Method and control unit for controlling an overdetermined system, system and aircraft

Abstract

The present invention relates to a method and a control unit, a system, and an aircraft for controlling an overdetermined system, the method comprising: a) determining a pseudo-control command according to a physical model of the system #imgabs0# The pseudo-control command particularly represents the torque and the total thrust acting on the system; b) determining a control matrix D according to u p = D u wherein u represents an actuator control command; c) decomposing the control matrix D into sub-control matrices D i according to #imgabs2# q ≤ p′, so that #imgabs3# and u p,i = D i u; d) determining an actuator control command for performing a primary task according to #imgabs4#; e) projecting non-primary tasks, i > 1, onto the null space of the primary task, i = 1, and onto the respective corresponding null spaces of all non-primary tasks with higher priorities (if any); and f) providing the actuator control commands from d) and e) to the actuator.

Description

Field of the Invention

[0001] The present invention relates to a method for controlling an overdetermined system having a plurality of actuators, for example, the system is an aircraft having a plurality of drive units.

[0002] The present invention also relates to a control unit for controlling an overdetermined system having a plurality of actuators, for example, the system is an aircraft having a plurality of drive units.

[0003] The present invention also relates to an overdetermined system having a plurality of actuators.

[0004] The present invention finally also relates to an aircraft having a plurality of drive units and optionally other actuators, such as movable flaps or winches, and these drive units and actuators together form an overdetermined system. Background Art

[0005] Aircraft, flying vehicles or aircraft with overdetermined actuation (i.e., having a greater number of actuators than required to perform the so-called main task in its control space) provide the possibility of performing the main task with more than one solution. This intuitively indicates that, depending on the type of aircraft, the type of actuator and the task defined in the control space, there may be additional space for performing one or more other (non-main) tasks.

[0006] Depending on the aircraft's handling, environmental conditions, failure scenarios or other influences, the operation of the aircraft may approach the limits of its control space. This means that the physical forces and (rotational) torques that can be provided by the actuators and control surfaces (flaps, wings, etc.) may not be sufficient to control all the control axes (or axes of maneuver) of the aircraft at all times. For the multi-rotor aircraft "VoloCity" produced by the applicant, these axes are the roll axis (longitudinal axis), the pitch axis (transverse axis), the yaw axis (vertical axis) and the (total) thrust. Other aircraft types may have different control axes depending on the actuator arrangement, especially two additional horizontal thrust axes. In these cases, the safety and controllability of the aircraft can ensure one or more control axes prior to other control axes. For example, the roll axis and the pitch axis are prioritized over the yaw axis. Importantly, it is necessary to ensure that the control axes with lower priority do not affect the control axes with higher priority (for example, when the priority of the yaw axis is lower than that of the roll axis and the pitch axis, the control of the yaw axis cannot affect the roll axis and the pitch axis).

[0007] This separation in control of different priorities is a relatively important task. Generally speaking, combining different tasks with their respective priorities so that tasks with low priorities do not affect tasks with high priorities is a complex requirement. The way and form in which secondary or tertiary (tertiary or generally non-primary) tasks are added to the control and configuration problem (allocation problem) can significantly affect the ability to solve the primary task and the stability of such a solution.

[0008] In European Patent Application 19 212 935.1, the applicant proposed a method for operating an eVTOL aircraft with 18 rotors, wherein the main control task uses a so-called "L-2" minimization solution to provide the required thrust and torque, while applying secondary and less prioritized (non-primary) constraints to reduce the power of the maximum LTU (Lift-Trust-Unit). This is achieved by changing the gain parameter of the allocation problem to a function of the LTU value (rotational speed - RPM) and the corresponding average value of the total LTU (so-called "L-inf" minimization). Here, two tasks are performed in one step, which makes it impossible to assign different priorities or importance to different objectives. In addition, a failure or incorrect behavior in achieving a lower importance objective (such as a secondary objective) may have an adverse impact on solving a task with higher importance (such as a primary objective). Summary of the Invention

[0009] The object of the present invention is to solve the above problems and provide a method, a control unit, a system and an aircraft of the type mentioned in each case, wherein in addition to achieving at least one main task, at least one non-main task can also be achieved without affecting the main task or its solution. Generally speaking, the same object applies to tasks with higher priorities relative to tasks with lower priorities.

[0010] The above object is achieved by the method, control unit, system and aircraft provided by the present invention.

[0011] The present invention also defines preferred improvement schemes.

[0012] According to the present invention, a method for controlling an overdetermined system having a plurality of actuators with limited power (the number is k) is proposed, the system being in particular an aircraft having a plurality of drive units, the actuators performing at least one main task and at least one non-main task, the method comprising:

[0013] a) determining a pseudo control instruction according to the physical model of the system The pseudo control instruction particularly represents the torques (L, M, N) and the total thrust (F) acting on the system,

[0014] b) Determine the control matrix D according to u p = Du, where u represents the actuator control command,

[0015] c) According to q ≤ p′, decompose the control matrix D into sub-control matrices D i such that and u p,i = D i u,

[0016] where, for i = 1, the sub-control matrix D i and the corresponding sub-pseudo control command u p,i correspond to the primary task, and for i > 1, the sub-control matrix D i and the corresponding sub-pseudo control command u p,i correspond to at least one non-primary task, and the priority of the non-primary task decreases as the index i increases,

[0017] d) Determine the actuator control command for performing the primary task according to where # represents matrix inversion, and includes the actuator control command for performing the primary task, where there is

[0018] e) Project the non-primary tasks, i > 1, onto the null space of the primary task, i = 1, and onto the null space of each of all non-primary tasks with higher priority (if any), such that D i u j = 0, where j > i, includes the actuator control command for performing the non-primary task, and

[0019] f) Provide the actuator control commands from d) and e) to the actuator.

[0020] The term "finite" or "power-limited" in this context means that the actuator has a physical power limit, that is, it cannot achieve any conceivable technical task (this applies in principle to any machine).

[0021] Correspondingly, for the actuator control command u,

[0022] means that the actuator control command is restricted within a certain numerical range.

[0023] According to the present invention, a control unit for controlling an overdetermined system having a plurality of power-limited actuators (numbering k) is proposed, said system being in particular an aircraft having a plurality of drive units, said actuators performing at least one main task and at least one non-main task, and being in particular constructed and arranged in software technology for:

[0024] a) determining a pseudo-control instruction according to a physical model of the system The pseudo-control instruction in particular represents the torques (L, M, N) and the total thrust (F) acting on the system.

[0025] b) determining a control matrix D according to u p = Du where u represents an actuator control instruction.

[0026] c) decomposing the control matrix D into sub-control matrices D according to q ≤ p′, such that i and u = D p,i u, i where, for i = 1, the sub-control matrix D

[0027] i and the corresponding sub-pseudo-control instruction u p,i correspond to the main task, and for i > 1, the sub-control matrix D i and the corresponding sub-pseudo-control instruction u p,i p,i correspond to at least one non-main task, and the priority of the non-main task decreases as the index i increases.

[0028] d) determining the actuator control instruction for performing the main task according to where # represents matrix inversion, and includes the actuator control instruction for performing the main task, where

[0029] e) projecting the non-main tasks, i > 1, onto the null space of the main task, i = 1, and onto the respective null spaces of all non-main tasks with higher priority (if any), such that D i u j = 0, where includes the actuator control instruction for performing the non-main task, and

[0030] f) supplying the actuator control instructions from d) and e) to the actuators.

[0031] Furthermore, the control unit can be constructed and arranged to perform the improvement schemes described below for the method according to the present invention.

[0032] Furthermore, the control unit can be operatively connected to means for measuring and / or determining parameters and states of the system and / or the actuator, which parameters and states are required for determining the pseudo control commands according to step a), in particular by the main flight control unit of the aircraft.

[0033] The overdetermined system according to the invention comprises a plurality of actuators operatively connected to a control unit according to the invention.

[0034] The aircraft according to the invention comprises a plurality of drive units and optionally other actuators, such as movable flaps or winches, and the drive units and the actuators together form the overdetermined system according to the invention, and the aircraft is in particular a multi-rotor aircraft having a plurality of preferably electrically driven rotor units.

[0035] "Actuator" in the present context particularly, but not exclusively, refers to drive units, such as rotor units or the like. Depending on the design of the system (aircraft), it also includes other mechanisms, such as flaps, winches, etc., or generally the operating mechanisms required for the system to perform defined physical tasks.

[0036] There is also proposed a method for assigning control priorities to an overdetermined system, in particular an aircraft, in which tasks with lower priority are projected into the null space of tasks with higher priority. In this way, it is ensured that tasks with lower priority do not affect tasks with higher priority.

[0037] In particular, there is proposed a method for differentiating priorities of control axes of the system (aircraft) by using the null space of a system with overdetermined actuators. The method described here, for the case of an aircraft, can assign a higher priority to the control roll axis than to the control pitch axis, or assign a higher priority to the control roll axis and the control pitch axis than to the control yaw axis, or assign a higher priority to the control roll axis and the control pitch axis than to the control yaw axis and altitude control, and so on. The combination of priorities can be arbitrarily selected, and preferably the algorithms underlying the design of the control unit according to the invention in software form can be applied to all these combinations.

[0038] A preferred feature is that due to the use of the null space of the control matrix, tasks / objectives with lower priority do not affect tasks with higher priority. For example, tasks of the third level do not affect secondary and primary tasks, and secondary tasks do not affect primary tasks.

[0039] If there is still space in the null space and under reasonable circumstances, the proposed method can also be used for tasks of the fourth level, fifth level or other tasks. If there is no more space in the null space, these low-priority tasks are advantageously simply ignored based on the definition of the null space.

[0040] In the present context, the "null space" should refer to the kernel of a (linear) mathematical mapping. The kernel of a linear mapping f: V → W between vector spaces V and W consists of the vectors in V that are projected to the zero vector in W; that is, the kernel is the solution set of the homogeneous linear equation f(x) = 0 and is thus also called the null space.

[0041] If one examines the example in EP 19 212 935.1, the main task then lies in finding a solution for the control allocation for generating the required (total) thrust and torque using "L-2 minimization". Accordingly, the secondary task, i.e., the non-main task, can be to reduce the maximum LTU power using "L-inf minimization". If the secondary task is projected into the null space of the main task according to the present invention, it is ensured that the secondary task does not affect the solution of the main task. This is desirable for safety reasons because the main task must be completed, while the secondary task is only preferably to be completed. In addition, further subordinate tasks (e.g., tertiary tasks) can be specified, for example, to reduce the power of a certain (or several) LTU to, for example, 75% because the associated drive unit is overheating or is classified as faulty. According to a corresponding improvement of the present invention, the tertiary task is projected into the null space of the main task and the secondary task, so that the tertiary task does not have an adverse effect on the tasks with higher priority.

[0042] In the above example, the secondary and tertiary tasks can be interchanged according to specific requirements and priorities. Within the scope of the present application, the priorities of the individual (control) tasks result from the corresponding specific application scenarios (which will be described in detail below).

[0043] It should be emphasized that the concept presented here provides a highly advantageous differentiation of tasks according to their respective importance, and it can be used to assign different design assurance levels (DAL) to functions with different importance and objectives. This has a significant impact on reducing the development costs of safety-critical devices, specifically, such as aircraft.

[0044] Although the aircraft is repeatedly cited here and below, the described method generally also applies to controlling any type of overdetermined actuator system.

[0045] For the sake of easy understanding, the mathematical and physical background of the present invention, particularly with regard to the aircraft, will be briefly explained in detail here.

[0046] The system equations of motion obtained using Newton-Euler's theorem or the Lagrangian method can be expressed as follows:

[0047]

[0048] where is the m-dimensional configuration vector of the system, e.g., position and rotation in three dimensions, is the state-dependent generalized inertia matrix, represents the state-dependent Coriolis forces, stands for the gravitational forces, is the external forces and torques, e.g., caused by aerodynamics, contact, etc. The physical control commands (or pseudo control commands) required by the system are represented as For example, the control commands are calculated using a feedback control method and are used to control the system. The pseudo control commands are fixed forces and torques acting on the system through different actuators, and they are all included in the system dynamics system given by Equation 1, with a control input matrix These matrices contain information about over-actuation or under-actuation.

[0049] A control method (or rule) is used to calculate u p (e.g., direct correlation or feedback control rules, etc.). The association between these calculated control commands and the actual actuator control commands is completed through an allocation or configuration problem, which is especially the geometric knowledge about the positioning of the actuators in the system and other configurations and properties related to the actuators. Applicable here is:

[0050] u p = Du, Equation 2

[0051] Here, where defines the so-called control effectiveness matrix (abbreviation: control matrix). As described above, after using the control method, the pseudo control commands are first calculated but the pseudo control commands must be allocated to the physical actuators in the form of actual control commands (actuator control commands), which is generally known as a control allocation problem or configuration problem. Therefore, an inverse matrix calculation (denoted by the superscript "#" below) is required in order to calculate u from u p This is expressed as:

[0052] u = D # (W, u min , u max (u p , Equation 3

[0053] This inversion is usually carried out considering the weights or weighting matrix and the physical limits of each actuator, e.g., and where,

[0054] is referred to as the "control allocation matrix" (or configuration matrix).

[0055] Note: is a matrix with rank(M) = p. At this time, M # represents the right inverse matrix, so that MM # = I. This involves the standard inverse matrix M # = M -1 for k = p', and when ignoring the weight matrix W and the extreme values u min , u max for k > p', this involves the pseudo-inverse matrix M # = M T (MM T ) -1 .

[0056] For an aircraft such as the 18-rotor (models "VC200", "VoloCity" or "VoloDrone") produced by the applicant, represents a vector that contains the required (control) thrust and the three-dimensional (operating) moment acting on the aircraft with respect to the center of gravity of the aircraft. In addition, is a vector containing eighteen (18) required rotor control commands.

[0057] The distributed actuator control command u was previously calculated with the aid of the allocation matrix , which is the result of a matrix inversion problem. For a system with a redundant number of actuators (i.e., k > p'), if the control matrix has sufficiently linearly dependent columns (which is known to those skilled in linear algebra), there may be more than one solution to the inversion problem. In this application, such a system is called an "overdetermined system".

[0058] The existence of more than one solution to the inversion problem provides the possibility of a non-zero "null space", which can be used for other (secondary or tertiary, or generally lower-priority) tasks without affecting higher-level objectives (tasks or their solutions).

[0059] Definition of the control axis

[0060] (Control) matrix D establishes the relationship between the physical control axes (e.g., torque and thrust) and the actual actuator command u based on the relationship u p = Du. To determine the priority of the control axes, the following allocation method is proposed:

[0061]

[0062] Here, it applies that: up,i = D i u. Here, u p,i represents a subset of the relevant control axes. When dim(u p,i ) = 1, it can be an isolated control axis, and when 1 < dim(u p,i ) < p, it can be multiple control axes.

[0063] For example, u p,1 can be the roll moment and the pitch moment (dim(u p,1 ) = 2), u p,2 can be the yaw moment (dim(u p,2 ) = 1), and u p,3 can be the thrust (dim(u p,3 ) = 1).

[0064] Null space

[0065] The null space of the matrix , also known as the kernel, is the set of all matrices v such that D i v = 0. Thus, the null space of the matrix D i can be defined as:

[0066] N(D i ) = {v | D i v = 0}.

[0067] Calculation of the null space

[0068] A possible expression for the null space of the matrix D can be calculated according to the following formula:

[0069]

[0070] where is the k×k identity matrix. The superscript # represents the inverse matrix (when the matrix is square, it is the standard inverse matrix, and when it is not square, it is the pseudo-inverse matrix), and the superscript T represents the transpose operation.

[0071] Determining task priorities through null space projection

[0072] The control matrix D can be subdivided (decomposed) into smaller matrices, and the number of such subdivisions, separations, or decompositions is related to the number of tasks / goals to be managed:

[0073]

[0074] Here, q ≤ p is the number of tasks or goals to be completed. The smaller its subscript, the more important the task to be completed, and the relevant task (goal) takes precedence over other tasks / goals.

[0075] For example, in the case of using D1 (corresponding to u p,1 ), the highest priority is assigned to the target. Thereafter, D2 (corresponding to u p,2 ) is assigned to the secondary target, and so on.

[0076] Example of an application scenario with three tasks / goals

[0077] Primary target

[0078] What applies here is:

[0079]

[0080] Among them, is a vector containing actuator instructions (or actuator control instructions), and these actuator instructions achieve the primary target of generating the required physical control command u p,1 . The executable instructions generated by this task are:

[0081]

[0082] Secondary target

[0083] Now consider the calculated to achieve the secondary target p,2 so as to generate the required physical control command u without interfering with the primary target. For this purpose, u2 is appropriately calculated and projected onto the null space of the control matrix D1 for the primary target, preferably the following projection:

[0084]

[0085]

[0086] u2 = N2u2 org .

[0087] According to a corresponding improvement of the present invention, it is first preferably calculated according to to execute the first non-primary task, and then, according to project onto the null space N2(D1) of the sub-control matrix D1, where preferably

[0088] To ensure the executability of the total instruction, i.e., u ∈ U, the following limits are preferably observed in the secondary allocation step:

[0089]

[0090] According to a corresponding improvement of the method of the present invention, for it is stipulated that​ It follows that: u1 + u2 ∈ U.

[0091] To ensure that the primary goal is not affected by the secondary goal (when there is no tertiary goal), the total actuator command preferably has the following form:

[0092] u = u1 + u2.

[0093] According to a corresponding improvement of the method according to the invention, the total actuator control command is calculated as follows: u = u1 + u2.

[0094] Tertiary goal

[0095] Consider calculating for the purpose of achieving the tertiary goal to generate the required physical control command u without disturbing the primary or secondary goals. p,3 Then, preferably project u3 onto the null spaces of the control matrices D1, D2 for the primary and secondary goals according to the following formula:

[0096]

[0097] u3 = N3u3 org .

[0098] Therefore, according to a corresponding improvement of the method according to the invention, next preferably calculate according to to perform the second non-primary task, and then project onto the null space N3(D1, D2) of the sub-control matrices D1, D2 according to u3 = N3u3 org where preferably There is

[0099] To ensure the executability of the total command, i.e., u ∈ U, the following restrictions are preferably observed in the tertiary allocation step:

[0100]

[0101] According to a corresponding improvement of the method according to the invention, for it is predefined that It follows that: u1 + u2 + u3 ∈ U.

[0102] To ensure that the primary goal is not affected by the secondary and tertiary goals, and the secondary goal is not affected by the tertiary goal, the total actuator command preferably has the following form:

[0103] u = u1 + u2 + u3.

[0104] Accordingly, a corresponding improvement of the method according to the invention provides that the total actuator control command u is calculated as follows: u = u1 + u2 + u3.

[0105] This approach can be generalized:

[0106] For tasks with the highest priority, the following always applies:

[0107]

[0108] For secondary tasks, the following applies:

[0109]

[0110] u2 = N2u2 org 。

[0111] For all other tasks (where i > 2), the following applies:

[0112]

[0113] u i =N i u i org 。

[0114] Accordingly, a corresponding improvement of the method according to the invention provides that the null space N i (D), i > 1 is calculated according to the following formula:

[0115]

[0116] Finally, the total actuator command is:

[0117]

[0118] The extreme value is:

[0119]

[0120] where

[0121] That is to say, specifically, in order to execute non-primary tasks, i > 1, the following calculation is performed in the improvement of the method according to the invention:

[0122]

[0123] u i =N i u i org ;

[0124] wherein

[0125] and wherein

[0126]

[0127] Preferably, the method according to the invention is applied to an aircraft having a plurality, i.e. k, drive units, preferably 18, i.e. k = 18, drive units, which drive units form at least some of the actuators of the system.

[0128] For example, in an improvement of the method according to the invention, it can be stipulated that attitude control related to roll (especially roll angle) and pitch (especially pitch angle) has priority over direction control related to yaw (especially yaw rate) and vertical control related to flight altitude (especially climb rate and descent rate). For specific cases, reference will also be made below to Figure 1 and 2 for a detailed description thereof.

[0129] In particular, it can be stipulated that is selected as the projection of the actuator control command u onto the roll moment and the pitch moment, wherein and is selected as the projection of the actuator control command u onto the thrust moment and the yaw moment, wherein (Variant 1).

[0130] In another improvement of the method, it can be stipulated that attitude control related to roll and pitch (especially roll angle and pitch angle) has priority over direction control related to yaw movement (especially yaw rate) and total thrust.

[0131] At this time, in particular, it can be stipulated that is selected as the projection of the actuator control command u onto the roll moment and the pitch moment, wherein is selected as the projection of the actuator control command u onto the yaw moment, wherein and is selected as the projection of the actuator control command u onto the total thrust, wherein (Variant 2).

[0132] In another improvement of the method, it can also be stipulated that the total thrust has priority over attitude control related to roll and pitch (especially roll angle and pitch angle), and direction control related to yaw movement (especially yaw rate).

[0133] For this purpose, it can be stipulated that is selected as the projection of the actuator control command u onto the total thrust, wherein is selected to represent the projection of the actuator control instruction u onto the pitch moment, where is selected to represent the projection of the actuator control instruction u onto the roll moment, where and is selected to represent the projection of the actuator control instruction u onto the yaw moment, where (variant embodiment 3).

[0134] The purpose of the first two variant embodiments is to restore a stable flight attitude once the roll and pitch angles have been reduced to a reasonable extent, as this may result in a loss of altitude, and this strategy may not be suitable for the case where the aircraft is approaching the ground.

[0135] In contrast, the third variant embodiment is very suitable for the case where a collision is inevitable, so that the collision speed can be reduced by giving priority to thrust in order to minimize the damage to the aircraft. In addition, an attempt can be made to reduce the pitch angle in order to improve the collision safety of the pilot and / or passengers. The same applies to the roll angle, while the yaw angle (heading angle) or yaw rate has only a low priority in this case. Description of the Drawings

[0136] Other features and advantages of the present invention result from the following description of the drawings.

[0137] Figure 1 shows a system or aircraft according to the present invention;

[0138] Figure 2 shows the coupling of the limit values of the pseudo-control instructions;

[0139] Figure 3 shows the aircraft Figure 1 in extreme flight conditions;

[0140] Figure 4 shows a way of decomposing the control matrix; and

[0141] Figure 5 shows a possible flow of the method according to the present invention. Detailed Description of the Invention

[0142] Figure 1 shows a system or aircraft 1 according to the present invention, in the form of a multi-rotor aircraft manufactured by the applicant and having 18 drive units (actuators). In Figure 1In this context, L, M, and N denote the moments about the axes x, y, and z (roll axis, pitch axis, and yaw axis) of the aircraft 1, and F denotes the total thrust. The reference numeral 2 denotes the main aircraft control unit of the aircraft 1, which preferably includes the control unit 2a of the present invention. The control unit preferably has a control algorithm 2a' and is thus configured to perform the method of the present invention and its improvements in software technology. The reference numeral 2b additionally shows a human pilot, who does not require further attention in the current situation. The reference numeral 3 denotes one of 18 (not limited to the same) drive units or actuators, each of which includes an (electric) motor 3a and a rotor 3b. That is to say, the aircraft 1 is an eVTOL, i.e., an electrically driven aircraft capable of taking off and landing vertically (vertical take-off and landing). The reference numeral 4 exemplarily denotes a sensor unit operatively connected to the main flight control unit 2. In order to be able to take into account the available aircraft states in corresponding improvements of the method according to the present invention, a plurality of such sensor units 4 may be provided, in particular inertial instruments, GNSS, barometers, vibration sensors on the actuators, temperature sensors on the actuators, and the like.

[0143] The present invention is not limited in principle to the application to the aircraft 1 as an overdetermined system.

[0144] Figure 2 Illustrating the situation described above, according to which, in a determined state, especially in an aircraft according to Figure 1 the control of the roll angle and the pitch angle takes precedence over the yaw angle or the yaw rate and the thrust. That is to say, according to Figure 2 , the extreme values of the respective pseudo-control commands are coupled, so that a large thrust requirement causes a reduction in the control range (control space, i.e., the shaded area) relating to the roll moment and the pitch moment (abscissa).

[0145] Furthermore, for a conventional multi-rotor aircraft, the attitude of the aircraft determines the direction of the thrust vector. Therefore, when the attitude angle has a large value, the thrust requirement for compensating the weight of the aircraft increases significantly, as shown in Figure 3 the illustration in. When the thrust requirement exceeds the permitted extreme value, a large attitude angle necessarily causes the aircraft 1 to lose altitude. This loss of altitude can only be compensated when the attitude angle decreases.

[0146] If these viewpoints are combined, it results that, in extreme flight conditions, as shown in Figure 3 , the attitude correction relating to the roll angle and the pitch angle takes precedence over the control relating to the other control axes (yaw and thrust). Therefore, according to Figure 4 , in the illustrated aircraft with 18 rotors (see Figure 1) can be processed or allocated as follows:

[0147] As Figure 4 shown, the control matrix is decomposed (dissociated) into two sub - matrices D1, D2. Here, correspond to the roll moment and the pitch moment. Thus, k = 1, …, 18, describes the projection of the actuator command u onto the roll moment and the pitch moment. correspond to the yaw moment and the total thrust, and correspondingly k = 1, …, 18, projects the actuator command u onto the yaw moment and the thrust.

[0148] Figure 5 shows a possible flow of the method according to the present invention. The method starts at step S1, where the pseudo - control command u p is calculated. As described in detail above, in step S2, the control matrix D is decomposed based on the control priorities, as exemplified above. For this purpose, (sensor) measurements from step S2' etc. can be used, as has also been described. The order of the control priorities can also be changed according to the measurements, as has been described. In step S3, as described, the sub - control matrix D1 is used to calculate to perform the main task, as has been described. In step S4, the control command for the secondary task is calculated. For this purpose, (sensor) measurements from step S4' etc., such as temperature measurements, can be used, as has also been described. Then, in step S5, the non - main (secondary) task or the corresponding control command is projected into the null space N(D) of the main task, so that when u2, represents the control command for the actuator to implement the non - main task, Du2 = 0. This has also been described in detail above and correspondingly applies to other low - priority tasks.

[0149] Step S6 includes querying whether there are further secondary (non - main, e.g., third - level) tasks to be solved. If "yes (j)", then steps S4 (and if necessary S4') and S5 are adaptively adjusted (e.g., with etc.) and the steps are repeated for said other tasks. Once the query in step S6 yields a "no (n)" response, the method jumps to step S7, where the total control command is determined according to the number of tasks solved (see above): = u1 + u2+…. In step S8, this total control command is used to control the actuator, and the method ends with step S9.

Claims

1. A method for controlling an overdetermined system having a plurality of power - limited actuators, the system being an aircraft (1) having a plurality of drive units (3), the actuators performing at least one main task and at least one non - main task, the method comprising: a) Determine the pseudo-control command according to the physical model of the system The pseudo-control command represents the torques (L, M, N) and the total thrust (F) acting on the system b) Determine the control matrix D according to u p = Du, where u represents the actuator control command, and k represents the number of the driving units (3); c) According to q ≤ p′, decompose the control matrix D into sub-control matrices D i , so that there are and u p,i = D i u, Among them, for i = 1, the sub-control matrix D i and the corresponding sub-pseudo control instruction u p,i correspond to the main task. For i > 1, the sub-control matrix D i and the corresponding sub-pseudo control instruction u p,i correspond to at least one of the non-main tasks, and the priority of the non-main tasks decreases as the index i increases. d) According to determine the actuator control instructions for performing the said main task, where # represents matrix inversion, and include the actuator control instructions for performing the said main task, where e) Project the non-primary tasks, i > 1, onto the null space of the primary task, i = 1, and if there are non-primary tasks with higher priorities, project them onto the respective null spaces of all non-primary tasks with higher priorities, so that there is D i u j = 0, where j > i, includes the actuator control instructions for performing the non-primary tasks, and f) Providing the actuator control instructions from d) and e) to the actuators.

2. The method according to claim 1, wherein, First, according to calculate to perform the first non-primary task, and then according to project onto the null space N2(D1) of the sub-control matrix D1, where Among them, u2 org represents the control instruction for executing the first non-primary task.

3. The method according to claim 2, wherein, Then calculate the total actuator control instruction u according to the following formula: u = u1+u2.

4. The method according to claim 2 or 3, wherein For Preset:

5. The method according to claim 2 or 3, wherein According to Calculate to perform a second non-primary task, and then according to u3 = N3u3 org Project onto the null space N3(D1, D2) of the sub-control matrices D1, D2, where Among them, represents a control instruction for executing the second non-primary task.

6. The method according to claim 5, wherein, Then calculate the total control instruction u according to the following formula: u = u1+u2+u3.

7. The method according to claim 5, wherein, For Preset:

8. The method according to any one of claims 1 to 3, wherein Calculate the null space N according to the following formula i (D), i > 1:

9. The method according to claim 8, wherein In order to perform the non - main task, i>1, calculate the following: u i = N i u i org ; Among them and therein 10. The method according to any one of claims 1 to 3, wherein, k = 18, the method is applied to an aircraft (1) having 18 drive units (3), and these drive units form at least some of the actuators of the system.

11. The method according to claim 10, wherein, Attitude control related to roll and pitch, which is used to control the roll angle and the pitch angle, takes precedence over yaw - related direction control, which is used to control the yaw rate, and altitude - related vertical control, which is used to control the climb rate and the descent rate.

12. The method according to claim 11, wherein is selected to represent the projection of the actuator control command u onto the roll moment and the pitch moment, where, and is selected to represent the projection of the actuator control command u onto the thrust moment and the yaw moment, where, 13. The method according to claim 10, wherein Attitude control related to the roll and pitch, which is used to control the roll angle and the pitch angle, takes precedence over yaw - related direction control, which is used to control the yaw rate and the total thrust.

14. The method according to claim 13, wherein, is selected to represent the projection of the actuator control command u onto the roll moment and the pitch moment, where, and is selected to represent the projection of the actuator control command u onto the yaw moment, where, and is selected to represent the projection of the actuator control command u onto the total thrust, where, 15. The method according to claim 10, wherein The total thrust takes precedence over attitude control related to roll and pitch, which is used to control the roll angle and the pitch angle, and yaw - related direction control, which is used to control the yaw rate.

16. The method according to claim 15, wherein, is selected to represent the projection of the actuator control command u onto the total thrust, where is selected to represent the projection of the actuator control command u onto the pitch moment, where is selected to represent the projection of the actuator control command u onto the roll moment, where is selected to represent the projection of the actuator control command u onto the yaw moment, where 17. A control unit (2a) for controlling an overdetermined system having a plurality of power - limited actuators, the system being an aircraft (1) having a plurality of drive units (3), the actuators performing at least one main task and at least one non - main task, and being constructed and arranged in software technology for: a) Determine the pseudo-control command according to the physical model of the system The pseudo-control command represents the torques (L, M, N) and the total thrust (F) acting on the system b) Determine the control matrix D according to u p = Du where u represents the actuator control instruction, c) According to q ≤ p′, decompose the control matrix D into sub-control matrices D i , so that there are and u p,i = D i u, Among them, for i = 1, the sub-control matrix D i and the corresponding sub-pseudo control instruction u p,i correspond to the main task, while for i > 1, the sub-control matrix D i and the corresponding sub-pseudo control instruction u p,i correspond to at least one of the non-main tasks, and the priority of the non-main tasks decreases as the index i increases. d) According to determine the actuator control instructions for performing the main task, where # represents matrix inversion, and include the actuator control instructions for performing the main task, where e) Project the non-primary tasks, i > 1, onto the null space of the primary task, i = 1, and onto the respective null spaces of all non-primary tasks with higher priorities (if any), so that D i u j = 0, where j > i, includes the actuator control instructions for performing the non-primary tasks, and f) Providing the actuator control instructions from d) and e) to the actuators.

18. The control unit (2a) according to claim 17, the control unit is further constructed and arranged to perform the method according to any one of claims 2 to 16.

19. The control unit (2a) according to claim 17 or 18, the control unit is operably connected to means (4) for measuring and / or determining parameters and states of the system and / or the actuators, which are required for determining the pseudo - control instruction by the main flight control unit (2) according to step a).

20. An overdetermined system having a plurality of actuators, the system being operably connected to the control unit (2a) according to any one of claims 17 to 19.

21. An aircraft (1), the aircraft having a plurality of drive units (3) and optionally other actuators, such as movable flaps or winches, the drive units and the actuators together constituting the overdetermined system according to claim 20, the aircraft being a multi - rotor aircraft having a plurality of electrically - driven rotor units.

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