CN116594308A - Robust asynchronous control method for time-delay turbine regulation system with pulse perturbation - Google Patents
Robust asynchronous control method for time-delay turbine regulation system with pulse perturbation Download PDFInfo
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Abstract
本发明公开了具有脉冲摄动的时滞水轮机调节系统鲁棒异步控制方法，包括如下步骤：第一步：建立具有脉冲摄动的非线性时滞水轮机调节系统的数学模型；第二步：选取合适的前件变量和隶属度函数，构建具有脉冲摄动的模糊时滞奇异混杂水轮机调节系统；第三步：建立异步状态反馈控制器，实现具有脉冲摄动的时滞奇异混杂水轮机调节系统鲁棒异步镇定。本发明的有益效果在于：本发明建立的具有脉冲摄动的模糊时滞奇异混杂水轮机调节系统，不需要逼近时滞代数方程，并能抵抗水流突然增多/少、电路元件的失效、环境噪声而对系统造成的损伤；通过隐马尔科夫模型策略设计异步模糊状态反馈控制器，解决了受控系统与控制器之间异步现象；将脉冲算子值域从推广到
The invention discloses a robust asynchronous control method for a time-delay water turbine regulation system with pulse perturbation, comprising the following steps: the first step: establishing a mathematical model of a nonlinear time-delay water turbine regulation system with pulse perturbation; second step: selecting Appropriate antecedent variables and membership functions to construct a fuzzy time-delay singular hybrid turbine regulating system with pulse perturbation; the third step: establish an asynchronous state feedback controller to realize a time-delay singular hybrid turbine regulation system with pulse perturbation. Great async calm. The beneficial effect of the present invention is that: the fuzzy time-delay singular hybrid hydraulic turbine regulating system with pulse perturbation established by the present invention does not need to approach the time-delay algebraic equation, and can resist sudden increase/decrease of water flow, failure of circuit elements, and environmental noise. The damage caused to the system; the asynchronous fuzzy state feedback controller is designed through the hidden Markov model strategy, which solves the asynchronous phenomenon between the controlled system and the controller; the value range of the pulse operator is changed from promote to
Description
Technical Field
The invention relates to the field of robust asynchronous controllers, in particular to a robust asynchronous control method of a time-lag hydroturbine adjusting system with pulse perturbation.
Background
In recent decades, sustainable power generation strategies have received increasing attention, and hydropower has become an increasingly important role in world energy strategies. As is well known, a hydraulic turbine regulating system is one of important links of a hydropower station, and the running condition of the hydraulic turbine regulating system directly influences the stable running of the hydropower station. Thus, modeling, analysis, and control problems of hydraulic turbine tuning systems are a hotspot for researchers to study. In recent years, many researchers have tried to build a nonlinear model of a hydraulic turbine tuning system. However, most scholars approximate the time-lag algebraic equation, and only a few scholars consider the time-lag singularities. Therefore, in order to describe the dynamic behavior of the pipeline more accurately, the invention is more in line with engineering practice, and the time lag singularities of the pipeline are considered. In recent decades, singular systems have played an important role in many fields such as aircraft modeling, crosslinking systems, power systems, missile systems, and the like. According to different application fields, the singular system is described as a constraint system, a generalized variable system, a half-state system and the like. The singular system has the advantage over the conventional system that the configuration of the physical system can be maintained, depicting both dynamic and static constraints. Notably, tolerability (including stability, non-impulsivity/causality and regularity) must be considered for singular systems, whereas the latter two problems do not exist for regular systems. Thus, the control of the singular system is much more difficult and complex than in the regular case.
Pulse systems have received considerable attention due to their wide application in the fields of communication networks, control technology, engineering science, biology, etc. In general, from the point of view of the impulse effect, the impulse system can be studied both from the point of view of impulse perturbation and impulse control. The former describes a system that is subject to transient disturbances at discrete times, where transient disturbance pulses can degrade system performance and possibly lead to instability. The latter corresponds to the case where intermittent control pulses can stabilize the controlled system and improve the system performance. In addition, a class of hybrid systems driven by Markov jumps has also recently come into the field of view of many scholars, as it can simulate many of the various real systems with abrupt structure and/or parameter changes.
On the other hand, takagi-Sugeno (T-S) fuzzy control has attracted a wide academic interest in recent decades, because the T-S fuzzy control method is very effective on certain mathematically uncertain, uncertain and nonlinear objects. The nonlinear dynamic system can be approximated by a T-S fuzzy model, wherein the local dynamics of the different state space regions are represented by a linear model, which are mixed together by fuzzy membership functions to obtain an overall fuzzy model. The parallel distribution compensation technique is then applied to the fuzzy model based controller design. Thus, a linear controller can be designed for each local linear model. It should be noted that most of the present inventions focus on synchronization problems, but ignore unavoidable asynchronous problems caused by time delay, network mechanism, measurement error, and the like, and in recent years, hidden markov model mechanisms have been proposed and widely used for asynchronous control problems in which the mode of a controller is not matched with the mode of an original controlled system.
Disclosure of Invention
In order to solve the problems, the invention discloses a robust asynchronous control method of a time lag hydroturbine regulating system with pulse perturbation
The specific scheme is as follows:
a robust asynchronous control method for a time lag hydroturbine adjusting system with pulse perturbation comprises the following steps: establishing a mathematical model of a nonlinear time-lag singular hybrid water turbine adjusting system with pulse perturbation; selecting proper front variables and membership functions, and constructing a fuzzy time-lag singular hybrid water turbine adjusting system with pulse perturbation; and establishing an asynchronous state feedback controller to realize robust asynchronous stabilization of the fuzzy time-lag singular hybrid water turbine regulating system with pulse perturbation. By constructing a novel pulse time dependent lyapunov functional; robust stabilization of a fuzzy time-lag singular hybrid turbine adjusting system with pulse perturbation is realized; finally, through a simulation example, the effectiveness of the proposed asynchronous control method is verified.
As a further improvement of the present invention, the method specifically comprises the following steps:
(a) The correlation between the turbine relative head h and the flow q is expressed as:
wherein the water hammer wave reflection time constant and the water inertia time constant are respectively T q and hw A representation; and carrying out Laplace inverse transformation on the hyperbolic tangent function to obtain a time-lag algebraic equation in a time domain:
h(t)＝-h(t-T q )+2h w q(t-T q )-2h w q(t)， (2)
the turbine model with less variation under steady state conditions can be linearized as:
wherein the relative deviation of the moment is m s (t) the relative deviations of the generator speed and the servo output are denoted by x p (t) and y (t);
then, six transfer coefficients of the water turbine can be obtained through the characteristic curves of the moment and the flow:
while the nonlinear characteristics of synchronous generators are described as:
wherein the rotor angle and the generator damping coefficient are respectivelyReplaced with (t) and χ. T (T) s and mp Respectively representing the inertia time constant and the electromagnetic torque of the generator motor;
in analyzing the dynamic characteristics of the generator system, the influence of the rotational speed variation on the generator is taken into account. Electromagnetic power is generally considered to be equal to electromagnetic torque;
m p (t)＝P e (t), (6)
the electromagnetic power is expressed as:
wherein the armature transient internal voltage, the bus infinite voltage and the direct axis transient reactance are respectively E' q 、V s and x′d A representation; x is x q 、x T and xL (r t ) Respectively representing the reactance of the tetrad axis, the short-circuit reactance of the transformer and the reactance of different transmission lines;
driving the turbine guide vane by a servo system, and converting a weak control signal u (t) into a mechanical displacement signal y (t); the dynamics of the hydraulic servo system can be expressed as:
wherein Ty (r t ) Representing a main relay connector response time;
let x be 1 、x 2 、x 3 and x4 Respectively representx p Y and h; meanwhile, it is considered that the malfunction of circuit elements, the ambient noise and the abrupt increase or decrease of water flow may cause a "pulse" phenomenon. Combining (1) - (9) to obtain a toolThe mathematical model of the nonlinear time-lag singular hybrid water turbine adjusting system with pulse perturbation is as follows:
wherein ,
f 1 (x(t),r t )＝x 0 x p (t),
f 4 (x(t),r t )＝(2h w e qx x p (t)+2h w e qy y(t)+(2h w e qh +1)h(t)),
x(t)＝[x 1 (t)x 2 (t)x 3 (t)x 4 (t)] T is a state vector, u (t) is a control input, ω (t) is an external disturbance, z (t) is an estimated output,is a pulse operator, { t k The sequence represents the pulse instants and satisfies 0=t 0 ＜t 1 ＜t 2 ＜···＜t k ＜t k+1 ＜···；
{r t The markov jump procedure is represented and takes a value in the set s= {1,2, M, pi= [ pi ] rl ]A transfer rate matrix for satisfying general conditions;
(b) Consider x in system (10) 1 ∈[-p,p]Based on the T-S fuzzy method, the linear model is adopted to represent the local dynamics of different state space regions. The local linear models are mixed through a fuzzy membership function, and a time-lag singular hybrid water turbine adjusting system with pulse perturbation can be constructed by utilizing two fuzzy rules of the system (10). Selecting rotor angleAs a membership function of the precursor variables:
rule 1: if x 1 (t) is affiliated toThen
Rule 2: if x 1 (t) is affiliated toThen
To conveniently obtain coefficient matrix A of system (10) i (r t ) (i=1, 2) using Maclaurin series;
wherein
When r is t ＝r∈S，In the process, considering (12), selecting the first three items of Maclaurin series, and obtaining an overall fuzzy model of the system (10) as follows:
wherein ,
I kil generalized pulse operator I under ith fuzzy rule kl ；
(c) Designing an asynchronous fuzzy state feedback controller;
rule 1: if x 1 (t) is affiliated toThen
u(t)＝K 1 (κ t )x(t)；
Rule 2: if x 1 (t) is affiliated toThen
u(t)＝K 2 (κ t )x(t)；
According to the parallel distributed compensation technology and the hidden Markov model mechanism, the overall fuzzy model of the asynchronous fuzzy state feedback controller is obtained as follows:
{κ t is dependent on { r } t Markov jump procedure atTaking a value of the middle value;
P{κ t ＝κ|r t ＝r}＝q rκ (15)
representing conditional probability, p= [ q ] rκ ]Representing a conditional probability matrix, for each r.epsilon.S, there is(r t ,κ t Pi, P) represents a hidden Markov model, K j (κ t ) The gain of the asynchronous fuzzy state feedback controller under the condition of a fuzzy rule j is obtained;
(d) In order to make the results more generic, a general form of the fuzzy time-lag singular confounding system with impulse perturbation is given below:
fuzzy rule i (i=1, 2,., m)
If lambda is 1 (t) is affiliated toλ 2 (t) belonging to->…λ n (t) belonging to->Then
wherein ,representing fuzzy sets, lambda v (t) (v=1, 2,., n) is a front piece variable;
(e) Based on the T-S fuzzy strategy, the fuzzy time-lag singular confounding system (16) with impulse perturbation is expressed as:
wherein ,
and m is the number of IF-THEN rules,represents a normalized fuzzy weighting function, λ (t) = [ λ ] 1 (t),λ 2 (t),...,λ n (t)]，Is->Lambda in (lambda) j Membership function of (t). At the pulse time, < >>Representing a normalized fuzzy weighting function, lambda (t k )＝[λ 1 (t k ),λ 2 (t k ),...,λ n (t k )]，Represented by lambda v (t k ) At->Membership functions in (a);
(f) The generalized asynchronous fuzzy state feedback controller is expressed as:
fuzzy rule j (j=1, 2,., m.)
If lambda is 1 (t) is affiliated toλ 2 (t) belonging to->…λ n (t) belonging to->Then
(g) Combining (16) - (18), when r t ＝r∈S， and κt =κ e Θ, resulting in a closed loop fuzzy time-lag singular hybrid system with pulsed perturbation:
wherein ,
(h) Definition:
(A) For each r t ＝r∈S，κ t =κ∈Θ, pairIs regular, pulse-free, a closed loop fuzzy time-lag singular confounding system (19) with pulse perturbation is said to be non-forced, regular, pulse-free;
(B) If there is a scalar quantityA closed loop fuzzy time-lapse singular hybrid system (19) with non-forced impulse perturbation is considered randomly stable if the following formula holds;
(C) If the closed loop fuzzy time-lapse singular confounding system (19) with non-forced impulse perturbation is regular, non-impulse and randomly stable, then the closed loop fuzzy time-lapse singular confounding system (19) with non-forced impulse perturbation is said to be randomly tolerant.
(i) For a given pulse sequence whereinFirst some auxiliary functions are introduced for +.>
Note thatThere is a function +.>So that
ρ 2 (t)＝1-ρ 1 (t)；
(j) Given a class of pulse time sequences, for all r t ＝r∈S，κ t Defining matrix P with =κ∈Θ and g=1, 2 r > 0, Q > 0 and scalar sigma > 0, T q ＞0，Sigma = min {1, sigma }, designing a lyapunov functional dependent on pulse time, and studying the stability condition of a closed-loop fuzzy time-lag singular hybrid system (19) with pulse perturbation:
wherein ,
wherein phi (t) =sigma ρ1(t) ；
Defining a random procedure { x } t ,r t ,κ t Acts on V (x) t ,r t ,κ t ) Weak infinity small operator on
Note thatHas the following components
Combining (21) - (25), when ω (t) =0, there are
wherein ,
on the other hand, consider V (t k) and relation of (2)
There is a scalar quantitySo that
According to the Deng Jin formula, for t > t s > 0, have
Thus there is
On the other hand, there are
Thus, the first and second substrates are bonded together,
wherein ,
(k) Is available according to the schulp lemma and the lyapunov theorem, when the following conditions are satisfied,
Λ ghrκ ＜0, (30)
(I+I khl ) T E T P r (I+I khl )≤σE T P l , (32)
wherein ,
the system can meet the random tolerance and has H ∞ Performance index;
(l) Designing an asynchronous fuzzy state feedback controller:
order the
wherein ,
simultaneous command
wherein ,
(m) according to Moore-Penrose inverse method, when the following linear matrix inequality is satisfied
wherein ,
the gain of the asynchronous fuzzy state feedback controller (18) may then be expressed as:
the system satisfies the random tolerance and satisfies H ∞ Performance index.
The method combines with some practical problems, and designs an asynchronous fuzzy state feedback controller aiming at a nonlinear time-lag singular hybrid water turbine adjusting system with pulse perturbation; compared with the prior art, the technical scheme provided by the invention has the beneficial effects that:
1. the modeling fuzzy time-lag singular hybrid water turbine adjusting system with pulse perturbation can simultaneously consider the influence of different reactance on the system due to different line switching in the working process of the water turbine system, the system with different reactance is modeled as a subsystem of a Markov system, and jump among the subsystems is compliant with the Markov chain; meanwhile, the method does not need to approach a time lag algebraic equation, and can resist damage to a water turbine system caused by sudden increase/decrease of water flow, failure of circuit elements and environmental noise; compared with the conventional water turbine regulating system modeling as a general linear system researching robust asynchronous control, the method can more effectively cope with the actual engineering problem;
2. the modal information of the fuzzy time-lag singular hybrid turbine tuning system is not fully accessible due to unavoidable delays, networking mechanisms, measurement errors, etc., which results in asynchronous problems between the controller and the controlled system. According to the invention, an asynchronous fuzzy state feedback controller is designed under a hidden Markov model mechanism, so that the modal asynchronous problem is successfully overcome, and the robust asynchronous control of the time-lag singular hybrid water turbine regulating system is realized;
3. the invention constructs a Lyapunov functional which is dependent on pulse time, and can effectively capture the characteristics and information of a Markov jump mode and the pulse moment; at the same time, the pulse operator value range is promoted to n×n Therefore, the method provided by the invention is more universal.
Drawings
Fig. 1 is a block diagram of a hydraulic turbine tuning system according to the present invention.
Fig. 2 is a robust asynchronous control flow chart of the fuzzy time-lag singular hybrid turbine regulating system with pulse perturbation.
FIG. 3 is a graph of a robust asynchronous control algorithm for a fuzzy time-lapse singular hybrid turbine tuning system with impulse perturbation.
FIG. 4 is a graph of fuzzy membership functions according to the present invention.
FIG. 5 is a schematic diagram of a lag hydroturbine tuning system with impulse perturbation according to the present invention 1 (t) trajectory.
FIG. 6 is a schematic diagram of a lag hydroturbine tuning system with impulse perturbation according to the present invention 2 (t) trajectory.
FIG. 7 is a schematic diagram of a lag hydroturbine tuning system with impulse perturbation according to the present invention 3 (t) trajectory.
FIG. 8 is a schematic diagram of an exemplary lag hydroturbine tuning system with impulse perturbation 4 (t) trajectory.
FIG. 9 is a z (t) trace of a lag hydroturbine tuning system with impulse perturbation, as presented in the present invention.
Detailed Description
The following description of the embodiments of the invention is presented in conjunction with the accompanying drawings to provide a better understanding of the invention to those skilled in the art. It is noted that in the following description, detailed descriptions of known functions and designs will be omitted herein as perhaps obscuring the subject matter of the present invention.
As shown in the figure, the invention provides a robust asynchronous control method for a time lag hydroturbine adjusting system with pulse perturbation, which specifically comprises the following steps:
(a) The correlation between the turbine relative head h and the flow q is expressed as:
wherein the water hammer wave reflection time constant and the water inertia time constant are respectively T q and hw A representation; and carrying out Laplace inverse transformation on the hyperbolic tangent function to obtain a time-lag algebraic equation in a time domain:
h(t)＝-h(t-T q )+2h w q(t-T q )-2h w q(t)，
the turbine model with less variation under steady state conditions can be linearized as:
wherein the relative deviation of the moment is m s (t) the relative deviations of the generator speed and the servo output are denoted by x p (t) and y (t);
then, six transfer coefficients of the water turbine can be obtained through the characteristic curves of the moment and the flow:
while the nonlinear characteristics of synchronous generators are described as:
wherein rotor angle and generator damping coefficient are respectively usedAnd χ. T (T) s and mp Respectively representing the inertia time constant and the electromagnetic torque of the generator motor;
in analyzing the dynamic characteristics of the generator system, the influence of the rotational speed variation on the generator is taken into account. Electromagnetic power is generally considered equal to electromagnetic torque:
m p (t)＝P e (t),
the electromagnetic power is expressed as:
wherein the armature transient internal voltage, the bus infinite voltage and the direct axis transient reactance are respectively E' q 、V s and x′d A representation; x is x q 、x T and xL (r t ) Respectively representing the reactance of the tetrad axis, the short-circuit reactance of the transformer and the reactance of different transmission lines;
driving the turbine guide vane by a servo system, and converting a weak control signal u (t) into a mechanical displacement signal y (t); the dynamics of the hydraulic servo system can be expressed as:
wherein Ty (r t ) Representing a main relay connector response time;
let x be 1 、x 2 、x 3 and x4 Respectively represent x p Y and h; meanwhile, considering that the phenomenon of pulse is possibly caused by fault circuit elements, environmental noise and sudden increase and decrease of water flow, the mathematical model of the nonlinear time-lag singular hybrid water turbine adjusting system with pulse perturbation is obtained as follows:
wherein ,
f 1 (x(t),r t )＝x 0 x p (t),
f 4 (x(t),r t )＝(2h w e qx x p (t)+2h w e qy y(t)+(2h w e qh +1)h(t)),
x(t)＝[x 1 (t)x 2 (t)x 3 (t)x 4 (t)] T is a state vector, u (t) is a control input, ω (t) is an external disturbance, z (t) is an estimated output,is a pulse operator, { t k The sequence represents the pulse instants and satisfies 0=t 0 ＜t 1 ＜t 2 ＜···＜t k ＜t k+1 ＜···；
{r t The markov jump procedure is represented and takes a value in the set s= {1,2, M, pi= [ pi ] rl ]A transfer rate matrix for satisfying general conditions;
(b) Consider x in a system 1 ∈[-p,p]Based on the T-S fuzzy method, the linear model is adopted to represent the local dynamics of different state space regions. The local linear models are mixed through fuzzy membership functions, and time lag odd abnormal mixing with pulse perturbation can be constructed by utilizing two fuzzy rules of the systemAnd a hybrid water turbine regulating system. Rotor angle (t) is selected as a membership function of the front piece variable:
rule 1: if x 1 (t) is affiliated toThen
Rule 2: if x 1 (t) is affiliated toThen
To conveniently obtain coefficient matrix A of system i (r t ) (i=1, 2) using Maclaurin series;
wherein
When r is t ＝r∈S，When the system is used, the first three items of Maclaurin series are selected, and the overall fuzzy model of the system is obtained as follows:
wherein , I kil generalized pulse operator I under ith fuzzy rule kl ；/>
(c) Designing an asynchronous fuzzy state feedback controller;
rule 1: if x 1 (t) is affiliated toThen
u(t)＝K 1 (κ t )x(t)；
Rule 2: if x 1 (t) is affiliated toThen
u(t)＝K 2 (κ t )x(t)；
According to the parallel distributed compensation technology and the hidden Markov model mechanism, the overall fuzzy model of the asynchronous fuzzy state feedback controller is obtained as follows:
{κ t is dependent on { r } t Markov jump procedure atTaking a value of the middle value;
P{κ t ＝κ|r t ＝r}＝q rκ
representing conditional probability, p= [ q ] rκ ]Representing a conditional probability matrix, for each r.epsilon.S, there is(r t ,κ t Pi, P) represents a hidden Markov model, K j (κ t ) The gain of the asynchronous fuzzy state feedback controller under the condition of a fuzzy rule j is obtained;
(d) In order to make the results more generic, a general form of the fuzzy time-lag singular confounding system with impulse perturbation is given below:
fuzzy rule i (i=1, 2,., m)
If lambda is 1 (t) is affiliated toλ 2 (t) belonging to->…λ n (t) belonging to->Then
wherein ,representing fuzzy sets, lambda v (t) (v=1, 2,., n) is a front piece variable;
(e) Based on the T-S fuzzy strategy, the fuzzy time-lag singular confounding system (16) with impulse perturbation is expressed as:
wherein ,
and m is the number of IF-THEN rules,represents a normalized fuzzy weighting function, λ (t) = [ λ ] 1 (t),λ 2 (t),...,λ n (t)]，Is->Lambda in (lambda) j Membership function of (t). At the pulse time, < >>Representing a normalized fuzzy weighting function, lambda (t k )＝[λ 1 (t k ),λ 2 (t k ),...,λ n (t k )]，Represented by lambda v (t k ) At->Membership functions in (a);
(f) The generalized asynchronous fuzzy state feedback controller is expressed as:
fuzzy rule j (j=1, 2,., m.)
If lambda is 1 (t) is affiliated toλ 2 (t) belonging to->…λ n (t) belonging to->Then
(g) When r is t ＝r∈S， and κt =κ e Θ, resulting in a closed loop fuzzy time-lag singular hybrid system with pulsed perturbation:
wherein ,
(h) Definition:
(A) For each r t ＝r∈S，κ t =κ∈Θ, pairThe closed loop fuzzy time lag singular hybrid system with pulse perturbation is regular and pulse-free;
(B) If there is a scalar quantityA closed loop fuzzy time-lag singular hybrid system with non-forced impulse perturbation is considered to be randomly stable if the following formula holds; />
(C) If the closed loop fuzzy time-lapse singular confounding system with non-forced impulse perturbation is regular, pulse-free and randomly stable, then the closed loop fuzzy time-lapse singular confounding system with non-forced impulse perturbation is said to be randomly tolerant.
In this embodiment, the parameters shown in table 1 were selected:
table 1: system parameters and design parameters
| x 0 | T s | e x | e y |
| 1 | 9 | 0 | 1 |
| e h | e qx | e qy | e qh |
| 1.5 | 0 | 1 | 0.5 |
| χ | E′ q | V s | h w |
| 2 | 1.35 | 1 | 0.5 |
| T y1 | T y2 | T y3 | x′ dΣ1 |
| 0.1 | 0.2 | 0.5 | 1.15 |
| x′ dΣ2 | x′ dΣ3 | x qΣ1 | x qΣ2 |
| 1.25 | 1 | 1.474 | 1.600 |
| x qΣ3 | p | σ | T q |
| 1 | 4 | 1.2 | 0.2 |
The technical means disclosed by the scheme of the invention is not limited to the technical means disclosed by the embodiment, and also comprises the technical scheme formed by any combination of the technical features. It should be noted that modifications and adaptations to the invention may occur to one skilled in the art without departing from the principles of the present invention and are intended to be within the scope of the present invention.
Claims (2)
1. The robust asynchronous control method for the time lag hydroturbine adjusting system with pulse perturbation is characterized by comprising the following steps of:
the first step: establishing a mathematical model of a nonlinear time-lag singular hybrid water turbine adjusting system with pulse perturbation;
and a second step of: selecting proper front variables and membership functions, and constructing a fuzzy time-lag singular hybrid water turbine adjusting system with pulse perturbation;
and a third step of: and establishing an asynchronous state feedback controller to realize robust asynchronous stabilization of the fuzzy time-lag singular hybrid water turbine regulating system with pulse perturbation.
2. The robust asynchronous control method of a lag turbine tuning system with impulse perturbation of claim 1, comprising the steps of:
(a) The correlation between the turbine relative head h and the flow q is expressed as:
wherein the water hammer wave reflection time constant and the water inertia time constant are respectively T q and hw Representing, inverse Laplace transform is performed on the hyperbolic tangent function, so as to obtain a time-lag algebraic equation in the time domain:
h(t)＝-h(t-T q )+2h w q(t-T q )-2h w q(t)，
the turbine model with less variation under steady state conditions can be linearized as:
wherein the relative deviation of the moment is m s (t) the relative deviations of the generator speed and the servo output are denoted by x p (t) and y (t);
then, six transfer coefficients of the water turbine are obtained through characteristic curves of moment and flow:
while the nonlinear characteristics of synchronous generators are described as:
wherein rotor angle and generator damping coefficient are respectively usedAnd χ substitution; t (T) s and mp Respectively representing the inertia time constant and the electromagnetic torque of the generator motor;
when analyzing the dynamic characteristics of the generator system, the influence of the rotation speed change on the generator is considered; the electromagnetic power is equal to the electromagnetic torque:
m p (t)＝P e (t),
the electromagnetic power is expressed as:
wherein the armature transient internal voltage, the bus infinite voltage and the direct axis transient reactance are respectively E' q 、V s and x′d A representation; x is x q 、x T and xL (r t ) Respectively representing the reactance of the tetrad axis, the short-circuit reactance of the transformer and the reactance of different transmission lines;
driving the turbine guide vane by a servo system, and converting a weak control signal u (t) into a mechanical displacement signal y (t); the dynamics of the hydraulic servo system are expressed as:
wherein Ty (r t ) Representing a main relay connector response time;
let x be 1 、x 2 、x 3 and x4 Respectively representx p Y and h; meanwhile, considering that the phenomenon of pulse is possibly caused by fault circuit elements, environmental noise and sudden increase and decrease of water flow, the mathematical model of the nonlinear time-lag singular hybrid water turbine adjusting system with pulse perturbation is obtained as follows:
wherein ,
f 1 (x(t),r t )＝x 0 x p (t),
f 4 (x(t),r t )＝(2h w e qx x p (t)+2h w e qy y(t)+(2h w e qh +1)h(t)),
x(t)＝[x 1 (t) x 2 (t) x 3 (t) x 4 (t)] T is a state vector, u (t) is a control input, ω (t) is an external disturbance, z (t) is an estimated output,is a pulse operator, { t k The sequence represents the pulse instants and satisfies 0=t 0 ＜t 1 ＜t 2 ＜···＜t k ＜t k+1 ＜···；
{r t The markov jump procedure is represented and takes a value in the set s= {1,2, M, pi= [ pi ] rl ]A transfer rate matrix for satisfying general conditions;
(b) Consider x in a system 1 ∈[-p,p]Based on the T-S fuzzy method, the linear model is adopted to represent the local dynamics of different state space areas; mixing these local linear models by fuzzy membership functions, using two modes of the systemPasting rules, constructing a time lag singular hybrid water turbine adjusting system with pulse perturbation; selecting rotor angleAs a membership function of the precursor variables:
rule 1: if x 1 (t) is affiliated toThen
Rule 2: if x 1 (t) is affiliated toThen
To conveniently obtain coefficient matrix A of system i (r t ) (i=1, 2) using Maclaurin series;
wherein
When r is t ＝r∈S，When the system is used, the first three items of Maclaurin series are selected, and the overall fuzzy model of the system is obtained as follows:
wherein , I kil generalized pulse operator I under ith fuzzy rule kl ；
(c) Designing an asynchronous fuzzy state feedback controller;
rule 1: if x 1 (t) is affiliated toThen
u(t)＝K 1 (κ t )x(t)；
Rule 2: if x 1 (t) is affiliated toThen
u(t)＝K 2 (κ t )x(t)；
According to the parallel distributed compensation technology and the hidden Markov model mechanism, the overall fuzzy model of the asynchronous fuzzy state feedback controller is obtained as follows:
{κ t is dependent on { r } t Markov jump procedure atTaking a value of the middle value;
P{κ t ＝κ|r t ＝r}＝q rκ
representing conditional probability, p= [ q ] rκ ]Representing a conditional probability matrix, for each r.epsilon.S, there is q rκ ≥0,(r t ,κ t Pi, P) represents a hidden Markov model, K j (κ t ) The gain of the asynchronous fuzzy state feedback controller under the condition of a fuzzy rule j is obtained;
(d) In order to make the results more generic, a fuzzy time-lag singular confounding system with impulse perturbation is given below: fuzzy rule i (i=1, 2,., m)
If lambda is 1 (t) is affiliated toλ 2 (t) belonging to->…λ n (t) belonging to->Then
wherein ,representing fuzzy sets, lambda v (t) (v=1, 2,., n) is a front piece variable;
(e) Based on the T-S fuzzy strategy, the fuzzy time-lag singular confounding system (16) with impulse perturbation is expressed as:
wherein ,
and m is the number of IF-THEN rules,represents a normalized fuzzy weighting function, λ (t) = [ λ ] 1 (t),λ 2 (t),...,λ n (t)]，Is->Lambda in (lambda) j A membership function of (t); at the pulse time, < >>Representing a normalized fuzzy weighting function, lambda (t k )＝[λ 1 (t k ),λ 2 (t k ),...,λ n (t k )]，Represented by lambda v (t k ) At->Membership functions in (a);
(f) The generalized asynchronous fuzzy state feedback controller is expressed as:
fuzzy rule j (j=1, 2,., m.)
If lambda is 1 (t) is affiliated toλ 2 (t) belonging to->…λ n (t) belonging to->Then
(g) When r is t ＝r∈S， and κt =κ e Θ, resulting in a closed loop fuzzy time-lag singular hybrid system with pulsed perturbation:
wherein ,
(h) Definition:
(A) For each r t ＝r∈S，κ t =κ∈Θ, pairThe closed loop fuzzy time lag singular hybrid system with pulse perturbation is regular and pulse-free;
(B) If there is a scalar quantityA closed loop fuzzy time-lag singular hybrid system with non-forced impulse perturbation is considered to be randomly stable if the following formula holds;
(C) If the closed loop fuzzy time-lapse singular confounding system with non-forced impulse perturbation is regular, pulse-free and randomly stable, then the closed loop fuzzy time-lapse singular confounding system with non-forced impulse perturbation is said to be randomly tolerant.
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