CN114326383B - Ocean platform vibration reduction control algorithm for on-line compensation of uncertain structure - Google Patents
Ocean platform vibration reduction control algorithm for on-line compensation of uncertain structure Download PDFInfo
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Abstract
An ocean platform vibration reduction control algorithm for on-line compensation of an uncertain structure, comprising: s1, according to ocean platform motion model parameters, providing linear feedback for additionControl law of line compensation; s2, designing a Lyapunov function, and combining an H infinity index to obtain a linear matrix inequality and a linear matrix equation; s3, solving an H infinity index gamma meeting the inequality of the linear matrix; s4, gradually reducing the numerical value of an H infinity index gamma; s5, judging whether the H infinity index gamma meets the preset condition, if so, repeating the step 4, and if not, acquiring the minimum index within the range of the linear matrix inequality solution; s6, determining a value K of the control gain according to the inequality of the linear matrix; s7, determining a preset parameter P according to the inequality of the linear matrix 1 The method comprises the steps of carrying out a first treatment on the surface of the S8, solving according to the obtained H infinity indexAnd updating W in the linear matrix equation on line to obtain the ocean platform vibration reduction control law. The invention improves the vibration reduction effect of the ocean platform by applying an on-line compensation strategy.
Description
Technical Field
The invention relates to an ocean platform vibration reduction control system, belongs to the technical field of ocean engineering, and particularly relates to an ocean platform vibration reduction control algorithm for on-line compensation of an uncertain structure.
Background
Offshore drilling platforms operate in offshore environments, and platform steel structures are susceptible to ocean waves and tides and produce structural vibrational responses. The wave interference it is subjected to can be difficult to measure. Most control systems have noise or other periodic disturbances, and the geographical location of the ocean platform determines that it is subject to wave disturbances of a significant order of magnitude and with non-periodic variations. Wave forces may have an impact on the strength, mooring etc. of the steel structure of the platform, and structural changes in the platform during operation activities may cause the vibration damping stabilization system it is equipped with to be asynchronous with the actual system.
At present, for ocean platform vibration damping control, structural uncertainty item assumption upper bound is generally required to carry out algorithm design. When the dynamic characteristics of a structure are specifically analyzed, the action load caused by waves is difficult to capture by a sensor in real time, so that the modeling of a system containing external interference is often inaccurate; when describing the actual control process, uncertainty factors such as structural changes of platform parameters, measurement errors and the like further influence the vibration reduction control effect. Therefore, it is necessary to quantify system disturbances during vibration damping and to develop research specifically for uncertain structures.
The existing interference suppression strategy mostly applies the internal mode principle, namely, external disturbance is introduced into the design of a control law, and an internal model of a control system is constructed, so that the part of bad disturbance is counteracted. However, the internal model principle relies on accurate estimation and reconstruction of internal model to external interference, and is suitable for a system under the influence of white noise and periodic interference, and is difficult to realize in practical application. In addition, for the dynamics equation and the control object which is likely to have asynchronous phenomenon in practice, the internal model principle is difficult to select a proper model. In addition, the prior art generally adopts a fixed gain value for control, and the control parameters are difficult to adjust in time according to actual conditions, so that the application effect is greatly reduced, and the defects are more obvious when modeling errors are larger.
Disclosure of Invention
The invention aims to provide an ocean platform vibration reduction control algorithm aiming at on-line compensation of an uncertain structure, which is used for solving the problems that the existing control algorithm is difficult to select a proper model for interference, control parameters cannot be adjusted according to actual conditions and the like, and influencing application and vibration reduction effects.
The vibration damping method combined with the internal mold principle generally comprises the following steps:
u(t)＝K x x(t)+K f f(t) (8)
wherein u (t) is the control force input into the platform at the moment t, x (t) is the structural response embodied by the main mode of the platform, f (t) is the wave interference received by the platform, and K x ，K f For a corresponding control gain.
It can be seen that the determination of the vibration damping control law needs to know time-varying random wave force in advance, and in the case that real-time wave interference is not measurable, the vibration damping control law is not available, for example, a platform is not provided with a high-precision wave real-time sensor, or a wave sensor has delay and the like, the control law can lack wave force item input, so that the final control law cannot realize vibration damping control of the ocean platform.
The invention is realized by the following technical scheme:
an ocean platform vibration reduction control algorithm for on-line compensation of an uncertain structure comprises the following steps:
s1, according to ocean platform motion model parameters, providing a control law of linear feedback additional online compensation;
s2, designing a Lyapunov function, and combining an H infinity index to obtain a linear matrix inequality and a linear matrix equation;
s3, solving an H infinity index gamma meeting the inequality of the linear matrix;
s4, gradually reducing the numerical value of an H infinity index gamma;
s5, judging whether the H infinity index gamma meets the preset condition, if so, repeating the step 4, and if not, acquiring the minimum index within the range of the linear matrix inequality solution;
s6, determining a value K of the control gain according to the inequality of the linear matrix;
s7, determining a preset parameter P according to the inequality of the linear matrix 1 ；
S8, solving according to the obtained H infinity indexAnd updating W in the linear matrix equation on line to obtain the ocean platform vibration reduction control law.
In order to achieve the purpose of the invention, the following technical scheme can be adopted:
in the ocean platform vibration reduction control algorithm for on-line compensation of the uncertain structure, in step S1, an ocean platform motion model equation is as follows:
wherein x is an n-dimensional displacement vector, x ε R n The method comprises the steps of carrying out a first treatment on the surface of the u is m-dimensional control force vector, u E R m The method comprises the steps of carrying out a first treatment on the surface of the f is a p-dimensional wave force vector, f E R p The method comprises the steps of carrying out a first treatment on the surface of the A. B, D is a coefficient matrix of the relevant dimension, Δa, Δb, Δd is a structural perturbation parameter.
In the ocean platform vibration reduction control algorithm for on-line compensation of the uncertain structure, in step S1, linear feedback is to replace each combination of uncertain perturbation parameters of an ocean platform motion model equation, and a new motion equation is obtained as follows:
wherein G (t) is a newly defined uncertainty term;
the control law of online compensation is that
u(t)＝u 1 (t)+u 2 (t) (3)
Wherein u is 1 (t) =w (t) H (t) is the online compensation part, W (t) is the compensation parameter of the online compensation term, H (t) =2 (1-e -2x(t) ) -1 is a nonlinear characteristic term added for the uncertainty term, u 2 (t) =kx (t) is a fixed gain feedback section, K is a fixed feedback term coefficient, and W (t) and K are obtained from a linear matrix equation and a linear matrix inequality, respectively, which satisfy the H infinity index.
The specific process of step S2 includes the following steps:
A1. the influence of interference on the ocean platform model is quantized into an H infinite index gamma, and a Lyapunov function is designed as follows:
wherein V (t)>0 is one of conditions that an ocean platform motion model equation is gradually stabilized under the action of an H infinite on-line control law, epsilon is given non-negative constant and positive definite matrix P 1 >0，Q 1 >0，R>0，P 1 -E>0；
A2. The second component of the ocean platform motion model equation under the action of an H infinite on-line control law is a derivativeDefinition α= [ x ] T (t)x T (t-ε)f T (t)]And deriving formula (4) to obtain
Wherein phi is 1 ＝x T (t)PBW(t)H(t)，Φ 2 ＝x T (t)PG(t)，
A3. Let epsilon-0 and H infinity be the condition, apply Schur's complement theorem to equation (5) to obtain linear matrix equation and linear matrix inequality to makeIs true, where p=p 1 -1 ，Q＝P 1 -1 Q 1 P 1 -1 ，/>
As described above, the linear matrix equation is:
the linear matrix inequality is:
wherein the positive definite matrix P>0，P 1 >0，Q>0，R>0，E>0 and P 1 >E，
In step S8, the specific process of online updating the linear matrix equation is as follows:
B1. determining a state feedback control section based on a value K of the control gain;
B2. according to preset parameter P 1 Setting parameters, and updating the nonlinear part of the linear matrix equation online;
B3. and superposing the fixed gain part in the step B1 and the online compensation part in the step B2, determining a control input, and updating the control input to a control object.
Compared with the prior art, the invention has the following beneficial effects and advantages:
for control systems where external disturbances cannot be measured, there are cases in the prior art where disturbance observers are designed to obtain an accurate internal model. For time-varying random wave forces, the accurate modeling is difficult, so that the control effect is difficult to ensure. Aiming at other uncertain factors, the prior art has cases of designing the vibration damping controller by means of fuzzy rules, but the cases need to rely on a segmented data model of each subsystem after fuzzy when solving the optimal control law, and the calculated amount is large. Aiming at the structure perturbation problem, other H infinite controllers often consider the worst case when selecting the Lyapunov function, and the system deformation maximum value is listed in a matrix, and the online compensation measurement provided by the invention is more flexible, and parameter values do not need to be set in advance. The method applies an online compensation strategy, does not introduce upper and lower limit limits of parameters, and carries out targeted repair compensation on uncertain items. Specifically:
1. according to the invention, interference is not required to be directly acquired, an interference model is not required to be established, and the application range of the control algorithm for resisting external interference phenomenon is widened. Compared with the existing vibration damping algorithm which needs accurate interference data to establish an internal model, the vibration damping algorithm can be applied to a specific system with unknown interference, and stability under random interference can be maintained after the completion of presetting.
2. The controlled object does not need to accurately acquire a specific part or degree of structural change, a lyapunov function is designed without adopting the worst case of a traditional algorithm, namely setting upper and lower bounds, and the structural perturbation part is simplified through a linear matrix inequality. On the basis of the existing fixed gain control algorithm, an on-line compensation control part aiming at structural perturbation is additionally arranged, and system modeling and asynchronous errors are made up.
3. The control law design comprises a linear part and a nonlinear part, wherein the linear part and the nonlinear part comprise control gain with nonlinear characteristics and an online compensation law, and the control law can be applied to other control scenes except the control law design method, and has good adaptability to wider control requirements.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below.
FIG. 1 is a diagram of a marine platform model structure according to the present invention;
FIG. 2 is a graph of simulation of vibration damping displacement response of an ocean platform according to an embodiment;
fig. 3 is a simulation diagram of vibration reduction acceleration response values of the ocean platform according to an embodiment.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention.
The embodiment discloses an ocean platform vibration reduction control algorithm for on-line compensation of an uncertain structure, which comprises the following steps:
s1, according to ocean platform motion model parameters, providing a control law of linear feedback additional online compensation;
s2, designing a Lyapunov function, and combining an H infinity index to obtain a linear matrix inequality and a linear matrix equation;
s3, solving an H infinity index gamma meeting the inequality of the linear matrix;
s4, gradually reducing the numerical value of an H infinity index gamma;
s5, judging whether the H infinity index gamma meets the preset condition, if so, repeating the step 4, and if not, acquiring the minimum index within the range of the linear matrix inequality solution;
s6, determining a value K of the control gain according to the inequality of the linear matrix;
s7, determining a preset parameter P according to the inequality of the linear matrix 1 ；
S8, solving according to the obtained H infinity indexAnd updating W in the linear matrix equation on line to obtain the ocean platform vibration reduction control law.
Specifically, as shown in fig. 1, a pipe-line ocean platform system is simplified into a simplified model under the action of time-varying and periodic wave forces by using an MATLAB platform.
The ocean platform motion model equation is as follows:
wherein x is an n-dimensional displacement vector, x ε R n The method comprises the steps of carrying out a first treatment on the surface of the u is m-dimensional control force vector, u E R m The method comprises the steps of carrying out a first treatment on the surface of the f is a p-dimensional wave force vector, f E R p The method comprises the steps of carrying out a first treatment on the surface of the A. B, D is a coefficient matrix of the relevant dimension, Δa, Δb, Δd is a structural perturbation parameter.
The following H infinity control problem is defined based on the ocean platform motion model equation,
(i) The closed loop control system represented by equation (1) is progressively stable at disturbance f=0.
(ii) Under the zero initial condition, a non-negative constant gamma is used as an H infinity index to meet the condition, namely, the formula (9):
the closed loop control system is made progressively stable, where C is the system output system matrix and the non-zero disturbance at time t, f (t), is energy bounded.
Definition of the definition
Wherein the linear feedback, i.e. the system perturbation term, is
G(t)＝ΔAx(t)+ΔBu(t)+ΔDf(t) (10)
The design of the H infinity-based online control law is as follows:
u(t)＝u 1 (t)+u 2 (t) (3)
wherein u is 1 (t) =w (t) H (t) is the online compensation part, H (t) =2 (1-e) -2x(t) ) -1 adding a nonlinear characteristic to the uncertainty term, u 2 (t) =kx (t) is a fixed part, W (t) and K are obtained from the following linear matrix equation (6) and linear matrix inequality (7) satisfying the H infinity index, respectively, where positive definite matrix P>0，P 1 >0，Q>0，R>0，E>0 and P 1 >E，
The linear matrix equation is:
the linear matrix inequality is:
wherein the positive definite matrix P>0，P 1 >0，Q>0，R>0，E>0 and P 1 >E，
The principle and the operation process of the invention are described as follows:
the ocean platform vibration reduction control law constructed by considering simple linear feedback is as follows by applying the internal model principle:
u(t)＝K x x(t)+K x f(t) (8)
wherein K is x ，K f For corresponding control gain, if the wave interference term f cannot be obtained, the control law is difficult to realize.
Therefore, an H infinite control strategy is selected, and the algorithm process for acquiring the ocean platform vibration reduction control law is as follows:
A1. the influence of interference on the ocean platform is quantized into an H infinite index gamma, and a Lyapunov function is designed as follows:
wherein V (t)>0 is one of conditions that an ocean platform motion model equation is gradually stabilized under the action of an H infinite on-line control law, epsilon is given non-negative constant and positive definite matrix P>0，P 1 >0，Q>0，R>0，E>0 and P 1 >E；
A2. The second component of the ocean platform motion model equation under the action of an H infinite on-line control law is a derivativeDefinition α= [ x ] T (t)x T (t-ε)f T (t)]And deriving formula (4) to obtain
Wherein phi is 1 ＝x T (t)PBW(t)H(t)，Φ 2 ＝x T (t)PG(t)，
A3. Let ε.fwdarw.0, combine H infinity to apply Schur's complement theorem to equation (18) to obtain linear matrix equation and linear matrix inequality to makeIs true, where p=p 1 -1 ，Q＝P 1 -1 Q 1 P 1 -1 ，/>
A4. The H infinity index γ of the linear matrix inequality (7) is calculated and smaller γ values are continually found over the range of solutions.
A5. Finding gamma and then solvingAnd updating the linear matrix equation (6) on line to obtain the ocean platform vibration reduction control law.
As shown in fig. 2 and 3, numerical simulation was performed using the linear matrix equation (6) and the linear matrix inequality (7) as an H-infinity online compensation controller. The wave height of the ocean environment is 5.2m, the wave crest frequency is 0.73rad/s, and the asynchronous time difference is 45 times of the sampling period, namely, the control state lag is 0.45s.
At this time, only the linear matrix inequality (7) is used for online supplementing to obtain K=1.0e+06 [1.7669 0.0011-0.0230-0.0121] to exert control, such as waveforms represented by virtual dot lines far from the middle line in the displacement response of fig. 2 and the acceleration response of fig. 3, which indicate that the vibration damping control of the ocean platform is invalid. On this basis, after adding the linear matrix equation (6) control, the online compensation parameter r=2e—5 [1 00 0; 01 0 0; 001 0; 00 01], such as the waveform represented by the displacement response of fig. 2 and the acceleration response of fig. 3, which are closer to the middle solid line, indicating that the vibration damping control on the ocean platform is effective. In both modes, specific comparison results of the numerical simulation are shown in table 1 below.
Table 1 comparison of vibration damping effect
The technical content that is not described in detail in the invention is known in the prior art.
Claims (5)
1. The ocean platform vibration reduction control algorithm for on-line compensation of the uncertain structure is characterized by comprising the following steps of:
s1, according to ocean platform motion model parameters, providing a control law of linear feedback additional online compensation;
s2, designing a Lyapunov function, and combining an H infinity index to obtain a linear matrix inequality and a linear matrix equation; the specific process of step S2 includes:
A1. the influence of interference on the ocean platform is quantized into an H infinite index gamma, and a Lyapunov function is designed as follows:
wherein V (t) > 0 is one of conditions of progressive stability of ocean platform motion model equation under the action of H infinity on-line control law, epsilon is given non-negative constant, and positive definite matrix P 1 >0，Q 1 >0，R>0，P 1 -E>0；
A2. The second component of the ocean platform motion model equation under the action of an H infinite on-line control law is a derivativeDefinition α= [ x ] T (t)x T (t-ε)f T (t)]And deriving formula (4) to obtain
Wherein phi is 1 ＝x T (t)PBW(t)H(t)，φ 2 ＝x T (t)PG(t)，
A3. Let epsilon-0 and H infinity be the condition, apply Schur's complement theorem to equation (5) to obtain linear matrix equation and linear matrix inequality to makeIs true, wherein->
S3, solving an H infinity index gamma meeting the inequality of the linear matrix;
s4, gradually reducing the numerical value of an H infinity index gamma;
s5, judging whether the H infinity index gamma meets the preset condition, if so, repeating the step 4, and if not, acquiring the minimum index within the range of the linear matrix inequality solution;
s6, determining a value K of the control gain according to the inequality of the linear matrix;
s7, determining a preset parameter P according to the inequality of the linear matrix 1 ；
S8, solving according to the obtained H infinity indexAnd updating W in the linear matrix equation on line to obtain the ocean platform vibration reduction control law.
2. The ocean platform vibration reduction control algorithm for on-line compensation of uncertain structures according to claim 1, wherein in step S1, the ocean platform motion model equation is:
wherein x is an n-dimensional displacement vector, x ε R n The method comprises the steps of carrying out a first treatment on the surface of the u is m-dimensional control force vector, u E R m The method comprises the steps of carrying out a first treatment on the surface of the f is a p-dimensional wave force vector, f E R p The method comprises the steps of carrying out a first treatment on the surface of the A. B, D is a coefficient matrix of the relevant dimension, Δa, Δb, Δd is a structural perturbation parameter.
3. The ocean platform vibration reduction control algorithm for on-line compensation of uncertain structures according to claim 1, wherein in step S1, the linear feedback is to replace each combination of uncertain perturbation parameters of an ocean platform motion model equation, and the new motion equation is obtained by:
wherein G (t) is a newly defined uncertainty term;
the control law of online compensation is that
u(t)＝u 1 (t)+u 2 (t) (3)
Wherein u is 1 (t) =w (t) H (t) is the online compensation part, W (t) is the compensation parameter of the online compensation term, H (t) =2 (1-e -2x(t) ) -1 is a nonlinear characteristic term added for the uncertainty term, u 2 (t) =kx (t) is a fixed gain feedback section, K is a fixed feedback term coefficient, W(t) and K are obtained from a linear matrix equation and a linear matrix inequality, respectively, that satisfy the H infinity index.
4. The ocean platform vibration damping control algorithm for on-line compensation of uncertain structures according to claim 1, wherein the linear matrix equation is:
the linear matrix inequality is:
wherein the positive definite matrix P>0，P1>0，Q>0，R>0，E>0 and P1>E，
5. The ocean platform vibration reduction control algorithm for on-line compensation of uncertain structures according to claim 1, wherein in step S8, the specific process of on-line updating the linear matrix equation is as follows:
B1. determining a state feedback control section based on a value K of the control gain;
B2. according to preset parameter P 1 Setting parameters, and updating the nonlinear part of the linear matrix equation online;
B3. and superposing the fixed gain part in the step B1 and the online compensation part in the step B1, determining a control input, and updating the control input to a control object.
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| CN108646798A (en) * | 2018-06-13 | 2018-10-12 | 南京理工大学 | A kind of Vibration Control of Offshore Platform strategy based on handover control system |
| CN112650056A (en) * | 2020-10-14 | 2021-04-13 | 中国海洋大学 | Method, device and equipment for determining vibration reduction control law of ocean platform and storage medium |
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| CN108646798A (en) * | 2018-06-13 | 2018-10-12 | 南京理工大学 | A kind of Vibration Control of Offshore Platform strategy based on handover control system |
| CN112650056A (en) * | 2020-10-14 | 2021-04-13 | 中国海洋大学 | Method, device and equipment for determining vibration reduction control law of ocean platform and storage medium |
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