Due to the fact that
And
affected by motor parameters, considering the identification error of the motor parameters, and taking phase angle
The law of variation with time t is:
2) next, as shown in FIG. 4, with the rotor speed of 1000rpm as the starting point and 10000rpm as the end point, 1 speed point is selected every 500rpm in the middle, and G is used open (s) to obtain a resonance gain epsilon for critically stabilizing the system at 19 rotor speeds SΩ The value is obtained. For epsilon SΩ Fitting the values with the selected rotation speed points to obtain the critical stable epsilon of the inner and outer frame systems respectively SΩ Law of variation of value with ΩComprises the following steps: inner frame of epsilon SΩ (Ω) ═ 0.42 Ω -18.61; outer frame of epsilon SΩ (Ω) ═ 0.99 Ω + 418.82. In order to further keep the system stable after the resonance controller is added, the change law of the resonance gain is finally selected as follows: inner frame of epsilon Ω (Ω) ═ 0.42 Ω -18.61)/5; outer frame of epsilon Ω (Ω)＝(0.99Ω+418.82)/10。
TABLE 2 proportional integral control term parameters
Fourthly, a fixed angle control block diagram of a frame servo system under a dual-frame variable speed control moment gyro flywheel mode provided by the invention is shown in fig. 5. And compounding the interference observer in the second step with the improved proportional-integral resonance controller in the third step, enhancing the capability of the frame servo system for coping with multi-source interference, and ensuring the locking precision of the double-frame servo system in a flywheel mode. The resulting composite controller was:
wherein u is IPIR (s) is the output of the improved proportional-integral resonant controller; e.g. of the type ω (s) is the angular velocity tracking error;
is an estimate of the low frequency interference;
is a composite control quantity of the speed loop.
In the flywheel working mode, the initial angle of the inner and outer frame servo systems is taken as (theta) gx ) 0 ＝10.00°、(θ jy ) 0 0.00 deg. periodThe expected rotation speed is
The change rule of the rotating speed of the gyro chamber rotor is as follows: omega is 0.00rpm, t is less than or equal to 2 s; omega 1000 x (t-2) rpm, 2 < t < 12 s. Based on the conventional proportional-integral resonance control, the article "reject of time-varying frequency-dependent resonance using refined-for-a class of uncertain systems based on a fine disturbance observer" and the locking effect of the inner and outer frames of the present invention are shown in fig. 6-9. Fig. 6 shows an estimation and estimation error of the disturbance observer for the low-frequency disturbance of the outer frame (the first sub-graph is a real value of the low-frequency disturbance, the second sub-graph is an estimation amount of the disturbance observer, and the third sub-graph is a compensation error of the low-frequency disturbance), fig. 7 shows a variation curve of the phase and the resonant gain parameter of the improved proportional-integral resonant controller (the left graph is a variation curve of the phase, the right graph is a variation curve of the resonant gain), fig. 8 shows a rotational speed locking effect of the inner frame servo system, and fig. 9 shows a rotational speed locking effect of the outer frame servo system. As can be seen from FIG. 6, the disturbance observer is designed to cope with low-frequency disturbance d l2 Effective estimation and compensation are performed. Although there is a high frequency component in the interference estimation error, it can be suppressed by the improved proportional-integral resonant controller. As can be seen from fig. 7, the phase and resonance gain parameters of the improved proportional-integral resonance controller vary with the rotor speed. From fig. 8 and 9, it can be seen that the conventional proportional-integral resonance control cannot better cope with the variable frequency and variable amplitude high frequency interference d h1 ,d h2 (ii) a Compared with two methods of improved proportional-integral resonance control and improved proportional-integral resonance control plus a disturbance observer, the disturbance observer can better compensate the variable speed disturbance of the rotor and reduce the offset of the rotating speed of the frame; under the condition of the same energy consumption, the control precision of the rotating speed of the inner frame is relatively higher and the control precision of the rotating speed of the outer frame is lower in the method of ' state feedback plus fine disturbance observer ', but the control precision of the rotating speed of the inner frame and the outer frame is not influenced by the speed change of the rotor under the method of ' improved proportional-integral resonance control plus disturbance observerAnd high-precision locking of the double-frame servo system under multi-source interference is realized.
In order to compare the control effects of the two control methods of the state feedback plus the fine disturbance observer and the improved proportional-integral resonance control plus the disturbance observer more specifically, under the condition of the same energy consumption, two indexes of a standard deviation sigma (°/s) of a locking error of a rotating speed and a mean value e (°/s) of an absolute value of the locking error are adopted for evaluation, and performance indexes of the two control methods are shown in table 3.
TABLE 3 Performance index for two control methods
As can be seen from Table 3, when the same energy is consumed, the standard deviation of the rotation speed locking errors of the inner and outer frames of the invention is reduced by 72.19% and 91.97% compared with the comparison method, and the rotation speed locking errors of the inner and outer frames are reduced by 62.87% and 90.29% compared with the comparison method. This shows that, when the consumed energy is similar, the invention has stronger anti-interference ability; when the frame locking precision is similar, the invention saves more energy.
Those skilled in the art will appreciate that the invention may be practiced without these specific details. It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. A fixed angle control method for a frame system under a DGVSCMG flywheel mode is characterized by comprising the following steps:
the method comprises the steps of firstly, considering the influence of dynamic unbalance interference, establishing a mathematical model of a DGVSCMG frame servo system, and classifying according to the frequency distribution characteristics of multi-source interference;
secondly, designing a disturbance observer according to the mathematical model in the first step, and estimating three low-frequency moments of rotor variable-speed disturbance, coupling moment between frames and friction moment in real time in a flywheel mode to obtain an estimated value of the low-frequency disturbance;
thirdly, designing an improved proportional-integral resonance controller to inhibit dynamic unbalance high-frequency interference in a flywheel mode by using known rotor rotation speed information according to the mathematical model in the first step;
and fourthly, combining the interference observer in the second step with the improved proportional-integral resonance controller in the third step, and improving the anti-interference capability and locking precision of the DGVSCMG frame servo system.
2. The angle-fixing control method for the frame system under DGVSCMG flywheel mode as claimed in claim 1, wherein: the first step comprises: in the dynamic analysis process, the influence of dynamic unbalance interference is considered, a mathematical model of a controlled object is determined, and multi-source interference is classified according to the frequency distribution characteristics of the interference; the mathematical model of the DGVSCMG frame servo system is established as follows:
wherein d is 1 ＝d h1 +d l1 ，d 2 ＝d h2 +d l2 ，
Wherein, theta gx 、
And
the angular position, angular velocity and angular acceleration of the rotation of the inner frame coordinate system relative to the outer frame coordinate system; theta jy 、
And
the angular position, the angular velocity and the angular acceleration of the rotation of the outer frame coordinate system relative to the inertial coordinate system; u. of qgx ,u qjy Q-axis components of the stator voltages of the driving motor of the inner frame and the outer frame respectively; j. the design is a square rx ,J ry ,J rz For the moment of inertia of the high-speed rotor of the spinning top room about three axes of the rotor coordinate system, and J rx ＝J ry ＝J rr ；J gx ,J gy ,J gz The moment of inertia of the inner frame system around the three axes of the inner frame coordinate system; j is a unit of x ,J y Equivalent rotational inertia of the inner frame system and the outer frame system around the frame shaft respectively; l is a radical of an alcohol qgx ,L qjy Q-axis inductance components of the inner frame driving motor and the outer frame driving motor respectively; r gx ,R jy Stator resistors of the driving motor of the inner frame and the outer frame respectively; k is tgx ,K tjy The electromagnetic torque coefficients of the driving motors of the inner frame and the outer frame are respectively; i.e. i qgx ,i qjy Q-axis components of stator currents of the driving motor of the inner frame and the outer frame are respectively; k egx ,K ejy Back electromotive force coefficients of the inner and outer frame driving motors, respectively, and K tgx ＝1.5·K egx ，K tjy ＝1.5·K ejy ；d 1 ,d 2 For multi-source interference acting on the inner and outer frames, wherein d h1 ,d h2 For high frequency interference, d l1 ,d l2 Low frequency interference;
the coupling moment of the inner frame servo system is acted on by the outer frame;
is insideThe frame acts on the coupling moment of the outer frame servo system; t is fgx ,T fjy Friction torque in the inner frame servo system and the outer frame servo system respectively;
the variable speed disturbance is carried out on the gyro room rotor; t is dx ,T dy The dynamic unbalance interference of the rotor of the gyro room is a component of an x axis and a y axis of an inner ring system; u shape d The dynamic unbalance amount of the gyro room rotor is obtained; omega is the rotating speed of the gyro room rotor;
is the phase angle of the dynamically unbalanced mass at the initial instant.
3. The method of claim 1, wherein the step of controlling the angle of the DGVSCMG flywheel mode lower frame system comprises the steps of: in the second step, the estimation of the low frequency interference is implemented as follows:
to compensate for low frequency disturbances d l1 ,d l2 Designing a frequency domain interference observer to carry out real-time estimation on the low-frequency interference observer to obtain an estimated value of the low-frequency interference:
wherein s is a Laplace transform complex variable operator;
is a low frequency interference estimation value;
angular velocity of the frame servo system;
a composite control quantity of a speed loop of a frame servo system; q(s) is a filter in a frequency domain disturbance observer; g 0 (s) is the nominal value of the frame servo systemA model;
in order to avoid that the compensation effect of the low-frequency interference is limited by the bandwidth of the current loop, in the nominal model G 0 The dynamics of the current loop are taken into account in(s). Meanwhile, in order to effectively estimate low-frequency interference and reduce the introduction of detection noise, Q(s) should be taken as a low-pass filter;
G 0 (s) and Q(s) are represented by:
wherein, ω is n And ξ are the cut-off frequency and the damping ratio of Q(s), respectively; k t And K e Respectively a moment coefficient and a counter electromotive force coefficient; c i (s) a controller for the current loop; g i (s)＝1/(L q +R)，L q And R is the q-axis inductance component and the stator resistance of the driving motor respectively; g(s) ═ 1/(Js), and J is the moment of inertia in the axial direction of the drive motor.
4. The angle-fixing control method for the frame system under DGVSCMG flywheel mode as claimed in claim 1, wherein: the third step includes: high-frequency interference d for suppressing simultaneous change of frequency and amplitude by improving traditional proportional-integral resonance controller h1 ,d h2 (ii) a The conventional proportional-integral resonant controller is:
wherein s is a Laplace transform complex variable operator; u. of PIR (s) is a proportional-integral resonant controller; k is a radical of formula sp ,k si Proportional and integral control coefficients, respectively;
is the resonant gain;
for adjusting the phaseAngle trimming; e.g. of the type ω (s) is angular velocity tracking error;
is the resonance frequency.
1) Firstly, in order to make up for the defect that the traditional proportional-integral resonance controller can not deal with the harmonic interference of the variable frequency, the resonant frequency is enabled
Simultaneous phase angle pair
Real-time regulation is carried out, when the speed loop adopts PI control and ensures the stability of the system, the closed loop transfer function G of the speed loop is controlled cl (s) performing identification;
wherein, C sPI (s) is a PI controller for the speed loop. Next, after the resonant controller is added, according to the open-loop transfer function G open The emergence angle of the root track at the(s) multiple pole point is in the range of (90 DEG, 270 DEG), and the phase angle is obtained
Range for system stability at different rotor speeds:
wherein G is cl0 (s)＝G cl (s)/C sPI (s)，G cl0 (s) is a transfer function of the speed loop control quantity to the frame rotational speed due to the desired rotational speed under PI control; open loop transfer function
ε Ω Is the resonant gain;
∠G cl0 (j Ω) is G cl0 (s) the phase angle at the frequency Ω, j being the unit length of the imaginary axis.
Due to the fact that
And
affected by motor parameters, considering the identification error of the motor parameters, and taking phase angle
The law of variation with time t is:
2) secondly, to further stabilize the system after the addition of the resonance controller, G is used open (s) selecting a certain number of rotation speed points in the known rotor rotation speed variation range to obtain the resonance gain epsilon for making the system critical stable under different rotor rotation speeds SΩ A value; for the obtained epsilon SΩ Fitting the value with the selected rotation speed point to obtain the resonance gain epsilon Ω Law of variation with time t:
ε Ω (t)＝ε SΩ (Ω)/N
wherein N is a constant greater than 1.
5. The method of claim 1, wherein the step of controlling the angle of the DGVSCMG flywheel mode lower frame system comprises the steps of: in the fourth step, the composite controller is:
wherein s is a Laplace transform complex variable operator; u. of IPIR (s) is the output of the improved proportional-integral resonant controller; e.g. of the type ω (s) is the angular velocity tracking error;
is an estimate of low frequency interference;
is a composite control quantity of the speed loop.
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| CN116430713B (en) * | 2023-04-18 | 2024-01-05 | 青岛哈尔滨工程大学创新发展中心 | Method for improving control loop bandwidth of full-angle hemispherical resonator gyroscope |
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