CN108267956B - Flight control method based on sliding formwork control - Google Patents
Flight control method based on sliding formwork control Download PDFInfo
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- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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- G—PHYSICS
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
- G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
- G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
- G05D1/0825—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models
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Abstract
The flying vehicles control method based on sliding formwork control that the invention discloses a kind of, being used for lump interference value, there are the flight of upper limit disturbances to control.The flight control method includes: the correlation function for establishing interference coefficient and sliding-mode surface；The interference coefficient is introduced to the control law function of sliding formwork control, and aircraft flight is controlled according to the control rate function.The flight control method is associated with control variable by making interference coefficient, to make disturbance quantity closer to the live flying state of aircraft, and then improves the control precision of aircraft.
Description
Technical Field
The invention relates to the technical field of aircraft control, in particular to an aircraft control method based on sliding mode control.
Background
Flight control of an aircraft is one of the core technologies of an aircraft. The motion of the aircraft in space is very complex, and in order to simplify the control of the aircraft, the attitude of the aircraft in space can be generally divided into pitch, roll and yaw. Therefore, the flight attitude of the aircraft is controlled by controlling the flight angle of the aircraft.
Sliding mode control, also known as variable structure control, is a special type of nonlinear control. Unlike other control modes, the system structure of the control strategy is not fixed, but the system can be forced to move according to the state track of the preset sliding mode in a dynamic process according to the purposeful and continuous change of the current state of the system. The sliding mode can be designed and is irrelevant to the parameters and the disturbance of an object, so that the sliding control has the advantages of quick response, insensitive corresponding parameter change and disturbance, no need of system online identification, simple physical implementation and the like.
However, for bounded disturbances in flight control, lumped disturbances are often greatly simplified in practical engineering designs. I.e. by making the interference coefficient of the term dependent on the system state zero, the lumped interference can be reduced to be independent of the system state. The simplified flight control mode often brings the problems of the reduction of the control precision of the aircraft, the weakening of the self-adaptive capacity of the aircraft and the like.
Disclosure of Invention
Aiming at the technical problems in the flight control technology of the aircraft, the invention provides a flight control method based on sliding mode control. According to the flight control method, the disturbance quantity is closer to the real flight state of the aircraft by associating the disturbance coefficient with the control variable, and the control precision of the aircraft is further improved.
One aspect of the invention provides an aircraft control method based on sliding mode control, which is used for flight disturbance control with an upper limit of lumped disturbance values. The flight control method comprises the following steps: establishing a correlation function of the interference coefficient and the sliding mode surface; and introducing the interference coefficient into a control law function of sliding mode control, and controlling the flight of the aircraft according to the control rate function.
In one embodiment, the interference coefficients include a first interference coefficient, a second interference coefficient, and a third interference coefficient; the upper limit value of the lumped interference is the sum of a first interference amount caused by the first interference coefficient, a second interference amount caused by the second interference coefficient and a third interference amount caused by the third interference coefficient; and in the lumped interference, the first interference amount is independent of a system state, and the second interference amount and the third interference amount are dependent on the system state.
In one embodiment, the second disturbance variable is a linear function of the control variable, and the third disturbance variable is a linear function of the control variable.
In one embodiment, the second amount of interference2＝d1| x |, the third interference amount3＝d2||x||2(ii) a Wherein d is1Is the second interference coefficient, d2Is the third interference coefficient.
At one endIn one embodiment, the lumped interference satisfies: d is less than or equal to | | | | delta | | |0+d1||x||+d2||x||2(ii) a Wherein d is0Is the first interference coefficient.
In one embodiment, the first interference coefficient d0The second interference coefficient d1And said third interference coefficient d2The following conditions are satisfied with the sliding mode control variable s:whereind0， d1，d2，Are all constants and satisfy: and c is0，p0，c1，p1，c2，p2Are all constants.
In one embodiment, the control law function is:whereinAnd u isControl law, x is the state set of the controlled object, s is the sliding mode surface selected for the controlled object, f0,g0Is the nominal value of the system, Δ is called lumped interference, k is the adaptive parameter, and v is*Is the coefficient of interferenceThe amount of assist control is concerned.
In one embodiment, the auxiliary control quantity v*The following conditions are satisfied:wherein α is a normal number.
In one embodiment, for example
According to the aircraft control method provided by the embodiment of the invention, the interference coefficient is associated with the flight control variable, so that the flight control precision of the aircraft can be improved.
Those skilled in the art will recognize additional features and advantages upon reading the detailed description, and upon viewing the accompanying drawings.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a flow chart of a flight control method according to an embodiment of the invention.
Detailed Description
The technical scheme of the invention is further explained by the specific implementation mode in combination with the attached drawings. Spatially relative terms such as "below," "… below," "lower," "above," "… above," "upper," and the like are used for convenience in describing the positioning of one element relative to a second element and are intended to encompass different orientations of the device in addition to different orientations than those illustrated in the figures. Further, for example, the phrase "one element is over/under another element" may mean that the two elements are in direct contact, or that there is another element between the two elements. Furthermore, terms such as "first", "second", and the like, are also used to describe various elements, regions, sections, etc. and should not be taken as limiting. Like terms refer to like elements throughout the description.
In the field of flight control of aircraft, a general affine nonlinear system is of the form:
considering various disturbances, it can be considered that f ═ f0+Δf，g＝g0+ Δ g, of which f0,g0Is the nominal value of the system, and af, ag are disturbance or uncertainty terms of the system,
so equation of state (1) of the system can become:
if let Δ ═ Δ f (x) + Δ g (u) u, then the following common form applies:
in this case, Δ is called lumped disturbance, and a general control law design is developed based on this form.
Suppose 1 g in the System State equation (1)0(u) is reversible, i.e. there is an inverse function
Assume 2 that the lumped disturbance Δ is bounded and satisfies the following form:
||Δ||≤d0+d1||x||+d2||x||2 (4)
in the formula (4), if d is1＝0,d2Equation (4) then becomes the commonly used interference-bounded form, i.e. the interference term is considered to be independent of the system state.
The form of the interference constraint represented by the lumped interference inequality (4) is more general and follows the general situation when the aircraft is disturbed. If the usual constant limit form is adopted, i.e. | | Δ | ≦ d, then d is implied0+d1||x||+d2||x||2D is less than or equal to d. In this way, if d is considered separately in designing the flight control laws0,d1,d2The designed control law reduces conservatism (for example, for sliding mode control), that is, the flight control precision and adaptivity of the aircraft are reduced, so that the precise control of the aircraft flight is not facilitated.
In general, the lumped interference inequality (4) considers the uncertainty Δ g (u) u of the control input at d0Among them.
In the practical engineering, the interference upper bound is often unknown and can not be given, the interference upper bound is estimated by a self-adaptive method, and then the estimated value is compensated into sliding mode control, so that the adaptability of the control law is stronger.
One aspect of the invention provides an aircraft control method based on sliding mode control, which is used for flight disturbance control with an upper limit of lumped disturbance values. The flight control method comprises the following steps:
establishing a correlation function of the interference coefficient and the sliding mode surface;
introducing the disturbance factor into a control law function of sliding mode control, an
And controlling the flight of the aircraft according to the control rate function.
According to the aircraft control method, the interference coefficient is associated with the sliding mode surface, and the interference coefficient is introduced into the control law function of sliding mode control, so that the adaptability of the control law is stronger, and the flight control precision and reliability of the aircraft are improved.
In one embodiment, the interference coefficients include a first interference coefficient, a second interference coefficient, and a third interference coefficient. The upper limit value of the lumped interference is a sum of a first interference amount caused by the first interference coefficient, a second interference amount caused by the second interference coefficient, and a third interference amount caused by the third interference coefficient. In the lumped interference, the first interference amount is independent of a system state, and the second interference amount and the third interference amount are dependent on the system state. For example, the first amount of interference may be equal to the first interference factor. The second disturbance variable increases as the control variable of the system increases. Also, the third disturbance variable increases as the control variable of the system increases. For example, the rate of increase of the second disturbance variable with the increase of the control variable may be smaller than the rate of increase of the third disturbance variable with the increase of the control variable.
It should be noted that, since the disturbance of the aircraft can occur in two directions, the first disturbance variable, the second disturbance variable and the third disturbance variable should be the same positive or the same negative.
In this embodiment, for example, the second disturbance variable is a linear function of the control variable, and the third disturbance variable is a linear function of the control variable.
In this embodiment, for example, the second interference amount2＝d1| x |, the third interference amount3＝d2||x||2(ii) a Wherein d is1Is the second interference coefficient, d2Is the third interference coefficient. I.e. the lumped interference satisfies: d is less than or equal to | | | | delta | | |0+d1||x||+d2||x||2(ii) a Wherein d is0Is the first interference coefficient.
In one embodiment, the first interference coefficient d0The second interference coefficient d1And said third interference coefficient d2The following conditions are satisfied with the sliding mode control variable s:wherein d1，d2，Are all constants and satisfy: and c is0，p0，c1，p1，c2，p2Are all constants. E.g. p0，p1And p is2Is not zero, so that the interference coefficients are each a function associated with the plane s of sliding mode control. According to the embodiment of the invention, the relation function of the interference coefficient and the sliding mode control variable s is set, so that the interference coefficient and the sliding mode control variable s can be displayedThe adaptability of the control law is improved, and therefore the control precision of the aircraft is improved.
In this embodiment, c0，p0，c1，p1，c2，p2The weight values are respectively weight values, and for different controlled objects, the difference of the weight values is large, and the weight values can be specifically determined according to the actual conditions of the controlled objects.
In one embodiment, the control law function is:whereinU is a control law, x is a state set of the controlled object, s is a sliding mode surface selected for the controlled object, and f0,g0Is the nominal value of the system, Δ is called lumped interference, k is the adaptive parameter, and v is*Is the coefficient of interferenceThe amount of assist control is concerned.
In one embodiment, the auxiliary control quantity v*The following conditions are satisfied:wherein α is a normal number.
In one embodiment, for exampleThe control result is equivalent to the situation that the sliding mode surface happens, so that the ideal control effect is achieved.
According to the aircraft control method provided by the embodiment of the invention, the interference coefficient is associated with the flight control variable, so that the flight control precision of the aircraft can be improved.
The above-described embodiments of the present invention may be combined with each other with corresponding technical effects.
As mentioned above, if the sliding mode is s ═ x, then the control law form is taken as
Wherein,
where k is an adaptive parameter and v*Is an auxiliary control quantity and has a coefficient of interferenceIt is related. WhileGiven by:
the specific form and stability of the flight control method of the embodiment of the invention is demonstrated as follows:
theorem 1 for equation of state (3) of the system, if one takes
Wherein α > 0, γ > 0, ω > 0, θ > 0 are normal numbers, wherein the parametersObtained from equation (a), then the system converges the finite time into the s-0 neighborhood.
Evidence takes the Lyapunov function as
Wherein,
substituting the formula and the formula into the system equation to obtain the formula
The Lyapunov function is derived and substituted into a formula to obtain
From Young's inequality, pairThe items are scaled to obtain
Wherein,
and (3) substituting the formula into a Lyapunov function derivation formula, and further processing to obtain:
according to the usual inequality
(x2+y2+z2)1/2≤|x|+|y|+|z|
For formula (I) to obtain
Wherein ξ min { α, ω, r ═ miH, i is 0,1,2 so have
Wherein,
case 1: k > kmTime of flight
When in useWhen there is
Therefore, the system converges to the neighborhoodAnd (4) the following steps.
Case 2: k is less than or equal to kmTime of flight
When in useWhile the parameter k is always increasing, the sliding mode s is decreasing; when the sliding mode enters | s | ≦ μ, the sliding mode will still stabilize in a region with a radius greater than μ, as referenced to Yuri analysis.
The system necessarily converges to within a certain neighborhood.
Note 4 if the adaptation law is modified
Then the neighborhood Q → 0 and the sliding mode surface also gradually go to zero, i.e. s → 0. In practice, however, it is difficult for the sliding-mode surface to accurately reach s-0, so the parameter k is always increasing as long as the system has not converged to s-0.
The self-adaptive sliding mode control method realizes the self-adaptability of the sliding mode control parameters and reduces the conservative property of control. If desired, k ≦ kmThe approach law can also be redesigned, but in essence the system will still converge into some small neighborhood.
The control law of the invention can be applied to the situation that the interference is unknown and the upper limit of the interference cannot be determined, such as the control of a tactical missile in the process of high-speed maneuvering motion, and the stability and the adaptability of the control law can be improved, thereby improving the reliability and the hit precision of a flight test.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (8)
1. An aircraft control method based on sliding mode control is used for flight disturbance control with an upper limit of lumped disturbance values, and is characterized by comprising the following steps: establishing a correlation function of the interference coefficient and the sliding mode surface;
introducing the disturbance factor into a control law function of sliding mode control, an
Controlling the aircraft to fly according to the control law function;
wherein the interference coefficients comprise a first interference coefficient, a second interference coefficient, and a third interference coefficient; the upper limit value of the lumped interference is the sum of a first interference amount caused by the first interference coefficient, a second interference amount caused by the second interference coefficient and a third interference amount caused by the third interference coefficient;
and in the lumped interference, the first interference amount is independent of a system state, and the second interference amount and the third interference amount are dependent on the system state.
2. The aircraft control method according to claim 1, characterized in that the second disturbance variable is a linear function of a control variable and the third disturbance variable is a linear function of a control variable.
3. The aircraft control method according to claim 2, characterized in that the second disturbance variable Δ2＝d1| x |, the third interference amount Δ3＝d2||x||2；
Wherein d is1Is the second interference coefficient, d2Is the third interference coefficient.
4. The aircraft control method according to claim 3, characterized in that the lumped disturbances satisfy: d is less than or equal to | | | | delta | | |0+d1||x||+d2||x||2(ii) a Where d0 is the first interference coefficient.
5. The aircraft control method according to any one of claims 1 to 4,
the first interference coefficient d0The second interference coefficient d1And said third interference coefficient d2The following conditions are satisfied with the sliding mode control variable s:
whereinAre all constants and satisfy:
and c is0，p0，c1，p1，c2，p2Are all constants.
6. The aircraft control method according to claim 5, characterized in that the control law function is:
wherein
U is a control law, x is a state set of the controlled object, s is a sliding mode surface selected for the controlled object, and f0,g0Is the nominal value of the system, Δ is called lumped interference, k is the adaptive parameter, and v is the interference coefficientThe amount of assist control is concerned.
7. The aircraft control method according to claim 6, characterized in that the auxiliary control quantity v*The following conditions are satisfied:
wherein α is a normal number.
8. The aircraft control method according to claim 7,
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