CN106444815A - Input forming control method of single-shaft maneuverable spacecraft - Google Patents

Abstract

The invention relates to an input forming control method of a single-shaft maneuverable spacecraft. The method comprises the steps that S1, the posture and posture angular velocity motion path of the spacecraft are planned according to the task requirement of the spacecraft with a flexible accessory, and the state equation of posture motion of the spacecraft is set up; S2, a simplified system feature matrix is applied to approximately calculating a feature value corresponding to the flexible accessory of the spacecraft, and the equivalent vibration frequency of the flexible accessory is calculated; S3, the conjugating feature value of an input former is calculated, parameters of the input former are obtained, and design of the input former is completed; S4, an angular acceleration feedback item is added into a controller of the spacecraft, and residual vibration caused by simplification of the posture motion state equation is compensated for. The method is suitable for the single-shaped motorized equation around the Euler shaft, the solving purpose of a nonlinear system equation is achieved by simplifying a system feature matrix, and the residual motion caused by simplification of the system feature matrix is eliminated through angular acceleration compensation.

Description

A kind of molding control method of single shaft maneuverable spacecraft

Technical field

The present invention relates to a kind of molding control method, specifically refer to a kind of being applied to around the motor-driven boat of Euler's axle single shaft The molding control method of its device, can suppress the vibration exciting in mobile process, realize attitude fast reserve and quickly steady Fixed.

Background technology

Task and function with modern spacecraft platform become more diversified, to the control accuracy of spacecraft, degree of stability, special It is not that fast reserve ability is put forward higher requirement.But for the spacecraft with flexible appendage, in fast reserve process In how to reduce the vibration of flexible appendage and affect on produced by control system, be particularly important.

Traditional molding method is a kind of forming method for opened loop control moment, if directly in closed loop control The moment outfan of device adds molding device, not only will not eliminate vibration, can lead to the concussion of system on the contrary.And apply at present Comparison extensive molding method primary limitation in linear control system, for attitude fast reserve control system Speech, the no matter kinematical equation of the spacecraft or attitude controller of spacecraft is required for adding nonlinear link, and for Vibration suppressing method containing nonlinear element is it is impossible to apply existing molding method.

Based on above-mentioned, need badly at present and propose a kind of molding control method of single shaft maneuverable spacecraft, machine can be suppressed The vibration exciting during dynamic, realizes attitude fast reserve and fast and stable.

Content of the invention

It is an object of the invention to provide a kind of molding control method of single shaft maneuverable spacecraft is it is adaptable to around Euler's axle The motor-driven spacecraft of single shaft, realizes the Solve problems of nonlinear system equation by simplified system eigenmatrix, by angle plus Velocity compensation is eliminating system features matrix because simplifying brought residual oscillation.

For achieving the above object, the present invention provide a kind of molding control method of single shaft maneuverable spacecraft it is adaptable to Around the motor-driven spacecraft of Euler's axle single shaft, comprise the steps of：

S1, the mission requirements according to the spacecraft containing flexible appendage, plan attitude and the attitude angle speed of this spacecraft Degree motion path, sets up the state equation of this attitude motion of spacecraft；

The system features matrix that S2, application simplify carrys out the corresponding eigenvalue of approximate calculation spacecraft flexible appendage；

S3, calculate the Con-eigenvalue of molding device, ask for the parameter of molding device, complete molding device Design；

S4, in the controller of spacecraft add Angular Acceleration Feedback item, compensate attitude motion state equation because simplify institute The residual oscillation causing.

In described S1, the state equation of the attitude motion of spacecraft containing flexible appendage is：

Wherein, 0 is the null matrix of corresponding dimension；E is the unit matrix of corresponding dimension；

q₀Represent Satellite Attitude The scalar component of state quaternary number；E₃Represent 3 rank unit matrixs；u_cRepresent control moment；q_vRepresent the vector of attitude of satellite quaternary number Part；Represent the projection in measuring satellite angular velocities three directions under co-ordinates of satellite system；Brot is the coupling moment of flexible appendage Battle array；ω_cIt is the diagonal matrix with each rank flexible vibration frequency as element；I represents the inertia matrix of satellite；ξ_cResistance for flexible vibration Buddhist nun's ratio, η_iArray for the mode of oscillation composition of i-th flexible appendage.

In described S2, the attitude motion state equation of simplification is：

Wherein,For the system features matrix simplifying；Solve the attitude motion state equation of this simplification, obtain spacecraft and scratch The property corresponding eigenvalue λ of adnexa.

In described S3, the parameter of molding device is two, and the action time of one of parameter is 0, and amplitude is 1/ (1+K), the action time of another parameter is T, and amplitude is K/ (1+K)；Wherein, the expression formula of K and T is：

ξ and ω according to obtaining after calculating in S3 is Con-eigenvalue, and ξ and ω represents the equivalent resistance of flexible appendage respectively Buddhist nun's ratio and frequency of vibration, thus obtaining parameter value T and K of molding device, it is Shaper that design completes molding device.

In described S4, in the controller of spacecraft, add angular acceleration molding item, compensate attitude motion state Equation affects because of the residual oscillation caused by simplification error, obtains the control moment u of controller_cFor：

In formula, Shaper represents molding device；K_pAnd K_dRepresent PD control parameter, q_vRepresent attitude of satellite quaternary number Vector section；q_vdRepresent that satellite expects the vector section of attitude quaternion；q_v0Represent the arrow of initial time attitude of satellite quaternary number Amount part；Represent the projection in measuring satellite angular velocities three directions under co-ordinates of satellite system；Represent initial satellite attitude The projection in angular velocity three directions under co-ordinates of satellite system；a_dRepresent desired angular acceleration；ω_dRepresent desired angular velocity；e₀ Represent initial Euler's axle.

In sum, the molding control method of the single shaft maneuverable spacecraft that the present invention provides is it is adaptable to around Euler's axle The motor-driven spacecraft of single shaft, realizes the Solve problems of nonlinear system equation by simplified system eigenmatrix, by angle plus Velocity compensation is eliminating system features matrix because simplifying brought residual oscillation.

Brief description

Fig. 1 is the flow chart of the molding control method of single shaft maneuverable spacecraft in the present invention.

Specific embodiment

Below in conjunction with Fig. 1, describe a preferred embodiment of the present invention in detail.

As shown in figure 1, the molding control method of the single shaft maneuverable spacecraft providing for the present invention is it is adaptable to around Euler The motor-driven spacecraft of axle single shaft, comprises the steps of：

S1, the mission requirements according to the spacecraft containing flexible appendage, plan attitude and the attitude angle speed of this spacecraft Degree motion path, sets up the state equation of this attitude motion of spacecraft；

The system features matrix that S2, application simplify carrys out the corresponding eigenvalue of approximate calculation spacecraft flexible appendage, and calculates The equivalent frequency of vibration of flexible appendage；

S3, calculate the Con-eigenvalue of molding device, ask for the parameter of molding device, complete molding device Design；

S4, in the controller of spacecraft add Angular Acceleration Feedback item, compensate attitude motion state equation because simplify institute The residual oscillation causing.

In described S1, the state equation of the attitude motion of spacecraft containing flexible appendage is：

Wherein, 0 is the null matrix of corresponding dimension；E is the unit matrix of corresponding dimension；I_c=E-Brot Brot^T；H= (E-Brot^TI^-1Brot)^-1；q₀Represent the scalar component of attitude of satellite quaternary number；E₃Represent 3 rank units Matrix；u_cRepresent control moment；q_vRepresent the vector section of attitude of satellite quaternary number；Represent measuring satellite angular velocities in satellite The projection in lower three directions of coordinate system；Brot is the coupling matrix of flexible appendage；ω_cIt is with each rank flexible vibration frequency as element Diagonal matrix；I represents the inertia matrix of satellite；ξ_cFor the damping ratio of flexible vibration, η_iMode of oscillation for i-th flexible appendage The array of composition.

In described S2, the attitude motion state equation of simplification is：

Wherein,For the system features matrix simplifying；Solve the attitude motion state equation of this simplification, obtain spacecraft and scratch The property corresponding eigenvalue λ of adnexa.

In described S3, the parameter (minimum pulse number) of molding device is two, the action time of one of parameter A For 0, amplitude is 1/ (1+K), and the action time of another parameter B is T, and amplitude is K/ (1+K), specifically refers to following table：

Molding device parameter	A	B
			Action time	0	T
Amplitude	1/(1+K)	K/(1+K)

Wherein, the expression formula of K and T is：

ξ and ω according to obtaining after calculating in S3 is Con-eigenvalue, and ξ and ω represents the equivalent resistance of flexible appendage respectively Buddhist nun's ratio and frequency of vibration, thus obtaining parameter value T and K of molding device, it is Shaper that design completes molding device.

In described S4, in the controller of spacecraft, add angular acceleration molding item, compensate attitude motion state Equation affects because of the residual oscillation caused by simplification error, obtains the control moment u of controller_cFor：

In formula, Shaper represents molding device；K_pAnd K_dRepresent PD (ratio according to designed by system performance for the designer Example differential) control parameter, q_vRepresent the vector section of attitude of satellite quaternary number；q_vdRepresent that satellite expects the vector of attitude quaternion Part；q_v0Represent the vector section of initial time attitude of satellite quaternary number；Represent measuring satellite angular velocities in co-ordinates of satellite system The projection in lower three directions；Represent the projection in initial satellite attitude angular velocity three directions under co-ordinates of satellite system；a_dRepresent Desired angular acceleration；ω_dRepresent desired angular velocity；e₀Represent initial Euler's axle.

The molding control method of the single shaft maneuverable spacecraft that the present invention provides, compared with prior art, has following Advantage and beneficial effect：1st, it is applied to the control system containing nonlinear element；2nd, can completely suppress motor-driven in theory During the vibration that excites；3rd, fast reserve and stable effect can be reached；4th, because vibration will be pressed down after motor-driven completely System, therefore can be bigger by the bandwidth Design of spacecraft；5th, reliability is high, and algorithm is simple, and on star, software is easily realized.

Although present disclosure has been made to be discussed in detail by above preferred embodiment, but it should be appreciated that above-mentioned Description is not considered as limitation of the present invention.After those skilled in the art have read the above, for the present invention's Multiple modifications and substitutions all will be apparent from.Therefore, protection scope of the present invention should be limited to the appended claims.

Claims (5)

1. a kind of molding control method of single shaft maneuverable spacecraft is it is characterised in that be applied to motor-driven around Euler's axle single shaft Spacecraft, comprise the steps of：

S1, the mission requirements according to the spacecraft containing flexible appendage, plan attitude and the attitude angular velocity fortune of this spacecraft Dynamic path, sets up the state equation of this attitude motion of spacecraft；

The system features matrix that S2, application simplify carrys out the corresponding eigenvalue of approximate calculation spacecraft flexible appendage, and calculates flexibility The equivalent frequency of vibration of adnexa；

S3, calculate the Con-eigenvalue of molding device, ask for the parameter of molding device, complete setting of molding device Meter；

S4, in the controller of spacecraft, add Angular Acceleration Feedback item, compensate attitude motion state equation caused because simplifying Residual oscillation.

2. the molding control method of single shaft maneuverable spacecraft as claimed in claim 1 is it is characterised in that described S1 In, the state equation of the attitude motion of spacecraft containing flexible appendage is：

$\stackrel{\·}{x}=A_{t}x+B_t{u}_c;$

$x={\[q_v,{\mathrm{\ω}}_{bt}^b,{\mathrm{\η}}_1^T,{\mathrm{\η}}_2^T...{\mathrm{\η}}_n^T,{\stackrel{\·}{\mathrm{\η}}}_1^T,{\stackrel{\·}{\mathrm{\η}}}_2^T...{\stackrel{\·}{\mathrm{\η}}}_n^T\]}^T;$

$A_t=\left[\begin{array}{cccc}0& q^{\#}& 0& 0\\ 0& 0& {I_c}^{-1}Brot\·{{\mathrm{\ω}}_c}^2& {I_c}^{-1}Brot\·2{\mathrm{\ξ}}_c{\mathrm{\ω}}_c\\ 0& 0& 0& E\\ 0& 0& -H\·{{\mathrm{\ω}}_c}^2& -H2{\mathrm{\ξ}}_c{\mathrm{\ω}}_c\end{array}\right];$

$B_t=\left[\begin{array}{c}0\\ {I_c}^{-1}\\ 0\\ -H\·{\mathrm{Brot}}^T{I}^{-1}\end{array}\right];$

Wherein, 0 is the null matrix of corresponding dimension；E is the unit matrix of corresponding dimension；I_c=E-Brot Brot^T；H=(E- Brot^TI^-1Brot)^-1；q₀Represent the scalar component of attitude of satellite quaternary number；E₃Represent 3 rank unit squares Battle array；u_cRepresent control moment；q_vRepresent the vector section of attitude of satellite quaternary number；Represent that measuring satellite angular velocities are sat in satellite The projection in lower three directions of mark system；Brot is the coupling matrix of flexible appendage；ω_cIt is with each rank flexible vibration frequency as element Diagonal matrix；I represents the inertia matrix of satellite；ξ_cFor the damping ratio of flexible vibration, η_iMode of oscillation group for i-th flexible appendage The array becoming.

3. the molding control method of single shaft maneuverable spacecraft as claimed in claim 2 is it is characterised in that described S2 In, the attitude motion state equation of simplification is：

$P_t^{*}=\left[\begin{array}{cc}0& E\\ -H\·{{\mathrm{\ω}}_c}^2& -H2{\mathrm{\ξ}}_c{\mathrm{\ω}}_c\end{array}\right];$

$\left|\begin{array}{cc}\mathrm{\λ}& -E\\ H\·{{\mathrm{\ω}}_c}^2& \mathrm{\λ}+H2{\mathrm{\ξ}}_c{\mathrm{\ω}}_c\end{array}\right|=0;$

Wherein, P_t ^*For the system features matrix simplifying；Solve the attitude motion state equation of this simplification, obtain spacecraft flexibility attached The corresponding eigenvalue λ of part.

4. the molding control method of single shaft maneuverable spacecraft as claimed in claim 3 is it is characterised in that described S3 In, the parameter of molding device is two, and the action time of one of parameter is 0, and amplitude is 1/ (1+K), another parameter Action time be T, amplitude be K/ (1+K)；Wherein, the expression formula of K and T is：

$K=e^{-\frac{\mathrm{\π}\mathrm{\ξ}}{\sqrt{1-{\mathrm{\ξ}}^2}}};$

$T=\frac{\mathrm{\π}}{\mathrm{\ω}\sqrt{1-{\mathrm{\ξ}}^2}};$

Be Con-eigenvalue according to ξ and ω that obtain after calculating in S3, ξ and ω represent respectively the equivalent damping ratio of flexible appendage and Frequency of vibration, thus obtaining parameter value T and K of molding device, it is Shaper that design completes molding device.

5. the molding control method of single shaft maneuverable spacecraft as claimed in claim 4 is it is characterised in that described S4 In, add angular acceleration molding item in the controller of spacecraft, compensate attitude motion state equation because of simplification error institute The residual oscillation impact causing, obtains the control moment u of controller_cFor：

$\begin{array}{c}{u}_c={\mathrm{IK}}_p\left(Shaper\right(q_{vd})-q_v)+{\mathrm{IK}}_d\left(Shaper\left({\mathrm{\ω}}_d\right)e_0-{\mathrm{\ω}}_{bt}^b\right)\\ -K_{p}IShaper\left(q_{v0}\right)+K_p{\mathrm{Iq}}_{v0}-K_{d}IShaper\left({\mathrm{\ω}}_{bt0}^b\right)+K_p{\mathrm{I\ω}}_{bt}^b+Shaper\left(a_d\right){\mathrm{Ie}}_0\end{array};$

In formula, Shaper represents molding device；K_pAnd K_dRepresent PD control parameter, q_vRepresent the vector of attitude of satellite quaternary number Part；q_vdRepresent that satellite expects the vector section of attitude quaternion；q_v0Represent the vector portion of initial time attitude of satellite quaternary number Point；Represent the projection in measuring satellite angular velocities three directions under co-ordinates of satellite system；Represent initial satellite attitude angle speed The projection in degree three directions under co-ordinates of satellite system；a_dRepresent desired angular acceleration；ω_dRepresent desired angular velocity；e₀Represent Initial Euler's axle.