CN102352812B - Sliding mode-based hydro turbine governing system dead zone nonlinear compensation method - Google Patents

Sliding mode-based hydro turbine governing system dead zone nonlinear compensation method Download PDF

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CN102352812B
CN102352812B CN201110200593.2A CN201110200593A CN102352812B CN 102352812 B CN102352812 B CN 102352812B CN 201110200593 A CN201110200593 A CN 201110200593A CN 102352812 B CN102352812 B CN 102352812B
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rbf
sliding formwork
dead band
variable
turbine governor
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CN102352812A (en
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钱殿伟
张博雅
刘向杰
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North China Electric Power University
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Abstract

The invention discloses a sliding mode-based hydro turbine governing system dead zone nonlinear compensation method in the technical field of hydro turbine control. The method comprises the following steps of: constructing a state space model for a hydro turbine governing system, and introducing an additional state variable; designing a sliding mode governor, and making an ideal hydro turbine governing system approximately stable by regulating the controlling quantity of the sliding mode governor; and designing a dead zone nonlinear compensator to compensate dead zone nonlinearity of an actual hydro turbine governing system. By the method, the automation level of the hydro turbine governing system is improved, the safety of a set is improved, the mechanical wear of the set is reduced, the equipment maintenance cost is reduced, and the economic performance of a hydro electric generating set is improved.

Description

A kind of Turbine Governor System dead band non-linear compensation method based on sliding formwork
Technical field
The invention belongs to Cut-edge Turbine Control Technology field, relate in particular to a kind of Turbine Governor System dead band non-linear compensation method based on sliding formwork.
Background technique
Turbine Governor System is a waterpower, machinery, the electric complex system being coupled, and it can automatically regulate the rotating speed of hydraulic generator unit, makes unit remain on the interior operation of deviation that rated speed allows, to meet the requirement of electrical network to electric energy frequency quality.In Turbine Governor System, comprise dead band non-linear, be mainly manifested in generating unit speed variation responsive not to the small-signal of speed control system, if uncompensation can badly influence the stability of Turbine Governor System.Conventionally, water wheels speed control system adopts PID speed regulator.This speed regulator is ignored the nonlinear impact in dead band, and the method that employing " is proofreaied and correct under design, the poorest operating mode under rated load " is asked for the parameter of PID speed regulator, cannot guarantee theoretically the stability that comprises the nonlinear Turbine Governor System in dead band.
Turbine Governor System can be divided into based on feedback of status with based on output feedback two large classes.PID speed regulator belongs to the speed regulator based on output feedback, because this type of speed regulator only utilizes output information (frequency departure), calculates controlled quentity controlled variable, and this has restricted the raising of Turbine Governor System performance and the design of dead band non-linear compensator from method.Strategy implementation along with China's " active development HYDROELECTRIC ENERGY ", hydraulic generator unit is towards high head, large capacity, high-revolving trend development, this performance to Turbine Governor System is had higher requirement, method in the urgent need to introducing based on feedback of status is to solve the design problem of Turbine Governor System, compensate the nonlinear impact in dead band, guarantee theoretically the stability of Turbine Governor System.
It is a kind of variable structure control method based on feedback of status that sliding formwork is controlled, and has strong robustness.When Satisfying Matching Conditions, on sliding hyperplane, to the external disturbance of system and Inter parameter, perturbation has invariance, and an alternative approach is provided for design Turbine Governor System, compensation dead band are non-linear.The people such as Ye have designed the change structure speed regulator of the fricton-tight mode of Turbine Governor System in article < < Variable structure and time-varying parameter control for hydroelectric generating unit > > and < < An intelligent discontinuous control strategy for hydroelectric generating unit > >, and the article of relevant sliding formwork Governor Design still rarely has report at present.For dead band compensation of nonlinearity problem, the people such as Chen Jie are at patent < < essentially nonlinear compensation controller of servo system > > (Chinese patent, publication number CN 101488010A) in, designed RBF Neural Network Online identification dead band non-linear, but this compensating controller, for Direct Current Governor System design, is difficult to directly apply to waterpower, machinery, the electric Turbine Governor System being coupled.
In order to improve the performance of Turbine Governor System, guarantee the stability of system, the present invention adopts the sliding formwork speed regulator of the sliding formwork control technique design water wheels speed control system based on feedback of status, non-linear with the dead band of compensation Turbine Governor System in conjunction with sliding formwork nerual network technique design compensation device, adopt the present invention can guarantee the stability that comprises the nonlinear Turbine Governor System in dead band.
Summary of the invention
For mentioning existing controlling method in above-mentioned background technology, cannot guarantee, containing the deficiency of the stability of the nonlinear Turbine Governor System in dead band, to the present invention proposes a kind of Turbine Governor System dead band non-linear compensation method based on sliding formwork.
Technological scheme of the present invention is that a kind of Turbine Governor System dead band non-linear compensation method based on sliding formwork, is characterized in that the method comprises the following steps:
Step 1: build the state-space model of Turbine Governor System, introduce additivity variable;
Step 2: design sliding formwork speed regulator on the basis of step 1, by adjusting the controlled quentity controlled variable of sliding formwork speed regulator, make desirable Turbine Governor System Asymptotic Stability;
Step 3: on the basis of step 2, design dead band non-linear compensator, non-linear in order to compensate the dead band of actual Turbine Governor System.
The formula of described additivity variable is:
Figure 846049DEST_PATH_IMAGE001
Wherein:
Figure 130399DEST_PATH_IMAGE002
for additivity variable;
Figure 605243DEST_PATH_IMAGE003
for normal number;
Figure 367663DEST_PATH_IMAGE004
for rotational speed of water turbine variable quantity.
The formula of the controlled quentity controlled variable of described sliding formwork speed regulator is:
Figure 549245DEST_PATH_IMAGE005
Wherein:
controlled quentity controlled variable for sliding formwork speed regulator;
Figure 966637DEST_PATH_IMAGE007
for equivalent control amount;
Figure 532748DEST_PATH_IMAGE008
for switching controls amount.
Described dead band non-linear compensator is that the radial primary function network based on sliding formwork designs.
The right value update formula of described radial primary function network is:
Figure 568837DEST_PATH_IMAGE009
Wherein:
Figure 194990DEST_PATH_IMAGE010
variable quantity for the weight vector of RBF RBF network;
Figure 644426DEST_PATH_IMAGE011
for upgrading constant;
Figure 748648DEST_PATH_IMAGE012
for sliding formwork plane variable;
Figure 904823DEST_PATH_IMAGE013
for RBF vector.
Feature of the present invention is:
1. for the feature of water turbine speed adjustment process, introduce an additivity;
2. the mathematical model that the RBF RBF network building out device in the present invention need not controlled device, omits identification, real-time;
3. according to the more new law of Lyapunov stable theory design RBF RBF network weight, compensator parameter adjustment and the stable unification of control system have been accomplished.
4. the present invention combines sliding formwork control technique and nerual network technique, inquired into the right value update rule of the RBF RBF network building out device based on sliding formwork, both guarantee theoretically the stability of control system, overcome again the robustness that nonlinear impact has improved control system.
The present invention has improved the automatization level of Turbine Governor System, has increased the Safety performance of unit, has alleviated the mechanical wear of unit, has reduced the cost of equipment maintenance, has improved the economic performance of hydroelectric power unit.
accompanying drawing explanation
Fig. 1 is hydroelectric power system illustraton of model;
Fig. 2 is dead band nonlinear model;
Fig. 3 is dead band nonlinear compensation structural drawing;
Fig. 4 is RBF RBF network structure;
Fig. 5 is
Figure 701878DEST_PATH_IMAGE014
individual RBF;
Fig. 6 is the output of each state variable of unit under 10% load disturbance;
Fig. 7 is sliding formwork speed regulator and the output of sliding formwork compensator under 10% load disturbance;
Fig. 8 is the controlled quentity controlled variable that puts on hydroelectric power unit
Figure 373031DEST_PATH_IMAGE015
with sliding formwork plane
Figure 546523DEST_PATH_IMAGE016
.
embodiment
Below in conjunction with accompanying drawing, preferred embodiment is elaborated.Should be emphasized that, following explanation is only exemplary, rather than in order to limit the scope of the invention and to apply.
In order to solve the dead band nonlinear compensation problem of Turbine Governor System, the present invention proposes a kind of Turbine Governor System dead band non-linear compensation method based on sliding formwork, for improving the performance of Turbine Governor System, guarantee the stability of Turbine Governor System.
The present invention can be divided into the following steps:
One: build the state-space model of Turbine Governor System, introduce additivity variable;
Two: on one basis, design sliding formwork speed regulator, by adjusting the controlled quentity controlled variable of sliding formwork speed regulator, make desirable Turbine Governor System Asymptotic Stability;
Three: on two basis, design dead band non-linear compensator, non-linear in order to compensate the dead band of actual Turbine Governor System.
Specifically be divided into:
1: diversion system mathematical model
Ignore friction, under the hypothesis of rigidity water hammer theory, the transfer function of diversion system can be written as:
Figure 557204DEST_PATH_IMAGE017
(1)
Wherein:
Figure 525160DEST_PATH_IMAGE018
for Laplace conversion;
Figure 686539DEST_PATH_IMAGE019
for Laplace operator;
Figure 132564DEST_PATH_IMAGE020
for change of water level amount;
for flow change rate;
Figure 402188DEST_PATH_IMAGE022
for water hammer time constant.
2: Mathematical Model for Hydraulic Turbine
For Francis turbine:
Figure 47933DEST_PATH_IMAGE023
(2)
Wherein:
variable quantity for water turbine torque;
Figure 282922DEST_PATH_IMAGE025
variable quantity for rotational speed of water turbine;
variable quantity for servomotor stroke;
Figure 725722DEST_PATH_IMAGE027
for water turbine torque variable quantity is to rotational speed of water turbine variable quantity;
Figure 779129DEST_PATH_IMAGE028
for servomotor stroke variable quantity;
Figure 618909DEST_PATH_IMAGE029
for change of water level amount carry-over factor;
Figure 99569DEST_PATH_IMAGE030
for changes in flow rate amount is to rotational speed of water turbine variable quantity;
Figure 454327DEST_PATH_IMAGE031
for servomotor stroke variable quantity;
Figure 311424DEST_PATH_IMAGE032
carry-over factor for change of water level amount.
3: Hydrauservo System mathematical model
In Turbine Governor System, servomotor is driven by hydraulic system, control system signal
Figure 5711DEST_PATH_IMAGE033
with servomotor stroke variable quantity
Figure 657272DEST_PATH_IMAGE026
between the relation first order inertial loop that can be expressed as:
(3)
Wherein:
Figure 160115DEST_PATH_IMAGE035
for servomotor responsive time constant.
4: mathematical models of power system
Suppose the operating conditions of electric power system in unit band island load, the first order inertial loop that this electric power system can be expressed as:
Figure 708908DEST_PATH_IMAGE036
(4)
Wherein:
Figure 796949DEST_PATH_IMAGE037
it is the variable quantity of generator electromagnetic torque;
Figure 126299DEST_PATH_IMAGE038
it is generator set time constant;
Figure 59620DEST_PATH_IMAGE039
it is generator set self-regulation coefficient.
5: additivity
The hydroelectric power system block diagram consisting of diversion system, water turbine, Hydrauservo System, electric power system is as shown in the solid line part of Fig. 1.From the control system viewpoint based on feedback of status, this system is 3 rank systems, and wherein each state variable is respectively rotational speed of water turbine variable quantity
Figure 728499DEST_PATH_IMAGE040
, water turbine torque variable quantity
Figure 49759DEST_PATH_IMAGE041
, the variable quantity of servomotor stroke
Figure 538509DEST_PATH_IMAGE042
.In state space, in order to make rotational speed of water turbine variable quantity go to zero, introduce its integration as an additivity (dotted portion in Fig. 1), be defined as follows and show:
Figure 64485DEST_PATH_IMAGE043
(5)
Wherein:
Figure 291067DEST_PATH_IMAGE044
for additivity variable;
Figure 532693DEST_PATH_IMAGE003
for normal number.
6: sliding formwork Governor Design
Complete after aforementioned five steps, according to the hydroelectric power system illustraton of model shown in Fig. 1, can push away to such an extent that the state-space model of this system is as follows:
Figure 73396DEST_PATH_IMAGE045
(6)
Wherein:
Figure 451287DEST_PATH_IMAGE046
state vector,
Figure 105561DEST_PATH_IMAGE047
;
Figure 568903DEST_PATH_IMAGE015
for control inputs;
Figure 913297DEST_PATH_IMAGE048
for water turbine torque disturbance, it is exactly in fact the variable quantity of generator electromagnetic torque
Figure 411274DEST_PATH_IMAGE049
;
Figure 979659DEST_PATH_IMAGE050
for state matrix, ;
Figure 78382DEST_PATH_IMAGE052
for gating matrix,
Figure 430866DEST_PATH_IMAGE053
;
Figure 170152DEST_PATH_IMAGE054
for sytem matrix, ;
Figure 294283DEST_PATH_IMAGE056
for perturbation matrix,
Figure 501273DEST_PATH_IMAGE057
.
The controlled quentity controlled variable of sliding formwork speed regulator is conventionally by equivalent control amount
Figure 677040DEST_PATH_IMAGE058
with switching controls amount
Figure 602270DEST_PATH_IMAGE059
two-part form, and are defined as:
Figure 826578DEST_PATH_IMAGE005
(7)
Wherein:
controlled quentity controlled variable for sliding formwork speed regulator;
for equivalent control amount;
Figure 647270DEST_PATH_IMAGE059
for switching controls amount.
Figure 675268DEST_PATH_IMAGE058
effect be that each state variable of keeping system is moved in sliding formwork plane, and
Figure 856851DEST_PATH_IMAGE059
effect be to make each state of system depart from sliding formwork plane
Figure 374420DEST_PATH_IMAGE016
time towards sliding formwork plane motion.
Definition sliding formwork plane is shown as follows:
Figure 274243DEST_PATH_IMAGE060
(8)
Wherein:
Figure 840353DEST_PATH_IMAGE016
for sliding formwork plane variable;
Figure 876443DEST_PATH_IMAGE061
, for constant.
For the nonlinear desirable speed control system in dead band of not considering as shown in Figure 2, order in formula (1.6)
Figure 686453DEST_PATH_IMAGE063
after, can obtain equivalent control amount
Figure 56254DEST_PATH_IMAGE058
for:
Figure 212429DEST_PATH_IMAGE064
(9)
Utilize Lyapunov direct method, choose energy function
Figure 9484DEST_PATH_IMAGE065
, guaranteeing sliding formwork plane variable
Figure 680636DEST_PATH_IMAGE016
under asymptotically stable condition, can obtain switching law for:
Figure 599231DEST_PATH_IMAGE066
(10)
In formula (1.10),
Figure 567187DEST_PATH_IMAGE067
,
Figure 728566DEST_PATH_IMAGE068
,
Figure 440170DEST_PATH_IMAGE069
for
Figure 570937DEST_PATH_IMAGE070
the upper bound.So far, do not consider that the nonlinear desirable Turbine Governor System in dead band exists
Figure 709794DEST_PATH_IMAGE006
effect under Asymptotic Stability.
7: the dead band non-linear compensator design based on sliding formwork
After completing steps one to six, designed sliding formwork speed regulator can regulate does not consider the nonlinear idealized system in Turbine Governor System dead band, and the stability of Guarantee control system theoretically; But actual Turbine Governor System is that the dead band comprising is as shown in Figure 2 nonlinear, therefore in order to guarantee the stability of real system, necessary design compensation device is with the compensation non-linear impact on the stability of a system in dead band.Because actual Turbine Governor System forms jointly by desirable Turbine Governor System+dead band is non-linear, the mentality of designing (system architecture as shown in Figure 3) that adopts in the present invention sliding formwork speed regulator to add dead band non-linear compensator solves the control problem that comprises the nonlinear Turbine Governor System in dead band.
Already having proved that neuron network has with arbitrary accuracy approaches any nonlinear characteristic, adopt in the present invention the dead band non-linear compensator of the RBF RBF network design Turbine Governor System based on sliding formwork, as shown in Figure 4, it is a three-layer network with input layer, hidden layer and output layer to this RBF RBF topology of networks.In Fig. 4,
Figure 89960DEST_PATH_IMAGE006
for compensator input,
Figure 605255DEST_PATH_IMAGE071
for compensator output,
Figure 590528DEST_PATH_IMAGE072
for the non-linear input in dead band,
Figure 900287DEST_PATH_IMAGE015
for the non-linear output in dead band.
Choose a nonlinear function
Figure 767749DEST_PATH_IMAGE073
description dead band is non-linear, and the nonlinear inverse dynamics in this dead band can be expressed as:
Figure 821155DEST_PATH_IMAGE074
, wherein, ideal output for the RBF RBF network building out device based on sliding formwork.Due to , so estimated value be
Figure 353451DEST_PATH_IMAGE071
, i.e. the output of dead band non-linear compensator can be expressed as the output of RBF RBF network as shown in Figure 4:
(11)
Wherein:
Figure 964878DEST_PATH_IMAGE071
for the actual output of RBF RBF network, it is desirable output
Figure 806932DEST_PATH_IMAGE075
estimated value;
Figure 202141DEST_PATH_IMAGE078
for the weight vector of RBF RBF network, ,
Figure 838976DEST_PATH_IMAGE080
it is the hidden layer node number of RBF RBF network;
Figure 168326DEST_PATH_IMAGE013
for RBF vector,
Figure 367226DEST_PATH_IMAGE081
.
Figure 36105DEST_PATH_IMAGE013
as shown in Figure 5, it is defined as individual RBF:
(12)
Wherein:
be
Figure 372091DEST_PATH_IMAGE014
the center of individual RBF;
be
Figure 777982DEST_PATH_IMAGE014
the width of individual RBF.
Suppose to exist an optimum weight vector
Figure 381001DEST_PATH_IMAGE085
, meet
Figure 758893DEST_PATH_IMAGE086
, wherein,
Figure 359639DEST_PATH_IMAGE087
it is normal number.For containing the nonlinear Turbine Governor System in dead band, under Lyapunov stable theory, choose a new energy function and be:
Figure 822981DEST_PATH_IMAGE088
(13)
Wherein:
Figure 232621DEST_PATH_IMAGE089
；
Figure 465020DEST_PATH_IMAGE011
for upgrading constant,
Figure 236667DEST_PATH_IMAGE090
.
The right value update formula of getting this RBF RBF network is:
Figure 187305DEST_PATH_IMAGE009
(14)
Have
Figure 132127DEST_PATH_IMAGE091
.Visible, adopt designed in the present invention dead band non-linear compensator, can guarantee that Turbine Governor System is under the effect of sliding formwork speed regulator,
Figure 484611DEST_PATH_IMAGE092
time full remuneration Turbine Governor System dead band non-linear.Since then, in the present invention, the Turbine Governor System dead band non-linear compensator design based on sliding formwork is complete.
Embodiment is as follows:
The structural drawing of hydroelectric power system as shown in Figure 1.By measurement and reference device specification, obtaining the parameter of certain hydroelectric power unit that adopts mixed flow type generator group under a certain operating mode is
Figure 427159DEST_PATH_IMAGE093
,
Figure 865094DEST_PATH_IMAGE094
,
Figure 551290DEST_PATH_IMAGE095
,
Figure 820598DEST_PATH_IMAGE096
,
Figure 934047DEST_PATH_IMAGE097
,
Figure 921595DEST_PATH_IMAGE098
,
Figure 145903DEST_PATH_IMAGE099
,
Figure 472979DEST_PATH_IMAGE100
,
Figure 491750DEST_PATH_IMAGE101
,
Figure 966594DEST_PATH_IMAGE102
.According to engineering experience and the understanding to controlled system, by trial and error method, get
Figure 994593DEST_PATH_IMAGE103
.Further by model conversion, can obtain the matrix in the equation of state of system
Figure 238492DEST_PATH_IMAGE050
and matrix
Figure 693745DEST_PATH_IMAGE052
be respectively:
Figure 327988DEST_PATH_IMAGE104
；
Figure 894099DEST_PATH_IMAGE105
The expectation limit of getting in Ackermann formula is ,
Figure 884237DEST_PATH_IMAGE107
,
Figure 5777DEST_PATH_IMAGE108
, can obtain sliding formwork floor coefficient
Figure 375579DEST_PATH_IMAGE109
for
Figure 594070DEST_PATH_IMAGE110
.According to the performance index meter of control system, determine switching control parameter
Figure 391125DEST_PATH_IMAGE111
,
Figure 999961DEST_PATH_IMAGE112
.The sliding formwork speed regulator of final definite this hydroelectric power unit is
Figure 907874DEST_PATH_IMAGE113
.
The relevant parameter of getting the designed dead band non-linear compensator of step 7 is
Figure 918555DEST_PATH_IMAGE114
,
Figure 951758DEST_PATH_IMAGE115
in each element be closed interval
Figure 47890DEST_PATH_IMAGE116
between equally distributed random numbers, be closed interval
Figure 686999DEST_PATH_IMAGE117
between equally distributed random numbers,
Figure 825856DEST_PATH_IMAGE118
,
Figure 409284DEST_PATH_IMAGE119
.All parameters by hydroelectric power unit under a certain operating mode, sliding formwork speed regulator and the dead band non-linear compensator substitution emulation platform based on sliding formwork, at load disturbance
Figure 986896DEST_PATH_IMAGE120
situation under carry out emulation experiment, obtain each state variable of unit as shown in Figure 6, the output of sliding formwork speed regulator and sliding formwork compensator as shown in Figure 7, puts on the controlled quentity controlled variable of hydroelectric power unit
Figure 706590DEST_PATH_IMAGE015
with designed sliding formwork plane
Figure 16349DEST_PATH_IMAGE016
as shown in Figure 8.
The above; be only the present invention's embodiment preferably, but protection scope of the present invention is not limited to this, is anyly familiar with in technical scope that those skilled in the art disclose in the present invention; the variation that can expect easily or replacement, within all should being encompassed in protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (1)

1. the Turbine Governor System dead band non-linear compensation method based on sliding formwork, the method comprises the following steps:
Step 1: build the state-space model of Turbine Governor System, introduce additivity variable;
Step 2: design sliding formwork speed regulator on the basis of step 1, by adjusting the controlled quentity controlled variable of sliding formwork speed regulator, make desirable Turbine Governor System Asymptotic Stability;
Step 3: on the basis of step 2, design dead band non-linear compensator, non-linear in order to compensate the dead band of actual Turbine Governor System;
It is characterized in that, the formula of described additivity variable is:
Figure FDA0000439091710000011
Wherein: x 4for additivity variable; K efor normal number; X (t) is rotational speed of water turbine variable quantity;
The formula of the controlled quentity controlled variable of described sliding formwork speed regulator is:
u smc=u eq+u sw
Wherein: u smccontrolled quentity controlled variable for sliding formwork speed regulator; u eqfor equivalent control amount; u swfor switching controls amount;
Described dead band non-linear compensator adopts the dead band non-linear compensator of the RBF RBF network design Turbine Governor System based on sliding formwork, the output of its RBF RBF network:
Figure FDA0000439091710000012
Wherein:
Figure FDA0000439091710000013
for the actual output of RBF RBF network, it is desirable output Δ E *estimated value; W is the weight vector of RBF RBF network,
Figure FDA0000439091710000014
n cit is the hidden layer node number of RBF RBF network; Φ (u smc) be RBF vector,
Figure FDA0000439091710000015
it is defined as:
Figure FDA0000439091710000016
Wherein: γ kit is the center of k RBF; δ kit is the width of k RBF;
Suppose to exist an optimum weight vector
Figure FDA0000439091710000021
meet
Figure FDA0000439091710000022
wherein, ε is normal number; For containing the nonlinear Turbine Governor System in dead band, under Lyapunov stable theory, choose a new energy function and be:
Wherein:
Figure FDA0000439091710000024
α is for upgrading constant, α >0;
The right value update formula of getting this RBF RBF network is:
Figure FDA0000439091710000025
Wherein:
Figure FDA0000439091710000026
variable quantity for the weight vector of RBF RBF network; α is for upgrading constant; S is sliding formwork plane variable; Φ (u smc) be RBF vector;
Above-mentioned u eqeffect be that each state variable of keeping system is moved in sliding formwork plane, and u sweffect be make each state of system when departing from sliding formwork planar S towards sliding formwork plane motion;
Definition sliding formwork plane is shown as follows:
S=c Tx
Wherein:
S is sliding formwork plane variable;
C=[c 1c 2c 3c 4] t, c i(i=1 ..., 4) be constant;
For not considering the nonlinear desirable speed control system in dead band, equivalent control amount u eqfor:
u eq=-(c TB) -1c TAx
Utilize Lyapunov direct method, choose energy function V (t)=S 2/ 2, under guaranteeing that sliding formwork plane variable S is to asymptotically stable condition, can obtain switching law u swfor:
u sw=-(c TB) -1[KS+ηsgn(S)]
In above formula, K>0, η >sup|c tfd|>0, sup|c tfd| is c tthe upper bound of Fd, so far, does not consider that the nonlinear desirable Turbine Governor System in dead band is at u smceffect under Asymptotic Stability, guarantee that Turbine Governor System is under the effect of sliding formwork speed regulator, when t → ∞, the dead band of full remuneration Turbine Governor System is non-linear.
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