CN116360274A - Obstacle Lyapunov function-based full-state constraint wind turbine cabin suspension control method - Google Patents
Obstacle Lyapunov function-based full-state constraint wind turbine cabin suspension control method Download PDFInfo
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Abstract
The invention relates to a full-state constraint wind turbine cabin suspension control method based on a barrier Lyapunov function, and belongs to the technical field of automation. The method comprises the steps that a wind power cabin suspension system is divided into an axial suspension system and a pitching suppression system, and is decomposed into a cabin suspension position system, a cabin suspension speed system, a pitching angle system and a pitching angle speed system by a back-stepping method, and constraint boundaries are respectively designed for the four systems; the method comprises the steps of designing a finite time disturbance observer to estimate the suspension speed, the pitch angle speed and the external disturbance of a cabin; an axial levitation controller and a synchronous controller are designed based on the obstacle Lyapunov function. The invention can effectively inhibit the influence of external disturbance and parameter uncertainty on the system operation while ensuring the quick tracking capability of the system, can well consider transient and steady-state performances, and ensures that the engine room runs stably and reliably under the influence of external disturbance.
Description
Technical Field
The invention relates to a control method, in particular to a control method for restraining a wind turbine cabin suspension system state based on a barrier Lyapunov function, and belongs to the technical field of automation.
Background
The magnetic levitation system is a nonlinear and weak damping unstable system in nature, and the wind power cabin magnetic levitation system works on a tower with the height of 80 meters, so that the suspension working condition is severe and the wind speed and the wind direction are time-varying, and the stable suspension of the cabin is very challenging. Because of the large windward area difference between the blade side and the tail wing side of the wind power engine room, the extremely large overturning moment exists on the two sides of the engine room, so that the engine room is extremely easy to pitch, and the operation safety of the wind turbine generator is seriously influenced. Particularly, mechanical impact is caused by too high speed in the process of falling and rising in the suspension process, and the service life of a magnetic suspension system is seriously influenced, so that the stable suspension of the cabin, synchronous control and the improvement of transient performance are important points of research. Compared with the PID control with self-adaptive compensation, the self-adaptive robust control strategy with synchronous compensation has faster dynamic response speed, smaller steady-state error and synchronous error. However, the control strategy does not effectively restrict the system state, and still has the problems of poor interference suppression capability, low dynamic response speed and the like, and cannot effectively cope with high-frequency disturbance and external interference existing in an actual system.
The method based on the Lyapunov function is used for restraining the state of the wind turbine suspended system, so that the tracking error and the synchronization error of the suspended air gap are guaranteed to meet given transient performance indexes, good tracking performance and synchronization effect of the system are guaranteed, and when the system is disturbed, a large control effect is generated, so that the system is restored to a stable running state. However, it is worth pointing out that the conventional Lyapunov function method sets a constant performance index, and a severe performance index is required to be set for improving the response speed of the system, so that the buffeting phenomenon of the system is caused, and singular problems are easily caused due to the fact that the buffeting phenomenon exceeds the limit of the performance index, so that the algorithm is invalid. In order to avoid the buffeting of the system, the control output needs to be provided with smaller gain, and the actual system is inevitably influenced by external interference and uncertainty in the running process, so that the singular problem caused by overrun is very easy to occur, the requirement of lower performance index is required to be set for avoiding the occurrence of the singular problem, the transient performance of the system is improved on the basis, and the control output gain is required to be increased. The state information is introduced into the design of constraint boundaries, so that the constraint sensitive interval can be dynamically adjusted, and the method has good transient performance and steady-state performance.
Disclosure of Invention
The main purpose of the invention is that: aiming at the blank and deficiency of the prior art, the invention provides a full-state constraint wind turbine cabin suspension control method based on a barrier Lyapunov function. Dividing a wind engine room suspension system into an axial suspension system and a pitching suppression system, designing a limited-time interference observer, and restricting the wind engine room suspension controller design based on a full state of a Lyapunov function; the axial suspension system is decomposed into a cabin suspension position system and a cabin suspension speed system by a back-stepping method, and the pitch suppression system is decomposed into a pitch angle system and a pitch angle speed system by a back-stepping method; the cabin suspension position system adopts a boundary function containing cabin suspension position feedback information to restrain suspension positions, the cabin suspension speed system adopts a fixed boundary to restrain suspension speeds, the pitch angle system adopts a boundary function containing pitch angle feedback information to restrain pitch angles, and the pitch angle speed system adopts a fixed boundary to restrain pitch angle speeds; the finite time disturbance observer is designed to estimate the suspension speed, pitch angle speed and external disturbance of the cabin by adopting a disturbance observer with a fractional order form, and is divided into an axial finite time disturbance observer and a pitch finite time disturbance observer; the method comprises the steps that a wind power cabin levitation controller design is based on a constraint boundary designed to constrain the state of a wind power cabin levitation system, the wind power cabin levitation controller design is divided into an axial levitation controller design and a synchronous controller design, the axial levitation controller design obtains a virtual control law based on the constraint of a cabin levitation position system, the virtual control law is used as a virtual reference of a cabin levitation speed system, the axial levitation speed system constraint obtains an actual control input of the axial levitation system, the synchronous controller design obtains a virtual control law based on the constraint of a pitching angle system, the virtual control law is used as a virtual reference of a pitching angle system, the pitch suppression system actual control input is obtained based on the constraint of the pitching angle system, and an uncertain item in the system is compensated by adopting an adaptive method containing fractional order.
In order to achieve the above purpose, the invention provides a full-state constraint wind turbine cabin suspension control method based on a barrier Lyapunov function, which comprises the following steps:
Establishing an axial suspension height system model:
pitch angle suppression system model:
wherein H is the center suspension height H= (H) A +H B )/2，H A And H B Suspension heights of blade side and tail side respectively, L is the sum of suspension air gap and height, (L-H) A ) And (L-H) B ) Respectively a blade side suspension air gap and a tail wing side suspension air gap, wherein theta is a pitching angle mu 0 Is vacuum magnetic conductivity, N is number of turns of suspension windings on two sides, S is magnetic pole area, i A And i B Excitation currents on the blade side and the tail wing side respectively, wherein J is the pitching moment of inertia of the engine room, and T is r Is the nacelle overturning moment, r is the nacelle rotating radius, m is the wind turbine mass, g is the gravitational acceleration, f d For nacelle axial disturbances ΔH x ＝H x -H 0 ，Δi x ＝i x -i 0 Wherein x is A or B, i 0 And H 0 Target current and target air gap, (L-H) 0 ) For axially suspending the air gap.
A) Axial finite time interference observer:
b) Pitch limited time disturbance observer:
wherein x is 1 、x 2 Respectively axial suspension height and axial suspension speed,
observed values of suspension height and suspension speed, x, respectively 3 、x 4 Respectively, pitch angle and pitch angle rate, +.>
Observed values of pitch angle and pitch rate, respectively,/->
For observing errors of suspension height and pitching angle, l 11 、l 21 、l 12 、l 22 、l 13 、l 23 Is a positive scalar, deltau 1 、Δu 2 Is an axial control law and a synchronous control law, +.>
For the external interference estimation value of the axial side and the synchronous side, < >>
b 10 ＝μ 0 N 2 Si 0 /(2m(L-H 0 ) 2 )，a 20 ＝μ 0 N 2 Si 0 2 /(2m(L-H 0 ) 3 )，b 20 ＝μ 0 N 2 Si 0 /(2m(L-H 0 ) 2 )。
A) Axial levitation controller design
Definition variable e 1 ＝x 1 -x 1d ，e 2 ＝x 2 -α 1 Wherein x is 1d Is the desired height, alpha 1 Is a virtual control input variable that is provided by a user,
a1 A) constructing an obstacle Lyapunov function as:
the boundary function containing the suspension position feedback information is constructed as follows:
wherein k is b1_0 ，k b1_∞ ，k t1 ，X 1 ，a 1 ，c 1 ，ξ 1 ，λ 1 Is a normal number, k b1_0 Represents the initial value, k, of the boundary function b1_∞ Representing a boundary function convergence target, k t1 Specifying the function convergence speed, X 1 Defining dynamic intervals of boundary functions e 1 For flying height tracking error, a 1 Influencing the gradient of the boundary function with respect to the fly height tracking error c 1 Influence steady state error interval, ζ 1 ＞1。
k b1 And (3) deriving t:
will V 1 And (3) deriving t to obtain:
wherein,,
errors were observed for levitation speed.
Order the
Wherein τ 1 ，k 1 For a positive scalar, 0 < β < 1 then formula (8) can be changed to:
a2 A constraint boundary for constructing the axial levitation speed system is:
k b2 ＝k b2_∞ (10)
wherein k is b2_∞ Is a positive constant.
Constructing an obstacle Lyapunov function as
Wherein, gamma 1 Is a positive scalar quantity, and the output is a positive scalar quantity,
adaptive estimation error on axial side, will V 2 And (3) deriving t to obtain:
wherein eta 1 As an axial side parameter uncertainty term,
for the axial side adaptation term, the control input variable Deltau is selected 1 The control law is as follows:
wherein τ2, k 2 Is a positive scalar.
The self-adaptive law is selected as follows:
wherein,,
is a positive scalar.
B) Synchronous controller design
Definition variable e 3 ＝x 3 -x 3d ，e 4 ＝x 4 -α 2 (e 3 ) Wherein x is 3d Is the desired angle alpha 2 Is a virtual control input variable that is provided by a user,
b1 Constructing an obstacle Lyapunov function as
The boundary function containing the pitching angle feedback information is constructed as follows:
wherein X is 3 ，a 3 ，c 3 ，ξ 3 ，λ 3 ，k b3_∞ Is of normal number, X 3 Defining dynamic intervals of boundary functions e 3 A is pitch angle tracking error 3 Influencing the gradient of the boundary function with respect to the pitch angle tracking error c 3 Influence steady state error interval, ζ 3 >1。
k b3 And (3) deriving t:
will V 3 And (3) deriving t to obtain:
wherein,,
error is observed for pitch angle speed, +.>
Order the
Wherein τ 3 ，k 3 For a positive scalar, then equation (19) may become:
b2 Constructing an obstacle Lyapunov function as
Wherein,,
for pitch-side adaptive estimation errors, constructing a constraint boundary of a pitch angle speed system is as follows:
k b4 ＝k b4_∞ (22)
wherein k is b4_∞ Is a positive constant;
will V 4 Deriving t to obtain
Wherein eta 2 Is a pitch-side parameter uncertainty term;
selecting a control input variable Deltau 1 The control law is as follows:
wherein τ 4 、k 4 Is a positive scalar quantity, and the output is a positive scalar quantity,
for the pitching side self-adaptive term, selecting a self-adaptive law as follows:
wherein gamma is 2 ，β，
Is a positive scalar;
the main control current of the blade side and the tail side can be obtained by the steps (14) and (25)
The beneficial effects of the invention are as follows:
1) Dividing a wind power cabin suspension system into an axial suspension system and a pitching suppression system; the axial suspension system is divided into a cabin suspension position system and a cabin suspension speed system by a back-stepping method, and the pitching synchronous system is divided into a pitching angle system and a pitching angle speed system.
2) A boundary function containing cabin suspension position feedback information is designed for a cabin suspension position system, a fixed boundary is designed for a cabin suspension speed system, a boundary function containing pitch angle feedback information is designed for a pitch angle system, and a fixed boundary is designed for a pitch angle speed system.
3) The boundary function and the higher-order term thereof designed in the control method are continuous, and no singular problem exists in dynamic adjustment.
4) The finite time disturbance observer is designed to estimate the external disturbance experienced by the system.
5) And finally compensating the uncertain term in the system based on the adaptive method containing fractional order. The method has excellent robustness, so that the tracking error of the system is converged for a limited time. The method has good robustness, and provides powerful guarantee for the wind turbine magnetic levitation system to cope with external high-frequency disturbance and uncertain items.
Drawings
FIG. 1 is a control block diagram of a horizontal axis wind turbine nacelle suspension system of the present invention.
FIG. 2 is a schematic diagram illustrating the analysis of the boundary function of the present invention as a function of the tracking error of the system.
FIG. 3 is a graph of air gap length versus axial disturbance applied by the nacelle under control of the present invention and under control of a comparison algorithm.
FIG. 4 is a graph of an experimental comparison of the air gap length of the nacelle applying pitch disturbance force under the control of the present invention and the control of the comparison algorithm.
FIG. 5 is a graph of a comparative experiment of the synchronization error of the nacelle applied pitch disturbance force under the control of the present invention and the control of the comparative algorithm.
FIG. 6 is a graph of air gap length versus experimental for two sides of a nacelle under control of the present invention applying a pitch disturbance force.
Reference numerals in the drawings: 1-axial air gap constraint boundary function, 2-air gap tracking error, 3-axial speed constraint boundary, 4-pitch angle constraint boundary function, 5-pitch angle error, 6-pitch angle speed constraint boundary, 7-axial air gap, 8-pitch angle, 9-axial finite time disturbance observer, 10-pitch finite time disturbance observer, 11-axial controller, 12-pitch controller, 13-current transformer, 14-blade side current tracking controller, 15-blade side suspension winding, 16-tail side current tracking controller, 17-tail side suspension winding, 18-wind nacelle.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, the levitation electromagnet is composed of windings 15, 17 and a core. When a voltage u (t) is applied to the windings 15 and 17, a current i flows through the windings 15 and 17 1 (t)、i 2 (t) the levitation electromagnet will generate electromagnetic attraction and the yaw stator will be attracted. In the floating process, after the windings 15 and 17 are electrified, the suspension electromagnet moves upwards under the action of electromagnetic attraction, and when interference is applied, u (t) is adjusted along with the change of a suspension air gap, so that i (t) is tracked and changed until stable suspension is achieved.
The invention discloses a finite time suspension control method of a smooth asymmetric obstacle Lyapunov function containing closed loop feedback information, which aims to restrict the state of a cabin suspension system so as to realize a good control effect, and specifically comprises the following steps:
the modeling process is as follows:
according to fig. 1, the windings 15, 17 will generate an upward axial levitation force F (i x (t),δ x ) The method comprises the following steps:
F(i x (t),δ x )＝ki x 2 (t)/δ x 2
according to FIG. 1, the magnetic levitation system is axially subjected to a levitation suction force F with both ends upward A 、F B Downward gravity mg and axial disturbance force f d The method comprises the steps of carrying out a first treatment on the surface of the In the floating process, the rising acceleration is
During landing, the landing acceleration is +.>
The mechanical equation of the magnetic suspension system in the axial direction is as follows:
the length of the air gap is converted into the axial height:
the mechanical equation of the magnetic suspension system about the pitching angle is as follows:
to sum up, a model of a two-degree-of-freedom fly height taking into account the axial fly height and the pitch angle can be obtained:
dividing a two-degree-of-freedom suspension system into an axial suspension system and a pitching suppression system;
axial levitation height system model:
pitch angle suppression system model:
wherein H is the center suspension height H= (H) A +H B )/2，H A And H B Suspension heights of blade side and tail side respectively, L is the sum of suspension air gap and height, (L-H) A ) And (L-H) B ) Respectively a blade side suspension air gap and a tail wing side suspension air gap, wherein theta is a pitching angle mu 0 Is vacuum magnetic conductivity, N is number of turns of suspension windings on two sides, S is magnetic pole area, i A And i B Exciting currents on the blade side and the tail side respectivelyJ is the pitch moment of inertia of the engine room, T r Is the nacelle overturning moment, r is the nacelle rotating radius, m is the wind turbine mass, g is the gravitational acceleration, f d For nacelle axial disturbances ΔH x ＝H x -H 0 ，Δi x ＝i x -i 0 Wherein x is A or B, i 0 And H 0 Target current and target air gap, (L-H) 0 ) For axially suspending the air gap.
A) Axial finite time interference observer:
b) Pitch limited time disturbance observer:
wherein x is 1 、x 2 Respectively axial suspension height and axial suspension speed,
observed values of suspension height and suspension speed, x, respectively 3 、x 4 Respectively, pitch angle and pitch angle rate, +.>
Observed values of pitch angle and pitch rate, respectively,/->
For observing errors of suspension height and pitching angle, l 11 、l 21 、l 12 、l 22 、l 13 、l 23 Is a positive scalar, deltau 1 、Δu 2 Is an axial control law and a synchronous control law, +.>
For the external interference estimation value of the axial side and the synchronous side, a 10 ＝μ 0 N 2 Si 0 2 /(2m(L-H 0 ) 3 )，b 10 ＝μ 0 N 2 Si 0 /(2m(L-H 0 ) 2 )，a 20 ＝μ 0 N 2 Si 0 2 /(2m(L-H 0 ) 3 )，b 20 ＝μ 0 N 2 Si 0 /(2m(L-H 0 ) 2 )。
B) Axial levitation controller design
Definition variable e 1 ＝x 1 -x 1d ，e 2 ＝x 2 -α 1 Wherein x is 1d Is the desired height, alpha 1 Is a virtual control input variable that is provided by a user,
a1 A) constructing an obstacle Lyapunov function as:
the boundary function containing the suspension position feedback information is constructed as follows:
wherein k is b1_0 ，k b1_∞ ，k t1 ，X 1 ，a 1 ，c 1 ，ξ 1 ，λ 1 Is a normal number, k b1_0 Represents the initial value, k, of the boundary function b1_∞ Representing a boundary function convergence target, k t1 Specifying the function convergence speed, X 1 Defining dynamic intervals of boundary functions e 1 For flying height tracking error, a 1 Influencing the gradient of the boundary function with respect to the fly height tracking error，c 1 Influence steady state error interval, ζ 1 ＞1。
k b1 And (3) deriving t:
will V 1 And (3) deriving t to obtain:
wherein,,
errors were observed for levitation speed.
Order the
Wherein τ 1 ，k 1 For a positive scalar, 0 < β < 1 then formula (8) can be changed to:
a2 A constraint boundary for constructing the axial levitation speed system is:
k b2 ＝k b2_∞ (10)
wherein k is b2_∞ Is a positive constant.
Constructing an obstacle Lyapunov function as
Wherein, gamma 1 Is a positive scalar quantity, and the output is a positive scalar quantity,
adaptive estimation error on axial side, will V 2 And (3) deriving t to obtain:
wherein eta 1 As an axial side parameter uncertainty term,
for the axial side adaptation term, the control input variable Deltau is selected 1 The control law is as follows:
wherein τ2, k 2 Is a positive scalar.
The self-adaptive law is selected as follows:
wherein,,
is a positive scalar.
B) Synchronous controller design
Definition variable e 3 ＝x 3 -x 3d ，e 4 ＝x 4 -α 2 (e 3 ) Wherein x is 3d Is the desired angle alpha 2 Is a virtual control input variable that is provided by a user,
b1 Constructing an obstacle Lyapunov function as
The boundary function containing the pitching angle feedback information is constructed as follows:
wherein X is 3 ，a 3 ，c 3 ，ξ 3 ，λ 3 ，k b3_∞ Is of normal number, X 3 Defining dynamic intervals of boundary functions e 3 A is pitch angle tracking error 3 Influencing the gradient of the boundary function with respect to the pitch angle tracking error c 3 Influence steady state error interval, ζ 3 >1。
k b3 And (3) deriving t:
will V 3 And (3) deriving t to obtain:
wherein,,
error is observed for pitch angle speed, +.>
Order the
Wherein τ 3 ，k 3 For a positive scalar, then equation (19) may become:
b2 Constructing an obstacle Lyapunov function as
Wherein,,
for pitch-side adaptive estimation errors, constructing a constraint boundary of a pitch angle speed system is as follows:
k b4 ＝k b4_∞ (22)
wherein k is b4_∞ Is a positive constant;
will V 4 Deriving t to obtain
Wherein eta 2 Is a pitch-side parameter uncertainty term;
selecting a control input variable Deltau 1 The control law is as follows:
wherein τ 4 、k 4 Is a positive scalar quantity, and the output is a positive scalar quantity,
for the pitching side self-adaptive term, selecting a self-adaptive law as follows:
wherein gamma is 2 ，β，
Is a positive scalar;
the main control current of the blade side and the tail side can be obtained by the steps (14) and (25)
The invention is further illustrated by the following preferred embodiment.
Example 1: the system parameters of the magnetic suspension system are as follows: effective area s= 235050mm of pole surface of suspension electromagnet 2 The total mass m of the suspension body is=500 kg, the number of turns of the exciting coil of the suspension electromagnet is n=6400 turns, the resistance R of the exciting coil is 4.4Ω, and the vacuum magnetic permeability is mu 0 ＝4π×10 -7 H/m; suspension electromagnet height H when stabilizing suspension equilibrium point 0 Suspension electromagnet height H at rest position =0.013 m 1 ＝0.009m。
Based on the above system parameters, system simulation conditions: (1) simulation experiment of axial interference resistance: the running time is t=0-15 s, and the expected track tracking function of the process is selected as H ref (t) =0.013, and 1000N axial interferences were added at t=5 s, and interferences were removed at t=10 s; (2) anti-pitch interference simulation experiment: the running time is t=0-15 s, and the expected track tracking function of the process is selected as H ref (t) =0.013, 1000N pitch disturbances are added at t=5 s, and the disturbances are removed at t=15 s. And simulating the system according to the simulation conditions, so as to verify the anti-interference capability of the system to external disturbance at the moment of operation. As shown in fig. 3, 4, 5 and 6.
FIG. 3 shows a simulation curve of a track tracking suspension air gap in an anti-axial interference 1000 simulation experiment, wherein the simulation effects of two types of algorithms are distinguished linearly. As can be seen from the graph, when axial interference is applied, the maximum air gap rising value of the method is only 0.015mm, the recovery time is only 0.025s, and compared with the traditional obstacle Lyapunov function method, the method has stronger anti-interference capability and quicker response speed.
FIG. 4 shows a trace tracking suspension air gap simulation curve in a pitch disturbance resisting 1000N simulation experiment, wherein the simulation effect of two types of algorithms is distinguished by the line type. As can be seen from the graph, when pitch interference is applied, the maximum rising of the air gap is only 0.017mm, the recovery time is only 0.03s, and compared with the traditional obstacle Lyapunov function, the method has stronger anti-interference capability and quicker response speed.
FIG. 5 shows a simulation curve of synchronous errors in a 1000N simulation experiment of anti-pitch disturbance, wherein the simulation effects of two types of algorithms are distinguished linearly. As can be seen from the graph, when pitch interference is applied, the maximum synchronization error is only 0.019mm, the recovery time is only 0.01s, and compared with the traditional obstacle Lyapunov function method, the method has a better synchronization effect.
FIG. 6 shows a suspension air gap simulation curve of the proposed algorithm with both end trajectory tracking in anti-pitch disturbance simulation experiments, in which the blade side and tail wing side are distinguished linearly. As can be seen from the figure, the maximum air gap offset is 0.021mm and the recovery time is 0.03s when pitch disturbance is applied.
The results show that the control method of the invention can effectively inhibit the influence of external disturbance and parameter uncertainty on the system operation while ensuring the rapid tracking capability and stability of the system, has good robustness and ensures the stable and reliable operation of the magnetic suspension system.
Claims (4)
1. A full-state constraint wind turbine generator suspension control method based on an obstacle Lyapunov function is characterized by comprising the following steps of: dividing a wind engine room suspension system into an axial suspension system and a pitching suppression system, designing a limited-time interference observer, and restricting the wind engine room suspension controller design based on a full state of a Lyapunov function; the axial suspension system is decomposed into a cabin suspension position system and a cabin suspension speed system by a back-stepping method, and the pitch suppression system is decomposed into a pitch angle system and a pitch angle speed system by a back-stepping method; the cabin suspension position system adopts a boundary function containing cabin suspension position feedback information to restrain suspension positions, the cabin suspension speed system adopts a fixed boundary to restrain suspension speeds, the pitch angle system adopts a boundary function containing pitch angle feedback information to restrain pitch angles, and the pitch angle speed system adopts a fixed boundary to restrain pitch angle speeds; the finite time disturbance observer is designed to estimate the suspension speed, pitch angle speed and external disturbance of the cabin by adopting a disturbance observer with a fractional order form, and is divided into an axial finite time disturbance observer and a pitch finite time disturbance observer; the full-state constraint wind power cabin suspension controller design based on the obstacle Lyapunov function is used for constraining the state of a wind power cabin suspension system based on a designed constraint boundary and comprises an axial suspension controller design and a synchronous controller design, wherein the axial suspension controller design is used for obtaining a virtual control law based on the constraint of a cabin suspension position system, the virtual control law is used as a virtual reference of a cabin suspension speed system, the axial suspension system actual control input is obtained based on the constraint of an axial suspension speed system, the synchronous controller design is used for obtaining the virtual control law based on the constraint of a pitch angle system, the virtual control law is used as a virtual reference of a pitch angle speed system, the pitch suppression system actual control input is obtained based on the constraint of the pitch angle speed system, and an uncertainty item in the system is compensated by adopting an adaptive method containing fractional steps, and the method comprises the following steps:
step 1, dividing a wind power cabin suspension system into an axial suspension system and a pitching suppression system;
step 2, designing a finite time interference observer;
and 3, designing a full-state constraint wind turbine generator suspension controller based on the obstacle Lyapunov function.
2. The obstacle-Lyapunov function-based full-state constraint wind turbine nacelle levitation control method as set forth in claim 1, wherein: the step 1 specifically comprises the following steps:
establishing an axial suspension height system model:
pitch angle suppression system model:
wherein H is the center suspension height H= (H) A +H B )/2，H A And H B Suspension heights of blade side and tail side respectively, L is the sum of suspension air gap and height, (L-H) A ) And (L-H) B ) Respectively a blade side suspension air gap and a tail wing side suspension air gap, wherein theta is a pitching angle mu 0 Is vacuum magnetic conductivity, N is number of turns of suspension windings on two sides, S is magnetic pole area, i A And i B Excitation currents on the blade side and the tail wing side respectively, wherein J is the pitching moment of inertia of the engine room, and T is r Is the nacelle overturning moment, r is the nacelle rotating radius, m is the wind turbine mass, g is the gravitational acceleration, f d For nacelle axial disturbances ΔH x ＝H x -H 0 ，Δi x ＝i x -i 0 Wherein x is A or B, i 0 And H 0 Target current and target air gap, (L-H) 0 ) For axially suspending the air gap.
3. The obstacle-based Lyapunov function full-state constraint wind turbine nacelle suspension control method as claimed in claim 2, wherein the method comprises the following steps of: the step 2 specifically comprises the following steps:
a) Axial finite time interference observer:
b) Pitch limited time disturbance observer:
wherein x is 1 、x 2 Respectively axial suspension height and axial suspension speedThe degree of the heat dissipation,
observed values of suspension height and suspension speed, x, respectively 3 、x 4 Respectively, pitch angle and pitch angle rate, +.>
Observed values of pitch angle and pitch rate, respectively,/->
For observing errors of suspension height and pitching angle, l 11 、l 21 、l 12 、l 22 、l 13 、l 23 Is a positive scalar, deltau 1 、Δu 2 Is an axial control law and a synchronous control law, +.>
For the external interference estimation value of the axial side and the synchronous side, a 10 ＝μ 0 N 2 Si 0 2 /(2m(L-H 0 ) 3 )，b 10 ＝μ 0 N 2 Si 0 /(2m(L-H 0 ) 2 )，a 20 ＝μ 0 N 2 Si 0 2 /(2m(L-H 0 ) 3 )，b 20 ＝μ 0 N 2 Si 0 /(2m(L-H 0 ) 2 )。
4. A method of barrier Lyapunov function based full state constraint wind nacelle suspension control as defined in claim 3 wherein: the step 3 specifically comprises the following steps:
a) Axial levitation controller design
Definition variable e 1 ＝x 1 -x 1d ，e 2 ＝x 2 -α 1 Wherein x is 1d Is the desired height, alpha 1 Is a virtual control input variable that is provided by a user,
a1 A) constructing an obstacle Lyapunov function as:
the boundary function containing the suspension position feedback information is constructed as follows:
wherein k is b1_0 ，k b1_∞ ，k t1 ，X 1 ，a 1 ，c 1 ，ξ 1 ，λ 1 Is a normal number, k b1_0 Represents the initial value, k, of the boundary function b1_∞ Representing a boundary function convergence target, k t1 Specifying the function convergence speed, X 1 Defining dynamic intervals of boundary functions e 1 For flying height tracking error, a 1 Influencing the gradient of the boundary function with respect to the fly height tracking error c 1 Influence steady state error interval, ζ 1 ＞1；
k b1 And (3) deriving t:
will V 1 And (3) deriving t to obtain:
wherein,,
observing errors for the suspension speed;
order the
Wherein τ 1 ，k 1 For a positive scalar, 0 < β < 1 then formula (8) can be changed to:
a2 A constraint boundary for constructing the axial levitation speed system is:
k b2 ＝k b2_∞ (10)
wherein k is b2_∞ Is a positive constant;
constructing an obstacle Lyapunov function as
Wherein, gamma 1 Is a positive scalar quantity, and the output is a positive scalar quantity,
adaptive estimation error on axial side, will V 2 And (3) deriving t to obtain:
wherein eta 1 As an axial side parameter uncertainty term,
for the axial side adaptation term, the control input variable Deltau is selected 1 The control law is as follows:
wherein τ2, k 2 Is a positive scalar;
the self-adaptive law is selected as follows:
wherein,,
is a positive scalar;
b) Synchronous controller design
Definition variable e 3 ＝x 3 -x 3d ，e 4 ＝x 4 -α 2 (e 3 ) Wherein x is 3d Is the desired angle alpha 2 Is a virtual control input variable that is provided by a user,
b1 Constructing an obstacle Lyapunov function as
The boundary function containing the pitching angle feedback information is constructed as follows:
wherein X is 3 ，a 3 ，c 3 ，ξ 3 ，λ 3 ，k b3_∞ Is of normal number, X 3 Defining dynamics of boundary functionsInterval e 3 A is pitch angle tracking error 3 Influencing the gradient of the boundary function with respect to the pitch angle tracking error c 3 Influence steady state error interval, ζ 3 >1；
k b3 And (3) deriving t:
will V 3 And (3) deriving t to obtain:
wherein,,
error is observed for pitch angle speed, +.>
Order the
Wherein τ 3 ，k 3 For a positive scalar, then equation (19) may become:
b2 Constructing an obstacle Lyapunov function as
Wherein,,
is self-adaptive to pitching sideThe error should be estimated, and the constraint boundaries for constructing the pitch angle rate system are:
k b4 ＝k b4_∞ (22)
wherein k is b4_∞ Is a positive constant;
will V 4 Deriving t to obtain
Wherein eta 2 Is a pitch-side parameter uncertainty term;
selecting a control input variable Deltau 1 The control law is as follows:
wherein τ 4 、k 4 Is a positive scalar quantity, and the output is a positive scalar quantity,
for the pitching side self-adaptive term, selecting a self-adaptive law as follows:
wherein gamma is 2 ，β，
Is a positive scalar;
the main control current of the blade side and the tail side can be obtained by the steps (14) and (25)
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| US20050096793A1 (en) * | 2003-10-30 | 2005-05-05 | Kabushiki Kaisha Toshiba | Reference model tracking control system and method |
| US20060293817A1 (en) * | 2005-06-23 | 2006-12-28 | Takahide Hagiwara | Intelligent electronically-controlled suspension system based on soft computing optimizer |
| CN111682815A (en) * | 2020-06-17 | 2020-09-18 | 曲阜师范大学 | Wind power engine room yaw control method containing high-frequency interference reconstruction |
| CN113051834A (en) * | 2021-04-13 | 2021-06-29 | 曲阜师范大学 | Model reference-based cabin suspension system RBF neural network adaptive decoupling control method |
| CN113204190A (en) * | 2021-04-19 | 2021-08-03 | 东北大学 | Design method of active suspension controller |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US20050096793A1 (en) * | 2003-10-30 | 2005-05-05 | Kabushiki Kaisha Toshiba | Reference model tracking control system and method |
| US20060293817A1 (en) * | 2005-06-23 | 2006-12-28 | Takahide Hagiwara | Intelligent electronically-controlled suspension system based on soft computing optimizer |
| CN111682815A (en) * | 2020-06-17 | 2020-09-18 | 曲阜师范大学 | Wind power engine room yaw control method containing high-frequency interference reconstruction |
| CN113051834A (en) * | 2021-04-13 | 2021-06-29 | 曲阜师范大学 | Model reference-based cabin suspension system RBF neural network adaptive decoupling control method |
| CN113204190A (en) * | 2021-04-19 | 2021-08-03 | 东北大学 | Design method of active suspension controller |
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