CN107589671B - Satellite attitude control method based on event driving - Google Patents
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Abstract
The invention relates to a satellite attitude control method based on event driving, which relates to a satellite attitude control system model and aims to solve the problem that unnecessary data transmission in the existing time-driven control method increases the load pressure of data transmission and wastes limited available resources due to limited resources of communication and information transmission.
Description
Technical Field
The invention relates to a satellite attitude control method.
Background
Satellites have gained increasing use since the middle of the 20 th century: the exploration satellite can explore the terrain; the meteorological satellite can detect the cloud picture and observe the wind direction and the wind speed; the spy satellite can collect military intelligence; the experimental satellite can help scientists to do a plurality of experiments which cannot be completed on the earth in the outer space, and the posture of the satellite after the in-orbit service is important to be aligned to complete corresponding tasks, so that the experimental satellite plays a very important role in the service life and the use of the experimental satellite. Attitude control is a method for realizing attitude stabilization by using the dynamic characteristics and environmental moments of satellites. Because the ground does not have the condition for simulating the actual operation environment of the satellite, the simulation of the satellite attitude control problem by using mathematical modeling and numerical simulation experiments becomes an important and effective research means.
In the field of control system research, a control method based on time drive is generally applied, a sensor periodically transmits the measurement state of a system to a controller port, and a controller calculates a series of controller outputs according to received data and then transmits the controller outputs back to system equipment so as to achieve the expected control performance. The control method based on time driving is easy to implement and operate, but often results in unnecessary data transmission, and because resources for communication and information transmission are limited, redundant data transmission increases load pressure of data transmission, and wastes limited available resources.
Disclosure of Invention
The invention aims to solve the problems that in the existing time-driven control method, unnecessary data transmission is caused, because resources for communication and information transmission are limited, redundant data packet transmission can increase load pressure of data transmission and waste limited available resources, and provides a satellite attitude control method based on event driving.
A satellite attitude control method based on event driving comprises the following specific processes:
the method comprises the following steps: establishing a satellite attitude dynamic behavior (a satellite rotation process) as a flexible arm model, and carrying out theoretical analysis on the flexible arm model to obtain a state space equation of the flexible arm model;
step two: designing a hybrid event-driven condition based on a state space equation of the flexible arm model;
thirdly, obtaining a condition for ensuring the passivity of the flexible arm model by utilizing L yapunov (Lyapunov) stability theory based on the driving condition of the mixed event;
step four: and designing a controller criterion of the flexible arm model based on the passivity condition obtained in the step three.
The invention has the beneficial effects that:
in order to reduce the sending of data packets and ensure the realization of control performance, the packet sending process does not regularly operate along with the time lapse under the event-driven control method. Whether or not to transmit a packet will depend on whether or not the set event-driven conditions are triggered. Only the measured state value that triggers the driving condition will be transmitted to the controller, and if the driving condition is not triggered, the controller will not be updated and the system will always use the last received control output; the method solves the problems that the existing time-driven control method causes unnecessary data packet transmission and wastes limited available resources. In the time-driven control method, the sampling period is selected to be 0.05 second, and the total operation time is selected to be 20 seconds, so that 400 data packets need to be sent by the sensor. In fact, these 400 packets are not all valuable, and many of the transmitted packets are redundant, which is not important for improving the control performance, but rather increases the communication pressure of the system. In the same case, by using the hybrid event-driven control method of the present invention, the packet sending amount of the sensors can be reduced to 73 based on the controller and the event-driven law designed by the present invention. Compared with a time-driven control method, the volume of the sent packets is greatly reduced. Therefore, the control method based on event driving can effectively save the bandwidth of the communication network and save the resource of information transmission. The application of the event-driven method also has very important practical significance to the research of the satellite attitude control problem.
In summary, the present invention provides a control method based on hybrid event driven for controlling the satellite attitude, which can reduce the number of data packets transmitted to the controller, and ensure the control performance required by the satellite attitude, thereby achieving efficient utilization of communication and information transmission resources.
Drawings
FIG. 1 is a schematic diagram of a basic structure of a satellite according to the present invention, wherein X is a horizontal axis of a rectangular spatial coordinate system, Y is a vertical axis of the rectangular spatial coordinate system, and Z is a vertical axis of the rectangular spatial coordinate system;
FIG. 2 is a schematic diagram of a flexible arm model constructed according to the present invention;
FIG. 3 is a simplified representation of a flexible arm model of the present invention placed in a coordinate system, OsXsYsAnd OXY are respectively defined as an inertial coordinate system and a relative position coordinate system fixed at the shaft end, tip mass mαFor the end mass of the flexible arm model, the flexible beam is the flexible beam of the flexible arm model, w (x, t) is the flexible deformation of the flexible beam relative to the XY coordinate system, x represents the displacement, and t is shown in the tableShowing time, O is the origin of the XY coordinate system, X is the horizontal axis of the XY coordinate system, Y is the vertical axis of the XY coordinate system, OsIs OsXsYsOrigin of the coordinate system, XsIs OsXsYsTransverse axis of the coordinate system, YsIs OsXsYsThe vertical axis of the coordinate system, hub, disk of the flexible arm model, τhTo control the torque, JhThe moment of inertia is adopted, r is the radius of the joint, l is the length of the beam body, and theta (t) is an expected adjusting angle;
FIG. 4 shows a first state in an embodiment of the present invention
A state trajectory diagram of a flexible arm model state space equation based on a hybrid event driven method;
FIG. 5 shows a second state in an embodiment of the present invention
A state trajectory diagram of a flexible arm model state space equation based on a hybrid event driven method;
FIG. 6 shows a third state in the embodiment of the present invention
A state trajectory diagram of a flexible arm model state space equation based on a hybrid event driven method;
FIG. 7 shows a fourth state in the embodiment of the present invention
A state trajectory diagram of a flexible arm model state space equation based on a hybrid event driven method;
FIG. 8 shows a fifth state in the embodiment of the present invention
A state trajectory diagram of a flexible arm model state space equation based on a hybrid event driven method;
FIG. 9 shows a sixth state in the embodiment of the present invention
A state trajectory diagram of a flexible arm model state space equation based on a hybrid event driven method;
fig. 10 is a diagram of a packet sending time interval based on a hybrid event driven method according to an embodiment of the present invention, where Inter-eventerval is the packet sending time interval.
Detailed Description
The first embodiment is as follows: the event-driven satellite attitude control method based on the embodiment comprises the following specific processes:
the method comprises the following steps: establishing a satellite attitude dynamic behavior (a satellite rotation process) as a flexible arm model, and carrying out theoretical analysis on the flexible arm model to obtain a state space equation of the flexible arm model;
step two: designing a hybrid event-driven condition based on a state space equation of the flexible arm model;
thirdly, obtaining a condition for ensuring the passivity of the flexible arm model by utilizing L yapunov (Lyapunov) stability theory based on the driving condition of the mixed event;
step four: and designing a controller criterion of the flexible arm model based on the passivity condition obtained in the step three.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: in the first step, a satellite attitude dynamic behavior (a satellite rotation process) is established as a flexible arm model, and the flexible arm model is subjected to theoretical analysis to obtain a state space equation of the flexible arm model; the specific process is as follows:
the flexible arm flexibly deforms into:
wherein w (x, t) is the elastic deformation of the flexible beam relative to the XY coordinate system, n in the formula (1) represents that the elastic deformation w (x, t) is decomposed into n vibrations with different frequencies, namely a so-called n-order mode, n is the number of the elastic deformation modes, and the value is a positive integer,
for the mode shape function corresponding to the i-th mode determined according to the boundary conditions of the flexible beam, qi(t) is a modal coordinate corresponding to the ith mode, i is a mode of the ith elastic deformation under consideration and takes a value of 1-n;
firstly, researching the potential energy of the flexible arm model, and calculating the potential energy v (t) of the flexible arm model according to a calculation formula (material mechanics) of elastic potential energy, namely the potential energy of the flexible beam is expressed as:
wherein D isα(. cndot) is the Caputo fractional derivative with respect to time, α is the order of the derivative, in the interval [0,1]Taking the value above, h is the height of the flexible arm, E is the Young modulus, l represents the length of the flexible arm,
the moment of inertia of the tangent plane of the flexible arm beam is represented, and S is the area of the tangent plane of the flexible arm beam; x is displacement and t is time;
considering the kinetic energy of the flexible arm model below, the kinetic energy t (t) of the entire model is concentrated on the rotating joints, flexible arms and end mounted actuators. That is, the kinetic energy t (t) of the flexible arm model is expressed as the sum of the kinetic energy of the coupling joint, the kinetic energy of the flexible arm and the kinetic energy of the tip:
where ρ isbRepresents the flexible arm density; j. the design is a squarehTheta (t) is a desired adjustment angle for the moment of inertia of the coupling,
is the first derivative of theta (t),
is the first derivative of w (x, t), r represents the flexible arm joint radius, mαIs the mass of the executing end of the flexible arm, w (l, t) is the value of w (x, t) when the displacement x is l,
is the first derivative of w (l, t);
bringing the formula (1) into the expressions of potential energy (2) and kinetic energy (3) of the flexible arm model respectively, the potential energy v (t) of the flexible arm model will be converted into:
wherein j is the mode of the j-th elastic deformation under consideration, j takes the value of 1-n, i is the mode of the i-th elastic deformation under consideration, and i takes the value of 1-n; q. q.sj(t) is a mode coordinate corresponding to the j-th mode, qi(t) is a modality coordinate corresponding to the ith modality,
the second derivative of the mode shape function corresponding to the jth mode shape determined according to the boundary condition of the flexible beam with respect to the displacement,
the second derivative of the corresponding mode shape function of the ith mode determined according to the boundary condition of the flexible beam with respect to the displacement;
the kinetic energy t (t) of the flexible arm model will be converted into:
wherein,
is qi(ii) the first derivative of (t),
is qj(ii) the first derivative of (t),
the value of the mode shape function corresponding to the ith mode when the displacement is l,
the displacement is l for the corresponding mode shape function of the jth mode,
the mode shape function corresponding to the jth mode determined according to the boundary condition of the flexible beam;
control moment tau of flexible arm modelh(t) the work done under the influence of the disturbance moment d (t) of the flexible arm model is expressed as:
W＝(τh(t)+d(t))θ(t) (6)
by synthesizing the potential energy v (t) of the flexible arm model, the kinetic energy t (t) of the flexible arm model and the work expression, using Hamilton's principal (Hamilton principle), the following equation is obtained:
H＝T(t)-V(t) (7)
wherein H is a scalar potential of work W;
since the degree of bending of the flexible arm is small compared to the angle of rotation, the modeling process ignores higher order terms and coupling terms, i.e., nonlinear components, in order to simplify the problem, and thus obtains the kinetic equation of the flexible arm model:
wherein q (t) { q ═ q1(t),q2(t)...qn(t)}TN is the number of elastic deformation modes, and the value is a positive integer,
is the second derivative of q (t),
is the second derivative of θ (t), J represents the moment of inertia matrix, MθqRepresenting a coupling matrix, MqqRepresenting the structural quality matrix, KqqRepresenting a stiffness matrix;
let z (t) be [ θ (t), q ═ qT(t)]TThen equation (8) is converted to a matrix equation as follows:
z (t) is an intermediate variable,
is the second derivative of z (T), T is transposed, d (T) is the disturbance moment of the flexible arm model;
is an intermediate variable;
establishing a state space equation of the flexible arm model according to the matrix equation (10):
selecting
As the state of the flexible arm model, the following state space equation of the flexible arm model is obtained:
wherein,
the matrix A and the matrix B are constant coefficient matrixes obtained by calculating parameters in the actual satellite attitude control process;
for the control problem of the flexible arm model, an input saturation state feedback control method is adopted, the observed control performance index is an passivity index reflecting the relation of input and output energy, and then the state space equation of the flexible arm model is rewritten as follows:
wherein,
in the state of the flexible arm model,
is composed of
First derivative of, τh(t) is the control moment of the flexible arm model, sat (DEG) is the saturation function of the control moment of the flexible arm model, D (t) is the interference moment of the flexible arm model, y (t) is the measurement output of the flexible arm model, the matrixes C and D are constant coefficient matrixes obtained by parameter calculation in the actual satellite attitude control process, and the matrix K is the gain of the controller to be designed.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: j, M in said equation 8θq、Mqq、KqqThe expression of (a) is as follows:
in said equation 10
The expression of (a) is:
wherein
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: before the satellite attitude dynamics behavior (satellite rotation process) is established as the flexible arm model in the first step, the following assumptions need to be made: the specific process is as follows:
the half structure of a satellite model with a symmetrical structure is modeled as a flexible arm, and the satellite model is schematically shown in FIG. 1. The flexible arm is composed of a joint, a flexible connecting rod and an execution end, and the basic structure of the flexible arm model is shown in figure 2. To analyze the flexible arm model, it was placed under a coordinate system frame, as shown in FIG. 3.
1. Only the transverse vibration in the flexible arm model plane is considered;
2. the influence of gravity on the deformation of the flexible arm model is ignored;
3. the shaft end joint and the flexible beam are assumed to be completely made of the same material and have the same isotropy;
4. the damping characteristics of the flexible part in the flexible arm model were ignored.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: designing a mixed event driving condition based on a state space equation of the flexible arm model in the second step; the specific process is as follows:
the event-driven driving condition is called hybrid event-driven because the used event-driven driving condition combines the characteristics of two methods of periodic sampling and continuous event-driven. The mixed event drive combining the periodic sampling and the continuous event drive solves the problem of redundant packet sending of the periodic sampling and avoids the Zeno phenomenon driven by the continuous event.
As in the second embodiment, a state space equation (13) of the flexible arm model is obtained, wherein each term is continuous with respect to time t. In practical application, only data packets at discrete time points can be sent to the controller by the sensor of the flexible arm model, and the controller updates the control input according to the received data packets and sends the control input back to the flexible arm model, so that the expected control performance is realized. Therefore, the state space equation (13) of the flexible arm model needs to be further rewritten as follows:
wherein s iskK is 0,1,2, … N for discrete time points of sending data packets, and N is a positive integer; tau ish(sk) A control moment for the flexible arm model; based on expression (14), hybrid event-driven driving conditions are designed as follows:
wherein,
in the state of the flexible arm model,
is composed of
At skThe value of the moment, omega, is the event-driven law to be determinedMatrix, event-driven correlation parameter, h1The length of silence after each successful packet transmission;
when the state of the flexible arm model
When the driving condition is satisfied, the sensor of the flexible arm model sends a data packet, and when the state variable of the flexible arm model is satisfied
When the driving condition is not met, the sensor of the flexible arm model does not generate a package.
Other steps and parameters are the same as those in the first to second embodiments.
Sixth specific implementation mode, the difference between the first specific implementation mode and the fifth specific implementation mode is that the third step obtains the condition for ensuring the passivity of the flexible arm model by using L yapunov (lyapunov) stability theory based on the mixed event driving condition, and the specific process is as follows:
step three, firstly, the following definitions are given to the saturation function in the state space equation (13) of the flexible arm model:
sat(τh)＝[sat(τh1) sat(τh2) … sat(τhm)]T(16)
wherein tau ish＝[τh1τh2… τhm]T，sat(τhi)＝sign(τhi)min{τ hi,|τhiI ═ 1, …, m, m being the dimension of the control input to the flexible arm model, sign (·) being a sign function,τ hiat the saturation level;
according to the definition of the saturation function, there must be a diagonal matrix T1So that-I is less than or equal to T1Is < 0 and
ψT(τh)[ψ(τh)-T1τh]0 ≦ 0 (17) holds, where ψ (τ)h)＝sat(τh)-τhI is an identity matrix; the state space equation (14) of the flexible arm model is transformed into
Step three, performing the following deformation on a state space equation (18) of the flexible arm model:
wherein,
τ(t)＝t-sk≤h1
χ(t)、τ(t)、e1(t) is an intermediate variable; psi (τ)h(sk))＝sat(τh(sk))-τh(sk)；
Step three, constructing L yapunov (Lyapunov) functions based on the state space equation (19) of the flexible arm model:
when χ (t) ═ 1, the state space equation of the flexible arm model is
Wherein τ (t) is an intermediate variable, and τ (t) is t-sk；
To pair
Derivation, using reciprocal method, Jensen inequality (Zhansen inequality), Schur complementary property,
And
to obtain
Wherein,
is composed of
The first derivative of (a); given a positive number (e.g. a value between 0 and 1)And,) represents exponential decay rate, gamma is a positive number, represents passivity performance index, G1For a matrix of variables of suitable dimensions, phi1,Σ,ξ1(t) is an intermediate variable;
when χ (t) ═ 0, the state space equation of the flexible arm model is
In the formula, e1(t) is a variable in the middle of the equation,
to pair
Derivation, using event-driven conditions and Ψ < 0
Where the parameters are event driven correlations, Ψ, ξ2(t) is an intermediate variable;
in the case of integrating χ (t) ═ 1 and χ (t) ═ 0, the following equation holds
Integrating the inequality (20) from 0 to t to obtain
Wherein μ is an integral variable;
when x (0) is 0, the following equation holds
Thus, when there is a positive definite matrix P1,S1,R1Ω and matrix variable G1So that
Ψ < 0 and
when established, the flexible arm model is passive.
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The seventh embodiment: the difference between this embodiment and one of the first to sixth embodiments is: the intermediate variable phi1,Σ,ξ1The expressions of (t) are respectively:
Σ＝h1[R1A R1BK 0 R1B R1B]T,
wherein, the symbol represents the transposed part on the corresponding position of the matrix;
intermediate variables Ψ, ξ2The expressions of (t) are respectively:
the specific implementation mode is eight: the present embodiment differs from one of the first to seventh embodiments in that: in the fourth step, a controller criterion of the flexible arm model is designed based on the passivity condition obtained in the third step; the specific process is as follows:
inequality for the above embodiment
Ψ < 0 and
making congruent transformation, and multiplying the matrix diag { P) on two sides of phi < 01 -1,P1 -1,P1 -1,I,I,R1 -1Multiplying by matrix diag { P) at two sides of psi < 01 -1,P1 -1I, I }, in
Multiplication of both sides by the matrix diag { P }1 -1,P1 -1Get separately
Wherein diag {. denotes a diagonal matrix,
as an intermediate variable, the expression is
Wherein,
as intermediate variables, matrix variables
Is defined as follows
Due to the fact that
Then
Wherein κ is a positive number, therefore
Wherein,
as an intermediate variable, the expression is
Thus, when a positive definite matrix exists
And matrix variables
So that
And
when established, the flexible arm model is passive and designed to yield controller gain
And pending event driven law matrix
Other steps and parameters are the same as those in one of the first to seventh embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the method for controlling the satellite attitude based on event driving is specifically prepared according to the following steps:
the structural parameters of the flexible arm model for the test are shown in table 1
Table 1 flexible arm structure parameter table for test
Based on the state space obtained by satellite modeling and the physical parameters of the satellite, MAT L AB software is used for calculating each parameter matrix of the satellite state space to obtain the following satellite parameter matrix
B＝[0 0 0 0.0885 0.1390 0.0315]T.
Solving the linear matrix inequality using the YA L MIP toolkit of MAT L AB, based on step four of the present invention
And
selecting a parameter h10.05, ═ 0.01, ═ 0.1, γ ═ 5, optimized event-driven correlation parameters were obtainedmax0.46, whereinmaxRepresents the maximum value allowed by the event-driven related parameters under the condition of ensuring the solution in the solving process, and the gain and the event-driven law of the solved controller are
K＝[-0.3014 7.4485 354.6386 -12.0395 -10.3123 -327.3108],
And carrying out simulation experiments on the constructed satellite model. The designed controller and event-driven law omega are applied to a system model, state tracks of a state space equation of the flexible arm model are drawn, and the bale release amount in the whole control process is calculated, as shown in the attached figures 4-10. In the simulation, the total operation time is 20 seconds, and the disturbance d (t) is e-0.1t. As can be seen from fig. 4-9, the state of the flexible arm model is convergent under the designed controller and drive laws,to achieve the desired control effect. Figure 10 reflects the control process in the case of a bundle.
TABLE 2 comparison of the amount of packets sent in different ways
Further, table 2 compares the parameter values of the same flexible arm model, and the number of data packets to be sent is determined by using the methods of periodic sampling and mixed event driving, and the results show that the event driving method plays a significant role in reducing the packet sending amount, thereby realizing efficient utilization of communication resources.
The above description is only an example of the present invention, and is not intended to limit the scope of the present invention. The modifications, the partial replacements and the application expansion of the contents of the description and the attached drawings of the invention, or the application of the invention in other related technical fields directly or indirectly, shall be included in the protection scope of the patent of the invention.
Claims (6)
1. A satellite attitude control method based on event driving is characterized in that: the method comprises the following specific processes:
the method comprises the following steps: establishing satellite attitude dynamic behaviors as a flexible arm model, and carrying out theoretical analysis on the flexible arm model to obtain a state space equation of the flexible arm model;
step two: designing a hybrid event-driven condition based on a state space equation of the flexible arm model;
step three: based on the driving conditions of the mixed events, utilizing the Lyapunov stability theory to obtain the conditions for ensuring the passivity of the flexible arm model;
step four: designing a controller criterion of the flexible arm model based on the passivity condition obtained in the step three;
in the first step, satellite attitude dynamic behaviors are established as a flexible arm model, and the flexible arm model is theoretically analyzed to obtain a state space equation of the flexible arm model; the specific process is as follows:
the flexible arm flexibly deforms into:
wherein w (x, t) is the elastic deformation of the flexible beam relative to the OXY coordinate system, n is the number of elastic deformation modes, the value is a positive integer,
for the mode shape function corresponding to the i-th mode determined according to the boundary conditions of the flexible beam, qi(t) is a modal coordinate corresponding to the ith mode, i is a mode of the ith elastic deformation under consideration and takes a value of 1-n;
according to the calculation formula of the elastic potential energy, calculating the potential energy V (t) of the flexible arm model as follows:
wherein D isα(. cndot.) is the Caputo fractional derivative with respect to time, α is the order of the derivative, in the interval [0,1]Taking the value above, h is the height of the flexible arm, E is the Young modulus, l represents the length of the flexible arm,
the moment of inertia of the tangent plane of the flexible arm beam is represented, and S is the area of the tangent plane of the flexible arm beam; x is displacement and t is time;
the kinetic energy t (t) of the flexible arm model is expressed as:
where ρ isbRepresents the flexible arm density; j. the design is a squarehTheta (t) is a desired adjustment angle for the moment of inertia of the coupling,
is the first derivative of theta (t),
is the first derivative of w (x, t), r represents the flexible arm joint radius, mαIs the mass of the executing end of the flexible arm, w (l, t) is the value of w (x, t) when the displacement x is l,
is the first derivative of w (l, t);
bringing the formula (1) into the expressions of potential energy (2) and kinetic energy (3) of the flexible arm model respectively, the potential energy v (t) of the flexible arm model will be converted into:
wherein j is the mode of the j-th elastic deformation under consideration, j takes the value of 1-n, i is the mode of the i-th elastic deformation under consideration, and i takes the value of 1-n; q. q.sj(t) is a mode coordinate corresponding to the j-th mode, qi(t) is a modality coordinate corresponding to the ith modality,
the second derivative of the mode shape function corresponding to the jth mode shape determined according to the boundary condition of the flexible beam with respect to the displacement,
the second derivative of the corresponding mode shape function of the ith mode determined according to the boundary condition of the flexible beam with respect to the displacement;
the kinetic energy t (t) of the flexible arm model will be converted into:
wherein,
is qi(ii) the first derivative of (t),
is qj(ii) the first derivative of (t),
the value of the mode shape function corresponding to the ith mode when the displacement is l,
the displacement is l for the corresponding mode shape function of the jth mode,
the mode shape function corresponding to the jth mode determined according to the boundary condition of the flexible beam;
control moment tau of flexible arm modelh(t) the work done under the influence of the disturbance moment d (t) of the flexible arm model is expressed as:
W＝(τh(t)+d(t))θ(t) (6)
by integrating the potential energy V (t) of the flexible arm model, the kinetic energy T (t) of the flexible arm model and the work expression, the following equation is obtained by using the Hamilton principle:
H＝T(t)-V(t) (7)
wherein H is a scalar potential of work W;
the kinetic equation for the flexible arm model:
wherein q (t) { q ═ q1(t),q2(t)...qn(t)}TN is the number of elastic deformation modes, and the value is a positive integer,
is the second derivative of q (t),
is the second derivative of θ (t), J represents the moment of inertia matrix, MθqRepresenting a coupling matrix, MqqRepresenting the structural quality matrix, KqqRepresenting a stiffness matrix;
let z (t) be [ θ (t), q ═ qT(t)]TThen equation (8) is converted to a matrix equation as follows:
z (t) is an intermediate variable,
is the second derivative of z (T), T is transposed, d (T) is the disturbance moment of the flexible arm model;
is an intermediate variable;
establishing a state space equation of the flexible arm model according to the matrix equation (10):
selecting
As the state of the flexible arm model, the following state space equation of the flexible arm model is obtained:
wherein,
the matrix A and the matrix B are constant coefficient matrixes obtained by calculating parameters in the actual satellite attitude control process;
the state space equation of the flexible arm model is rewritten as:
wherein,
in the state of the flexible arm model,
is composed of
First derivative of, τh(t) is the control moment of the flexible arm model, sat (DEG) is the saturation function of the control moment of the flexible arm model, D (t) is the interference moment of the flexible arm model, y (t) is the measurement output of the flexible arm model, the matrixes C and D are constant coefficient matrixes obtained by parameter calculation in the actual satellite attitude control process, and the matrix K is the gain of the controller to be designed;
designing a mixed event driving condition based on a state space equation of the flexible arm model in the second step; the specific process is as follows:
the state space equation (13) for the flexible arm model is further rewritten as follows:
wherein s iskK is 0,1,2, … N for discrete time points of sending data packets, and N is a positive integer; tau ish(sk) A control moment for the flexible arm model; based on expression (14), hybrid event-driven driving conditions are designed as follows:
wherein,
in the state of the flexible arm model,
is composed of
At skThe value of the moment, omega, is the event-driven law matrix to be determined, and is the parameter related to the event drive, h1The length of silence after each successful packet transmission;
when the state of the flexible arm model
When the driving condition is satisfied, the sensor of the flexible arm model sends a data packet, and when the state variable of the flexible arm model is satisfied
When the driving condition is not met, the sensor of the flexible arm model does not generate a package.
2. The method of claim 1, wherein the method comprises: j, M in said equation 8θq、Mqq、KqqThe expression of (a) is as follows:
in said equation 10
The expression of (a) is:
wherein
3. The method of claim 2, wherein the method comprises: before the satellite attitude dynamics behavior is established as the flexible arm model in the first step, the following assumptions need to be made:
1) only the transverse vibration in the flexible arm model plane is considered;
2) the influence of gravity on the deformation of the flexible arm model is ignored;
3) the shaft end joint and the flexible beam are assumed to be completely made of the same material and have the same isotropy;
4) the damping characteristics of the flexible part in the flexible arm model were ignored.
4. The method of claim 1, wherein the method comprises: the third step is based on the driving condition of the mixed event, and utilizes the Lyapunov stability theory to obtain the condition for ensuring the passivity of the flexible arm model; the specific process is as follows:
step three, firstly, the following definitions are given to the saturation function in the state space equation (13) of the flexible arm model:
sat(τh)＝[sat(τh1) sat(τh2) … sat(τhm)]T(16)
wherein tau ish＝[τh1τh2… τhm]T，sat(τhi)＝sign(τhi)min{τ hi,|τhiI ═ 1, …, m, m being the dimension of the control input to the flexible arm model, sign (·) being a sign function,τ hiat the saturation level;
according to the definition of the saturation function, there must be a diagonal matrix T1So that-I is less than or equal to T1Is < 0 and
ψT(τh)[ψ(τh)-T1τh]≤0 (17)
in which ψ (τ)h)＝sat(τh)-τhI is an identity matrix; the state space equation (14) of the flexible arm model is transformed into
Step three, performing the following deformation on a state space equation (18) of the flexible arm model:
wherein,
τ(t)＝t-sk≤h1
χ(t)、τ(t)、e1(t) is an intermediate variable; psi (τ)h(sk))＝sat(τh(sk))-τh(sk)；
Thirdly, constructing a Lyapunov function based on a state space equation (19) of the flexible arm model:
when χ (t) ═ 1, the state space equation of the flexible arm model is
Wherein τ (t) is an intermediate variable, and τ (t) is t-sk；
To pair
Derivation, using reciprocal method, Jensen inequality, Schur's complement property,
And
to obtain
Wherein,
is composed of
The first derivative of (a); given a positive number representing the exponential decay rate, gamma is a positive number representing the passivity performance index, G1For a matrix of variables of suitable dimensions, phi1,Σ,ξ1(t) is an intermediate variable; when χ (t) ═ 0, the state space equation of the flexible arm model is
In the formula, e1(t) is a variable in the middle of the equation,
to pair
Derivation, using event-driven conditions and Ψ < 0
Where the parameters are event driven correlations, Ψ, ξ2(t) is an intermediate variable;
in the case of integrating χ (t) ═ 1 and χ (t) ═ 0, the following equation holds
Integrating the inequality (20) from 0 to t to obtain
Wherein μ is an integral variable;
when x (0) is 0, the following equation holds
Thus, when there is a positive definite matrix P1,S1,R1Ω and matrix variable G1So that
Ψ < 0 and
when established, the flexible arm model is passive.
5. The method of claim 4, wherein the method comprises: the intermediate variable phi1,Σ,ξ1The expressions of (t) are respectively:
Σ＝h1[R1A R1BK 0 R1B R1B]T,
wherein, the symbol represents the transposed part on the corresponding position of the matrix;
intermediate variables Ψ, ξ2The expressions of (t) are respectively:
6. the method of claim 5, wherein the method comprises: in the fourth step, a controller criterion of the flexible arm model is designed based on the passivity condition obtained in the third step; the specific process is as follows:
for the above inequality
Ψ < 0 and
making congruent transformation, and multiplying the matrix diag { P) on two sides of phi < 01 -1,P1 -1,P1 -1,I,I,R1 -1Multiplying by matrix diag { P) at two sides of psi < 01 -1,P1 -1I, I }, in
Multiplication of both sides by the matrix diag { P }1 -1,P1 -1Get separately
Wherein diag {. denotes a diagonal matrix,
as an intermediate variable, the expression is
Wherein,
as intermediate variables, matrix variables
Is defined as follows
Due to the fact that
Then
Wherein κ is a positive number, therefore
Wherein,
as an intermediate variable, the expression is
Thus, when a positive definite matrix exists
And matrix variables
So that
And
when established, the flexible arm model is passive and designed to yield controller gain
And pending event driven law matrix
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1876501A (en) * | 2006-05-31 | 2006-12-13 | 哈尔滨工业大学 | Three axis directional controlling method for stabilizing posture in deep space based on behavior mode |
| CN105930627A (en) * | 2016-06-27 | 2016-09-07 | 北京邮电大学 | Free-floating space manipulator modeling method under condition of considering spacial flexible deformation of arm lever |
| CN106094528A (en) * | 2016-07-13 | 2016-11-09 | 上海航天控制技术研究所 | A kind of spatial flexible robot arm vibration suppression algorithm |
Family Cites Families (1)
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-
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1876501A (en) * | 2006-05-31 | 2006-12-13 | 哈尔滨工业大学 | Three axis directional controlling method for stabilizing posture in deep space based on behavior mode |
| CN105930627A (en) * | 2016-06-27 | 2016-09-07 | 北京邮电大学 | Free-floating space manipulator modeling method under condition of considering spacial flexible deformation of arm lever |
| CN106094528A (en) * | 2016-07-13 | 2016-11-09 | 上海航天控制技术研究所 | A kind of spatial flexible robot arm vibration suppression algorithm |
Non-Patent Citations (2)
| Title |
|---|
| 基于混杂系统描述的卫星姿态控制系统研究;赖镇洲 等;《Proceedings of the 32nd Chinese Control Conference》;20130728;4452-4457 * |
| 时间事件混合驱动的实时容错卫星操作系统设计;李涛 等;《微处理机》;20001130(第04期);41-43 * |
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