CN108278323A - A kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage - Google Patents

Abstract

A zero-stiffness vibration isolation method for an electrostatically suspended two-stage dragless platform. By introducing the displacement of the suspended load platform, the output of the suspension control algorithm is nonlinearly modulated, and the electrostatic force change caused by the displacement is compensated, thereby eliminating the electrostatic negative stiffness. , to achieve suspension vibration isolation with zero stiffness. The method of the present invention can realize absolute zero stiffness vibration isolation, effectively suppress vibration energy in a wide frequency range, and due to the construction of zero stiffness, the two-level system can be completely decoupled, and the platform systems can be independently designed without affecting each other and stable The performance is better, and the method flow is simple.

Description

A Zero-Stiffness Vibration Isolation Method for Electrostatically Suspended Two-stage Dragless Platform

technical field

The invention relates to a zero-stiffness vibration isolation method for an electrostatic suspension type two-stage dragless platform, belonging to the technical field of electrostatic suspension control and precision vibration reduction.

Background technique

The in-depth development of activities such as high-precision space measurement, high-resolution earth remote sensing, and ultra-precision space science experiments have put forward new requirements and challenges for space-based vibration isolation and vibration reduction platforms. The two-stage dragless space-based ultra-static platform based on electrostatic suspension is a new type of vibration isolation and vibration reduction platform. The system is divided into three independent parts: the satellite parent body, the payload platform and the reference mass. The space operation mode of the system is: the satellite parent body and the load platform realize non-contact isolation through electrostatic suspension, and a differential capacitance is formed between the two, which can generate electrostatic control force according to the relative displacement between the load platform and the reference mass, and drive the load platform Track the reference mass to achieve the first level of no-drag, in which the reference mass is suspended in the vacuum cavity inside the load platform, completely free from the interference of external non-conservative forces, and the orbit running under the pure earth's gravity is a no-drag state The quiet reference source under the ground; and the micro-propeller can generate a reactionary control force according to the relative displacement between the satellite parent body and the load platform, and drive the satellite parent body to track the load platform to achieve the second stage without drag. The overall system adopts a two-stage drag-free structure, uses electrostatic suspension to achieve zero-stiffness vibration isolation, uses electrostatic drive to achieve active vibration reduction, and integrates to achieve vibration suppression.

However, electrostatic levitation will actually form negative electrostatic stiffness between the load platform and the satellite parent body, which is not a true zero-stiffness vibration isolation. The displacement disturbance of the satellite parent body can be transmitted to the load platform through this electrostatic negative stiffness, making the system form an isolated An absolute micro-vibration coupling path reduces the vibration isolation effect of the system.

The idea of zero-stiffness vibration isolation originated in the field of mechanical vibration reduction. Since the mechanical support structure is generally positive stiffness, the zero stiffness of the vibration isolation system is generally achieved by superimposing the negative stiffness of the nonlinear force. In the prior art, a negative stiffness construction method based on Euler buckling beam construction and a negative stiffness generation method using magnetic nonlinearity have been proposed. However, what this type of method achieves is a quasi-zero stiffness vibration isolation system, which is completely zero stiffness only at the position of the work balance point, and only quasi-zero stiffness near the balance work point, and its vibration isolation performance is related to the magnitude of the vibration excitation , it cannot be guaranteed that the electrostatic negative stiffness is zero under all conditions.

Contents of the invention

The technical problem solved by the present invention is: Aiming at the problems existing in the prior art, a zero-stiffness vibration isolation method for the electrostatically suspended two-stage non-drag platform is proposed, which solves the problem that the electrostatic negative stiffness of the electrostatically suspended platform is not all zero. The problem of complete vibration isolation cannot be formed.

The present invention solves the problems of the technologies described above and is achieved through the following technical solutions:

A zero-stiffness vibration isolation method for an electrostatically suspended two-stage dragless platform, comprising the following steps:

(1) Linearize the relationship between the feedback voltage of the electrostatic levitation platform system and the electrode electrostatic force, so that the forced electrostatic negative stiffness is 0;

(2) On the basis of the completion of step (1), for the electrostatic suspension type two-stage drag-free platform, the control algorithm design of the electrostatic drive and micro-push drive control is independently carried out;

(3) Non-linear modulation is performed on the output of the control algorithm of the electrostatic drive controller obtained in step (2), and the output of the control algorithm after nonlinear modulation is used as the actual output of the electrostatic drive controller.

In the step (1), the specific steps for linearizing the electrostatic levitation platform system are:

(1a) In the differential capacitance model, ignoring the high-order small amount of displacement in the electrode electrostatic force F _e , the formula for calculating the middle electrode electrostatic force F _e in the actual system is expressed as:

In the formula, ε _r is the relative permittivity, ε ₀ is the vacuum permittivity, A is the effective area of a capacitor plate, V _{s_eff} is the effective value of high-frequency AC excitation voltage, V _r is the preload voltage (bias DC voltage ), V _b is the feedback voltage, d ₀ is the nominal gap, and x is the displacement of the suspension from the center position;

(1b) Separating the electrostatic negative stiffness; the calculation formula of the electrostatic negative stiffness is:

(1c) Force the electrostatic negative stiffness to be 0, and complete the linearization of the feedback voltage and the electrode electrostatic force.

In the step (3), the modulated feedback voltage loaded on both sides of the differential capacitor includes an upper feedback voltage and a lower feedback voltage, wherein the calculation methods of the upper feedback voltage V _{b_up} and the lower feedback voltage V _{b_down} are respectively:

Among them, the relative displacement of the load platform The calculation formula of is as follows:

In the formula, _Vc is the output voltage of the control algorithm.

The advantage of the present invention compared with prior art is:

(1) The present invention provides a zero-stiffness vibration isolation method for an electrostatically suspended two-stage non-drag platform. The electrostatic negative stiffness is controlled to be zero through nonlinear modulation, so as to overcome the limitation of the static operating point in the zero-stiffness, and can be used in large Under the condition of amplitude, zero stiffness is formed, which can give linear modulation with high bandwidth and realize vibration isolation in wide frequency range;

(2) The electrostatic suspension type two-stage non-drag platform system adopting the method of the present invention, under the condition of zero stiffness, the two-pole system can be completely decoupled after nonlinear modulation, and it is easy to realize that each system does not affect each other, and the control environment is independent , the stability is better.

Description of drawings

Fig. 1 is a platform system structural diagram provided by the invention;

Fig. 2 is the flow chart of the vibration isolation method provided by the invention;

Fig. 3 is an equivalent differential capacitance model diagram of an electrostatic force generating device;

Fig. 4 is the control block diagram of the two-stage suspension system after linearization;

Fig. 5 is the control block diagram of the two-stage suspension system after the electrostatic negative stiffness can be regarded as zero;

Fig. 6 is the actual system control block diagram after constructing zero stiffness;

Fig. 7 is the simulation verification result figure of the inventive method;

Detailed ways

In the patent with the publication number CN104158431A, an electrostatic levitation space-based ultra-quiet platform system is proposed, including a quiet reference system, a load platform, an electrode cavity on the star, a capacitance detection circuit, a digital control system, a drive circuit and a micro-thruster , which realizes a two-stage drag-free system that uses weak electrostatic negative stiffness for low-stiffness vibration isolation and uses controllable feedback electrostatic force for active vibration reduction. The zero-stiffness vibration isolation method provided by the present invention is in this platform system Implemented, by introducing the displacement of the suspended load platform relative to the satellite parent body, the output of the suspension controller is nonlinearly modulated to compensate for the electrostatic force change caused by the displacement, so as to achieve zero stiffness and ensure that the modulated system electrostatic force is not affected by the load platform. Relative satellite parent displacement effect.

As shown in Figure 1, the space operation mode of the two-stage non-drag space-based ultra-quiet platform system of electrostatic suspension is: the satellite parent body and the load platform realize non-contact isolation through electrostatic suspension, and a differential capacitance is formed between the two, which can According to the relative displacement between the load platform and the reference mass, the electrostatic control force is generated, and the load platform is driven to track the reference mass, realizing the first-stage no-drag, in which the reference mass is suspended in the vacuum cavity inside the load platform, completely free from external non-conservative The interference of force, the orbit under the pure earth's gravity, is a quiet reference source in the non-drag state; and the micro-thruster can generate a reactionary control force according to the relative displacement between the satellite parent body and the load platform, and drive the satellite parent body to track the load platform , to achieve the second level without drag. The overall system adopts a two-stage drag-free structure, uses electrostatic suspension to achieve zero-stiffness vibration isolation, uses electrostatic drive to achieve active vibration reduction, and integrates to achieve the suppression of micro-vibration.

A zero-stiffness vibration isolation method for an electrostatically suspended two-stage dragless platform, as shown in Figure 2, the specific steps are as follows:

(1) Linearize the conversion link between the voltage and electrostatic force of the electrostatic levitation platform system; the specific steps are:

(1a) In the differential capacitance model, the formula for calculating the electrostatic force F _e of the middle electrode in the actual system is:

In the formula, ε _r is the relative permittivity, ε ₀ is the vacuum permittivity, A is the effective area of a capacitor plate, V _{s_eff} is the effective value of high-frequency AC excitation voltage, V _r is the preload voltage (bias DC voltage ), V _b is the feedback voltage, d ₀ is the nominal gap, and x is the displacement of the suspension from the center position;

(1b) Neglecting the high-order small amount of displacement in the electrode electrostatic force F _e , the calculation formula of the electrode electrostatic force F _e is:

(1c) Separating the electrostatic negative stiffness, the calculation formula of the electrostatic negative stiffness is:

(1d) Force the electrostatic negative stiffness to be 0, and complete the linearization of the feedback voltage and the electrode electrostatic force.

In the above formula, the electrode electrostatic force F _e is related to the displacement x of the suspension from the center position. When no linearization is performed, the electrostatic negative stiffness K _e of the electrostatic levitation system is the effect of the electrode electrostatic force F _e on the suspension from the center position Find the partial derivative with displacement x.

After the linearization design of the electrostatic levitation system, K _e can be regarded as 0.

(2) Design the control algorithm of electrostatic drive and micro-push drive for the electrostatic suspension two-stage non-drag platform;

The control algorithm design mentioned here, because the designed control algorithm is oriented to the system after the electrostatic negative stiffness is eliminated, that is, the relative displacement change between the load platform and the satellite body will not produce a change in the electrostatic force, so that the ultra-static platform The two-stage drag-free system is completely decoupled, so the existing technology (second-order optimal control model or design methods such as conventional PID controllers) can be used to independently design excellent controllers.

(3) According to the control algorithm obtained in step (2), the output of the control algorithm is nonlinearly modulated, and the output of the modulated control algorithm is used to replace the output of the original algorithm.

The feedback voltage loaded on both ends of the differential capacitor is nonlinearly modulated to obtain the modulated output upper feedback voltage and lower feedback voltage. The calculation methods of the upper feedback voltage V _{b_up} and the lower feedback voltage V _{b_down} are respectively:

Among them, the relative displacement of the load platform The calculation formula of is as follows:

The feedback voltage obtained by nonlinear modulation is used as the modulated feedback voltage loaded on both sides of the differential capacitor. At this time, the calculation formula of the actual electrode electrostatic force F _e ′ is:

The calculation formula of the actual electrode electrostatic force F _e ′ is not affected by the local linearization result, but the actual electrode electrostatic force after modulation. It can be seen from the formula that under the condition of zero stiffness, the actual electrode electrostatic force has the same value as the suspension The displacement x away from the center position is irrelevant, thus ensuring that the platform system is not affected by large amplitudes and achieving a better vibration isolation effect, as shown in Figure 3.

As shown in Figure 4, after the linearization design is carried out, the system block diagram after linearization is obtained. Among them, m is the mass of the load platform, F _n1 is the non-conservative force acting on the load platform, x ₁ is the displacement of the load platform relative to the reference mass; M is the mass of the satellite parent body, F _n2 is the force acting on the satellite parent body Non-conservative force, x ₂ is the displacement of the satellite parent body relative to the reference mass, K ₁ is the detection gain from the displacement of the load platform relative to the reference mass to the voltage, G ₁ is the electrostatic drive control algorithm, H ₁ is the difference between the feedback voltage and the electrostatic force The linear part of the drive gain, K ₂ is the detection gain from the displacement of the satellite parent body relative to the load platform to the voltage, G ₂ is the control algorithm of the micro-thruster, and H ₂ is the power/force conversion gain of the micro-thruster.

Since the controller will be applied to the zero-stiffness system in the end, in order to optimize the performance of the controller parameters in the zero-stiffness system, the electrostatic negative stiffness is forced to be regarded as zero, and the control block diagram of the zero-stiffness linear system is obtained as shown in Figure 5.

In the actual system control method after constructing zero stiffness as shown in Figure 6, a simulink simulation model of the system is established, and the simulation parameters are shown in Table 1.

Table 1 System Simulation Parameters

parameter value Mass of load platform m/kg 100 Satellite body mass M/kg 500 Gain K ₁ /(V/m) of the displacement detection circuit between the load platform and the mass block 500000 Gain K ₂ /(V/m) of the displacement detection circuit between the payload platform and the satellite body 30000 Effective area of capacitor plate A/m ² 1 Preload voltage V _r /V 1000 Nominal clearance d ₀ /m between payload platform and satellite body 0.001 Electromechanical conversion gain H ₂ /(V/N) of micro propulsion 1

Among them, the comprehensive effect of f ₁ f ₂ is equivalent to the H ₁ link in Figure 5;

The designed controller parameters are:

Set the amplitude of the disturbing force _Fn2 acting on the satellite parent body to 50N, the frequency to 50Hz, and set the disturbing force _Fn1 acting on the load platform to zero. The simulation can obtain the displacement of the suspended load platform on the disturbance acting on the satellite parent body. The time-domain response of the dynamic _Fn2 , that is, the response to the displacement disturbance of the satellite parent body, is shown in Figure 7. It can be seen from Figure 7 that the fluctuation value is almost zero, and the glitch is only an error caused by numerical calculation. It can be seen that this method achieves the vibration isolation effect of absolute zero stiffness.

The content that is not described in detail in the description of the present invention belongs to the well-known technology of those skilled in the art.

Claims (3)

1. a kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage, it is characterised in that including walking as follows Suddenly：

(1) linearization process is carried out to the relationship of electrostatic suspension plateform system feedback voltage and electrode electrostatic force so that force quiet Electric negative stiffness is 0；

(2) on the basis of step (1) is completed, for electrostatic suspension formula twin-stage without tow platform, electrostatic drive is independently carried out Dynamic and micro- control algorithm design for pushing away drive control；

(3) non-linear modulation carried out to the control algolithm output of electrostatic drive controller obtained by step (2), and by non-linear modulation Control algolithm afterwards exports the reality output as electrostatic drive controller.

2. a kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage according to claim 1, It is characterized in that：In the step (1), to electrostatic suspension plateform system linearized the specific steps are：

(1a) ignores electrode electrostatic force F in differential capacitance model_eMiddle displacement high-order is a small amount of, by real system target electrostatic Power F_eCalculation formula be expressed as：

In formula, ε_rFor relative dielectric constant, ε₀For permittivity of vacuum, A is one piece of capacitor plate effective area, V_{s_eff}For high frequency Ac-excited voltage effective value, V_rFor pre-load voltage, V_bFor feedback voltage, d₀For nominal gap, x is that suspended substance deviates centre bit The displacement set；

(1b) detaches electrostatic negative stiffness；The calculation formula of the electrostatic negative stiffness is：

It is 0 that (1c), which forces electrostatic negative stiffness, completes feedback voltage and is linearized with electrode electrostatic force.

3. a kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage according to claim 1 or 2, It is characterized in that：In the step (3), differential capacitance both sides load modulated feedback voltage include upper feedback voltage and under Feedback voltage, wherein upper feedback voltage V_{b_up}, lower feedback voltage V_{b_down}Computational methods be respectively：

Wherein, payload platform relative displacementCalculation formula it is as follows：

In formula, V_cAlgorithm output voltage in order to control.