CN111783311B - Helicopter scheduling controller design method based on arbitrary time algorithm - Google Patents

Helicopter scheduling controller design method based on arbitrary time algorithm Download PDF

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CN111783311B
CN111783311B CN202010667546.8A CN202010667546A CN111783311B CN 111783311 B CN111783311 B CN 111783311B CN 202010667546 A CN202010667546 A CN 202010667546A CN 111783311 B CN111783311 B CN 111783311B
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王国良
孙媛媛
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Liaoning Shihua University
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Abstract

The invention discloses a helicopter dispatching controller design method based on any time algorithm, which comprises the following steps: s1, establishing a random jump system; s2, designing a scheduling controller Γ based on any time scheduling algorithm according to the system established in the step S1 δ(t) ：K δ(t) And the determined control gain, delta (t), is a switching signal of the scheduling controller. The design method of the invention aims at the continuous time hopping linear system, and can ensure the stability of the system for the execution condition of the controllers in a period of residence time, whether the total execution time of all the dispatching controllers is less than the situation when the residence time is open-loop or the total execution time of all the dispatching controllers is equal to the residence time, and the special situation that the residence time of the non-hopping system is constant or time-varying is studied. The design method can be applied to a vertical lifting helicopter system, and conditions for stabilizing the system are established to obtain a corresponding dispatching controller.

Description

Helicopter scheduling controller design method based on arbitrary time algorithm
Technical Field
The invention relates to the technical field of helicopter control, in particular to a design method of a scheduling controller of a helicopter based on any time algorithm.
Background
The system of linear hopping has hybrid dynamics. It consists of a limited number of subsystems described by discrete (or continuous) time dynamics and rules controlling the hopping between them. The hopping system provides a unified framework for mathematical modeling of many physical or manual systems of hopping characteristics, which has proven to be a focus of continued interest in the control and systems community. In recent years, two main problems related to a jump linear system have been studied, namely, the development of the stability condition of the system under arbitrary switching and the design of the controller to ensure stable operation of the system and improvement of performance.
The dynamics of a vertical lift helicopter system is obtained from a continuous time hopping linear system, the main research purpose of which is to calm the system by a type of random dispatch controller that balances system performance requirements and resource constraints better than traditional stable controllers. Further, extensions to systems that are hop-free but have a constant dwell time and a time-varying dwell time are further contemplated. The proposed scheduling control concept is key, and an achievable controller is designed to ensure that the controller obtains a useful result after a period of operation, and the controller is utilized to the maximum extent. Traditionally, very conservative scheduling methods, i.e., static allocation of controller execution time, have been employed, which makes the overall architecture extremely stiff, difficult to reconfigure for additions or changes to components, and often poorly performing. In various scheduling methods, the scheduling algorithm at any time is suitable for providing a solution to process limited resources and optimizing when more resources are available, so that the availability of the resources is greatly improved. Scheduling control can improve system performance by deciding which task to perform, and is a communication network capable of transmitting information and processing elements to ensure stability thereof. In contrast to previous studies, when the system under consideration is continuous, the total execution time of the controller is not exactly equal to its residence time, and the proposed strategy cannot be applied directly.
Therefore, the invention provides a design method of a dispatch controller of a vertical lift helicopter, which is used for solving the problems.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a scheduling controller design method of a helicopter based on any time algorithm.
The invention provides a helicopter scheduling controller design method based on any time algorithm, which comprises the following steps:
s1, establishing a random jump system, wherein the system is shown in the following formula (1):
wherein the system is at [ t ] k ,t k+1 ) Run in time period, matrix A r(t) and Br(t) All are constant matrix, r (t) is the mode of the system, represents the random switching signal of the system, and is assembled in the setThe internal value, r (t), is a piecewise constant function, shown as +.>t k For the time of the kth system jump, i.e. the time of the kth jump, +.>Is residence time, and->Residence time->The residence time is dependent on the mode for a fixed time, as shown in the following formula (2):
i.e. for systems of the same modality, the residence times are the same, the minimum and maximum values of the residence times of the systems are τ respectively min and τmax ，u δ(t) Delta (t) is the mode of the dispatch controller and is also the switching signal of the dispatch controller, and is used for the input vector of the systemTaking an internal value;
s2, designing a scheduling controller Γ according to the system established in the step S1 δ(t) The following formula (3) shows:
wherein ,Kδ(t) In order to determine the control gain of the device,for fixed modality dependent residence timeBetween (I) and (II)>Set to the total execution time of all schedule controllers.
Further, according to the correlation of the total execution time of all the schedule controllers and the residence time of the system, there is one maximum label of the schedule controller at any interval, i.e., the time interval between systems, which satisfies the following formula (4):
wherein ,representing the execution time of the j-th dispatch controller in the control mode r (t), the j-th dispatch controller is provided with a control mode r (t)>The maximum label of the scheduling controller in the residence time is taken as a value in M; that is, at [ t ] k ,t k+1 ) From the scheduling controller Γ during system operation time period of (1) 1 Executing until the schedule controller +.>And dispatch controller->Cannot be performed. In one period of residence time, the total execution time of the scheduling controller is smaller than or equal to the residence time of the system, and once the residence time of the corresponding system is exceeded, the scheduling controller cannot stop in time, so that the execution of the next period of system and the scheduling controller is affected.
Further, the system is at [ t ] k ,t k+1 ) The running time is controlled by a plurality of scheduling controllers in a time period, and each scheduling controller is sequentially executed according to the sequence, namely the jth scheduling controller Γ j Cannot be performed until Γ j-1 Complete execution of task and first dispatch controller Γ 1 Execution time WCET of (4) 1 (worst case execution time) is mandatory, satisfies 0 < WCET 1 ≤τ min The execution times of the remaining sequentially executing schedule controllers are random.
Further, for a system in the same mode, the residence time is the same, the residence time is divided into a plurality of time slices deltat, and each time slice deltat is the same; similarly, the execution time of each scheduling controller is also divided into a plurality of time slices delta T, and the sum of the total execution time slices of all scheduling controllers isThe method comprises the following steps:total execution time of all scheduling controllers +.>The following formula (5):
during the system operation time period [ t ] k ,t k+1 ) In, total execution time of all scheduling controllersAnd residence time->The relationship of (2) is divided into two types: first, the total execution time of all scheduling controllers +.>Less than the residence time of the system->In this case, the system is open-loop, the running time of the open-loop system is +.>The other is the total execution time of all the dispatch controllersEqual to the residence time of the system->The system will not open loop at this point.
Further, during the system operation time period [0, t ], the random state transition matrix of the system is phi (t, 0). For the system, when k is greater than or equal to 0, a random state transition matrix is given, as shown in the following formula (6):
wherein ,Φ(tk ,t k-1 ) For a system run time period t k-1 ,t k ) The random state transition matrix of the internal system, according to equation (6), can be developed as shown in equation (7) below:
if r (t) k )＝q≠r(t k-1 ) By matrix exponential norms and parametersThe scaling relationship is as follows:
wherein ,representing the time period of operation of the system [0, t ] k ) In the system, the j-th scheduling controller controls the total number of times of execution under the system with the mode of i; />Representing the time period of operation of the system [0, t ] k ) In the system, the j-th scheduling controller performs accumulated execution time under the control mode of i system; based on the definition of the index almost certainly stable, the formula (8) is converted into the following formula (9):
wherein the scalar eta > 0 is the stability margin, and />Is the corresponding parameter of the open loop system mode i, and /> wherein ,
when the expression (9) is established, the stability of the system can be ensured.
Further, when all scheduling controllers total execution timeEqual to the residence time of the system->When this is done, the formula (9) is converted into the following formula (11):
when (when)When the expression (11) is satisfied, the system can be kept stable.
Further, the scheduling controller is designed by the following processing means, and LMI (linearmatrix inequalities) can be obtained according to the quotation:
presence matrixScalar->Is a numerical value less than 0, and the positive symmetric array ++can be obtained by solving equation (12)>Corresponding parameter value-> And controller gain K [j] . Compared with the traditional stable controller, the design mode of the scheduling controller can better utilize the controller and balance the performance requirement and resource constraint of the system.
Further, when the system in which no jump occurs replaces the random system, the system at this time is shown in the following formula (23):
(a) When the residence time of the system without jump is tau, and tau is a fixed value, the sum of the total execution time segments of all the dispatch controllers is q max Total execution time τ of all schedule controllers c ＝q max Run time τ of DeltaT, open loop System o ＝τ-τ c If the time relation is satisfied: τ c And (t) and still obtaining the condition for stabilizing the system.
Further, (b) when the system's residence time without hopping is time-varying τ k At the time, residence time constraint: τ min ≤τ k ≤τ max The sum of the total execution time segments of the scheduling controller is constrained: wherein ,/>The sum of the total execution time segments of all schedule controllers is in the form of +.>Andwhen the total execution time of all schedule controllers +.>Less than or equal to tau k Conditions that stabilize the system can still be obtained.
Compared with the prior art, the invention has the following beneficial effects:
(1) Aiming at the continuous time jump linear system, the design method of the invention can ensure the stability of the system for the execution condition of the scheduling controllers in a period of residence time, whether the total execution time of all the scheduling controllers is less than the situation when the residence time is open-loop or the total execution time of all the scheduling controllers is equal to the residence time;
(2) Aiming at the helicopter system, the invention provides a condition of considering a resolvable form of residence time and random scheduling probability to ensure the stability of the system by designing a scheduling controller based on a method of a random state transition matrix of the system, and the designed scheduling controller obtains a new controller form based on any time algorithm, thereby having more applicability;
(3) The invention fully considers the situation that the fixed mode of the helicopter system depends on the residence time, and further extends to the situation that the residence time of the system without jump is a constant value and the residence time is time-varying, and the stability of the system can be ensured by adopting the design method provided by the invention. The design method can be applied to a vertical lifting helicopter system, and conditions for stabilizing the system are established to obtain a corresponding dispatching controller.
Drawings
FIG. 1 is a block diagram of a dispatch controller for a helicopter of the invention based on an arbitrary time algorithm;
fig. 2 is a flow chart of the system setup of the present invention.
Detailed Description
The following describes embodiments of the present invention in detail with reference to the accompanying drawings, and the embodiments and specific operation procedures are given by the embodiments of the present invention under the premise of the technical solution of the present invention, but the scope of protection of the present invention is not limited to the following embodiments.
Referring to fig. 1-2, for the stability problem of continuous time hopping linear systems with a scheduling controller based on arbitrary time algorithms, based on the idea of arbitrary time algorithms, the invention considers the modeling of the scheduling controller for fixed modality dependent dwell time cases, mainly in two cases: the system residence time is equal to the total execution time of the scheduling controller, and the system residence time is greater than the total execution time of the scheduling controller, to establish the scheduling controller u with the switching signal delta (t) based on any time algorithm δ(t) Thereby solving the stability problem of the corresponding system.
First, a random hopping system is established as shown in the following formula (1):
in formula (1), matrix A r(t) and Br(t) All are constant matrix, r (t) is the mode of the system, and represents a random switching signal, and is in setTaking an internal value; r (t) is a piecewise constant function, shown as +.>t k I.e. the moment of the kth transition, +.>Is the residence time of the system, and +.>The residence time is dependent on the mode for a fixed time, as shown in the following formula (2):
that is, for systems of the same modality, the residence time is the same, the minimum value of the system residence time is τ min And a maximum value of tau max ，u δ(t) Delta (t) is the controller mode, which is the input vector of the system, and also the switching signal, inAnd (5) taking an internal value.
Then, according to the system established above, the random scheduling controller Γ is designed based on an arbitrary time scheduling algorithm δ(t) The following formula (3) shows:
wherein ,Kδ(t) For a determined control gain, delta (t) is the switching signal of the dispatch controller,set to the total execution time of all schedule controllers.
Depending on the correlation of the total execution time of all scheduling controllers with the residence time of the system, there is one maximum label of the scheduling controller at any interval, i.e. the time interval between systems, which satisfies the following formula (4):
wherein ,representing the execution time of the j-th dispatch controller in the control mode r (t), the j-th dispatch controller is provided with a control mode r (t)>The maximum label of the scheduling controller in the residence time is taken as a value in M; that is, at [ t ] k ,t k+1 ) From the scheduling controller Γ during system operation time period of (1) 1 Executing until the schedule controller +.>And dispatch controller->Cannot be performed. In one period of residence time, the total execution time of the scheduling controller is smaller than or equal to the residence time of the system, and once the residence time of the corresponding system is exceeded, the scheduling controller cannot stop in time, so that the execution of the next period of system and the scheduling controller is affected.
The above-mentioned systemIs unified at [ t ] k ,t k+1 ) The operation is carried out in the time period,dependent residence time for a fixed modality; due to the fact thatThere is no pre-requirement for the run time period, in which case the individual schedule controllers are executed sequentially in a sequential order, i.e. the jth schedule controller Γ j Cannot be performed until Γ j-1 The dispatch controller completes the execution task and the first controller Γ 1 Is the simplest, its execution time WCET 1 (worst case execution time) is mandatory. In order to ensure that each system is controlled to execute by at least one scheduling controller, 0 < WCET is required 1 ≤τ min Without loss of generality, the execution time of the scheduling controller allocated by the scheduler to the residence time of each system is random, and the residence time of the system can be divided into a plurality of time slices deltat which are integer multiples, and each time slice deltat is identical. Similarly, the execution time of each scheduling controller is also divided into a plurality of time slices DeltaT, and the sum of the total execution time slices of all the scheduling controllers is +.>The method comprises the following steps: />Total execution time of schedule controller->The following formula (5):
during the system operation time period [ t ] k ,t k+1 ) In, total execution time of all scheduling controllersAnd residence time->The relationship of (2) is divided into two types: first, total execution time of all scheduling controllers +.>Less than system residence time->At this time, the system will be open-loop, the running time of the open-loop system is +.>The other is total execution time of all scheduling controllers +.>Equal to system residence time->The system will not open loop at this point.
When the random state transition matrix of the system is phi (t, 0) in the system operation time period [0, t ], the random state transition matrix is given when k is more than or equal to 0 for the system, and the following formula (6) is shown:
wherein ,Φ(tk ,t k-1 ) For a system run time period t k-1 ,t k ) The random state transition matrix of the internal system, according to equation (6), can be developed as shown in equation (7) below:
if r (t) k )＝q≠r(t k-1 ) By matrix exponential norms and parametersThe scaling relationship is as follows:
wherein ,representing the time period of operation of the system [0, t ] k ) In the system, the j-th scheduling controller controls the total number of times of execution under the system with the mode of i; />Representing the time period of operation of the system [0, t ] k ) In the system, the j-th scheduling controller performs accumulated execution time under the control mode of i system; based on the definition of the index as almost affirmative, equation (8) can be converted into the following equation (9):
wherein the scalar eta > 0 is the stability margin, and />Is the corresponding parameter of the open loop system mode i, and /> wherein ,
when the expression (9) is established, the stability of the system can be ensured.
The design of the dispatch controller is based on any time algorithm, because and />Must be within the interval t k The limited number of times and the limited time in t), it follows that:
when (when)In interval [0, t k ) In, the dispatch controller Γ 1 And a scheduling controller Γ j Is executed in a system of the same modality, the number of executions is the same, wherein +.>According to this, equation (8) can become
wherein ,meaning when +.>Maximum execution scheduling controller is Γ γ At interval [0, t k ) System with internal mode i, scheduling controller Γ j Is performed a total number of times. />Then the controller total execution time is scheduled under the same conditions. The relationship between the execution time of the schedule controller and the execution number of times of the schedule controller is as follows:
then it is possible to obtain:
thus, the formula (15) can be sorted to obtain the formula (9).
(1) When the total execution time of all the dispatch controllersEqual to the residence time of the system->In this case, the above formula (9) is converted into the following formula (11):
the expression (11) is true, meaning whenThe system remains stable when it is used.
The scheduling controller is designed by the following processing means to ensure the stability of the system. According to the quotients, LMI (linear matrix inequalities) can be obtained:
presence matrixScalar->Is a numerical value less than 0, and the positive symmetric array ++is obtained by solving the above equation (12)>Corresponding parameter value-> And controller gain K [j] . Such a controller approach may better utilize the controller than a traditional approach to stabilizing the controller, balancing system performance requirements and resource constraints.
(2) When the total execution time of all the dispatch controllersLess than the residence time of the system->When there is an open loop system, the open loop system is represented by the following formula (21):
wherein , and />Is a parameter corresponding to the open loop system mode i; LMI can be obtained by quotients:
wherein ,is a given scalar, whereby the symmetric matrix P is positively defined i Solving can be achieved. The scaling theory of the index matrix norms is as follows: />Wherein the parameters->Obtained by the above formula (12).
In addition, the present invention also researches the case of a system in which no hopping occurs, in addition to the above-described system for random hopping, the system is represented by the following formula (23):
(a) When the system residence time is τ, τ is a fixed value, then the total execution of all the schedule controllersThe sum of the time slices is q max Total execution time τ of all schedule controllers c ＝q max Run time τ of DeltaT, open loop System o ＝τ-τ c If the time relation is satisfied: τ c And tau is less than or equal to tau, and stable conditions of the system can be obtained through the design method.
(b) When the residence time of the system without jump is time-varying tau k At the time, residence time constraint: τ min ≤τ k ≤τ max The sum of the total execution time segments of the scheduling controller is constrained: wherein ,/>The sum of the total execution time segments of all schedule controllers is in the form of +.>Andwhen the total execution time of all schedule controllers +.>Less than or equal to tau k The design method provided by the invention can still obtain the condition for stabilizing the system.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.

Claims (8)

1. A helicopter dispatch controller design method based on any time algorithm is characterized by comprising the following steps:
s1, establishing a random jump system, wherein the system is shown in the following formula (1):
wherein the system is at [ t ] k ，t k+1 ) Run in time period, matrix A r(t) and Br(t) All are constant matrix, r (t) is the mode of the system, represents the random switching signal of the system, and is assembled in the setThe internal value, r (t), is a piecewise constant function, shown as +.>t k For the time of the kth system jump, i.e. the time of the kth jump, +.>Is residence time, and->Residence time->The residence time is dependent on the mode for a fixed time, as shown in the following formula (2):
i.e. for systems of the same modality, the residence times are the same, the minimum and maximum values of the residence times of the systems are τ respectively min and τmax ，u δ(t) Delta (t) is the mode of the dispatch controller and is also the switching signal of the controller, and is used for the system
Taking an internal value;
s2, according to the stepsThe system established in step S1 designs a scheduling controller Γ δ(t) The following formula (3) shows:
wherein ,Kδ(t) For a determined control gain, delta (t) is the switching signal of the dispatch controller,for a fixed modality dependent residence time, +.>Setting the total execution time of all the dispatching controllers;
for a system in the same mode, the residence time is the same, the residence time is divided into a plurality of time slices delta T, and each time slice delta T is the same; similarly, the execution time of each scheduling controller is also divided into a plurality of time slices delta T, and the sum of the total execution time slices of all scheduling controllers isThe method comprises the following steps: />Total execution time of all scheduling controllers +.>The following formula (5):
the system is in time period t k ,t k+1 ) Internal run, total execution time of all schedule controllersAnd residence time->The relationship of (2) is divided into two types: first, the total execution time of all scheduling controllers +.>Less than the residence time of the system->In this case, the system is open-loop, the running time of the open-loop system is +.>The other is the total execution time of all scheduling controllers +.>Equal to the residence time of the system->The system will not open loop at this point.
2. A method of designing a dispatch controller for a helicopter based on an arbitrary time algorithm according to claim 1 wherein, based on the correlation of the total execution time of all dispatch controllers with the residence time of the system, at arbitrary intervals, i.e. the time intervals between systems, there is a maximum label for a dispatch controller which satisfies the following equation (4):
wherein ,indicating time->Modality of time->Representing the execution time of the j-th dispatch controller in the control mode r (t), the j-th dispatch controller is provided with a control mode r (t)>The maximum label of the dispatch controller for the dwell time, which takes the value in M, i.e. at [ t ] k ,t k+1 ) From the scheduling controller Γ during system operation time period of (1) 1 Executing until the schedule controller +.>And τ i The residence time is dependent for the i-modality.
3. A method of designing a dispatch controller for a helicopter based on an arbitrary time algorithm as defined in claim 1 wherein said system is set at [ t ] k ，t k+1 ) The operation time in the time period is controlled by a plurality of scheduling controllers, and each scheduling controller is sequentially executed according to the sequence, namely the jth controller Γ j Cannot be performed until Γ j-1 The controller completes the execution task and the first dispatch controller Γ 1 Execution time WCET of (4) 1 Is mandatory to satisfy 0<WCET 1 ≤τ min The execution times of the remaining sequentially executing schedule controllers are random.
4. The method for designing a scheduling controller for a helicopter according to any time algorithm according to claim 1, wherein in said system operation time period [0, t ], the random state transition matrix of the system is Φ (t, 0), and for the system, when k is not less than 0, the random state transition matrix is given, as shown in the following formula (6):
ln||Φ(t，0)||＝ln||Φ(t，t k )Φ(t k ，t k-1 )…Φ(t 1 ，0)||≤ln||Φ(t，t k )||+ln||Φ(t k ，t k-1 )||+…+ln||Φ(t 1 ，0)||(6)
wherein ,Φ(tk ，t k-1 ) For a system run time period t k-1 ，t k ) The random state transition matrix of the internal system, according to equation (6), can be developed as shown in equation (7) below:
if r (t) k )＝q≠r(t k-1 ) By matrix exponential norms and parameters The scaling relationship is as follows:
wherein ,representing the time period of operation of the system [0, t ] k ) In the system, the j-th scheduling controller controls the total number of times of execution under the system with the mode of i; />Representing the time period of operation of the system [0, t ] k ) In the system, the j-th scheduling controller performs accumulated execution time under the control mode of i system; based on the definition of the index as almost affirmative, equation (8) can be converted into the following equation (9):
wherein, the markQuantity eta>0 is the stability margin and, and />Is the corresponding parameter of the open loop system mode i, and /> wherein ,
when the expression (9) is established, the stability of the system can be ensured.
5. The method for designing a schedule controller for a helicopter based on an arbitrary time algorithm according to claim 4 wherein when the total execution time of all schedule controllers isEqual to the residence time of the system->When this is done, the formula (9) is converted into the following formula (11):
when (when)If equation (11) is true, the system remains stable.
6. The method for designing a dispatch controller for a helicopter according to any time algorithm of claim 5, wherein the dispatch controller is designed by the following processing means, and the LMI is obtained according to the quotients:
presence matrix P i [j] Scalar r i [j] For a given value less than 0, a positive symmetric array P is obtained by solving equation (12) i [j] Corresponding to the parameter value And controller gain K [j] 。
7. The method for designing a scheduling controller for a helicopter according to claim 1, wherein when a system in which no jump occurs replaces a random system, the system at this time is represented by the following formula (23):
(a) When the residence time of the system without jump is tau, and tau is a fixed value, the sum of the total execution time segments allocated to all the dispatch controllers is q max Total execution time τ of all schedule controllers c ＝q max Delta T, run time of open loop system τ o ＝τ-τ c If the time relation is satisfied: τ c And (t) and still obtaining the condition for stabilizing the system.
8. The method for designing a dispatch controller for a helicopter according to claim 7 wherein (b) when no jump is occurring system residencyTime is time-varying tau k At the time, residence time constraint: τ min ≤τ k ≤τ max The sum of the total execution time segments of the scheduling controller is constrained: wherein ,/>For the sum of the total execution time segments of all the dispatch controllers, in the form of
and />When the total execution time of all schedule controllers +.>Less than or equal to tau k Conditions that stabilize the system can still be obtained.
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Citations (3)

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