CN116819976A - Predetermined time fault-tolerant control design method for control input constrained dynamics system - Google Patents

Predetermined time fault-tolerant control design method for control input constrained dynamics system Download PDF

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CN116819976A
CN116819976A CN202311112547.6A CN202311112547A CN116819976A CN 116819976 A CN116819976 A CN 116819976A CN 202311112547 A CN202311112547 A CN 202311112547A CN 116819976 A CN116819976 A CN 116819976A
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function
formula
actuator
control
representing
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CN116819976B (en
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吕茂隆
董泽洪
沈堤
苟新禹
万路军
余付平
毛东辉
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Air Force Engineering University of PLA
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    • Y02P90/02Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

There is provided a predetermined time fault tolerant control design method for controlling an input constrained dynamics system, comprising the steps of: (1) Modeling a controlled object and rewriting its kinetic equation intoForm of (c); (2) Designing a predetermined time performance function parameter according to the desired control performance; (3) The controller parameters and the adaptive parameters are designed based on a priori knowledge of the controlled system. The invention can simultaneously compensate the influence of the saturation nonlinearity of the actuator and the actuator fault on the control system in the control system; expanding the fault type of the actuator which can be compensated by the controller to an infinite frequency jump fault type through a projection operator; fault-tolerant control of a predetermined time, preset performance of the control system is achieved by introducing a predetermined time performance function.

Description

Predetermined time fault-tolerant control design method for control input constrained dynamics system
Technical Field
The invention relates to a flight control technology, in particular to a predetermined time fault-tolerant control design method for a control input constrained dynamic system.
Background
In an actual control system, an actuator bears a key device for receiving a controller instruction and realizing a desired action. When the actuator fails, the control performance of the system is degraded, and even if the actuator fails, the system is crashed directly. This would directly cause immeasurable impact on some critical safety systems (e.g., aircraft, spacecraft, submarines, etc.). Therefore, the safety and reliability of the control system in the event of an actuator failure must be improved.
Regarding actuator faults, currently existing fault-tolerant method related patents (fault-tolerant control system with uncertainty system of actuator faults (CN 108646712B), mechanical arm actuator fault-tolerant control system based on double-layer structure and method thereof (CN 107121977B), etc.) all consider only a limited number of faults, but not an infinite number of jump types of actuator faults (the fault mode of an actuator changes from one fault mode to another fault mode an infinite number of times) that may exist. Meanwhile, almost all control systems (e.g., servo systems, flight control systems, power systems, etc.) are inevitably limited by hardware (e.g., amplitude limitations). However, no constraint on control inputs is considered in the current fault-tolerant control methods for unlimited number of transition type faults (W.Wang, and C.Wen, adaptive compensation for infinite number of actuator failures or faults, autoica, 47 (2011) 2197-2210; G.Lai, Z.Liu, C.L.P. Chen, Y.Zhang and X.Chen, adaptive compensation for infinite number of time-varying actuator failures in Fuzzy tracking control of uncertain nonlinear Systems, IEEE Trans. Fuzzy Systems, 26 (2018) 474-486).
In addition, transient performance (such as overshoot, convergence speed, convergence time, etc.) can also have a significant impact on the control system, and therefore, it is also desirable to constrain the transient performance of the fault tolerant control system.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a predetermined time fault-tolerant control design method for controlling an input constrained dynamic system, which specifically comprises the following steps:
step 1: dynamic system with limited control inputs as follows
(1)
in the formula ,indicating the status of the system->For real number set->The upper points represent the differentiation of the system state; />Representing time; />Is a known nonlinear function of the system; />For known system parameters->Is->The identity of the individual actuator(s),nrepresenting the number of actuators +.>;/>Represent the firstiThe amplitude of each actuatorInput in a limited situation; />Representing unknown bounded external disturbances;
step 2: consider the following actuator failure model
(2)
(3)
in the formula ,represent the firstiThe output of the actuators in the case of limited amplitude; />Is an unknown fault moment; />For the moment of occurrence of the next unknown fault, < +.>Represent the firstiThe individual actuators are in the time interval->An internal efficiency coefficient; />Represent the firstiThe individual actuators are in the time interval->Unknown stuck position within;
the fault models (2) and (3) contain two types of faults
And->,/>The actuator part fails;
and->The actuator is completely disabled and will no longer be controlled by the input +.>Is a function of (1);
the saturation nonlinearity of the actuator is expressed as
(4)
in the formula ,is a control law to be designed; />For control input +.>Consider the output of the actuator under the saturation nonlinear condition under the effect; />And->Respectively the firstiControl input->Upper and lower limit limits of (2); />Is a saturation function;
introducing a smoothA kind of electronic deviceFunction to replace saturation function->The saturation nonlinearity is expressed as
(5)
wherein ,
in the formula , representing control law->Under the action of +.>An output of the function; />Representing a maximum amplitude limit for the ith actuator; />Representing a minimum amplitude limit for the ith actuator; />To adopt->Function to replace saturation function->The resulting bounded approximation error, expressed as
Based on the mean theorem, equation (5) is expressed as
(6)
in the formula ,representing the equivalent control coefficient;
combining (2) and (6), the mathematical model of actuator failure and input saturation is expressed as
(7)
in the formula ,represent the firstiControl coefficients of the actuators under the nonlinear effects of faults and saturation;is a compound uncertainty term;
step 3: combining a kinetic system (1) with an actuator model (7) with
(8)
Defining tracking errors of a system
(9)
in the formula , representation->Is a reference signal of (a);
step 4: a new predetermined time performance function is designed as follows
(10)
in the formula ,、/>for the controller parameters to be designed, < >>Representing the initial value of the performance function, +.>Is the time of the predetermined convergence;
introducing a new errorAnd error transfer function->The method comprises the steps of carrying out a first treatment on the surface of the The system tracking error is expressed as
(11)
According to the nature of the error transfer function, there areTherefore, the tracking error of the system can be +.>Inner convergence to a predetermined interval->
Leads to two sides of (11) and has
(12)
in the formula ,is a transformed state function, +.>Is a transformed control coefficient function;
step 5: to compensate for actuator failure and saturation nonlinearity, the time interval is setThe following parameters are defined internally
,/>, />
in the formula , and 、/>Representing two newly defined state variables; />Representation->Reciprocal of->Is the infinitesimal of the function,/->Is the upper bound of the function;
definition of the definition, in the formula ,/>Representation->Is a function of the estimated value of (2); />Representation->In the time interval +.>Estimation error in, define->, in the formula ,/>Representation->Is a function of the estimated value of (2); />Is indicated as +.>Inner->Is determined by the estimation error of (a);
the following virtual control rate is designed
(13)
in the formula ,、/>are all controller parameters to be designed; />Is reference signal->Is the first derivative of (a);
design of actual control law
(14)
in the formula ,for the parameters to be designed, +.>Is a sign function;
the design parameter self-adaption law is as follows:
(15)
(16)
in the formula ,for the parameters to be designed, brackets->In (a) is multiplication of a plurality of states,/->、/>Are projection operators, wherein ∈>Expressed as:
wherein ,representation->Maximum value of>、/>Respectively indicate->Maximum and minimum of (2).
The method can realize the fault-tolerant control of the preset time and the preset performance of the control system under the condition of considering the control input limit and the actuator fault. The novel control method designed by the invention not only ensures the fault tolerance performance of the control system under the condition that the limited times of jump faults occur in the actuator, but also ensures the control performance of the actuator under the condition that the unlimited times of jump faults occur. The method of the invention comprises the following steps: establishing a dynamics model of a control system; establishing a mathematical model with unified actuator faults and input saturated phases; establishing a control system model considering the fault and input limit of the actuator; designing a new predetermined time performance function; the projection principle is adopted to design the self-adaptive law of the control system and the actual control law of the control system. Compared with the prior method, the method reduces the limit on the fault type, has wider application range and lower calculation amount.
Compared with the prior art, the invention has the advantages that:
(1) Introducing a smoothFunction to replace saturation function->And uniformly modeling the saturation nonlinearity of the actuator and the actuator fault as formula (7), so that the influence of the saturation nonlinearity of the actuator and the actuator fault on the control system can be compensated in the control system.
(2) And expanding the fault type of the actuator which can be compensated by the controller to the infinite frequency jump fault type through a projection operator.
(3) Fault-tolerant control of a predetermined time, preset performance of the control system is achieved by introducing a predetermined time performance function.
Drawings
FIG. 1 illustrates a control input response process with asymmetric constraints;
FIG. 2 shows performance index functions for asymmetric constraints.
Detailed Description
The present invention is described in detail below with reference to the accompanying drawings.
The invention provides a predetermined time fault-tolerant control design method for a control input constrained dynamics system, which specifically comprises the following steps.
Step 1: dynamic system with limited control inputs as follows
(1)
in the formula ,indicating the status of the system->For real number set->The upper dot represents the differentiation of the system state, the same as below; />Representing time; />Is a known nonlinear function of the system; />For known system parameters->Is->The identity of the individual actuator(s),nrepresenting the number of actuators +.>。;/>Representing unknown bounded external disturbances; />Represent the firstiThe input of the actuators in the case of limited amplitude.
Step 2: consider the following actuator failure model
(2)
(3)
in the formula ,represent the firstiThe output of the actuators in the case of limited amplitude; />Is an unknown fault moment;represent the firstiThe individual actuators are in the time interval->An internal efficiency coefficient; />Represent the firstiThe individual actuators are in the time interval->Unknown stuck position within.
Two types of common faults are contained in fault models (2) and (3)
And->,/>The actuator portion fails.
And->The actuator is completely disabled and will no longer be controlled by the input +.>Is a function of (a) and (b).
The saturation nonlinearity of the actuator can be expressed as
(4)
in the formula ,is a control law to be designed; />For control input +.>Consider the output of the actuator under the saturation nonlinear condition under the effect; />And->Respectively the firstiControl input->Upper and lower limit limits of (2).
To improve the performance, a smooth one is introducedFunction to replace saturation function->The saturation nonlinearity can be expressed as
(5)
wherein ,
in the formula , representing control law->Under the action of +.>An output of the function; />Representing a maximum amplitude limit for the ith actuator; />Representing a minimum amplitude limit for the ith actuator; />To adopt->Function to replace saturation function->The resulting bounded approximation error can be expressed as
Based on the mean theorem, (5) can be expressed as
(6)
in the formula ,representing the equivalent control coefficient.
Combining (2) and (6), the mathematical model of actuator failure and input saturation can be expressed as
(7)
in the formula ,represent the firstiControl coefficients of the actuators under the nonlinear effects of faults and saturation;is a compound uncertainty item.
Step 3: combining a kinetic system (1) with an actuator model (7) with
(8)
Defining tracking errors of a system
(9)
in the formula , representation->Is included in the reference signal of (a).
Step 4: a new predetermined time performance function is designed as follows
(10)
in the formula ,、/>for the controller parameters to be designed, < >>Representing the initial value of the performance function, +.>Is the time of the predetermined convergence.
Introducing a new errorAnd error transfer function->. The system tracking error can be expressed as
(11)
According to the nature of the error transfer function, there areTherefore, the tracking error of the system can be +.>Inner convergence to a predetermined interval->
Leads to two sides of (11) and has
(12)
in the formula ,is a transformed state function, +.>Is a function of the transformed control coefficients.
Step 5: to compensate for actuator failure and saturation nonlinearity, the time interval is setThe following parameters are defined internally
,/>, />
in the formula , and 、/>Representing two newly defined state variables; />Representation->Reciprocal of->Is the infinitesimal of the function,/->Is the upper bound of the function.
Definition of the definition, in the formula ,/>Representation->Is a function of the estimated value of (2); />Representation->In the time interval +.>Estimation error in, define->, in the formula ,/>Representation->Is a function of the estimated value of (2); />Is indicated as +.>Inner->Is used for the estimation error of (a).
The following virtual control rate is designed
(13)
in the formula ,,/>are all controller parameters to be designed. />Is reference signal->Is a first derivative of (a).
Design of actual control law
(14)
in the formula ,for the parameters to be designed, +.>Is a sign function.
The design parameter self-adaption law is as follows:
(15)
(16)
in the formula ,for the parameters to be designed, brackets->In (a) is multiplication of a plurality of states,/->For projection operators, this can be expressed as:
wherein ,representation->Is a maximum value of (a).
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
According to the specific implementation steps of the technical scheme of the invention, the following embodiment is provided.
Step 1: gives the following general second order dynamics system
(17)
in the formula ,as a known system nonlinear function +.>Indicating the state of the system and,representing an unknown bounded external disturbance. Control inputuIs restrained->
Step 2: a new predetermined time performance function is designed as follows
(18)
in the formula ,,/>,/>
step 3: to compensate for actuator failure and saturation nonlinearity, the time interval is setThe following parameters are defined internally
,/>, />
Definition of the definitionRepresentation->In the time interval +.>Estimation error in, define->Representation ofIn the time interval +.>An estimation error in the model.
The following virtual control rate is designed
(19)
in the formula ,,/>the method comprises the steps of setting parameters of a controller to be designed; />Representing reference instruction->Is a first derivative of (a).
Design of actual control law
(14)
in the formula ,is a parameter to be designed.
The design parameter self-adaption law is as follows:
(15)
(16)
in the formula ,for the parameters to be designed, +.>Representing the projection operator.
FIG. 1 shows the control input response process for asymmetric constraints. FIG. 2 shows performance index functions for asymmetric constraints. As can be seen from simulation results, the control algorithm designed by the invention can realize fault-tolerant control of the control system for a preset time and a preset performance under the condition of controlling the input-limited actuator and the fault of the actuator.

Claims (1)

1. A method for designing a fault tolerant control for a predetermined time for controlling an input constrained dynamics system, comprising the steps of:
step 1: dynamic system with limited control inputs as follows
(1)
in the formula ,indicating the status of the system->For real number set->The upper points represent the differentiation of the system state; />Representing time;is a known nonlinear function of the system; />For known system parameters->Is->The identity of the individual actuator(s),nrepresenting the number of actuators +.>;/>Represent the firstiInput of the actuators in the case of limited amplitude; />Representing unknown bounded external disturbances;
step 2: consider the following actuator failure model
(2)
(3)
in the formula ,represent the firstiThe output of the actuators in the case of limited amplitude; />Is an unknown fault moment; />For the moment of occurrence of the next unknown fault, < +.>Represent the firstiThe individual actuators are in the time interval->An internal efficiency coefficient;represent the firstiThe individual actuators are in the time interval->Unknown stuck position within;
the fault models (2) and (3) contain two types of faults
And->,/>The actuator part fails;
and->The actuator is completely disabled and will no longer be controlled by the input +.>Is a function of (1);
the saturation nonlinearity of the actuator is expressed as
(4)
in the formula ,is a control law to be designed; />For control input +.>Consider the output of the actuator under the saturation nonlinear condition under the effect; />And->Respectively the firstiControl input->Upper and lower limit limits of (2); />Is a saturation function;
introducing a smoothFunction to replace saturation function->The saturation nonlinearity is expressed as
(5)
wherein ,
in the formula , representing control law->Under the action of +.>An output of the function; />Representing a maximum amplitude limit for the ith actuator; />Representing a minimum amplitude limit for the ith actuator; />To adopt->Function to replace saturation functionThe resulting bounded approximation error, expressed as
Based on the mean theorem, equation (5) is expressed as
(6)
in the formula ,representing the equivalent control coefficient;
combining (2) and (6), the mathematical model of actuator failure and input saturation is expressed as
(7)
in the formula ,represent the firstiControl coefficients of the actuators under the nonlinear effects of faults and saturation;is a compound uncertainty term;
step 3: combining a kinetic system (1) with an actuator model (7) with
(8)
Defining tracking errors of a system
(9)
in the formula , representation->Is a reference signal of (a);
step 4: a new predetermined time performance function is designed as follows
(10)
in the formula ,、/>for the controller parameters to be designed, < >>Representing the initial value of the performance function, +.>Is the time of the predetermined convergence;
introducing a new errorAnd error transfer function->The method comprises the steps of carrying out a first treatment on the surface of the The system tracking error is expressed as
(11)
According to the nature of the error transfer function, there areTherefore, the tracking error of the system can be +.>Inner convergence to a predetermined interval->
Leads to two sides of (11) and has
(12)
in the formula ,is a transformed state function, +.>Is a transformed control coefficient function;
step 5: in the time intervalThe following parameters are defined internally
,/>, />
in the formula , and 、/>Representing two newly defined state variables; />Representation->Reciprocal of->Is the infinitesimal of the function,/->Is the upper bound of the function;
definition of the definition, in the formula ,/>Representation->Is a function of the estimated value of (2); />Representation->In the time interval +.>Estimation error in, define->, in the formula ,/>Representation->Is a function of the estimated value of (2); />Is indicated as +.>Inner->Is determined by the estimation error of (a);
virtual controlRate of production
(13)
in the formula ,、/>are all controller parameters to be designed; />Is reference signal->Is the first derivative of (a);
actual control law
(14)
in the formula ,for the parameters to be designed, +.>Is a sign function;
the parameter self-adaption law is as follows:
(15)
(16)
in the formula ,for the parameters to be designed, brackets->In (a) is multiplication of a plurality of states,/->、/>Are projection operators, wherein ∈>Expressed as:
wherein ,representation->Maximum value of>、/>Respectively indicate->Maximum and minimum of (2)Values.
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