CN110658724B - Self-adaptive fuzzy fault-tolerant control method for nonlinear system - Google Patents
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Abstract
The invention discloses a self-adaptive fuzzy fault-tolerant control method for a nonlinear system. And secondly, the fuzzy comprehensive observer comprises a fuzzy state observer, a fault failure factor observer and a disturbance observer. The adaptive sliding mode controller then uses the observed information to compensate for the effects of faults and disturbances on the system. In addition, the dual channel event triggering mechanism includes two sets of event triggering conditions, sensor to controller and controller to actuator. Finally, event-triggered based fault tolerant controllers incorporate a controller-to-actuator triggering mechanism, the output of which acts on a nonlinear system. The invention can effectively solve the problem of effective fault-tolerant control performance and track tracking control of a nonlinear system under the conditions of actuator failure and external disturbance.
Description
Technical Field
The invention belongs to the field of fault-tolerant control of a nonlinear system with actuator faults and external disturbance, and particularly relates to a nonlinear system subjected to actuator faults and external disturbance, a fuzzy synthetic observer, an adaptive sliding mode controller, a dual-channel event trigger mechanism and an event trigger-based controller, which are collectively called a nonlinear system adaptive fuzzy fault-tolerant control method.
Background
With the rapid development of the industry, more and more nonlinear units are included in modern industrial systems to achieve richer system performance, and thus, maintaining the reliability of the system is important for the nonlinear systems to complete the given work task. However, as the number of system components increases, the dynamics of unknown coupling factors and unknown system nonlinearities that occur when the system is modeled also increases. On the other hand, the nonlinear system is always difficult to avoid external interference in working operation, and the stability of the system is inevitably influenced by interference signals. In addition, when the system components work for too long, the system also has the problems of actuator aging, actuator parameter deviation, actuator partial failure and the like, and when a system fault occurs, the control performance of the system is influenced, and even the stability of the system is damaged. Therefore, it is important to study the reliability and fault tolerance control of the nonlinear system to achieve the given goal or maintain acceptable performance index.
At present, the study on the reliability, fault tolerance and stability of a nonlinear system based on a fault-tolerant control framework has relevant documents, such as: in the literature [ "discrete observer-based fault-tolerant adaptive control system for nonlinear parameter," (IEEE Transactions on Industrial Electronics, to be public, DOI:10.1109/tie.2018.2889634,2018.) ], a fault-tolerant control strategy of a nonlinear system under the condition of actuator fault and interference is researched, and an interference observer and a backstepping control method are designed. In the literature [ "Robust Adaptive Sliding Mode Control for Switched network Control Systems With interference and Faults ]" (IEEE Transactions on Industrial information, 201915 (1):193-204.) ], a network nonlinear system With actuator Faults and external interference is researched, and corresponding fault and interference compensation measures are designed for keeping the system stability. However, the above-mentioned literature results assume that the system state is measurable when designing the controller, and that the upper bound of the disturbance is known when designing the disturbance observation. This limits the use of the method to some extent. In recent years, a fault-tolerant control method based on sliding mode control is widely used, and particularly, a method based on a fuzzy logic theory, sliding mode control and observer combination is correspondingly researched. For example, in the document [ "Robust Adaptive Sliding Mode Control for Switched network Control Systems With dimensions and Faults ]" (IEEE Transactions on Industrial information, 201915 (1):193-204.) ], a class of aircraft Systems affected by actuator Faults is researched, the upper bound information of the Faults is approximated by using a fuzzy logic theory, and a controller is designed based on a Sliding Mode Control method so that the system can better realize the track tracking performance.
The above-mentioned literature results take into account the stability or tracking performance of certain non-linear systems. On the one hand, however, the literature assumes that the state of the system is measurable when designing the controller, and that the upper bound of the disturbance is known; on the other hand, relatively few literature has also considered event triggers to reduce system transmission load when designing controllers. It is still a challenge to design a reliable fault-tolerant control method for reducing the information transmission amount of a nonlinear system while maintaining stable control in the nonlinear system.
Disclosure of Invention
The invention aims to overcome the defects of the traditional technology and provide a self-adaptive fuzzy fault-tolerant control method of a nonlinear system, which aims to design a corresponding controller for the nonlinear system when the nonlinear system is influenced by actuator faults and interference, so that the system can stably run and the track tracking capability of the system is kept.
In order to achieve the purpose, the invention provides a self-adaptive fuzzy fault-tolerant control method of a nonlinear system, which is characterized by comprising the nonlinear system subjected to actuator faults and external disturbance, a fuzzy comprehensive observer, a self-adaptive sliding mode controller, a dual-channel event trigger mechanism and a controller based on event trigger;
(1) aiming at the influence of actuator faults and external interference on a nonlinear system, a nonlinear system tracking control model under the influence of the actuator faults and the interference is established;
(2) the fuzzy comprehensive observer comprises a fuzzy state observer, a fault failure factor observer and an interference observer, can realize the estimation of the state, the fault failure information and the interference of the nonlinear system, and does not need the upper bound value of the interference information in the interference information estimation process;
(3) the self-adaptive sliding mode controller is designed by utilizing the observation information to compensate the influence of faults and interference on the system; in the method, two self-adaptive sliding mode surface parameters are introduced, aiming at considering the influence of factors such as faults, interference and the like on the tracking performance;
(4) the dual-channel event trigger mechanism comprises two groups of event trigger conditions from a sensor to a controller and from the controller to an actuator, so that on one hand, fewer output information values are used for observing system variables, on the other hand, the transmission value of system information during control is reduced, and the real-time fault tolerance of the system is improved;
(5) the sliding mode control method based on event triggering combines a triggering mechanism from a controller to an actuator, and the output of the sliding mode control method acts on a nonlinear system. Under the influence of actuator faults, external interference and the like, the fault-tolerant capability of the system is ensured, the transmission load of the system is effectively reduced, and the real-time performance of the system is improved.
The purpose of the invention is realized as follows:
the invention relates to a self-adaptive fuzzy fault-tolerant control method of a nonlinear system, which comprises the nonlinear system subjected to actuator faults and external disturbance, a fuzzy comprehensive observer, a self-adaptive sliding mode controller, a dual-channel event trigger mechanism and a controller based on event trigger. The fault-tolerant control method aims to improve the effective fault-tolerant control capability of a nonlinear system when the nonlinear system is subjected to actuator faults and external disturbance. The specific method comprises the following steps: firstly, a nonlinear system state space model with actuator faults and external interference is established. And secondly, the fuzzy comprehensive observer comprises a fuzzy state observer, a fault failure factor observer and a disturbance observer. The adaptive sliding mode controller then uses the observed information to compensate for the effects of faults and disturbances on the system. In addition, the dual channel event triggering mechanism includes two sets of event triggering conditions, sensor to controller and controller to actuator. Finally, event-triggered based fault tolerant controllers incorporate a controller-to-actuator triggering mechanism, the output of which acts on a nonlinear system. The invention can effectively solve the problem of effective fault-tolerant control performance and track tracking control of a nonlinear system under the conditions of actuator failure and external disturbance.
Drawings
FIG. 1 is a control block diagram of an embodiment of a nonlinear system adaptive fuzzy fault-tolerant control method of the invention.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
The influence of actuator faults and external interference factors on a nonlinear system is considered, wherein the actuator faults consider actuator partial failures, deviation faults and other forms, and a fuzzy logic theory is combined to obtain the comprehensive control model of the nonlinear system. Considering the bias fault and interference of the system as the total interference, assuming the total disturbance xiz(t) satisfies the following condition,
wherein
Z (t) represents a new variable associated with the interference information for an unknown gain.
The fuzzy comprehensive observer comprises a fuzzy state observer, a fault failure factor observer and a disturbance observer, and does not need the upper bound information when observing disturbance. The design results are as follows:
in the formula,
and
is x2i-1(t)，x2i(t)，yi(t)，
And hiIs estimated. x is the number of2i-1(t)，x2i(t)，yi(t)，
And hiSystem state, system output, system nonlinear function, and failure factor, respectively.
The fault failure factor observer is as follows:
Wherein
h1，h2Is two constants.
The disturbance observer is:
wherein, pi (t) is a new variable introduced.
In addition, when the observer is designed, an observation error compensation term delta is introducedm(t), the design precision and the flexibility of the observer are improved, and the result is as follows:
wherein etak＝2(h2-h1)(hn+h2-h1) P positively defines a symmetric matrix.
Which is indicative of an error in the observation,
is composed of
Estimate of, LzIs a design matrix.
In the adaptive sliding mode controller, the design is as follows:
wherein,
to represent
Is estimated.
Wherein m is greater than 0, n is greater than 0, c1＞0，c2＞0。sik(t) represents a slip form surface designed to:
in a dual channel event trigger scheme, the sensor-to-controller trigger conditions are designed to: e.g. of the typey Tψey≤γmyi(tk)Tψyi(tk) In the formula, ψ represents a weight matrix, γm∈(0，1)，ey＝yi(tk)-yi(t), y (t) represents the current output, y (t)k)(k＝0，1，...，t00) represents the most recently transmitted value.
The controller to actuator triggering conditions are:
in the formula,
km＞0，kn＞0，δa＞0，δb＞0，δh＞0，tqis a trigger time sequence.
In an event trigger based controller, the design result is:
wherein,
represents an estimate of Γ, a design parameter, and ψ is a variable matrix.
The following describes the technical solution of the present invention in detail by taking a class of nonlinear system adaptive fuzzy fault-tolerant control methods as an example and combining with the accompanying drawings.
As illustrated in FIG. 1, the present invention includes a class of nonlinear systems subject to actuator failure and external disturbances, fuzzy synthetic observers, adaptive sliding mode controllers, dual channel event-triggered mechanisms, and event-trigger based controllers.
Model building
Consider a class of nonlinear control system models as follows:
wherein, X2i-1(t)＝[x1，x2，...，x2i-1]∈R2i-1Indicating the state of the system,. DELTA.f2i-1(X2i-1T, v) and Δ f2i(X2iT, v) represents a system unknown nonlinear function, and vi is an unknown constant. d2i-1(t) and d2i(t) represents external interference, udi(t) denotes a control input, biTo control the gain. 0 < h1≤hi≤h2< 1 indicates actuator failureFault factor, h1and h2Is two constants,. epsiloni∈{0，1}，tfFor the time of occurrence of a fault usi(t) indicates an actuator paranoia fault. Suppose | | | hi||≤hnWherein h isn＞0。
σiOften characterizing a paranoia fault.
Consider the fuzzy logic system theory as follows:
where r (x) represents an arbitrary nonlinear function, U is a compact set, and δ is a positive number.
χ(x)＝[χ1(x),χ2(x),...,χN(x)]TWherein
is a membership function.
Based on the fuzzy logic theory, the following system can be obtained:
sensor-to-controller channel trigger mechanism design:
ey Tψey≤γmyi(tk)Tψyi(tk) (4)
wherein e isy＝yi(tk)-yi(t), ψ is a weight matrix, γmE (0,1) is a given parameter, yi(t) denotes the current output, yi(tk)(k＝0,1,...,t00) represents the most recently transmitted value.
Design and certification of the observer:
aiming at the system, an observer is designed as follows:
wherein etak＝2(h2-h1)(hn+h2-h1) P positive definite symmetric matrix, LzIs a design matrix.
wherein
The error system thus obtained is:
wherein,
further, it is possible to obtain:
in the formula:
for estimating interfering signals, design
And (3) proving that: the Lyapuloff function is chosen as:
wherein,
derivatives of the above formula are available to persons (6) - (14):
known from the Lyapunov theorem, when (P (A)z-Lc)+(Az-Lc)TP), the observation error can be converged to zero, and the certification is finished.
Design and analysis of controller
Designing an adaptive sliding mode function:
the tracking error is defined as: e.g. of the typeki＝yi-yidThe slip form surface is designed as follows:
wherein: wherein eki＝yi-yidWhich is indicative of a tracking error,
two adaptive parameters are respectively expressed as
In the formula, m is more than 0, n is more than 0, c1＞0，c2＞0。
Triggering design from the controller to the actuator:
in the formula,
km＞0,kn＞0,δa＞0,δb＞0,δh＞0,tqis a trigger time sequence.
Controller design
The controller is designed as follows:
wherein:
denotes an estimate of Γ, which is a parameter that requires subsequent design, and ψ will be defined below.
Note that the following relationship holds:
wherein:
the controller is brought into the sliding mode surface to obtain:
in the above formula:
analyzing the tracking performance:
selecting a Lyapunov function as:
defining:
from fuzzy logic theory one can see:
wherein,
κsis an unknown parameter.
This gives:
in the formula,
the derivation of (22) and the substitution of (17) to (24) can be obtained as follows:
the sliding mode surface is accessible, and the certification is finished.
Further, from (18) can be obtained:
the carry-in (8) can result in:
wherein,
solving the above equation can obtain:
wherein, Tq＝tq+1-tq。
Therefore, the event triggering mechanism designed by the invention has a lower limit on two triggering times, namely the Zeno phenomenon can be avoided.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.
Claims (3)
1. A self-adaptive fuzzy fault-tolerant control method for a nonlinear system is characterized by comprising the nonlinear system subjected to actuator faults and external disturbance, a fuzzy comprehensive observer, a self-adaptive sliding mode controller, a dual-channel event trigger mechanism and a controller based on event trigger:
(1) aiming at the influence of actuator faults and external interference on a nonlinear system, a nonlinear system tracking control model under the influence of the actuator faults and the interference is established;
(2) the fuzzy comprehensive observer comprises a fuzzy state observer, a fault failure factor observer and an interference observer, can realize the estimation of the state, the fault failure information and the interference of the nonlinear system, and does not need the upper bound value of the interference information in the interference information estimation process;
the fuzzy state observer has the following design results:
in the formula,
and
is x2i-1(t)，x2i(t)，yi(t)，
And hi(ii) an estimate of (d); x is the number of2i-1(t)，x2i(t)，yi(t)，
And hiRespectively representing a system state, a system output, a system nonlinear function and a fault failure factor;
the fault failure factor observer is as follows:
wherein
ez＝[e2i-1 e2i]T，
h1，h2Are two constants;
the disturbance observer is:
wherein pi (t) is a new variable introduced;
in addition, when the observer is designed, an observation error compensation term delta is introducedm(t), the design precision and the flexibility of the observer are improved, and the result is as follows:
wherein etak＝2(h2-h1)(hn+h2-h1) P positively defines a symmetric matrix;
which is indicative of an error in the observation,
is composed of
Estimate of, LzA design matrix is formed;
(3) the self-adaptive sliding mode controller is designed by utilizing the observation information to compensate the influence of faults and interference on the system; in the method, two self-adaptive sliding mode surface parameters are introduced, aiming at considering the influence of fault and interference factors on the tracking performance;
the design result of the self-adaptive sliding mode controller is as follows:
wherein,
to represent
(ii) an estimate of (d);
wherein m is greater than 0, n is greater than 0, c1＞0，c2＞0；sik(t) represents a slip form surface designed to:
(4) the dual-channel event trigger mechanism comprises two groups of event trigger conditions from a sensor to a controller and from the controller to an actuator, so that on one hand, fewer output information values are used for observing system variables, on the other hand, the transmission value of system information during control is reduced, and the real-time fault tolerance of the system is improved;
the dual-channel event triggering mechanism is as follows; the triggering conditions from the sensor to the controller are designed as follows: e.g. of the typey Tψey≤γmyi(tk)Tψyi(tk) In the formula, ψ represents a weight matrix, γm∈(0,1)，ey＝yi(tk)-yi(t), y (t) represents the current output, y (t)k)(k＝0,1,...,t00) represents the most recently transmitted value;
the controller to actuator triggering conditions are:
in the formula,
km＞0,kn＞0,δa＞0,δb＞0,δh＞0,tqis a trigger time sequence;
(5) the sliding mode control method based on event triggering combines a triggering mechanism from a controller to an actuator, and the output of the sliding mode control method acts on a nonlinear system; when the system is influenced by actuator faults and external interference, the fault-tolerant capability of the system is ensured, the transmission load of the system is effectively reduced, and the real-time performance of the system is improved;
the controller based on event triggering is designed as follows:
wherein,
δb＞0，δc＞0，
represents an estimate of Γ, a design parameter, and ψ is a variable matrix.
2. The adaptive fuzzy fault-tolerant control method for the nonlinear system of the type as claimed in claim 1, characterized in that a control model of the nonlinear system of the type having an actuator failure and an external disturbance is established, the bias failure and the disturbance of the system are considered as an overall disturbance ξ in consideration of the actuator partial failure and the bias failurez(t); on the other hand, the fuzzy logic system theory is adopted to carry out fuzzy approximation on the nonlinear links of the nonlinear systems, and a nonlinear system control model based on the fuzzy logic system theory is established.
3. The adaptive fuzzy fault-tolerant control method of a nonlinear system as recited in claim 2, wherein the total disturbance ξ isz(t) provided that it satisfies the following condition,
wherein
Z (t) represents a new variable associated with the interference information for an unknown gain.
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