CN105116914A - Stratospheric-airship-analytic-model-based prediction path tracking control method - Google Patents
Stratospheric-airship-analytic-model-based prediction path tracking control method Download PDFInfo
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Abstract
The invention relates to a stratospheric-airship-analytic-model-based prediction path tracking control method. The method comprises the following steps: step one, providing a given expected tracking value; to be specific, providing a given expected space random parametric path and an expected airship speed; step two, carrying out stratospheric airship modeling; to be specific, carrying out dynamics modeling on a certain type of stratospheric airship to obtain a six-freedom-degree non-linear model; step three, carrying out guidance law calculation; to be specific, for each time, carrying out calculation of an angular speed expectation value at current time according to the current position and attitude of the stratospheric airship and a reference point position on an expected reference path; step four, carrying out control law calculation; to be specific, calculating a control law by using an analytic model prediction control algorithm according to the guidance law calculated by the step three as well as a state quantity and measurable output measured by sensors like an integrated inertial navigation unit, thereby obtaining controlled quantities of a control surface and a propeller thrust. And the inputs obtained by calculation are directly applied to the airship propeller, the rudder, and the elevator, thereby completing the path tracking control of the airship.
Description
Technical field
The invention provides a kind of stratospheric airship analytic model predicted path tracking and controlling method, it does not need online rolling optimization for drive lacking stratospheric airship provides a kind of and has the new control method in the tracking spatial parameterization path of closed analytic solution form, belongs to automatic control technology field.
Background technology
Stratospheric airship relies on aerostatic buoyancy to stay sky, at the aerostatics of the round-the-clock round-the-clock continuous working of stratosphere away from earth's surface, it is moderate that it has flying height, time of executing the task is long, viability is strong, carries the advantages such as useful load is large, and in communication, monitoring, the fields such as traffic administration have wide military and civilian prospect.The gordian technique of stratospheric airship development relates to many fields such as material, structure, the energy, navigation and control.In these gordian techniquies, the path following control of stratospheric airship is unusual part and parcel.Stratospheric airship path following control refers to that stratospheric airship can be followed the tracks of and finally be stabilized in predetermined reference path under the effect of controller.Stratospheric airship path following control system has drive lacking characteristic, strong nonlinearity, is vulnerable to the features such as model parameter change and external interference impact, is a kind of typical nonlinear system.
For the These characteristics of stratospheric airship path following control system, the present invention's " a kind of stratospheric airship analytic model predicted path tracking and controlling method ", proposes the path tracking control method based on non-linear dirigible model.The method combine based on coordinate transform guidance algorithm and resolve Model Predictive Control Theory.According to the controller of method proposed by the invention and Theoretical Design, stratospheric airship space path tracking control problem can well be solved, make drive lacking stratospheric airship asymptotically stability in the reference path of setting, the Project Realization for the path following control of stratospheric airship provides effective design means.
Summary of the invention
(1) object: the object of the present invention is to provide a kind of stratospheric airship analytic model predicted path tracking and controlling method, control engineering teacher can realize the space path tracing control of stratospheric airship according to the step of the method theory in actual design in conjunction with real system parameter.
(2) technical scheme: the present invention's " a kind of stratospheric airship analytic model predicted path tracking and controlling method ", its main contents and program are: first carry out guidance navigation by given expectation track path and calculate, generate and expect angular velocity; Dynamic Modeling is carried out to certain stratospheric airship, obtains the nonlinear model of six degree of freedom.Then using forward speed, side velocity, yaw rate, rate of pitch and angular velocity in roll as output variable, analytic application Model Predictive Control Algorithm solves input quantity, and input quantity is acted on system, realizing route tracing control.In actual applications, the quantity of state such as position, attitude, speed of dirigible is obtained by sensor measurements such as combined inertial nevigations, the controlled quentity controlled variable calculated is transferred to the actuating unit such as steering wheel and propelling screws can realize stratospheric airship path trace facility by the method.
The present invention's " a kind of stratospheric airship analytic model predicted path tracking and controlling method ", its concrete steps are as follows:
step onegiven expectation pursuit gain: arbitrary parameter path, given expectation space and expectation dirigible speed;
step 2stratospheric airship modeling: Dynamic Modeling is carried out to certain model stratospheric airship, obtains six degree of freedom nonlinear model;
step 3guidance Law calculates: in each moment according to the position of current stratospheric airship, attitude and expect that the reference point locations in reference path carries out the calculating of the angular velocity expectation value of current time;
step 4control law calculates: the Guidance Law calculated according to previous step, utilizes analytic model predictive control algorithm to calculate control law, obtains the controlled quentity controlled variable of rudder face and airscrew thrust;
wherein, described in step onegiven expectation pursuit gain, its pursuit gain comprises expected path and desired speed value.Given arbitrary parameter space expected path
,
,
for path parameter;
Given desired speed
,
for desired speed is along the decomposition amount of hull coordinate system.
wherein, described in step 2stratospheric airship modeling,
its computing method are as follows:
Definition position vector
for dirigible barycenter is at the coordinate of inertial system; Velocity
for the component that dirigible speed is fastened at body; Angular velocity vector
for the component that dirigible angular velocity is fastened at body; Eulerian angle
component represent the angle of pitch, crab angle and roll angle respectively;
Position kinematical equation is:
(1)
Wherein for body axis system is to the transition matrix of inertial system;
Attitude kinematics equations is:
(2)
Kinetics equation is:
(3)
Wherein
for constant matrices,
for about
with
nonlinear function matrix;
with
for airscrew thrust and angle of rudder reflection.
wherein, described in step 3guidance Law calculates,
its computing method are as follows:
As in Figure of description as described in Fig. 1, first define inertial coordinate be I}, speed coordinate is that { W} and path coordinate are { F}; Definition
for the projection that dirigible barycenter is fastened at path coordinate relative to the distance of reference point on path.Site error kinematical equation is:
(4)
In above formula
for the translational speed of track reference point on expected path;
for the projection that the angular velocity of path coordinate system relative inertness system is fastened at path coordinate; Definition auxiliary coordinates D}, this coordinate system is for describing the attitude of dirigible close to destination path; Definition
for speed coordinate is tied to the transition matrix of auxiliary coordinates; Definition
for actual value error, attitude error kinematical equation is:
(5)
In above formula
for attitude error,
for
the tertial element of the first row of matrix,
for the element of the first row secondary series of matrix;
;
for path coordinate is tied to the transition matrix of auxiliary coordinates;
for the projection that the angular velocity of path coordinate system relative inertness system is fastened at path coordinate;
for the projection that the angular velocity of auxiliary coordinates relative path coordinate system is fastened at auxiliary coordinate;
for the rate of pitch in velocity coordinate system and yaw rate.
Definition
for generalized error vector.We will design conductance processed and make
asymptotic convergence is to zero.Expect that Formula for Angular Velocity of Fuze is as follows:
(6)
Wherein,
for normal number.On expected path, the translational speed of reference point can be calculated by following formula:
(7) wherein
for normal number.Due to
for the expectation angular velocity under velocity coordinate system, so the expectation angular velocity under also needing to be converted to body axis system.Definition
for the expectation angular velocity of dirigible under body axis system.Its conversion formula is:
(8)
wherein, described in step 4solve control law,
its computing method are as follows:
The kinetic model of the six degree of freedom obtained by step one can be write as following expression matrix form:
(9)
Wherein
for quantity of state,
for system input quantity, be dirigible screw propeller thrust and yaw rudder, elevating rudder drift angle,
for the controlled output quantity of system;
with
for about quantity of state
nonlinear function vector,
it is the constant matrices that 6 row 5 arrange.
The degree of correlation that we define this system is
, controlling rank is
,
for prediction time domain length.Can obtain system input quantity according to analytic model predictive control algorithm is:
(10)
Wherein
with
lie derivative,
for the reference of current time exports;
represent
time is asked
subderivative;
Here
provided by following formula:
(11)
Wherein
it is matrix
front 5 row, and these two matrixes are calculated by following formula:
(12)
Wherein
(13)
(3) advantage and effect:
The present invention's " a kind of stratospheric airship analytic model predicted path tracking and controlling method ", compared with the prior art, its advantage is:
1) analytic model predictive control algorithm is identical with the ultimate principle of basic model prediction algorithm, it is all the strategy that have employed rolling optimization, the one-component of the optimization solution of each sampling instant is acted on system, its roll implement to take into account model mismatch, time the uncertainty that causes such as change, interference, make up in time, all the time new optimization is based upon on actual basis, makes control keep actual optimum;
2) place that analytic model predictive control algorithm is better than basic model predictive control algorithm is to which propose the predictive control algorithm of analytic solution form, make not need on-line optimization when solving nonlinear Control problem with this algorithm, thus save calculated amount, make it the system that may be used for corresponding speed being had to requirement;
3) the method directly designs based on the nonlinear model of stratospheric airship, simple for different dirigible model controller design comparison.
4) the method algorithm structure is simple, and Controller gain variations is simple, is easy to Project Realization.
The controlled quentity controlled variable calculated by the method according to the given any desired path of actual dirigible, and can directly be transferred to the function of topworks's realizing route tracing control by control engineering teacher in application process.
Accompanying drawing explanation
Fig. 1 is Guidance Law computational geometry graph of a relation of the present invention;
Fig. 2 is control method structured flowchart of the present invention;
Fig. 3 is stratospheric airship schematic diagram of the present invention;
expected path reference point;
the current centroid position of dirigible;
inertial coordinates system;
inertial coordinates system X-axis;
inertial coordinates system Y-axis;
inertial coordinates system Z axis;
path coordinate system;
path coordinate system is tangential along track;
path coordinate system along method of loci to;
path coordinate system along method of loci to;
velocity coordinate system;
velocity coordinate system X-axis;
velocity coordinate system Y-axis;
velocity coordinate system Z axis;
dirigible speed;
the coordinate of position in path coordinate system of dirigible;
the coordinate of position in path coordinate system of dirigible;
the coordinate of position in path coordinate system of dirigible;
the position vector of expected path reference point relative inertness coordinate system;
the position vector of dirigible relative inertness coordinate system;
the position vector of dirigible relative path coordinate system;
the position coordinates of dirigible barycenter under inertial system;
dirigible forward speed;
dirigible longitudinal velocity;
expect dirigible forward speed;
expect dirigible longitudinal velocity;
expect dirigible angular velocity;
dirigible angular velocity;
airscrew thrust;
dirigible angle of rudder reflection;
dirigible velocity;
dirigible Eulerian angle;
inertial coordinates system;
hull coordinate system;
dirigible barycenter;
hull coordinate system X-axis;
hull coordinate system Y-axis;
hull coordinate system Z axis;
inertial coordinates system initial point;
inertial coordinates system X-axis;
inertial coordinates system Y-axis;
inertial coordinates system Z axis;
dirigible angular velocity in roll;
dirigible rate of pitch;
dirigible yaw rate;
dirigible side velocity;
airscrew thrust;
Embodiment
Below in conjunction with accompanying drawing, each several part method for designing in the present invention is further described:
The present invention's " a kind of stratospheric airship analytic model predicted path tracking and controlling method ", as shown in Figure 2, its concrete steps are as follows for its concrete structure block diagram:
Step one: given expectation pursuit gain
1) as shown in Figure 1, first opening relationships coordinate system
, its three coordinate axis are
with
; Then arbitrary parameter path, given expectation space:
,
,
for path parameter; And set up path coordinate system along this path
; Three coordinate axis of definition path coordinate system are
with
, and these three vectors meet following equation:
(14)
Wherein
,
with the curvature of space curve
and torsion
meet following relationship:
(15)
The transition matrix being tied to inertial system from path coordinate is; Angular velocity being expressed as under path coordinate system of path coordinate system relative inertness system
.
2) given desired speed
,
for desired speed is along the decomposition amount of hull coordinate system.
Step 2: stratospheric airship modeling
Be illustrated in figure 3 stratospheric airship schematic diagram.This dirigible object adopts traditional spheroid configuration, symmetrical about fore-and-aft plane, and empennage adopts "+" font band elevating rudder and yaw rudder layout, and gondola is positioned at below ship capsule, and gondola both sides respectively fill a secondary screw propeller.
Definition inertial coordinates system
with hull coordinate system
; Definition position vector
for dirigible barycenter is at the coordinate of inertial system; Velocity
for the component that dirigible speed is fastened at body; Angular velocity vector
for the component that dirigible angular velocity is fastened at body; Eulerian angle
component represent the angle of pitch, crab angle and roll angle respectively;
Position kinematical equation is:
(16)
Wherein for body axis system is to the transition matrix of inertial system;
Attitude kinematics equations is:
(17)
Kinetics equation is:
(18)
Wherein
for constant matrices,
for about
with
nonlinear function matrix;
with
for airscrew thrust and angle of rudder reflection; Wherein
,
;
for the thrust of screw propeller is at hull coordinate system
the component of axle,
for the thrust of screw propeller is at hull coordinate system
the component of axle,
for the angle of rudder reflection of dirigible yaw rudder,
for the angle of rudder reflection of the elevating rudder on the dirigible left side, it is the angle of rudder reflection of the elevating rudder on the right of dirigible; Occurrence every in kinetic model equation is different with different dirigible structure and parameter, determines in actual applications according to actual conditions.
Step 3: Guidance Law calculates
As in Figure of description as described in Fig. 1, first define inertial coordinate be I}, speed coordinate is that { W} and path coordinate are { F}; What definition dirigible barycenter was fastened at path coordinate relative to the distance of reference point on path is projected as
; According to the geometric relationship in Fig. 1, can obtain
; Can obtain both sides differentiate:
(19)
So site error kinematical equation can be obtained be:
(20)
In above formula
for the translational speed of track reference point on expected path;
for the projection that the angular velocity of path coordinate system relative inertness system is fastened at path coordinate; Above formula relative path coordinate system is launched to obtain:
(21)
In order to derive attitude error equations, first need first to define auxiliary coordinates D}, this coordinate system is for describing the attitude of dirigible close to destination path; The initial point of auxiliary coordinates at the barycenter of dirigible, and by three mutually orthogonal vectors (
,
,
) represent; These three vectorial is defined as follows:
(22)
Wherein
being a constant, is very important design parameter; The transition matrix being tied to path coordinate system from auxiliary coordinate can be calculated by these three vectors
:
(23)
Definition
the transition matrix from velocity coordinate system to auxiliary coordinates, then
can be expressed as:
(24)
Definition
for actual value error, its computing formula is:
(25)
Wherein,
,
for
the element of the first row first row of matrix;
Carry out differentiate to above formula both sides can obtain:
(26)
Wherein,
for attitude error,
for the expression of angular velocity under velocity coordinate system of the relative auxiliary coordinates of velocity coordinate system; They calculate respectively by following formula:
(27)
(14) are brought into (13) attitude error equations can be obtained be:
(28)
Definition
for generalized error vector; We will design conductance processed and make
asymptotic convergence is to zero; Expect that Formula for Angular Velocity of Fuze is as follows:
(29)
Wherein,
for normal number; On expected path, the translational speed of reference point can be calculated by following formula:
(30)
Wherein
for normal number; Due to
for the expectation angular velocity under velocity coordinate system, so the expectation angular velocity under also needing to be converted to body axis system; Definition
for the expectation angular velocity of dirigible under body axis system; Its conversion formula is:
(31)。
Step 4: solve control law
The kinetic model of the six degree of freedom obtained by step one can be write as following expression matrix form:
(32)
Wherein
for quantity of state,
for system input quantity, be dirigible screw propeller thrust and yaw rudder, elevating rudder drift angle,
for the controlled output quantity of system;
with
for about quantity of state
nonlinear function vector,
it is the constant matrices that 6 row 5 arrange;
First defining rolling time horizon performance index is:
(33)
Wherein
for prediction of output value,
for expecting prediction of output value,
for prediction time domain length; Model Predictive Control Algorithm is exactly mainly to find prediction input
these performance index are made to obtain minimum value; Similar with other roll stablized loop, the control inputs of its reality is optimum control input
initial value, namely
time
value;
Carry out differentiate to output equation to obtain:
(34)
Can this system Relative order by above-mentioned equation
be 1, suppose that controlling rank is
; Obtained by Taylor expansion;
Can obtain system input quantity according to analytic model predictive control algorithm is:
(35)
Wherein
with
lie derivative,
for the reference of current time exports;
represent
time is asked
subderivative;
Here
provided by following formula:
(36)
Wherein
it is matrix
front 5 row, and these two matrixes are calculated by following formula:
(37)
Wherein
(38)
Here Relative order is 1; Controlling rank is variable elements, controls rank larger control accuracies better, but reasonably chooses and can ensure closed-loop system exponential convergence; Calculated by step 1 and step 3 at each moment desired output, wherein the expectation value of forward speed and longitudinal velocity does not become steady state value, the expectation value of angular velocity was calculated by outer shroud Guidance Law for each moment, and hypothesis desired output in prediction time domain is constant;
Desired output can be expressed as:
;
Suppose that the derivative of desired output is zero, we can obtain final system and be input as:
(39)
In each moment, quantity of state is obtained by sensor measurements such as combined inertial nevigations with surveying to export, and is calculated the system input quantity of current time by these measured values; The input quantity calculated is directly acted on dirigible screw propeller, yaw rudder and elevating rudder, the path following control of dirigible can be completed.
Claims (5)
1. a stratospheric airship analytic model predicted path tracking and controlling method, is characterized in that: its concrete steps are as follows:
step onegiven expectation pursuit gain: arbitrary parameter path, given expectation space and expectation dirigible speed;
step 2stratospheric airship modeling: Dynamic Modeling is carried out to certain model stratospheric airship, obtains six degree of freedom nonlinear model;
step 3guidance Law calculates: in each moment according to the position of current stratospheric airship, attitude and expect that the reference point locations in reference path carries out the calculating of the angular velocity expectation value of current time;
step 4control law calculates: the Guidance Law calculated according to previous step, utilizes analytic model predictive control algorithm to calculate control law, obtains the controlled quentity controlled variable of rudder face and airscrew thrust.
2. a kind of stratospheric airship analytic model predicted path tracking and controlling method according to claim 1, it is characterized in that: the given expectation pursuit gain described in step one, it is specially:
1) first opening relationships coordinate system
, its three coordinate axis are
with
; Then arbitrary parameter path, given expectation space:
,
,
for path parameter; And set up path coordinate system along this path
; Three coordinate axis of definition path coordinate system are
with
, and these three vectors meet following equation:
(1)
Wherein
,
with the curvature of space curve
and torsion
meet following relationship:
(2)
The transition matrix being tied to inertial system from path coordinate is; Angular velocity being expressed as under path coordinate system of path coordinate system relative inertness system
;
2) given desired speed
,
for desired speed is along the decomposition amount of hull coordinate system.
3. a kind of stratospheric airship analytic model predicted path tracking and controlling method according to claim 1, it is characterized in that: the stratospheric airship modeling described in step 2, its computing method are as follows:
Definition inertial coordinates system
with hull coordinate system
; Definition position vector
for dirigible barycenter is at the coordinate of inertial system; Velocity
for the component that dirigible speed is fastened at body; Angular velocity vector
for the component that dirigible angular velocity is fastened at body; Eulerian angle
component represent the angle of pitch, crab angle and roll angle respectively;
Position kinematical equation is:
(3)
Wherein for body axis system is to the transition matrix of inertial system;
Attitude kinematics equations is:
(4)
Kinetics equation is:
(5)
Wherein
for constant matrices,
for about
with
nonlinear function matrix;
with
for airscrew thrust and angle of rudder reflection; Wherein
,
;
for the thrust of screw propeller is at hull coordinate system
the component of axle,
for the thrust of screw propeller is at hull coordinate system
the component of axle,
for the angle of rudder reflection of dirigible yaw rudder,
for the angle of rudder reflection of the elevating rudder on the dirigible left side, it is the angle of rudder reflection of the elevating rudder on the right of dirigible; Occurrence every in kinetic model equation is different with different dirigible structure and parameter, determines in actual applications according to actual conditions.
4. a kind of stratospheric airship analytic model predicted path tracking and controlling method according to claim 1, is characterized in that: the Guidance Law described in step 3 calculates, and its computing method are as follows:
First define inertial coordinate be I}, speed coordinate is that { W} and path coordinate are { F}; What definition dirigible barycenter was fastened at path coordinate relative to the distance of reference point on path is projected as
; According to the geometric relationship in Fig. 1, can obtain
; Can obtain both sides differentiate:
(6)
So site error kinematical equation can be obtained be:
(7)
In above formula
for the translational speed of track reference point on expected path;
for the projection that the angular velocity of path coordinate system relative inertness system is fastened at path coordinate; Above formula relative path coordinate system is launched to obtain:
(8)
In order to derive attitude error equations, first need first to define auxiliary coordinates D}, this coordinate system is for describing the attitude of dirigible close to destination path; The initial point of auxiliary coordinates at the barycenter of dirigible, and by three mutually orthogonal vectors (
,
,
) represent; These three vectorial is defined as follows:
(9)
Wherein
being a constant, is very important design parameter; The transition matrix being tied to path coordinate system from auxiliary coordinate can be calculated by these three vectors
:
(10)
Definition
the transition matrix from velocity coordinate system to auxiliary coordinates, then
can be expressed as:
(11)
Definition
for actual value error, its computing formula is:
(12)
Wherein,
,
for
the element of the first row first row of matrix;
Carry out differentiate to above formula both sides can obtain:
(13)
Wherein,
for attitude error,
for the expression of angular velocity under velocity coordinate system of the relative auxiliary coordinates of velocity coordinate system; They calculate respectively by following formula:
(14)
(14) are brought into (13) attitude error equations can be obtained be:
(15)
Definition
for generalized error vector; We will design conductance processed and make
asymptotic convergence is to zero; Expect that Formula for Angular Velocity of Fuze is as follows:
(16)
Wherein,
for normal number; On expected path, the translational speed of reference point can be calculated by following formula:
(17)
Wherein
for normal number; Due to
for the expectation angular velocity under velocity coordinate system, so the expectation angular velocity under also needing to be converted to body axis system; Definition
for the expectation angular velocity of dirigible under body axis system; Its conversion formula is:
。(18)
5. a kind of stratospheric airship analytic model predicted path tracking and controlling method according to claim 1, it is characterized in that: the control law that solves in step 4, its computing method are as follows:
The kinetic model of the six degree of freedom obtained by step one can be write as following expression matrix form:
(19)
Wherein
for quantity of state,
for system input quantity, be dirigible screw propeller thrust and yaw rudder, elevating rudder drift angle,
for the controlled output quantity of system;
with
for about quantity of state
nonlinear function vector,
it is the constant matrices that 6 row 5 arrange;
First defining rolling time horizon performance index is:
(20)
Wherein
for prediction of output value,
for expecting prediction of output value,
for prediction time domain length; Model Predictive Control Algorithm is exactly mainly to find prediction input
these performance index are made to obtain minimum value; Similar with other roll stablized loop, the control inputs of its reality is optimum control input
initial value, namely
time
value;
Carry out differentiate to output equation to obtain:
(21)
Can this system Relative order by above-mentioned equation
be 1, suppose that controlling rank is
; Obtained by Taylor expansion;
Can obtain system input quantity according to analytic model predictive control algorithm is:
(22)
Wherein
with
lie derivative,
for the reference of current time exports;
represent
time is asked
subderivative;
Here
provided by following formula:
(23)
Wherein
it is matrix
front 5 row, and these two matrixes are calculated by following formula:
(24)
Wherein
(25)
Here Relative order is 1; Controlling rank is variable elements, controls rank larger control accuracies better, but reasonably chooses and can ensure closed-loop system exponential convergence; Calculated by step 1 and step 3 at each moment desired output, wherein the expectation value of forward speed and longitudinal velocity does not become steady state value, the expectation value of angular velocity was calculated by outer shroud Guidance Law for each moment, and hypothesis desired output in prediction time domain is constant;
Desired output can be expressed as:
;
Suppose that the derivative of desired output is zero, we can obtain final system and be input as:
(26)
In each moment, quantity of state is obtained by sensor measurements such as combined inertial nevigations with surveying to export, and is calculated the system input quantity of current time by these measured values; The input quantity calculated is directly acted on dirigible screw propeller, yaw rudder and elevating rudder, the path following control of dirigible can be completed.
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