阅读说明：本技术 一种基于升沉补偿平台多液压缸并联运动的同步控制方法 (Synchronous control method based on parallel motion of multiple hydraulic cylinders of heave compensation platform ) 是由 潘梦婷 张冰 赵强 周萌萌 左思雨 于 2021-06-17 设计创作，主要内容包括：本发明公开了一种基于升沉补偿平台多液压缸并联运动的同步控制方法,包括如下步骤：建立电液伺服阀控非对称液压缸系统的数学模型；基于建立的数学模型设计预测控制器,获得最优控制律,控制单电液伺服通道实现精确的位置跟踪；基于预测控制器结合环形耦合的控制策略设计同步补偿控制器,补偿六个液压缸之间的同步误差,实现对多电液伺服阀控非对称缸通道的同步控制。本发明实现对单电液伺服阀控非对称缸通道的位置控制,对多电液伺服控非对称缸通道的同步控制,提高系统的位置控制精度以及同步控制性能,保证升沉补偿平台的稳定运作补偿船舶的不规则运动。(The invention discloses a synchronous control method based on the parallel motion of a plurality of hydraulic cylinders of a heave compensation platform, which comprises the following steps: establishing a mathematical model of the electro-hydraulic servo valve control asymmetric hydraulic cylinder system; designing a prediction controller based on the established mathematical model to obtain an optimal control law and control a single electro-hydraulic servo channel to realize accurate position tracking; and designing a synchronous compensation controller based on a prediction controller and combined with a control strategy of annular coupling to compensate synchronous errors among six hydraulic cylinders, thereby realizing synchronous control on the channels of the multi-electro-hydraulic servo valve-controlled asymmetric cylinders. The invention realizes the position control of the single electro-hydraulic servo valve-controlled asymmetric cylinder channel and the synchronous control of the multi-electro-hydraulic servo control asymmetric cylinder channel, improves the position control precision and the synchronous control performance of the system, and ensures the stable operation of the heave compensation platform to compensate the irregular motion of the ship.)

1. A synchronous control method based on the parallel motion of a plurality of hydraulic cylinders of a heave compensation platform is characterized by comprising the following steps:

s1: establishing a mathematical model of the electro-hydraulic servo valve control asymmetric hydraulic cylinder system;

s2: designing a prediction controller based on the established mathematical model to obtain an optimal control law and control a single electro-hydraulic servo channel to realize position tracking;

s3: and designing a synchronous compensation controller based on the prediction controller of the step S2 and the control strategy of annular coupling to compensate the synchronous error between the hydraulic cylinders, thereby realizing the synchronous control of the channels of the multi-electro-hydraulic servo valve-controlled asymmetric cylinders.

2. The synchronous control method based on the parallel motion of the plurality of hydraulic cylinders of the heave compensation platform according to claim 1, wherein the electro-hydraulic servo valve-controlled asymmetric hydraulic cylinder system in step S1 comprises a servo amplifier, an electro-hydraulic servo valve, a hydraulic cylinder and a displacement sensor, and a mathematical model of the valve-controlled asymmetric hydraulic cylinder system is established according to a flow continuity equation of the valve-controlled asymmetric cylinder, a flow equation of the valve, a force balance equation of the hydraulic cylinder and a load, and a main element transfer function.

3. The synchronous control method based on the parallel motion of the plurality of hydraulic cylinders of the heave compensation platform according to claim 2, wherein the method for establishing the mathematical model in the step S1 specifically comprises:

the servo amplifier is a power amplifier for driving a valve core of the electro-hydraulic servo valve to move, converts a voltage signal into a current signal which can be accepted by the electro-hydraulic servo valve, can be regarded as a proportional link, and has a transfer function of:

ka in the formula (1) is proportional gain of the amplifier; i is an electro-hydraulic servo valve current control signal; u is a servo amplifier input voltage signal;

the transfer function of the electro-hydraulic servo valve depends on the size of the hydraulic natural frequency, when the hydraulic natural frequency is set times the bandwidth of the electro-hydraulic servo valve, the electro-hydraulic servo valve is regarded as a second-order oscillation link, and the transfer function is as follows:

in the formula (2), k_svIs the flow gain, w, of the electrohydraulic servo valve_svIs the inherent bandwidth, ζ, of an electrohydraulic servo valve_svFor electrohydraulic servoThe damping ratio of the servo valve;

a main valve core of the servo valve adopts a slide valve structure, the valve is assumed to be a zero-opening four-side slide valve, four throttling windows are matched and symmetrical, and a linearized flow equation of the valve is as follows:

q_L＝K_qx_v-K_cp_L (3)

in the formula (3), q_LIs the load flow; kc is the flow pressure coefficient of the slide valve; p is a radical of_LIs the load pressure;

the flow continuity equation from the servo valve to the hydraulic cylinder is:

in the formula (4), C_ipThe leakage coefficient in the hydraulic cylinder; v₁The volume of the rodless cavity of the hydraulic cylinder; beta is a_eEffective bulk modulus of elasticity;

the balance equation of the output force and the load force of the hydraulic cylinder is as follows:

in the formula (5), A₁、A₂The effective action areas of a rodless cavity and a rod cavity of the hydraulic cylinder are respectively; p₁、P₂Respectively the pressure of a rodless cavity and a rod cavity of the hydraulic cylinder; x is the number of_pIs the piston rod displacement, Bp is the viscous damping coefficient; f_LFor theoretical loading force, K is the loading stiffness;

in engineering, an actuating element and a controlled object when the elastic load is ignored are regarded as a combination of an integral and a second-order link; the transfer function of the hydraulic cylinder is:

in the formula (6), A₁Is the effective active area of the hydraulic cylinder，ξ_hDamping ratio, w, for a hydraulic cylinder-load mass system_hIs the natural frequency of the hydraulic cylinder-load mass system;

the displacement sensor converts the displacement signal into a voltage signal, and the proportionality coefficient of the displacement sensor is as follows:

in the formula (7), l is a hydraulic cylinder length change signal, u_fFor the output of a voltage signal, k, of the displacement sensor_fA displacement sensor gain;

the open-loop transfer function of the electro-hydraulic position servo system is as follows:

in the formula (8), ka is a proportional coefficient of the servo valve amplifier, k_fIs the displacement sensor gain.

4. The synchronous control method based on the parallel motion of the plurality of hydraulic cylinders of the heave compensation platform according to claim 3, wherein the design method of the predictive controller in the step S2 is as follows:

discretizing an open-loop transfer function of the electro-hydraulic position servo system, and performing time translation to obtain an input and output model difference equation of the system:

y(k)+a₁y(k-1)+…+a_ny(k-n)＝b₀u(k-1)+…+b_mu(k-m-1) (9)

thus determining A (z)^-1) And B (z)^-1) Order of na, nb;

the prediction control adopts a controlled autoregressive integral moving average process model, and the expression form of the model is as follows:

A(z^-1)y_i(k)＝B(z^-1)u_i(k-1)+C(z^-1)ξ(k)/(1-z^-1) (12)

namely:

in the formula (13), the reaction mixture is,

according to a difference equation of the system, na and nb are known as orders, the prediction length P can be determined according to a controlled object and requirements, the length M is controlled (M is less than or equal to P), the weighting matrix R is controlled, and the error weighting matrix Q is controlled;

discussion C (z)^-1) And (3) predicting the output of each system at the moment k + j under the control of 1, and introducing a loss-of-energy graph equation as follows:

formula (14) is E_j(z^-1),F_j(z^-1),G_j(z^-1),L_j(z^-1)，H_j(z^-1) Expressed in the following form:

e in the formula (15)_j(z^-1),F_j(z^-1),G_j(z^-1),L_j(z^-1),H_j(z^-1) Is obtained by recursive calculation, and the future k + of each system can be obtained from the formula 13-14The output prediction equation of the system at the moment j is as follows:

y_i(k+j)＝L_j(z^-1)Δu_i(k+j-1)+H_j(z^-1)Δu_i(k-1)+F_j(z^-1)y_i(k)+E_j(z^-1)ξ(k+j) (16)

the relationship between the output prediction of the system at the future time k + j of each system and the optimal output prediction of the system at the future time k + j based on the input and output data at the time k and the previous time is as follows:

y_i(k+j)＝y_i ^*(k+j|k)+E_j(z^-1)ξ(k+j) (17)

in the formula (17), y_i ^*(k + j | k) for each system, based on the input and output data at time k and at the previous time, the optimal output prediction of the system at the future time k + j is performed, that is, the output prediction model of each system is:

y_i ^*(k+j|k)＝L_j(z^-1)Δu_i(k+j-1)+H_j(z^-1)Δu_i(k-1)+F_j(z^-1)y_i(k) (18)

the optimal output vector predicted by each system future model is as follows:

Y_i ^*(k)＝[y_i ^*(k+1∣k),y_i ^*(k+2∣k),…,y_i ^*(k+P∣k)]^T (19)

wherein the content of the first and second substances,

y in formula (20)_i(k+j)＝H_j(z^-1)Δu_i(k-1)+F_j(z^-1)y_i(k)

From equations 18-20, the vector form of the output optimal predictor is:

in the formula (21), the compound represented by the formula,

to reduce overshoot, a reference trajectory y is selected_r(k) In the form:

y in formula (22)_i(k) Output for object, y_r(k + j) is an expected output, namely a reference track, at the future k + j moment, r is a set value, alpha is a softening factor influencing the dynamic response of the electro-hydraulic system, and alpha is more than 0 and less than 1;

the quadratic performance index function weighted by the output error and the control increment is used as the objective function of system optimization to ensure that the output y of the object_i(k) Along a reference trajectory y_r(k + j) approximation, the performance indicator function of which is:

in equation (23), E is the desired output, λ is the control weighting factor that affects the tracking error, and when λ > 0, the performance indicator function is expressed as:

minimize J to the extent that the current and future control increase vectors are:

the final control law is as follows: u. of_i(k)＝Δu_i(k)+u_i(k-1) (26)。

5. The synchronous control method based on the parallel motion of the plurality of hydraulic cylinders of the heave compensation platform according to claim 4, wherein the synchronous compensation controller in step S3 adopts a predictive controller to compensate the position tracking error of the channel and the synchronous error of the two adjacent channels in a ring coupling control manner, and the method comprises the following specific steps:

defining position following error and synchronization error:

position tracking error: e.g. of the type_i(k)＝y_r(k)-y^* _i(k)(i≤6)

Wherein

Synchronization error:

and feeding the synchronization error back to the generalized predictive controller, and processing the system by utilizing a generalized predictive control algorithm to obtain the optimal synchronization control increment of each servo channel, wherein the optimal synchronization control increment is expressed as follows:

wherein

In the equations (28) and (29), λ is a control parameter, k is a synchronous compensation coefficient, and k (Y)_i(k)-Y_i+1(k) Feedback compensation designed to counteract synchronization errors generated by coupling;

the first row of the matrix in equation (28) is denoted as Δ u_i(k) Then the control amount required for each system is:

u_i(k)＝u_i(k-1)+Δu_i(k) (30)

taking the hydraulic cylinder one as an example, the synchronization error generated between the servo channel one and the servo channel two is fed back to the generalized predictive controller of the servo channel one for compensation, and the control increment is obtained as follows:

wherein

Take Delta U in formula (31)₁Is marked as Deltau₁(k) Then, the optimal control quantity of the servo channel one is: u. of₁(k)＝u₁(k-1)+Δu₁(k) (ii) a The control quantities of the other five servo channels can be obtained by class-II extrapolation and are respectively u₂(k),u₃(k),u₄(k),u₅(k),u₆(k)。

Technical Field

The invention relates to the field of multi-cylinder synchronous control, in particular to a synchronous control method based on parallel motion of a plurality of hydraulic cylinders of a heave compensation platform.

Background

At present, the design life of offshore wind farms in China is generally 25 years, and for coastal wind farms, the sea state is relatively stable. For an ocean wind farm, when the ocean wind farm is operated on the sea, motions with six degrees of freedom of rolling, pitching, yawing, pitching and heaving are inevitably generated under the action of sea wind and sea waves, and the interference can influence the stable operation of the ocean wind farm and prolong the operation time between a fan platform and a ship. The six-freedom-degree heave compensation platform carrying gangway ladder can effectively isolate the motion on the carrier, and provides a relatively stable working platform. It is important to study how to keep the platform in a relatively stable state of motion.

The six-degree-of-freedom heave compensation platform has six identical channels of the electro-hydraulic servo valve-controlled hydraulic cylinder, and in order to ensure the stability of the platform, the six hydraulic cylinders need to be synchronously controlled, so that the six channels are mutually coordinated. At present, the multi-cylinder synchronous control is also concerned more and more, and a plurality of scientific achievements are obtained. There are still several disadvantages:

1. the adoption of a synchronous control strategy such as deviation coupling, ring coupling and adjacent cross coupling can reduce the complexity of a control structure, can quickly respond even if large interference exists, can compensate tracking errors, and can improve the synchronous control precision. At present, a plurality of motors are applied in a multi-motor synchronous control system, but the engineering application in an electro-hydraulic servo system is less;

2. the basic principle of a multi-cylinder synchronous electro-hydraulic servo control system used in engineering is not greatly different, the performance of an electro-hydraulic servo valve greatly affects the performance of the system, and the precision of the synchronous system is limited by the characteristics of elements to a certain extent.

3. The multi-cylinder synchronous control has the problems of large overshoot, low synchronous precision in the transition process, low system reliability and the like, and the electrohydraulic servo system also has the influences of nonlinearity, parameter uncertainty, model uncertainty and the like.

Therefore, a new technical solution is needed to solve the above problems.

Disclosure of Invention

The purpose of the invention is as follows: in order to overcome the defects in the prior art, a synchronous control method based on the parallel motion of a plurality of hydraulic cylinders of a heave compensation platform is provided, six electro-hydraulic servo valve-controlled asymmetric hydraulic cylinders are controlled by a generalized predictive control algorithm, the position control of a single electro-hydraulic servo valve-controlled asymmetric cylinder channel is realized, the synchronous control of a plurality of electro-hydraulic servo valve-controlled asymmetric cylinder channels is realized, the position control precision and the synchronous control performance of the system are improved, and the stable operation of the heave compensation platform is ensured to compensate the irregular motion of a ship.

The technical scheme is as follows: in order to achieve the purpose, the invention provides a synchronous control method based on the parallel motion of a plurality of hydraulic cylinders of a heave compensation platform, which comprises the following steps:

s1: establishing a mathematical model of the electro-hydraulic servo valve control asymmetric hydraulic cylinder system;

s2: designing a prediction controller based on the established mathematical model to obtain an optimal control law and control a single electro-hydraulic servo channel to realize accurate position tracking;

s3: and designing a synchronous compensation controller based on the prediction controller of the step S2 and the control strategy of annular coupling to compensate the synchronous errors among the six hydraulic cylinders, thereby realizing the synchronous control of the channels of the multi-electro-hydraulic servo valve-controlled asymmetric cylinders.

Further, in the step S1, the electro-hydraulic servo valve-controlled asymmetric cylinder system mainly uses an inertial load without an elastic load, and adopts a single-rod hydraulic cylinder, and the electro-hydraulic servo valve-controlled asymmetric cylinder system mainly includes a servo amplifier, an electro-hydraulic servo valve, a hydraulic cylinder, and a displacement sensor, and a mathematical model of the valve-controlled asymmetric cylinder system is established according to a flow continuity equation of the valve-controlled asymmetric cylinder, a flow equation of the valve, a force balance equation of the hydraulic cylinder and the load, and a transfer function of a main element.

Further, the method for establishing the mathematical model in step S1 specifically includes:

the servo amplifier is a power amplifier for driving a valve core of the electro-hydraulic servo valve to move, converts a voltage signal into a current signal which can be accepted by the electro-hydraulic servo valve, can be regarded as a proportional link, and has a transfer function of:

ka in the formula (1) is proportional gain of the amplifier; i is an electro-hydraulic servo valve current control signal; u is a servo amplifier input voltage signal;

the transfer function of the electro-hydraulic servo valve depends on the magnitude of the hydraulic natural frequency, and when the hydraulic natural frequency is 3-5 times of the bandwidth of the electro-hydraulic servo valve, the electro-hydraulic servo valve is generally regarded as a second-order oscillation link, and the transfer function is as follows:

in the formula (2), k_svIs the flow gain, w, of the electrohydraulic servo valve_svIs the inherent bandwidth, ζ, of an electrohydraulic servo valve_svThe damping ratio of the electro-hydraulic servo valve;

a main valve core of the servo valve adopts a slide valve structure, the valve is assumed to be a zero-opening four-side slide valve, four throttling windows are matched and symmetrical, and a linearized flow equation of the valve is as follows:

q_L＝K_qx_v-K_cp_L (3)

in the formula (3), q_LIs the load flow; kc is the flow pressure coefficient of the slide valve; p is a radical of_LIs the load pressure;

the flow continuity equation from the servo valve to the hydraulic cylinder is:

in the formula (4), C_ipThe leakage coefficient in the hydraulic cylinder; v₁The volume of the rodless cavity of the hydraulic cylinder; beta is a_eEffective bulk modulus of elasticity;

the balance equation of the output force and the load force of the hydraulic cylinder is as follows:

in the formula (5), A₁、A₂The effective action areas of a rodless cavity and a rod cavity of the hydraulic cylinder are respectively; p₁、P₂Respectively the pressure of a rodless cavity and a rod cavity of the hydraulic cylinder; x is the number of_pIs the piston rod displacement, Bp is the viscous damping coefficient; f_LIs theoretical load force (inertia force, viscous damping force, elastic force and any external load force), and K is load rigidity;

in engineering, an actuating element and a controlled object when the elastic load is ignored are regarded as a combination of an integral and a second-order link; the transfer function of the hydraulic cylinder is:

in the formula (6), A₁Is the effective area of action, ξ, of the hydraulic cylinder_hDamping ratio, w, for a hydraulic cylinder-load mass system_hIs the natural frequency of the hydraulic cylinder-load mass system;

the displacement sensor converts the displacement signal into a voltage signal, and the proportionality coefficient of the displacement sensor is as follows:

in the formula (7), l is a hydraulic cylinder length change signal, u_fFor the output of a voltage signal, k, of the displacement sensor_fA displacement sensor gain;

the open-loop transfer function of the electro-hydraulic position servo system is as follows:

in the formula (8), ka is a proportional coefficient of the servo valve amplifier, k_fIs the displacement sensor gain.

Further, the design method of the predictive controller in step S2 is as follows:

discretizing an open-loop transfer function of the electro-hydraulic position servo system to obtain a difference equation, determining a CARIMA model adopted for predictive control, and performing time translation to obtain an input and output model difference equation of the system:

y(k)+a₁y(k-1)+…+a_ny(k-n)＝b₀u(k-1)+…+b_mu(k-m-1) (9)

thus determining A (z)^-1) And B (z)^-1) Order of na, nb;

predictive control employs a controlled autoregressive integrated moving average process model (CARIMA) expressed in the form of:

A(z^-1)y_i(k)＝B(z^-1)u_i(k-1)+C(z^-1)ξ(k)/(1-z^-1) (12)

namely:

in the formula (13), the reaction mixture is,

according to a difference equation of the system, na and nb are known as orders, the prediction length P can be determined according to a controlled object and requirements, the length M is controlled (M is less than or equal to P), the weighting matrix R is controlled, and the error weighting matrix Q is controlled;

discussion C (z)^-1) And (3) predicting the output of each system at the moment k + j under the control of 1, and introducing a loss-of-energy graph equation as follows:

formula (14) is E_j(z^-1),F_j(z^-1),G_j(z^-1),L_j(z^-1)，H_j(z^-1) Can be expressed in the following form:

e in the formula (15)_j(z^-1),F_j(z^-1),G_j(z^-1),L_j(z^-1),H_j(z^-1) The coefficients of (a) can be obtained by recursive calculation, and the output prediction equation of the system at the future k + j time of each system can be obtained by equations 13-14 as follows:

y_i(k+j)＝L_j(z^-1)Δu_i(k+j-1)+H_j(z^-1)Δu_i(k-1)+F_j(z^-1)y_i(k)+E_j(z^-1)ξ(k+j) (16)

the relationship between the output prediction of the system at the future time k + j of each system and the optimal output prediction of the system at the future time k + j based on the input and output data at the time k and the previous time is as follows:

y_i(k+j)＝y_i ^*(k+j|k)+E_j(z^-1)ξ(k+j) (17)

in the formula (17), y_i ^*(k + j | k) for each system, based on the input and output data at time k and at the previous time, the optimal output prediction of the system at the future time k + j is performed, that is, the output prediction model of each system is:

y_i ^*(k+j|k)＝L_j(z^-1)Δu_i(k+j-1)+H_j(z^-1)Δu_i(k-1)+F_j(z^-1)y_i(k) (18)

the optimal output vector predicted by each system future model is as follows:

Y_i ^*(k)＝[y_i ^*(k+1∣k),y_i ^*(k+2∣k),…,y_i ^*(k+P∣k)]^T (19)

wherein the content of the first and second substances,

y in formula (20)_i(k+j)＝H_j(z^-1)Δu_i(k-1)+F_j(z^-1)y_i(k)

From equations 18-20, the vector form of the output optimal predictor is:

in the formula (21), the compound represented by the formula,

to reduce overshoot, a reference trajectory y is selected_r(k) In the form:

y in formula (22)_i(k) Output for object, y_r(k + j) is an expected output, namely a reference track at the future k + j moment, r is a set value, a is a softening factor influencing the dynamic response of the electro-hydraulic system, and a is more than 0 and less than 1;

the quadratic performance index function weighted by the output error and the control increment is used as the objective function of system optimization to ensure that the output y of the object_i(k) Along a reference trajectory y_r(k + j) approximation, the performance indicator function of which is:

in equation (23), where E is the desired output, λ is the control weighting factor that affects the tracking error, and λ > 0, the performance indicator function can be expressed as:

minimizing J, the current and future control increase vectors can be found as:

the final control law is as follows: u. of_i(k)＝Δu_i(k)+u_i(k-1)。 (26)

Further, the synchronous compensation controller in step S3 adopts a predictive controller, and compensates the position tracking error of its own channel and the synchronous error of two adjacent channels in a ring coupling control manner, and the specific steps are as follows:

defining position following error and synchronization error:

position tracking error: e.g. of the type_i(k)＝y_r(k)-y^* _i(k)(i≤6)

Wherein

Synchronization error:

the steps of the synchronous compensation controller are designed according to the predictive controller, and the steps are the same. The synchronous error is fed back to the generalized predictive controller, the generalized predictive control algorithm is utilized to carry out multi-step prediction, rolling optimization, feedback correction and other steps on the system, and the optimal synchronous control increment of each servo channel is obtained, and can be expressed as follows:

wherein

In the equations (28) and (29), λ is a control parameter, k is a synchronous compensation coefficient, and k (Y)_i(k)-Y_i+1(k) Feedback compensation designed to counteract synchronization errors generated by coupling; thereby canceling out the effect of synchronization errors due to coupling on each servo channel.

The first row of the matrix in equation (28) is denoted as Δ u_i(k) Then the control amount required for each system is:

u_i(k)＝u_i(k-1)+Δu_i(k) (30)

taking the hydraulic cylinder one as an example, the synchronization error generated between the servo channel one and the servo channel two is fed back to the generalized predictive controller of the servo channel one for compensation, and the control increment is obtained as follows:

wherein

Take Delta U in formula (31)₁Is marked as Deltau₁(k) Then, the optimal control quantity of the servo channel one is: u. of₁(k)＝u₁(k-1)+Δu₁(k) (ii) a The control quantities of the other five servo channels can be obtained by class-II extrapolation and are respectively u₂(k),u₃(k),u₄(k),u₅(k),u₆(k)。

Has the advantages that: compared with the prior art, the method has the advantages that the optimal control law is obtained by utilizing a generalized predictive control algorithm, the single-channel electro-hydraulic servo asymmetric hydraulic cylinder system is controlled, the position control performance of a single channel of the system is improved, the predictive control is further combined with the annular coupling to construct a synchronous error compensator, the structure of the controller is simplified, the tracking error of the channel and the synchronous error between adjacent channels are compensated, the six electro-hydraulic servo valve control asymmetric hydraulic cylinder channels synchronously move, the synchronous control precision and the dynamic response rate of the movement of the multiple hydraulic cylinders are improved, the static error and the instability of the system are reduced, the coordination performance among the multiple channels is improved, and the heave compensation platform stably operates.

Drawings

FIG. 1 is a control schematic of the process of the present invention;

FIG. 2 is a schematic structural diagram of an electro-hydraulic servo valve control asymmetric cylinder;

FIG. 3 is a schematic diagram of a position transfer function of an electro-hydraulic servo system;

FIG. 4 is a predictive controller schematic;

FIG. 5 is a simulation comparison diagram of the single channel output of the system to the expected command position tracking, with predictive control and fuzzy PID control acting on the system respectively;

fig. 6 to 14 are simulation comparison diagrams of position control, tracking error and synchronization error of the ring coupling control based on the generalized predictive control and the master-slave fuzzy PID control, respectively.

Detailed Description

The present invention is further illustrated by the following figures and specific examples, which are to be understood as illustrative only and not as limiting the scope of the invention, which is to be given the full breadth of the appended claims and any and all equivalent modifications thereof which may occur to those skilled in the art upon reading the present specification.

The invention provides a synchronous control method based on the parallel motion of a plurality of hydraulic cylinders of a heave compensation platform, which comprises the following steps with reference to fig. 1:

s1: establishing a mathematical model of the electro-hydraulic servo valve control asymmetric hydraulic cylinder system:

as shown in fig. 2 and 3, the structural schematic diagram of the electro-hydraulic servo valve control asymmetric cylinder and the position transfer function schematic diagram of the electro-hydraulic servo system are respectively shown, the electro-hydraulic servo valve control asymmetric cylinder system mainly takes inertial load without elastic load and adopts a single-rod hydraulic cylinder, the electro-hydraulic servo valve control asymmetric hydraulic cylinder system mainly comprises a servo amplifier, an electro-hydraulic servo valve, a hydraulic cylinder and a displacement sensor, and a mathematical model of the valve control asymmetric hydraulic cylinder system is established according to a flow continuity equation of the valve control asymmetric cylinder, a flow equation of the valve, a force balance equation of the hydraulic cylinder and the load and a main element transfer function;

the method for establishing the mathematical model specifically comprises the following steps:

the servo amplifier is a power amplifier for driving a valve core of the electro-hydraulic servo valve to move, converts a voltage signal into a current signal which can be accepted by the electro-hydraulic servo valve, can be regarded as a proportional link, and has a transfer function of:

ka in the formula (1) is proportional gain of the amplifier; i is an electro-hydraulic servo valve current control signal; u is a servo amplifier input voltage signal;

the transfer function of the electro-hydraulic servo valve depends on the magnitude of the hydraulic natural frequency, and when the hydraulic natural frequency is 3-5 times of the bandwidth of the electro-hydraulic servo valve, the electro-hydraulic servo valve is generally regarded as a second-order oscillation link, and the transfer function is as follows:

in the formula (2), k_svIs the flow gain, w, of the electrohydraulic servo valve_svIs the inherent bandwidth, ζ, of an electrohydraulic servo valve_svThe damping ratio of the electro-hydraulic servo valve;

a main valve core of the servo valve adopts a slide valve structure, the valve is assumed to be a zero-opening four-side slide valve, four throttling windows are matched and symmetrical, and a linearized flow equation of the valve is as follows:

q_L＝K_qx_v-K_cp_L (3)

in the formula (3), q_LIs the load flow; kc is the flow pressure coefficient of the slide valve; p is a radical of_LIs the load pressure;

the flow continuity equation from the servo valve to the hydraulic cylinder is:

in the formula (4), C_ipThe leakage coefficient in the hydraulic cylinder; v₁The volume of the rodless cavity of the hydraulic cylinder; beta is a_eEffective bulk modulus of elasticity;

the balance equation of the output force and the load force of the hydraulic cylinder is as follows:

in the formula (5), A₁、A₂The effective action areas of a rodless cavity and a rod cavity of the hydraulic cylinder are respectively; p₁、P₂Respectively the pressure of a rodless cavity and a rod cavity of the hydraulic cylinder; x is the number of_pIs the piston rod displacement, Bp is the viscous damping coefficient; f_LIs theoretical load force (inertia force, viscous damping force, elastic force and any external load force), and K is load rigidity;

in engineering, an actuating element and a controlled object when the elastic load is ignored are regarded as a combination of an integral and a second-order link; the transfer function of the hydraulic cylinder is:

in the formula (6), A₁Is the effective area of action, ξ, of the hydraulic cylinder_hDamping ratio, w, for a hydraulic cylinder-load mass system_hIs the natural frequency of the hydraulic cylinder-load mass system;

the displacement sensor converts the displacement signal into a voltage signal, and the proportionality coefficient of the displacement sensor is as follows:

in the formula (7), l is a hydraulic cylinder length change signal, u_fFor the output of a voltage signal, k, of the displacement sensor_fIs a positionMoving the sensor gain;

the open-loop transfer function of the electro-hydraulic position servo system is as follows:

in the formula (8), ka is a proportional coefficient of the servo valve amplifier, k_fIs the displacement sensor gain.

S2: designing a prediction controller based on the established mathematical model to obtain an optimal control law, and controlling a single electro-hydraulic servo channel to realize accurate position tracking:

as shown in fig. 4, the design method of the predictive controller is as follows:

discretizing an open-loop transfer function of the electro-hydraulic position servo system to obtain a difference equation, determining a CARIMA model adopted for predictive control, and performing time translation to obtain an input and output model difference equation of the system:

y(k)+a₁y(k-1)+…+a_ny(k-n)＝b₀u(k-1)+…+b_mu(k-m-1) (9)

thus determining A (z)^-1) And B (z)^-1) Order of na, nb;

predictive control employs a controlled autoregressive integrated moving average process model (CARIMA) expressed in the form of:

A(z^-1)y_i(k)＝B(z^-1)u_i(k-1)+C(z^-1)ξ(k)/(1-z^-1) (12)

namely:

in the formula (13), the reaction mixture is,

according to a difference equation of the system, na and nb are known as orders, the prediction length P can be determined according to a controlled object and requirements, the length M is controlled (M is less than or equal to P), the weighting matrix R is controlled, and the error weighting matrix Q is controlled;

discussion C (z)^-1) And (3) predicting the output of each system at the moment k + j under the control of 1, and introducing a loss-of-energy graph equation as follows:

formula (14) is E_j(z^-1),F_j(z^-1),G_j(z^-1),L_j(z^-1)，H_j(z^-1) Can be expressed in the following form:

e in the formula (15)_j(z^-1),F_j(z^-1),G_j(z^-1),L_j(z^-1),H_j(z^-1) The coefficients of (a) can be obtained by recursive calculation, and the output prediction equation of the system at the future k + j time of each system can be obtained by equations 13-14 as follows:

y_i(k+j)＝L_j(z^-1)Δu_i(k+j-1)+H_j(z^-1)Δu_i(k-1)+F_j(z^-1)y_i(k)+E_j(z^-1)ξ(k+j) (16)

the relationship between the output prediction of the system at the future time k + j of each system and the optimal output prediction of the system at the future time k + j based on the input and output data at the time k and the previous time is as follows:

y_i(k+j)＝y_i ^*(k+j|k)+E_j(z^-1)ξ(k+j) (17)

in the formula (17), y_i ^*(k + j | k) for each system, based on the input and output data at time k and at the previous time, the optimal output prediction of the system at the future time k + j is performed, that is, the output prediction model of each system is:

y_i ^*(k+j|k)＝L_j(z^-1)Δu_i(k+j-1)+H_j(z^-1)Δu_i(k-1)+F_j(z^-1)y_i(k) (18)

the optimal output vector predicted by each system future model is as follows:

Y_i ^*(k)＝[y_i ^*(k+1∣k),y_i ^*(k+2∣k),…,y_i ^*(k+P∣k)]^T (19)

wherein the content of the first and second substances,y in formula (20)_i(k+j)＝H_j(z^-1)Δu_i(k-1)+F_j(z^-1)y_i(k)

From equations 18-20, the vector form of the output optimal predictor is:

in the formula (21), the compound represented by the formula,

to reduce overshoot, a reference trajectory y is selected_r(k) In the form:

y in formula (22)_i(k) Output for object, y_r(k + j) is a reference trajectory which is the expected output at a future time k + j, r is a set value, and a isA softening factor influencing the dynamic response of the electro-hydraulic system, wherein a is more than 0 and less than 1;

the quadratic performance index function weighted by the output error and the control increment is used as the objective function of system optimization to ensure that the output y of the object_i(k) Along a reference trajectory y_r(k + j) approximation, the performance indicator function of which is:

in equation (23), where E is the desired output, λ is the control weighting factor that affects the tracking error, and λ > 0, the performance indicator function can be expressed as:

minimizing J, the current and future control increase vectors can be found as:

the final control law is as follows: u. of_i(k)＝Δu_i(k)+u_i(k-1) (26)

S3: and designing a synchronous compensation controller based on the prediction controller of the step S2 and the control strategy of annular coupling to compensate the synchronous errors among the six hydraulic cylinders, thereby realizing the synchronous control of the channels of the multi-electro-hydraulic servo valve-controlled asymmetric cylinders.

The synchronous compensation controller adopts a prediction controller, compensates the position tracking error of the channel and the synchronous error of two adjacent channels in a ring coupling control mode, and comprises the following specific steps:

defining position following error and synchronization error:

position tracking error: e.g. of the type_i(k)＝y_r(k)-y^* _i(k)(i≤6)

Wherein

Synchronization error:

the steps of the synchronous compensation controller are designed according to the predictive controller, and the steps are the same. The synchronous error is fed back to the generalized predictive controller, the generalized predictive control algorithm is utilized to carry out multi-step prediction, rolling optimization, feedback correction and other steps on the system, and the optimal synchronous control increment of each servo channel is obtained, and can be expressed as follows:

wherein

In the equations (28) and (29), λ is a control parameter, k is a synchronous compensation coefficient, and k (Y)_i(k)-Y_i+1(k) Feedback compensation designed to counteract synchronization errors generated by coupling; thereby canceling out the effect of synchronization errors due to coupling on each servo channel.

The first row of the matrix in equation (28) is denoted as Δ u_i(k) Then the control amount required for each system is:

u_i(k)＝u_i(k-1)+Δu_i(k) (30)

in this embodiment, taking the hydraulic cylinder one as an example, a synchronization error generated between the servo channel one and the servo channel two is fed back to the generalized predictive controller of the servo channel one for compensation, and a control increment thereof is obtained as follows:

wherein

Take Delta U in formula (31)₁Is marked as Deltau₁(k) Then, the optimal control quantity of the servo channel one is: u. of₁(k)＝u₁(k-1)+Δu₁(k) (ii) a The control quantities of the other five servo channels can be obtained by class-II extrapolation and are respectively u₂(k),u₃(k),u₄(k),u₅(k),u₆(k)。

Based on the technical scheme, in order to verify the effect of the method, the following simulation experiment is carried out:

the performance of a prediction controller designed in a simulated manner in matlab is compared with fuzzy PID control, and the parameters of the electro-hydraulic servo valve control asymmetric hydraulic cylinder system are selected as follows:

the diameter D of the rodless cavity of the hydraulic cylinder is 50mm, the diameter D of the rod cavity is 36mm, the effective stroke is 280mm, the inertial load mt of a single hydraulic cylinder is 60kg, and the damping ratio xi of the hydraulic cylinder-load mass system is xi_h0.15; volume modulus of hydraulic oil β e is 0.7 × 10⁹Pa; total volume V of two chambers of hydraulic cylinder_t＝2.7×10^-3m³(ii) a Natural frequency omega of electrohydraulic servo valve_sv85Hz, damping ratio xi_svRated flow Qsv is 30L/min, rated control current Ic is 8mA, and flow gain K of valve_sv＝0.0625m³V (s.A); the effective acting area of the hydraulic cylinder is 1.96 multiplied by 10 when A1 is equal to^-3m²

The prediction controller predicts the output according to a mathematical model of the electro-hydraulic servo system and simulates in matlab, wherein simulation parameters comprise 25 of control parameters, 5 of prediction time domain and control time domain, 0.2 of output softening coefficient and 0.5 of synchronous compensation coefficient. Simulating its tracking of the output desired value and the amount of control of the output.

The fuzzy PID controller is compared with the prediction controller by the fuzzy PID controller, the fuzzy PID controller is simulated in matlab, the PID parameters are optimized through fuzzy control to enable the output to better track the set expected value, and the optimized PID control parameters are as follows: kp 0.166, ki 0, kd 0.0598.

Fig. 5 shows that the predictive control and the fuzzy PID control track the step signal expected to be one, respectively, and it can be seen from fig. 5 that the response speed of the predictive control is faster than that of the fuzzy PID control, the stability is good, and the set expected value can be tracked quickly.

Fig. 6-14 are simulation comparison graphs of ring coupling GPC control and master-slave fuzzy PID control. Simulating position control, control quantity output, tracking error and synchronization error of the master cylinder after disturbance, and simulating position control, tracking error and synchronization error of a second hydraulic cylinder and a sixth hydraulic cylinder which are adjacent to the master cylinder. The input is set to a step input and the servo channel is subjected to a 10% step load disturbance at a time when k is 50. Under master-slave fuzzy PID control: the output of the first servo channel is used as the input of the other five servo channels, when the first hydraulic cylinder is disturbed, the output of the second hydraulic cylinder and the six positions of the hydraulic cylinder are delayed and larger, so that the output of the system can not be kept consistent, the tracking error and the synchronization error are larger in fluctuation, the sub hydraulic cylinders are mutually independent, and the synchronization error of the second hydraulic cylinder stably tends to 0. Ring coupling GPC under control: when the first hydraulic cylinder is disturbed, the second hydraulic cylinder and the sixth hydraulic cylinder are both influenced, but the output of the first hydraulic cylinder is smaller than that of the master-slave control, the position hysteresis phenomenon does not exist, the stability can be quickly recovered, the disturbance resistance is strong, when the first hydraulic cylinder is disturbed, the tracking error and the synchronization error are smaller, the fluctuation range is smaller, the maximum synchronization error is smaller than that of the master-slave control mode, and the position tracking control performance and the synchronization control performance are better.