CN108415239A - It is a kind of that distribution method is directly controlled based on dynamic construction reachable set - Google Patents

Abstract

Distribution method is directly controlled based on dynamic construction reachable set the invention discloses a kind of, the method of dynamic construction reachable set is divided by branch, builds the reachable set facet arrived involved in search process in real time, rather than the complete reachable set of structure, greatly reduce calculation amount, improve efficiency of algorithm, memory space also substantially reduces, and solves the control problem of the complex control system of reachable set real-time variable.

Description

It is a kind of that distribution method is directly controlled based on dynamic construction reachable set

Technical field

The invention belongs to control distribution technique field, and in particular to a kind of directly controlling based on dynamic construction reachable set Distribution method.

Background technology

Control distribution (Control Allocation, CA) technology is commonly used to solve the control problem of actuator redundancy, it The virtual controlling obtained by control law can be instructed and reasonably be assigned to each actuator, and then realize control targe.Control For assignment problem from the development course for proposing to have more than 20 years so far, control distribution technique is multiple in automobile, ship, spacecraft etc. Achieve achievement of attracting attention in the application in field, and control distribution technique itself also experienced be assigned to by Linear Control it is non-linear Control distribution is assigned to dynamic control allocation by static cost control, is assigned to complicated more mesh by the control of simple single object optimization Mark the evolution of optimal control allocation.Existing common control allocation algorithm has explicit allocation method, direct distribution method, non- Linear Control distribution method.

Explicit allocation method is to impose linear restriction relation to each actuator first before control distributes link, The dimension for reducing control distribution, makes the underdetermined system of equations be converted to positive definite equation group, to reduce the size of solution space, in addition it is straight It connects and obtains determining solution.But explicit allocation method is difficult processing actuator by maximum deflection position and maximum deflection rate limit The problem of, and its virtual controlling instruction that can be realized is far smaller than reachable set, is unable to give full play actuator redundant configuration Structural advantage.

Directly distribution (Direct Allocation, DA) algorithm be by Virginia Polytechnic Institute and State University Durham professor in First proposed within 1992, the realization of the algorithm be based on the structure of reachable set (Attainable Moment Subset, AMS) with Operation.The advantages of this method, is that it has specific geometric meaning, and can ensure to obtain through direct allocation algorithm Virtual controlling instruction is identical as desired virtual controlling command direction.But the disadvantages of this method is to work as system actuator redundancy When degree is higher, the time is calculated as the number of actuator is in quadratic power growth, real-time is wanted it is difficult to meet control system It asks.

Nonlinear Control Allocation (Nonlinear Control Allocation, NCA) is non-thread to solve executing agency Control assignment problem under implementations.Doman etc. approaches control surface controlled efficiency using affine function, and real based on this method The distribution target of Nonlinear Control Allocation is showed；For executing agency's angle it is unbalance and therefore caused by control efficiency matrix Unascertainable situation, Hu Qinglei etc. propose a kind of based on robust least square method in conjunction with TSM control method Finite-time control distribution method, realize effective control to spacecraft.

After decades of development, control distribution technique achieves significant achievement in theoretical research and engineering practice, and It has been further applicable to the various fields such as the aircraft of advance aerodynamic configuration, distributed electric drive automobile.But current control Distribution technique processed remains problems, is especially considering control surface by under inflection point and bitrate constraints Constrained control distribution and existing allocation algorithm real-time, accuracy raising etc..Therefore, skill is distributed to control Art is especially considering control surface by the constrained control distribution technique progress under inflection point and bitrate constraints more The development of in-depth study, the advanced technologies such as aircraft and distributed electric drive automobile for advance aerodynamic configuration has weight Big meaning.

Invention content

In view of this, distribution method is directly controlled based on dynamic construction reachable set the object of the present invention is to provide a kind of, Control efficiency can be improved.

It is a kind of that distribution method is directly controlled based on dynamic construction reachable set, include the following steps：

Step 1：Take any pair of different column vector b in control efficiency matrix B_iAnd b_jAs parameter, structure plane ginseng Number equation, can be obtained family of planes；Wherein, B=[b₁,b₂..., bm] i, j=1,2 ... the number of m and i ≠ j, m expression actuator Amount；

An initial facet is randomly assigned in family of planes, as facet f；

Step 2：Calculate each apex coordinates of facet f；

Step 3：Judge given expectation fictitious order v_dWhether positive direction and facet f intersect, if intersection, enter step Rapid four；If non-intersecting, fictitious order v is found_dPositive direction and the hithermost a lines of facet f, it is assumed that be AB, using AB as phase It is facet f, return to step two that adjacent side, which constructs adjacent facet f ' and enables it,；

Wherein, adjacent facet f ' is constructed in the process, it is assumed that the corresponding parameters of AB are b_i, then it needs to be determined that adjacent facet Another parameter b of f '_k, specially：

Point u ' on facet f ' to be built top AB_t,lIt is expressed as：

Wherein, u_min,lIndicate the minimum value of first of actuator output；u_t,lIndicate the point on facet f top AB；

First, b is removed_iAnd b_jIn addition, in b₁To b_mIn arbitrarily select a value as b_k, enable b_lIn b₁To b_mIn take successively Value, and formula is substituted into respectivelyIn, obtain a series of x_lValue, and Judge all x_lValue whether be the same symbol, if not the same symbol, then change b_kValue, by b_lValue according still further to Above-mentioned requirements traversal a series of x that is primary, then judging_lWhether value is jack per line；And so on, until a series of x_lValue It for the same symbol, stops search, obtains b at this time_kValue, i.e., according to b_kWith adjacent side b_iComplete the structure of facet f'；Wherein, l ∈ (1, m) and l ≠ i, l ≠ k；

Wherein, u_max,lIndicate the maximum value of first of actuator output；|b_i b_k b_l| indicate b_i、b_kAnd b_lThe mixing of three Product；

Step 5：It calculates and it is expected fictitious order v_dThe intersection point of positive direction and facet f；

Step 6：According to the intersection point calculation intersecting point coordinate v_d, the line between input is instructed and controlled according to virtual controlling Property conversion is anti-releases the practical control instruction u for distributing to each actuator_d, and distributed to drive system.

The present invention has the advantages that：

In actuator is by the control system of maximum deflection position and maximum deflection rate limit, reachable set in real time may be used Become, efficiency of algorithm can not be improved by the method for offline storage reachable set data, and build the calculation amount of complete reachable set in real time It is larger, it is difficult to meet requirement of the system to real-time, and larger memory space is needed, one kind of the invention is based on dynamic Structure reachable set directly controls distribution method, and the method for dynamic construction reachable set is divided by branch, builds search process in real time Involved in the reachable set facet that arrives, rather than build complete reachable set, greatly reduce calculation amount, improve algorithm effect Rate, memory space also substantially reduce, and solve the control problem of the complex control system of reachable set real-time variable.

Description of the drawings

Fig. 1 is to directly control allocation algorithm flow chart based on dynamic construction reachable set in the present invention；

Fig. 2 is to determine the adjacent facet schematic diagram on some side of reachable set facet；

Fig. 3 to Figure 11 is the process that reachable set is built successively respectively when being scanned for for some vector.

Specific implementation mode

The present invention will now be described in detail with reference to the accompanying drawings and examples.

For the system that actuator is limited by deflection speed, reachable set real-time variable.It is thus impossible to again by storage from Line number can only pass through control surface actual deflection situation testing agency and detect last moment and execute machine according to improving computational efficiency Thus the actual deflection situation of structure obtains control subset, and builds reachable set.However complete reachable set is built in real time and is necessarily led Cause overlength in the line computation time, so that direct allocation algorithm is lost practical value.

The method of a kind of branch proposed by the present invention point, in real time structure reachable set, it is a pair of flat to carve random structure at the beginning Capable reachable set facet determines the direction of search, only structure search ring according to the geometrical relationship of desired fictitious order and facet normal direction The facet arrived involved in section, algorithm time control in a reasonable range.Realize that the key of above-mentioned conception is to determine After the direction of search, known adjacent facet of the facet on some adjacent side how is established.

When each control surface is by maximum deflection rate limit, the practical reachable position at each moment is depending on upper Position, maximum deflection rate and the maximum deflection position of one moment control surface, at each moment, the reality of actuator is reachable Position be it 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 formula：U (t) is control instruction at this time, that is, indicates the vector of the position of current time each actuator, T₀For the time interval that each fictitious order arrives, u_max(t+T₀) and u_min(t+T₀) it is respectively each in next secondary control distribution The range that actuator can actually reach.

Since the actuator bound at each moment is different, leading to the control subset at each moment, reachable set is all different, I.e.：

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

Φ(t+T₀)={ v | v=Bu, u ∈ Ω (t+T₀)} (4)

Wherein B is control efficiency matrix, Ω (t+T₀) it is that the actual control that subsequent time carries out when control distributes is sub Collection, Φ (t+T₀) it is the actual reachable set of subsequent time.

When building reachable set facet, any pair of different column vector b in control efficiency matrix B is taken_iAnd b_jAs ginseng The identical family of planes of a normal vector, family of planes upper bound facet f then can be obtained in number₁With lower bound facet f₂Equation be respectively：

1≤i≤m, 1≤j≤m, i ≠ j；

Wherein：u_t1=[u_T1,1, u_T1,2..., u_{T1, m}] indicate upper bound facet f₁On point, u_t2=[u_T2,1, u_T2,2..., u_{T2, m}] indicate lower bound facet f₂On point；Then 4 apex coordinates in facet are：

Wherein, | a b c | indicate the mixed product of a b c；u_{Max, p}And u_{Min, p}Respectively indicate pth actuator maximum value and Minimum value；

Due to randomly select a facet, as long as so arbitrarily choosing one in upper bound facet and lower bound facet i.e. It can.It might as well set and have chosen upper bound facet：

f：|b_i b_jV |=(b_i×b_j)^TBu_t, u_t∈Ω_t

And

It is respectively v as Fig. 1 mustn't go to a facet f, each apex coordinate_A, v_B, v_CAnd v_D, wherein：

v_A=Bu_A, u_A∈Ω_tAnd u_{A, i}=u_{Min, i}, u_{A, j}=u_{Min, j}

v_B=Bu_B, u_B∈Ω_tAnd u_{B, i}=u_{Max, i}, u_{B, j}=u_{Min, j}

v_C=Bu_C, u_C∈Ω_tAnd u_{C, i}=u_{Max, i}, u_{C, j}=u_{Max, j}

v_D=Bu_D, u_D∈Ω_tAnd u_{D, i}=u_{Min, i}, u_{D, j}=u_{Max, j}

It is clear that can obtain：

Line segment AB is by Ω_tA proper subclass Ω_{T, 1}Mapping obtains, i.e.,：

Point on line segment AB is expressed as：

AndWherein, q =1,2 ..., m；

Assume that we need to search for the adjoining facet f ' on the sides AB below, as shown below.B at this time_iAnd b_jIt is corresponding with facet f Ω_tAll be known, determine facet f ' two vectors one of them must be b_i, we are set as b for another_k, we are only Find b_k, you can the structure of facet f ' is completed, as shown in Figure 2.

We can determine whether the point u ' on the corresponding rib AB of structure facet f '_tFor：

And according to formula (4) and (5), b_kDetermining search condition, i.e., to all l ≠ k, in the case of i：

Except b_iAnd b_jIn addition, in b₁To b_mIn arbitrarily select a value as b_k, enable b_lIn b₁To b_mIn value successively, and point Following formula is not substituted into,Obtain a series of x_lValue, and judge x_l Value whether be jack per line, if it is not, then change b_kValue, by b_lValue traversed according still further to above-mentioned requirements primary, then sentence Disconnected obtained a series of x_lWhether value is jack per line, and so on, until a series of x_lValue is jack per line, is stopped search, and is obtained B at this time_kValue, i.e., according to b_kWith adjacent side b_iComplete the structure of facet f '；Wherein, l ∈ (1, m) and l ≠ i, l ≠ k；According to above-mentioned Method scans for next facet.

It calculates and it is expected fictitious order v_dThe intersection point of positive direction and facet f；According to the intersection point calculation intersecting point coordinate v_d, according to Virtual controlling instructs the linear transformation between control input instead to release the practical control instruction u for distributing to each actuator_d, and Distributed to drive system.

It, can in order to show that dynamic construction reachable set, Fig. 3 to Figure 11 give when being scanned for for some vector The process built successively up to collection.

In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the protection model of the present invention It encloses.All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in this hair Within bright protection domain.

Claims (1)

1. a kind of directly controlling distribution method based on dynamic construction reachable set, which is characterized in that include the following steps：

Step 1：Take any pair of different column vector b in control efficiency matrix B_iAnd b_jAs parameter, plane parameter side is built Family of planes can be obtained in journey；Wherein, B=[b₁,b₂..., bm] i, j=1,2 ... the quantity of m and i ≠ j, m expression actuator；

An initial facet is randomly assigned in family of planes, as facet f；

Step 2：Calculate each apex coordinates of facet f；

Step 3：Judge given expectation fictitious order v_dWhether positive direction and facet f intersect, if intersection, enters step four； If non-intersecting, fictitious order v is found_dPositive direction and the hithermost a lines of facet f, it is assumed that be AB, using AB as adjacent edge structure It is facet f, return to step two to build out adjacent facet f ' and enable it；

Wherein, adjacent facet f ' is constructed in the process, it is assumed that the corresponding parameters of AB are b_i, then it needs to be determined that adjacent facet f's ' is another One parameter b_k, specially：

Point u ' on facet f ' to be built top AB_t,lIt is expressed as：

Wherein, u_min,lIndicate the minimum value of first of actuator output；u_t,lIndicate the point on facet f top AB；

First, b is removed_iAnd b_jIn addition, in b₁To b_mIn arbitrarily select a value as b_k, enable b_lIn b₁To b_mIn value successively, and point Formula is not substituted intoIn, obtain a series of x_lValue, and judge all x_lValue whether be the same symbol, if not the same symbol, then change b_kValue, by b_lValue according still further to above-mentioned requirements Traversal is primary, then a series of x judged_lWhether value is jack per line；And so on, until a series of x_lValue is identical symbol Number, it stops search, obtains b at this time_kValue, i.e., according to b_kWith adjacent side b_iComplete the structure of facet f '；Wherein, l ∈ (1, m) and l ≠ i,l≠k；

Wherein, u_max,lIndicate the maximum value of first of actuator output；|b_i b_k b_l| indicate b_i、b_kAnd b_lThe mixed product of three；

Step 5：It calculates and it is expected fictitious order v_dThe intersection point of positive direction and facet f；

Step 6：According to the intersection point calculation intersecting point coordinate v_d, the linear transformation between input is instructed and controlled according to virtual controlling It is anti-to release the practical control instruction u for distributing to each actuator_d, and distributed to drive system.