CN108415239B

CN108415239B - Direct control distribution method based on dynamic construction of reachable set

Info

Publication number: CN108415239B
Application number: CN201810131236.7A
Authority: CN
Inventors: 刘彤; 王美玲; 李海筝; 沈宏梁; 刘冬宇; 吴泰霖
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2018-02-09
Filing date: 2018-02-09
Publication date: 2020-08-11
Anticipated expiration: 2038-02-09
Also published as: CN108415239A

Abstract

The invention discloses a direct control allocation method based on dynamic reachable set construction, which greatly reduces the calculated amount, improves the algorithm efficiency, greatly reduces the storage space and solves the control problem of a complex control system with a reachable set which is variable in real time by constructing a reachable set facet involved in the searching process in part and in real time instead of constructing a complete reachable set.

Description

Direct control distribution method based on dynamic construction of reachable set

Technical Field

The invention belongs to the technical field of control distribution, and particularly relates to a direct control distribution method based on dynamic construction of an reachable set.

Background

Control Allocation (CA) technology is commonly used to solve the problem of redundant Control of actuators, and it can reasonably allocate virtual Control instructions obtained from a Control law to each actuator, thereby achieving a Control target. The problem of control distribution has been raised for over 20 years, the control distribution technology has gained attention in applications in various fields such as automobiles, ships, and spacecrafts, and the control distribution technology itself has undergone a development process from linear control distribution to nonlinear control distribution, from static control distribution to dynamic control distribution, from simple single-target optimization control distribution to complex multi-target optimization control distribution. Common control allocation algorithms include an explicit allocation method, a direct allocation method and a nonlinear control allocation method.

The explicit allocation method is that before the link of control allocation, a linear constraint relation is firstly applied to each actuator, the dimension of control allocation is reduced, and an underdetermined equation set is converted into a positive determined equation set, so that the size of a solution space is reduced, and even a determined solution is directly obtained. However, the explicit allocation method is difficult to handle the problem that the actuator is limited by the maximum deflection position and the maximum deflection rate, and the virtual control instruction which can be realized by the explicit allocation method is far smaller than the reachable set, so that the structural advantage of redundant configuration of the actuator cannot be fully exerted.

The Direct Allocation (DA) algorithm was first proposed in 1992 by Durham's teaching of virginia physics university, and its implementation is based on the construction and operation of an reachable motion Subset (AMS). The advantage of this approach is that it has a well-defined geometric meaning and can ensure that the virtual control commands derived via the direct assignment algorithm are in the same direction as the desired virtual control commands. However, this method has the disadvantage that when the redundancy of the system actuator is high, the calculation time increases quadratically with the number of actuators, and it is difficult to meet the real-time requirement of the control system.

Nonlinear Control Allocation (NCA) is used to solve the problem of Control Allocation in the case of non-linearity of the actuator. Doman et al approximate control surface control efficiency by an affine function and realize the distribution target of nonlinear control distribution based on the method; for the condition that the angle of an actuating mechanism is unbalanced and a control efficiency matrix caused by the angle unbalance cannot be determined, Hu Qinglei and the like provide a finite time control distribution method based on a robust least square method in combination with a terminal sliding mode control method, and effective control of the space vehicle is achieved.

After decades of development, the control distribution technology has achieved significant achievement in theoretical research and engineering practice, and is further applied to numerous fields such as aircrafts with advanced pneumatic layout, distributed electrically driven automobiles and the like. However, there are still many problems with the current control and distribution techniques, especially in considering the limited control and distribution of control surfaces subject to yaw position and velocity constraints, and the improvement of real-time performance and accuracy of existing distribution algorithms. Therefore, intensive research on control distribution technology, especially limited control distribution technology considering the condition that the control surface is limited by deflection position and speed, has great significance on the development of advanced technologies such as advanced pneumatic layout aircrafts and distributed electric drive automobiles.

Disclosure of Invention

In view of this, the present invention provides a direct control allocation method based on dynamic construction of reachable sets, which can improve control efficiency.

A direct control distribution method based on dynamic construction of reachable sets comprises the following steps:

the method comprises the following steps: taking any pair of different column vectors bi and bj in the control efficiency matrix B as parameters, and constructing a plane parameter equation to obtain a plane family; wherein, B ═ B₁,b₂,...,bm]i, j ≠ 1,2,. m, which represents the number of actuators;

randomly assigning an initial facet in the family of planes as facet f;

step two: calculating the coordinates of each vertex of the facet f;

step three: determining a given desired virtual instruction v_dWhether the positive direction is intersected with the facet f or not, if so, entering a fourth step; if not, find the virtual instruction v_dOne side, which is closest to the facet f in the positive direction, is assumed to be AB, AB is used as an adjacent side to construct an adjacent facet f 'and the adjacent facet f' is taken as the facet f, and the step II is returned;

wherein, in the process of constructing the adjacent facet f', the parameter corresponding to AB is assumed to be b_iThen another parameter b of the adjacent facet f' needs to be determined_kThe method specifically comprises the following steps:

point u ' on the AB on the upper side of the facet f ' to be constructed '_t,lExpressed as:

wherein u is_min,lRepresents the minimum of the ith actuator output；u_t,lRepresents a point on the edge AB on facet f;

first, remove b_iAnd b_jIn addition, in b₁To b_mArbitrarily selected as a value of b_kLet b_lAt b₁To b_mSequentially taking values and substituting into formulas

In (b), a series of x is obtained_lValue, and judge all x_lIs the same sign, and if not, changes b_kA value of (b)_lTraversing once again according to the requirements, and judging a series of obtained x_lWhether the value is the same number; and so on until a series of x_lThe value is the same sign, stop searching, obtain this moment b_kA value according to b_kAnd adjacent side b_iCompleting the construction of the facet f', wherein l ∈ (1, m) and l ≠ i, l ≠ k;

wherein u is_max,lRepresents the maximum value of the output of the ith actuator; | b_ib_kb_lI denotes b_i、b_kAnd b_lMixing product of the three;

step five: calculating an expected virtual instruction v_dThe intersection point of the positive direction and the facet f;

step six: calculating the coordinates v of the intersection point from the intersection point_dThe actual control commands u assigned to the actuators are deduced inversely from the linear transitions between the virtual control commands and the control inputs_dAnd distributed to the overdrive system.

The invention has the following beneficial effects:

in a control system of which an actuator is limited by a maximum deflection position and a maximum deflection rate, an reachable set is variable in real time, algorithm efficiency cannot be improved by a method of storing reachable set data offline, the calculation amount of constructing a complete reachable set in real time is large, the requirement of the system on real-time performance is difficult to meet, and a large storage space is needed.

Drawings

FIG. 1 is a flow chart of a direct control distribution algorithm based on dynamically constructed reachable sets in the present invention;

FIG. 2 is a schematic diagram of adjacent facets identifying an edge of a reachable set facet;

fig. 3 to 11 are processes of sequentially constructing reachable sets when searching is performed for a certain vector.

Detailed Description

The invention is described in detail below by way of example with reference to the accompanying drawings.

For systems where the actuator is limited by the deflection rate, the achievable set is variable in real time. Therefore, the calculation efficiency can not be improved by storing the off-line data, but only the actual deflection condition of the actuating mechanism at the last moment can be detected by the control surface actual deflection condition detection mechanism, so that the control subset is obtained, and the reachable set is constructed. However, constructing a complete reachable set in real time inevitably leads to an excessively long online computation time, which makes the direct allocation algorithm lose practical value.

The invention provides a method for constructing an reachable set in part and in real time, which comprises the steps of randomly constructing a pair of parallel reachable set facets at the initial moment, determining a search direction according to the geometric relation between an expected virtual instruction and the normal direction of the facets, only constructing the facets related in a search link, and controlling the algorithm time within a reasonable range. The key to implementing the above idea is how to establish the adjacent facets of the known facets on one of the adjacent sides after determining the search direction.

When the individual control surfaces are constrained by a maximum rate of deflection, the actual achievable position at each instant depends on the position of the control surface at the previous instant, the maximum rate of deflection and the maximum deflection position, and at each instant the actual achievable position of the actuator is variable, i.e.:

u_max(t+T₀)＝min{u_max，u(t)-T₀S_max} (1)

u_min(t+T₀)＝max{u_min，u(t)-T₀S_max} (2)

in the formula: u (T) is a control command at this time, i.e., a vector representing the positions of the actuators at the current time, T₀For each interval of arrival of virtual instructions, u_max(t+T₀) And u_min(t+T₀) The ranges that can be actually reached by each actuator in the next control allocation are respectively.

Because the upper and lower bounds of the actuator at each time are different, the control subsets at each time are different in reachable set, that is:

Ω(t+T₀)＝{u|u_min(t+T₀)≤u≤u_max(t+T₀)} (3)

Φ(t+T₀)＝{v|v＝B·u，u∈Ω(t+T₀)} (4)

where B is the control efficiency matrix, Ω (T + T)₀) The actual control subset, phi (T + T), at which control allocation is to take place for the next moment₀) Is the actual reachable set at the next time.

When constructing the reachable set facet, taking any pair of different column vectors B in the control efficiency matrix B_iAnd b_jAs a parameter, a family of planes with the same normal vector can be obtained, and the upper boundary facet f of the family of planes₁And a lower boundary facet f₂The equations of (a) are:

1≤i≤m，1≤j≤m，i≠j；

wherein: u. of_t1＝[u_t1,1,u_t1,2,…,u_t1,m]Representing the upper boundary facet f₁Point of (a) u_t2＝[u_t2,1,u_t2,2,…,u_t2,m]Representing the lower boundary facet f₂A point on; the 4 vertex coordinates on the facet are:

wherein, | ab c | represents the mixed product of ab c; u. of_max,pAnd u_min,pRespectively representing the maximum value and the minimum value of the pth actuator;

since one facet is randomly selected, any one of the upper-and lower-boundary facets may be selected. No upper-bound facet is selected:

f：|b_ib_jv|＝(b_i×b_j)^TBu_t，u_t∈Ω_t

and is

As shown in FIG. 1, a facet f is obtained with vertex coordinates v_A，v_B，v_CAnd v_DWherein:

v_A＝Bu_A，u_A∈Ω_tand u is_A，i＝u_min，i，u_A，j＝u_min，j

v_B＝Bu_B，u_B∈Ω_tAnd u is_B，i＝u_max，i，u_B，j＝u_min，j

v_C＝Bu_C，u_C∈Ω_tAnd u is_C，i＝u_max，i，u_C，j＝u_max，j

v_D＝Bu_D，u_D∈Ω_tAnd u is_D，i＝u_min，i，u_D，j＝u_max，j

It is therefore evident that:

segment AB is defined by Ω_tIs a proper subset omega of_t，1The mapping results in, that is:

the points on line segment AB are represented as:

and is

Wherein q is 1, 2.. multidot.m;

in the following it is assumed that the adjacent facet f' of the AB edge needs to be searched for, as shown in the following figure. At this time b_iAnd b_jΩ corresponding to facet f_tBoth are known, and one of the two vectors defining facet f' must be b_iAnd the other is set as b_kAs long as b is found_kThe construction of the facet f' is completed as shown in fig. 2.

Point u ' on the edge AB corresponding to the constructed facet f ' may be determined '_tComprises the following steps:

and according to formulae (4) and (5), b_kThe determined search conditions, i.e. for all l ≠ k, i cases:

except for b_iAnd b_jIn addition, in b₁To b_mArbitrarily selected as a value of b_kLet b_lAt b₁To b_mThe values are sequentially taken and respectively substituted into the following formulas,

a series of x is obtained_lValue, and judge x_lIf not, changing b_kA value of (b)_lTraversing once again according to the requirements, and judging a series of obtained x_lWhether the values are of the same sign, and so on, up to a series of x_lThe value is the same number, the search is stopped, and b at the moment is obtained_kA value according to b_kAnd adjacent side b_iThe construction of facet f' is completed, where l ∈ (1, m) and l ≠ i, l ≠ k, and the next facet is searched as described above.

Calculating an expected virtual instruction v_dThe intersection point of the positive direction and the facet f; calculating the coordinates v of the intersection point from the intersection point_dThe actual control commands ud assigned to the various actuators are back-derived from the linear transformation between the virtual control commands and the control inputs and assigned to the overdrive system.

In order to show that reachable sets are dynamically constructed, the processes of sequentially constructing reachable sets when searching for a certain vector are shown in fig. 3 to 11.

In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A direct control distribution method based on dynamic construction of reachable sets is characterized by comprising the following steps:

the method comprises the following steps: taking any pair of different column vectors B in the control efficiency matrix B_iAnd b_jAs parameters, a plane parameter equation is constructed, and a plane family can be obtained; wherein, B ═ B₁,b₂,...,bm]i, j ≠ 1,2,. m, which represents the number of actuators;

randomly assigning an initial facet in the family of planes as facet f;

step two: calculating the coordinates of each vertex of the facet f;

wherein u is_min,lRepresents the minimum value of the output of the ith actuator; u. of_t,lRepresents a point on the edge AB on facet f;

In (b), a series of x is obtained_lValue, and judge all x_lIs the same sign, and if not, changes b_kA value of (b)_lTraversing once again according to the requirements, and judging a series of obtained x_lWhether the values are the same sign; and so on until a series of x_lThe value is the same sign, stop searching, obtain this moment b_kA value according to b_kAnd adjacent side b_iCompleting the construction of the facet f', wherein l ∈ (1, m) and l ≠ i, l ≠ k;

step four: calculating an expected virtual instruction v_dThe intersection point of the positive direction and the facet f;

step five: calculating the coordinates v of the intersection point from the intersection point_dThe actual control commands u assigned to the actuators are deduced inversely from the linear transitions between the virtual control commands and the control inputs_dAnd distributed to the overdrive system.