CN113219841B - Nonlinear control method for underwater multi-joint hydraulic mechanical arm based on adaptive robustness - Google Patents
Nonlinear control method for underwater multi-joint hydraulic mechanical arm based on adaptive robustness Download PDFInfo
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Abstract
The invention discloses a nonlinear control method of an underwater multi-joint hydraulic mechanical arm based on self-adaptive robustness. The method comprises the following steps: establishing a system nonlinear dynamic model of the underwater multi-joint hydraulic mechanical arm; establishing a self-adaptive robust control law of the underwater multi-joint hydraulic mechanical arm to form a self-adaptive robust controller of the underwater multi-joint hydraulic mechanical arm; the tracking error value obtained by the measurement of the sensor is fed back to the adaptive robust controller in real time, the adaptive robust controller realizes self-adaptive iterative updating of self parameters, the adaptive robust controller controls the underwater multi-joint hydraulic mechanical arm in real time to form a complete closed-loop control system of the underwater multi-joint hydraulic mechanical arm, and the adaptive robust controller realizes effective control of the underwater multi-joint hydraulic mechanical arm. The invention reduces the tracking error of the tail end of the mechanical arm and improves the control performance; the influence caused by model uncertainty in the control process can be overcome, and the control precision of the tail end of the underwater multi-joint hydraulic mechanical arm is improved.
Description
Technical Field
The invention belongs to a nonlinear control method of a mechanical arm in the field of motion control of an underwater multi-joint hydraulic mechanical arm, and particularly relates to a nonlinear control method of an underwater multi-joint hydraulic mechanical arm based on self-adaptive robustness.
Background
With the continuous deepening of the development, utilization and research of oceans, the underwater operation environment is more and more severe and is not suitable for direct human intervention. On the other hand, the complexity of the underwater operation task is continuously increased, and the requirement on the operation accuracy is also continuously increased, so that the underwater operation task is completed by the aid of the underwater robot in the situation, and the underwater operation task is a feasible scheme. The underwater multi-joint hydraulic mechanical arm is an important component of an underwater robot and is also a necessary component for completing complex underwater operation tasks. At present, the method has various applications such as pipeline tracking, submarine cable burying, marine resource investigation, submarine oil platform detection, underwater salvage, rescue and rescue. However, most of the existing underwater hydraulic mechanical arm controllers do not fully consider system nonlinearity, model uncertainty and multi-input multi-output high-order model characteristics, and in addition, the underwater hydraulic mechanical arm is often subjected to the comprehensive influence of external interference such as sea waves, ocean currents and the like in the operation process. Therefore, the existing controller is difficult to ensure good control precision of the tail end of the underwater multi-joint hydraulic mechanical arm, and accordingly underwater operation performance is affected.
Disclosure of Invention
Aiming at the defects of the existing underwater multi-joint hydraulic mechanical arm control technology, the invention provides a nonlinear control method of the underwater multi-joint hydraulic mechanical arm based on self-adaptive robustness, which reduces the influence of model uncertainty (modeling error and parameter uncertainty) and uncertain nonlinearity (mechanical friction, hydraulic oil resistance and wave flow influence) on the control precision of the tail end of the mechanical arm in the movement process of the underwater hydraulic mechanical arm, reduces the tracking error of the tail end of the mechanical arm while ensuring the stability of a control system, and improves the control performance.
In order to achieve the purpose, the specific technical scheme of the invention is as follows:
the invention comprises the following steps:
1) establishing a system nonlinear dynamic model of the underwater multi-joint hydraulic mechanical arm;
2) establishing a self-adaptive robust control law of the underwater multi-joint hydraulic mechanical arm based on a system nonlinear dynamic model of the underwater multi-joint hydraulic mechanical arm; the system nonlinear dynamics model is connected with the adaptive robust control law to form an adaptive robust controller of the underwater multi-joint hydraulic manipulator;
3) the tracking error value obtained by the measurement of the sensor is fed back to the adaptive robust controller in real time, the adaptive robust controller realizes self-adaptive iterative updating of self parameters, the adaptive robust controller controls the underwater multi-joint hydraulic mechanical arm in real time to form a complete closed-loop control system of the underwater multi-joint hydraulic mechanical arm, and the adaptive robust controller realizes effective control of the underwater multi-joint hydraulic mechanical arm.
The step 1) is specifically as follows:
establishing a system nonlinear dynamical model of the underwater multi-joint hydraulic mechanical arm, wherein the system nonlinear dynamical model of the underwater multi-joint hydraulic mechanical arm mainly comprises a dynamic relation between a joint angle and a hydraulic cylinder push rod, a nonlinear dynamical model of a connecting rod mechanical arm, a nonlinear dynamical model of a hydraulic system and a dynamic relation between chamber flow and valve core displacement of a hydraulic valve;
1.1) establishing a dynamic relation between a joint angle and a hydraulic cylinder push rod, which specifically comprises the following steps:
each joint angle q of the underwater multi-joint hydraulic mechanical arm satisfies q ═ q1,q2,…,qi,…,qn]TThe extension x of the push rod of each joint hydraulic cylinder meets the condition that x is ═ x1,x2,…,xi,…,xn]TWherein q is1Representing the joint angle, q, of the first joint of an underwater multi-joint hydraulic manipulatoriRepresenting the joint angle, x, of the ith joint of an underwater multi-joint hydraulic manipulator1Shows the extension amount, x, of the push rod of the joint hydraulic actuator of the first joint of the underwater multi-joint hydraulic mechanical armiThe hydraulic actuator push rod elongation of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented, i represents the serial number of the joint, n represents the total number of the joints, i is 1,2,3, …, n, T represents the transposition operation, and each joint angle and the hydraulic actuator push rod elongation of the corresponding joint satisfy the following relations:
wherein the content of the first and second substances,
indicating the length between the i-1 th joint and the ith joint,
represents the length between the ith joint and the (i + 1) th joint;
1.2) establishing a nonlinear dynamics model of the connecting rod mechanical arm, and satisfying the following formula:
wherein the content of the first and second substances,
and G (q) are an inertia matrix, a Coriolis force and centrifugal force matrix and a gravity matrix of the underwater multi-joint hydraulic mechanical arm respectively;
the angular velocity of each joint of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirements are met
The joint angular velocity of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented,
the angular acceleration of each joint of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirements of the angular acceleration
Representing the joint angular acceleration of the ith joint of the underwater multi-joint hydraulic mechanical arm;
a full differential matrix representing the extension x of the push rod of each joint hydraulic cylinder to each joint angle q, and satisfies
PinThe oil pressure of an oil inlet cavity of each joint hydraulic cylinder is shown, and the requirement of oil pressure
The oil pressure of an oil inlet cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; poutThe oil pressure of an oil return cavity of each joint hydraulic cylinder is shown, and the requirement of oil pressure
The oil pressure of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; a. theinThe area of the oil inlet cavity of each joint hydraulic cylinder is shown, and the requirement is met
The area of an oil inlet cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; a. theoutThe area of an oil return cavity of each joint hydraulic cylinder is shown, and the requirement is met
The area of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; d represents an interference item in the motion of the underwater multi-joint hydraulic mechanical arm, wherein the interference item comprises mechanical arm interference factors influenced by mechanical friction, hydraulic oil resistance and wave flow;
1.3) establishing a hydraulic system nonlinear dynamics model, and satisfying the following formula:
wherein, VinThe volume of the oil inlet cavity of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirements of the oil inlet cavity volume of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm
VoutThe volume of an oil return cavity of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirement of the volume of the oil return cavity of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm is met
And
respectively representing the volume of an oil inlet cavity and the volume of an oil return cavity of each joint hydraulic cylinder under the initial condition; diag [ 2 ]]Representing a matrix diagonalization operation; beta is aeThe volume modulus of the hydraulic oil is shown; qinThe flow of the oil inlet cavity of each joint hydraulic cylinder is expressed, and the requirement of the flow
The flow of an oil inlet cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; qoutThe flow of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirement of the flow of the oil return cavity of the hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is met
The flow of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented;
the differential of the oil pressure of the oil inlet cavity of each joint hydraulic cylinder is represented;
the differential of the oil pressure of the oil return cavity of each joint hydraulic cylinder is represented;
1.4) establishing a dynamic relation between the chamber flow and the displacement of the valve core of the hydraulic valve, and satisfying the following formula:
Qin＝kqingin(Pin,xv)xv (5)
Qout＝kqoutgout(Pout,xv)xx (6)
wherein x isvIs the valve core displacement of each joint hydraulic control valve, and meets the requirements
A valve body displacement of a hydraulic control valve of the ith joint; k is a radical ofqinShows the flow gain constant of each joint oil inlet chamber and satisfies
A flow gain constant representing the oil inlet chamber of the ith joint; k is a radical ofqoutShows the flow gain constant of the oil inlet chamber and the oil return chamber, and satisfies
A flow gain constant of an oil return chamber of the i-th joint is represented; gin(Pin,xv) Indicating the spool displacement x of each joint hydraulic control valvevPressure P of oil inlet chamberinValve element displacement transfer function of gout(Pout,xv) Indicating the spool displacement x of each joint hydraulic control valvevAnd return chamber pressure PoutThe spool displacement transfer function of (1) satisfies the following equation:
wherein the content of the first and second substances,
valve element displacement of hydraulic control valve for ith joint
Pressure of oil inlet chamber
The transfer function of the spool displacement of (a),
valve element displacement of hydraulic control valve for ith joint
And pressure of oil return chamber
Valve element displacement transfer function of, PsIs the supply pressure coefficient, P, of the hydraulic pumprIs the reference pressure coefficient of the hydraulic return tank.
The step 2) is specifically as follows:
2.1) establishing a first adaptive robust control law P based on the system nonlinear dynamics model established in the step 1)LdThe following formula is satisfied:
PLd＝PLda+PLds1+PLds2 (16)
wherein, PLdaRepresenting a compensation parameter of the first adaptive model, PLds1Representing a first linear robust parameter, PLds2Representing a first uncertainty compensation parameter;
a matrix is estimated for parameters in a nonlinear dynamical model of the link arm,
compensating the parameter P for the first adaptive modelLdaIn the parameter estimation matrix
A coefficient regression matrix corresponding to each parameter in (1);
and
respectively an inertia matrix M (q), a Coriolis force matrix and a centrifugal force matrix in the nonlinear dynamics model of the connecting rod mechanical arm
A gravity matrix g (q) and an estimate of an interference matrix D; z is a radical of2Representing the angle conversion error of the underwater hydraulic mechanical arm; k is a radical of2Is a predetermined angle conversion error z2The coefficient feedback gain positive definite matrix; t represents a transpose operation; epsilon2Representing the first adaptationCompensation parameters of the stick control law; compensation parameter epsilon for first adaptive robust control law2Is set to be greater than the first adaptive model compensation parameter PLdaAnd a first linear robust parameter PLds1Is smaller by three or more orders of magnitude;
an error matrix representing uncertainty model parameters satisfying
Theta is a parameter matrix in the nonlinear dynamical model of the connecting rod mechanical arm;
the uncertain nonlinear error parameter of the underwater environment is expressed and satisfied
2.2) based on the first adaptive robust control law PLdEstablishing a second adaptive robust control law QLdThe following formula is satisfied:
QLd＝QLda+QLds1+QLds2 (30)
z3 TβeQLds2≤0 (35)
wherein Q isLdaRepresenting a second adaptive model compensation parameter, QLds1Representing a second linear robust parameter，QLds2Representing a second uncertainty compensation parameter;
the compensation parameter Q is represented in the second adaptive modelLdaIn the parameter estimation matrix
A coefficient regression matrix corresponding to each parameter in (1); z is a radical of3Representing the pressure parameter error, k, of an underwater hydraulic manipulator3Is a preset pressure parameter error z3The coefficient feedback gain positive definite matrix; oil inlet cavity flow Q of each joint hydraulic cylinderinNominal flow Q of the inlet chambers of the hydraulic cylinders of each jointinmAnd the error flow of the oil inlet cavity of each joint hydraulic cylinder
Flow Q of oil return cavity of each joint hydraulic cylinderoutNominal flow Q of the return chambers of the hydraulic cylinders comprising each jointoutmAnd error flow rate of oil return chamber
ε3A compensation parameter representing a second adaptive robust control law, the value of the compensation parameter ε x of the second adaptive robust control law being set to be greater than the value of the second adaptive model compensation parameter QLdaAnd a second linear robust parameter QLds1Is smaller by three or more orders of magnitude;
representing a first adaptive robust control law PLdDifferential of (2)
A non-calculation section;
2.3) based on the tracking error value obtained by the sensor measurement, carrying out self-adaptive iteration on the parameter matrix theta in the nonlinear dynamical model of the system by using a parameter self-adaptive adjusting method to obtain an updated parameter estimation matrix
Thereby updating the first adaptive model compensation parameter PLdaCompensating parameter Q with the second adaptive modelLda(ii) a By a first linear robust parameter PLds1A first uncertainty compensation parameter PLds2And updated first adaptive model compensation parameter PLdaForming an updated first adaptive robust control law PLdFrom the second linear robust parameter QLds1A second uncertainty compensation parameter QLds2And updated second adaptive model compensation parameter QLdaForming an updated second adaptive robust control law, and obtaining the updated second adaptive robust control law QLdaThe method is used as a self-adaptive robust control law of the underwater multi-joint hydraulic mechanical arm;
2.4) constructing the adaptive robust controller of the hydraulic mechanical arm based on the system nonlinear dynamical model and the adaptive robust control law, specifically, inputting a second adaptive model compensation parameter of the adaptive robust control law into the system nonlinear dynamical model, adding the output of the system nonlinear dynamical model, the second linear robust parameter and the uncertainty compensation parameter, and outputting the sum as the output of the adaptive robust controller, and obtaining the output of the adaptive robust controller by simultaneous equations (6) - (9) and (30), wherein the following relations are satisfied:
xv＝(AinVin -1kqingin(Pin,xv)+AoutVout -1kqoutgout(Pout,xv))-1QLd (36)
and the output of the adaptive robust controller is transmitted to a hydraulic system of the underwater multi-joint hydraulic mechanical arm, so that control is realized.
The step 2.3) is specifically as follows:
s1: determining the initial value of a parameter matrix theta according to a system nonlinear dynamic model, and recording as a parameter self-adaptive initial matrix
S2: angle conversion error z of underwater hydraulic mechanical arm obtained based on sensor measurement2And the pressure parameter error z of the underwater hydraulic mechanical arm3Adapting the initial matrix to the parameters by using the adaptive parameter adjustment method
Performing nonlinear model parameter adaptive iteration to obtain updated parameter adaptive initial matrix
And a parameter estimation matrix
Specifically, iteration is performed by the following formula:
wherein the content of the first and second substances,
expressing the differentiation of the parameter estimation matrix, namely the change rate of the parameter estimation matrix;
is a function of the discrete projection that is,
is a preset parameter adaptive gain matrix, tauθDenotes the adaptive adjustment quantity, tsIndicating the sampling time of the controller, thetamaxRepresenting the maximum value of a predetermined parameter matrix thetaminRepresenting the minimum value of a preset parameter matrix theta; in the formula (37), the first and second groups of the formula,
representing the updated parameter estimation matrix and serving as the parameter adaptive initial matrix of the next iteration
S3: in the process of controlling the motion of the underwater multi-joint hydraulic mechanical arm, the step S2 is continuously repeated, and a parameter estimation matrix is obtained
Performing a non-linear model parameter adaptive iteration to thereby update a parameter estimation matrix
And a second adaptive model compensation parameter QLdaThe second adaptive model compensation parameter Q is obtained while the parameter matrix theta of the model uncertainty is made to approach the actual valueLdaThe method approaches to an ideal control value, thereby overcoming the influence of model uncertainty on the control effect and improving the control precision.
The underwater multi-joint hydraulic mechanical arm is mainly formed by connecting a multi-joint connecting rod mechanical arm and a hydraulic system, sensors are arranged in the multi-joint connecting rod mechanical arm and the hydraulic system, and the sensors measure the state of the underwater hydraulic mechanical arm and transmit the state to the self-adaptive robust controller.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the nonlinear control method of the underwater multi-joint hydraulic mechanical arm, the nonlinear dynamics model of the underwater multi-joint hydraulic mechanical arm is established, the nonlinear control method of the underwater multi-joint hydraulic mechanical arm based on the adaptive robustness is provided, the stability of a control system is guaranteed, meanwhile, the tracking error of the tail end of the mechanical arm is reduced, and the control performance is improved.
2. In the invention, the model uncertainty of the nonlinear dynamics model of the underwater multi-joint hydraulic manipulator is considered, and the parameter estimation matrix is iteratively updated by using a parameter self-adaptive adjustment method
The influence caused by model uncertainty in the control process can be overcome, and therefore the control precision of the tail end of the underwater multi-joint hydraulic mechanical arm is further improved.
Drawings
Fig. 1 is a schematic view of a control target of the present invention.
Fig. 2 is a diagram of the hydraulic drive system of the present invention.
FIG. 3 is a block diagram of an adaptive robust based nonlinear control (ARC) system for an underwater multi-joint hydraulic manipulator of the present invention.
Fig. 4 is a target trajectory of the hydraulic robot arm joint motion of the present invention.
Fig. 5 is a graph comparing the control effect of the adaptive robust underwater articulated hydraulic robot nonlinear controller (ARC) based on the invention with the control effect of the conventional PID controller.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention will now be further described with reference to fig. 1,2,3, 4, 5:
the implementation technical scheme of the invention is as follows:
as shown in fig. 3, the present invention comprises the steps of:
1) aiming at the mechanical configuration and the hydraulic transmission mechanism of a connecting rod of the underwater multi-joint hydraulic mechanical arm, considering mechanical arm interference factors including mechanical friction, hydraulic oil resistance and wave flow influence, and establishing a system nonlinear dynamic model of the underwater multi-joint hydraulic mechanical arm; the underwater multi-joint hydraulic mechanical arm is mainly formed by connecting a multi-joint connecting rod mechanical arm and a hydraulic system, sensors are arranged in the multi-joint connecting rod mechanical arm and the hydraulic system, and the sensors measure the state of the underwater hydraulic mechanical arm and transmit the state to the self-adaptive robust controller.
The step 1) is specifically as follows:
establishing a system nonlinear dynamical model of the underwater multi-joint hydraulic mechanical arm, wherein the system nonlinear dynamical model of the underwater multi-joint hydraulic mechanical arm mainly comprises a dynamic relation between a joint angle and a hydraulic cylinder push rod, a nonlinear dynamical model of a connecting rod mechanical arm, a nonlinear dynamical model of a hydraulic system and a dynamic relation between chamber flow and valve core displacement of a hydraulic valve; as shown in fig. 1 and 2.
1.1) establishing a dynamic relation between a joint angle and a hydraulic cylinder push rod, which specifically comprises the following steps:
each joint angle q of the underwater multi-joint hydraulic mechanical arm satisfies q ═ q1,q2,…,qi,…,qn]TThe extension x of the push rod of each joint hydraulic cylinder meets the condition that x is ═ x1,x2,…,xi,…,xn]TWherein q is1Representing the joint angle, q, of the first joint of an underwater multi-joint hydraulic manipulatoriRepresenting the joint angle, x, of the ith joint of an underwater multi-joint hydraulic manipulator1Shows the extension amount, x, of the push rod of the joint hydraulic actuator of the first joint of the underwater multi-joint hydraulic mechanical armiThe hydraulic actuator push rod elongation of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented, i represents the serial number of the joint, n represents the total number of the joints, i is 1,2,3, …, n, T represents the transposition operation, and each joint angle and the hydraulic actuator push rod elongation of the corresponding joint satisfy the following relations:
wherein the content of the first and second substances,
indicating the length between the i-1 th joint and the ith joint,
represents the length between the ith joint and the (i + 1) th joint;
1.2) establishing a nonlinear dynamics model of the connecting rod mechanical arm, and satisfying the following formula:
wherein the content of the first and second substances,
and G (q) are an inertia matrix, a Coriolis force and centrifugal force matrix and a gravity matrix of the underwater multi-joint hydraulic mechanical arm respectively;
the angular velocity of each joint of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirements are met
The joint angular velocity of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented,
the angular acceleration of each joint of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirements of the angular acceleration
Representing the joint angular acceleration of the ith joint of the underwater multi-joint hydraulic mechanical arm;
to representThe full differential matrix of the extension x of the push rod of each joint hydraulic cylinder to each joint angle q meets the requirement
PinThe oil pressure of an oil inlet cavity of each joint hydraulic cylinder is shown, and the requirement of oil pressure
The oil pressure of an oil inlet cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; poutThe oil pressure of an oil return cavity of each joint hydraulic cylinder is shown, and the requirement of oil pressure
The oil pressure of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; a. theinThe area of the oil inlet cavity of each joint hydraulic cylinder is shown, and the requirement is met
The area of an oil inlet cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; a. theoutThe area of an oil return cavity of each joint hydraulic cylinder is shown, and the requirement is met
The area of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; d represents an interference item in the motion of the underwater multi-joint hydraulic mechanical arm, wherein the interference item comprises mechanical arm interference factors influenced by mechanical friction, hydraulic oil resistance and wave flow;
1.3) establishing a hydraulic system nonlinear dynamics model, and satisfying the following formula:
wherein, VinThe volume of the oil inlet cavity of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirements of the oil inlet cavity volume of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm
VoutThe volume of an oil return cavity of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirement of the volume of the oil return cavity of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm is met
And
respectively representing the volume of an oil inlet cavity and the volume of an oil return cavity of each joint hydraulic cylinder under the initial condition; diag [ 2 ]]Representing a matrix diagonalization operation; beta is aeThe volume modulus of the hydraulic oil is shown; qinThe flow of the oil inlet cavity of each joint hydraulic cylinder is expressed, and the requirement of the flow
The flow of an oil inlet cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; qoutThe flow of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirement of the flow of the oil return cavity of the hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is met
The flow of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented;
the differential of the oil pressure of the oil inlet cavity of the hydraulic cylinder of each joint is represented;
the differential of the oil pressure of the oil return cavity of the hydraulic cylinder of each joint is shown;
1.4) establishing a dynamic relation between the chamber flow and the displacement of the valve core of the hydraulic valve, and satisfying the following formula:
Qin＝kqingin(Oin,xv)xv (5)
Qout＝kqoutgout(Pout,xv)xv (6)
wherein x isvIs the valve core displacement of each joint hydraulic control valve, and meets the requirements
A valve body displacement of a hydraulic control valve of the ith joint; k is a radical ofqinShows the flow gain constant of each joint oil inlet chamber and satisfies
A flow gain constant representing the oil inlet chamber of the ith joint; k is a radical ofqoutShows the flow gain constant of the oil inlet chamber and the oil return chamber, and satisfies
A flow gain constant of an oil return chamber of the i-th joint is represented; gin(Pin,xv) Indicating the spool displacement x of each joint hydraulic control valvevPressure P of oil inlet chamberinValve element displacement transfer function of gout(Pout,xv) Indicating the spool displacement x of each joint hydraulic control valvevAnd return chamber pressure PoutThe spool displacement transfer function of (1) satisfies the following equation:
wherein the content of the first and second substances,
valve element displacement of hydraulic control valve for ith joint
Pressure of oil inlet chamber
The transfer function of the spool displacement of (a),
valve element displacement of hydraulic control valve for ith joint
And pressure of oil return chamber
Valve element displacement transfer function of, PsIs the supply pressure coefficient, P, of the hydraulic pumprIs the reference pressure coefficient of the hydraulic return tank.
2) Establishing a self-adaptive robust control law of the underwater multi-joint hydraulic mechanical arm based on a system nonlinear dynamic model of the underwater multi-joint hydraulic mechanical arm; the adaptive robust control law comprises adaptive model compensation parameters, linear robust parameters and uncertainty compensation parameters; the system nonlinear dynamics model is connected with the adaptive robust control law to form an adaptive robust controller of the underwater multi-joint hydraulic manipulator;
the step 2) is specifically as follows:
2.1) establishing a first adaptive robust control law P based on the system nonlinear dynamics model established in the step 1)LdThe following formula is satisfied:
PLd＝PLda+PLds1+PLds2 (16)
wherein, PLdaRepresenting a compensation parameter of the first adaptive model, PLds1Representing a first linear robust parameter, PLds2Representing a first uncertainty compensation parameter;
a matrix is estimated for parameters in a nonlinear dynamical model of the link arm,
compensating the parameter P for the first adaptive modelLdaIn the parameter estimation matrix
A coefficient regression matrix corresponding to each parameter in (1);
and
respectively an inertia matrix M (q), a Coriolis force matrix and a centrifugal force matrix in the nonlinear dynamics model of the connecting rod mechanical arm
A gravity matrix g (q) and an estimate of an interference matrix D; z is a radical of2Representing the angle conversion error of the underwater hydraulic mechanical arm; k is a radical of2Is a predetermined angle conversion error z2The coefficient feedback gain positive definite matrix; t represents a transpose operation; epsilon2A compensation parameter representing a first adaptive robust control law; compensation parameter epsilon for first adaptive robust control law2Is set to be greater than the first adaptive model compensation parameter PLdaAnd a first linear robust parameter PLds1Is smaller by three or more orders of magnitude;
an error matrix representing uncertainty model parameters satisfying
Theta is a parameter matrix in the nonlinear dynamical model of the connecting rod mechanical arm;
the uncertain nonlinear error parameter of the underwater environment is expressed and satisfied
First adaptive robust control law PLdThe calculation process specifically comprises the following steps:
tracking error z of joint angle of underwater hydraulic mechanical arm1Comprises the following steps:
z1＝qs-qd (11)
wherein q issRepresenting actual measurements of the joint angles of an underwater hydraulic manipulator, qdAnd the control target value of each joint angle of the underwater hydraulic mechanical arm is represented. In addition, the angle conversion error z of the underwater hydraulic mechanical arm2Comprises the following steps:
transforming angle parameters
Comprises the following steps:
wherein k is1Representing preset joint angle tracking error z of underwater hydraulic mechanical arm1Positive determining a diagonal matrix; k is a radical of1The purpose of establishing the adaptive robust controller is to ensure that the differential of the lyapunov control function of the first adaptive robust control law in the adaptive robust controller is less than or equal to zero, so that the stability of the whole adaptive robust controller is maintained.
Differentiating two sides of the equal sign of the formula (12) and multiplying the inertia matrix M (q) of the underwater hydraulic mechanical arm to the left, and combining the formulas (2), (11) and (13) to obtain the following results:
due to PinAin-PoutAoutThe method is characterized in that a nonlinear dynamics model of the connecting rod mechanical arm is a high-order item, so that an inversion establishment method is adopted based on the idea of order reduction, and the pressure virtual control input P of the underwater hydraulic mechanical armLComprises the following steps:
PL＝PinAin-PoutAout (15)
considering that the uncertainty of the parameters of the dynamic model exists in the nonlinear dynamic model of the connecting rod mechanical arm, a parameter estimation matrix is required to replace the accurate parameters of the unknown model in the self-adaptive robust controller establishment. Here, the pressure virtual control input P for the underwater hydraulic robot armLProposing a first adaptive robust control law PLdAnd the tracking error of each joint angle is reduced while the transient performance of the system is ensured. Established first adaptive robust control law PLdThe device consists of the following three parts:
PLd＝PLda+PLds1+PLds2 (16)
wherein, PLdaRepresenting a compensation parameter of the first adaptive model, PLds1Representing a first linear robust parameter, PLds2Representing a first uncertainty compensation parameter.
First adaptive model compensation parameter PLdaThe specific expression of (a) is written in the form of:
wherein the content of the first and second substances,
respectively an inertia matrix M (q), a Coriolis force matrix and a centrifugal force matrix in the nonlinear dynamics model of the connecting rod mechanical arm
The gravity matrix g (q) and an estimate of the disturbance matrix D.
In addition, the nonlinear dynamical model of the link mechanical arm has the following two properties:
Wherein theta is a parameter matrix in a link mechanical arm dynamic equation,
is a coefficient regression matrix corresponding to each parameter in the parameter matrix theta.
In the adaptive robust controller building process, the parameter matrix θ is:
according to the above properties, the first adaptive model compensates the parameter PLdaWriting into:
wherein the content of the first and second substances,
estimating a matrix for parameters in a multi-joint hydraulic mechanical arm dynamic model;
compensating the parameter P for the first adaptive modelLdaIn the parameter estimation matrix
The coefficient regression matrix corresponding to each parameter in (1).
First linear robust parameter PLds1The specific expression of (a) is written in the form of:
wherein k is2Is a predetermined angle conversion error z2The coefficient feedback gain positive definite matrix. Angle conversion error k2The purpose of (2) is also to ensure that the derivative of the lyapunov control function of the first adaptive robust control law is less than or equal to zero, so that the stability of the overall adaptive robust controller is maintained.
In addition, considering that uncertain nonlinear factors also exist in the nonlinear dynamical model of the connecting rod mechanical arm, the influence factors need to be compensated. As uncertainty compensation parameter, a first uncertainty compensation parameter PLds2Cannot be written as a concrete formula, but it requiresThe following constraints are to be satisfied:
condition 1:
condition 2:
wherein epsilon2Is a first adaptive robust control law compensation parameter, a first adaptive robust control law compensation parameter epsilon2Is set to be greater than the first adaptive model compensation parameter PLdaAnd a first linear robust parameter PLds1Is smaller by three (i.e. 10)-3) Or of the order of the above.
An error matrix representing uncertainty model parameters satisfying
Theta is a parameter matrix in the nonlinear dynamical model of the connecting rod mechanical arm;
an uncertain nonlinear error parameter representing underwater environment is satisfied
The condition 1 is met, so that the first adaptive robust control law can keep good control performance when parameter uncertainty and uncertainty nonlinearity exist; satisfying condition 2 guarantees a first uncertainty compensation parameter PLds2Finally approaches to 0 to compensate the parameter P for the first adaptive modelLdaThe interference of (2) is minimized.
2.2) based on the first adaptive robust control law PLdEstablishing a second adaptive robust control law QLdThe following formula is satisfied:
QLd＝QLda+QLds1+QLds2 (30)
z3 TβeQLds2≤0 (35)
wherein Q isLdaRepresenting a second adaptive model compensation parameter, QLds1Representing a second linear robust parameter, QLds2Representing a second uncertainty compensation parameter;
the compensation parameter Q is represented in the second adaptive modelLdaIn the parameter estimation matrix
A coefficient regression matrix corresponding to each parameter in (1); z is a radical of3Representing the pressure parameter error, k, of an underwater hydraulic manipulator3Is a preset pressure parameter error z3The coefficient feedback gain positive definite matrix; oil inlet cavity flow Q of each joint hydraulic cylinderinNominal flow Q of the inlet chambers of the hydraulic cylinders of each jointinmAnd the error flow of the oil inlet cavity of each joint hydraulic cylinder
Flow Q of oil return cavity of each joint hydraulic cylinderoutNominal flow Q of the return chambers of the hydraulic cylinders comprising each jointoutmAnd error flow rate of oil return chamber
ε3A compensation parameter representing a second adaptive robust control law, a second algorithmCompensation parameter epsilon adapted to robust control law3Is set to be greater than the second adaptive model compensation parameter QLdaAnd a second linear robust parameter QLds1Is smaller by three (i.e. 10)-3) Or of the order of the above;
representing a first adaptive robust control law PLdDifferential of (2)
A non-calculation section;
second adaptive robust control law QLdThe calculation process specifically comprises the following steps:
upon completion of virtual control input P to pressureLAfter the control law of (2) is established, the pressure parameter error z3＝PL-PLdAnd establishing a second adaptive robust control law to make the pressure parameter error z3The transient performance and the accuracy of the system are ensured while the system is converged to zero or a minimum value.
Firstly, the pressure parameter error z3Carrying out differentiation:
first adaptive robust control law PLdIs the pressure virtual control input P set in 3.1)LThe theoretical established value of (a) is fully differentiated to obtain:
differentiation of the first adaptive robust control law
Is calculated by
Is written as:
wherein the content of the first and second substances,
is an observed value of angular velocity of each joint of the mechanical arm acquired by an extended observer,
the observation value of the angular acceleration of each joint of the mechanical arm is calculated according to the nonlinear dynamics model of the connecting rod mechanical arm.
Differentiation of the first adaptive robust control law
Without calculating part of
Is written as:
wherein the content of the first and second substances,
and
respectively represent the estimation errors of each angular velocity and each angular acceleration, and respectively satisfy
And
simultaneous equations (3), (4), and (15) yield:
wherein, the oil inlet cavity flow Q of each joint hydraulic cylinderinNominal flow Q of the inlet chambers of the hydraulic cylinders of each jointinmAnd the error flow of the oil inlet cavity of each joint hydraulic cylinder
Flow Q of oil return cavity of each joint hydraulic cylinderoutNominal flow Q of the return chambers of the hydraulic cylinders comprising each jointoutmAnd error flow rate of oil return chamber
And pressure virtual control input PLSame, flow virtual control input QL：
QL＝AinVin -1Qinm+AoutVout -1Qoutm (28)
Simultaneous equations (22) - (26) to relate the pressure error parameter z3The differential of (d) is expressed as:
input Q for virtual control of flow, similar to the first adaptive robust control lawLThe second adaptive robust control law of (a) also includes three parts, specifically expressed in the form:
QLd＝QLda+QLds1+QLds2 (30)
wherein Q isLdaRepresenting a second adaptive model compensation parameter, QLds1Representing a second linear robust parameter, QLds2Representing a second uncertainty compensation parameter.
Second adaptive model compensation parameter QLdaThe specific expression of (a) is written in the form of:
according to the property 2 of the nonlinear dynamical model of the connecting rod mechanical arm, the second adaptive model compensates the parameter QLdaAlso in short:
wherein the content of the first and second substances,
the compensation parameter Q is represented in the second adaptive modelLdaIn the parameter estimation matrix
A coefficient regression matrix corresponding to each parameter in (1);
second linear robust parameter QLds1The specific expression of (a) is written in the form of:
wherein z is3Representing the pressure parameter error, k, of an underwater hydraulic manipulator3Is a preset pressure parameter error z3The coefficient feedback gain positive definite matrix; k is a radical of3Is established to ensure that the derivative of the lyapunov control function of the second adaptive robust control law is less than or equal to zero, thereby enabling the overall controller to maintain stability.
In addition, with the first uncertainty compensation parameter PLds2Same, second uncertainty compensation parameter QLds2Nor can it be written as a concrete formulation, but it needs to satisfy the following constraints:
condition 1:
condition 2: z is a radical of3 TβeQLds2≤0 (35)
Wherein epsilon3A compensation parameter representing a second adaptive robust control law is represented. Compensation parameter epsilon for the second adaptive robust control law3Is set to be greater than the second adaptive model compensation parameter QLdaAnd a second linear robust parameter QLds1Is smaller by three (i.e. 10)-3) Or of the order of the above.
2.3) considering model uncertainty of the system nonlinear dynamical model established in the step one, and adopting a parameter estimation matrix in the system nonlinear dynamical model
Not completely accurate, so to reduce the parameter estimation matrix
The method comprises the following steps of carrying out adaptive iteration on a parameter matrix theta in a system nonlinear dynamics model by using a parameter adaptive adjustment method based on a tracking error value obtained by sensor measurement to obtain an updated parameter estimation matrix
Thereby updating the first adaptive model compensation parameter PLdaCompensating parameter Q with the second adaptive modelLda(ii) a By a first linear robust parameter PLds1A first uncertainty compensation parameter PLds2And updated first adaptive model compensation parameter PLdaForming an updated first adaptive robust control law PLdFrom the second linear robust parameter QLds1A second uncertainty compensation parameter QLds2And updated second adaptive model compensation parameter QLdaForming an updated second adaptive robust control law, and obtaining the updated second adaptive robust control law QLdaThe method is used as a self-adaptive robust control law of the underwater multi-joint hydraulic mechanical arm;
the step 2.3) is specifically as follows:
s1: determining the initial value of a parameter matrix theta according to a system nonlinear dynamic model, and recording as a parameter self-adaptive initial matrix
Adapting an initial matrix using parameters
Calculating to obtain an initial first adaptive model compensation parameter PLdaCompensating parameter Q with the second adaptive modelLda。
S2: angle conversion error z of underwater hydraulic mechanical arm obtained based on sensor measurement2And the pressure parameter error z of the underwater hydraulic mechanical arm3Adapting the initial matrix to the parameters by using the adaptive parameter adjustment method
Performing nonlinear model parameter adaptive iteration to obtain updated parameter adaptive initial matrix
And a parameter estimation matrix
Specifically, iteration is performed by the following formula:
wherein the content of the first and second substances,
expressing the differentiation of the parameter estimation matrix, namely the change rate of the parameter estimation matrix;
is a function of the discrete projection that is,
is a preset parameter adaptive gain matrix, tauθDenotes the adaptive adjustment quantity, tsIndicating the sampling time of the controller, thetamaxRepresenting the maximum value of a predetermined parameter matrix thetamin represents the minimum value of a preset parameter matrix theta; in the formula (37), the first and second groups of the formula,
representing the updated parameter estimation matrix and serving as the parameter adaptive initial matrix of the next iteration
S3: in the process of controlling the motion of the underwater multi-joint hydraulic mechanical arm, the step S2 is continuously repeated, and a parameter estimation matrix is obtained
Performing a non-linear model parameter adaptive iteration to thereby update a parameter estimation matrix
And a second adaptive model compensation parameter QLda, making the uncertain parameter matrix theta of the model approach to the actual value and simultaneously compensating the parameter QL of the second adaptive modelda approaches to an ideal control value, thereby overcoming the influence of model uncertainty on the control effect and improving the control precision.
2.4) constructing the adaptive robust controller of the hydraulic mechanical arm based on the system nonlinear dynamical model and the adaptive robust control law, specifically, inputting a second adaptive model compensation parameter of the adaptive robust control law into the system nonlinear dynamical model, adding the output of the system nonlinear dynamical model, the second linear robust parameter and the uncertainty compensation parameter, and outputting the sum as the output of the adaptive robust controller, and obtaining the output of the adaptive robust controller by simultaneous equations (6) - (9) and (30), wherein the following relations are satisfied:
xv＝(AinVin -1kqingin(Pin，xv)+AoutVout -1kqoutgout(Pout，xv))-1QLd (36)
and the output of the adaptive robust controller is transmitted to a hydraulic system of the underwater multi-joint hydraulic mechanical arm, so that control is realized.
3) The tracking error value obtained by the measurement of the sensor is fed back to the adaptive robust control law of the adaptive robust controller in real time, the adaptive robust controller realizes adaptive iterative updating of self parameters, and the adaptive robust controller controls the underwater multi-joint hydraulic mechanical arm in real time to form a complete closed-loop control system of the underwater multi-joint hydraulic mechanical arm and realize the effective control of the adaptive robust controller on the underwater multi-joint hydraulic mechanical arm.
Finally, MATLAB/Simulink simulation based on the hydraulic mechanical arm with two degrees of freedom is carried out on the control method, a target track of the joint motion of the hydraulic mechanical arm shown in figure 4 is simulated, and the target track is compared with a PID controller, so that the control effect of the control method provided by the invention is verified.
In terms of controller gain factor design, the PID controller gain parameters for comparison are selected as: k is a radical ofp＝diag[150，180]，kI＝diag[40,40]，kD＝diag[17，10](ii) a The designed ARC controller gain parameters are selected as: k is a radical of1＝150，k2＝diag[150,90]，k3＝diag[100,60]The adaptive parameter matrix is set to: gamma-diag [ alpha ]2.5×10-6，0，6×10-6，8.6×10-6，0，0，0，2.5×10-6，0，7.2×10-6，8.6×10-6，0，0，0]The reason for some of the adaptation parameters in Γ being zero is: in practical application, some parameters can be uniquely determined by known parameters, the uncertainty is small, and therefore only the parameters with large uncertainty can be adaptively adjusted to improve the efficiency of the controller.
The parameters of the underwater multi-joint hydraulic mechanical arm simulation model are shown in table 1.
TABLE 1 simulation model parameters
Finally, the simulation result of the multi-joint hydraulic mechanical arm is shown in fig. 5, in the two sub-graphs in fig. 5, a thin line represents the control effect of the underwater multi-joint hydraulic mechanical arm nonlinear controller based on the adaptive robustness, and a thick line represents the control effect of the PID controller; in the next two sub-diagrams of fig. 5, the thin line represents the error of the nonlinear controller of the underwater articulated hydraulic mechanical arm based on adaptive robustness, and the thick line represents the control error of the PID controller.
The control effect subgraph shows that the underwater multi-joint hydraulic mechanical arm nonlinear controller based on the adaptive robustness can accurately track a target track curve under the conditions of model interference (mechanical friction, hydraulic oil resistance and wave flow influence) and unknown speed signals. Meanwhile, the control tracking error curve shows that the angle tracking error of each joint is kept to be zero (the angular velocity and the acceleration are kept unchanged) in a steady state in the whole movement process. Compared with the joint angle range, the tracking errors of the two joints have smaller fluctuation in the transient change process.
Compared with the traditional PID controller, the ARC has smaller joint tracking error and shorter transient response time, the nonlinear control method based on the adaptive robust underwater multi-joint hydraulic manipulator has superior transient response performance and better robustness, can effectively compensate the influence of model uncertainty (modeling error and parameter uncertainty) and model interference (mechanical friction, hydraulic oil resistance and wave flow influence) on the control precision of the tail end of the manipulator, reduces the tracking error of the tail end of the manipulator while ensuring the stability of a control system, and improves the control performance.
The above-mentioned contents are only technical ideas of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical ideas proposed by the present invention fall within the protection scope of the claims of the present invention.
Claims (4)
1. An underwater multi-joint hydraulic manipulator nonlinear control method based on self-adaptive robustness is characterized by comprising the following steps:
1) establishing a system nonlinear dynamic model of the underwater multi-joint hydraulic mechanical arm;
2) establishing a self-adaptive robust control law of the underwater multi-joint hydraulic mechanical arm based on a system nonlinear dynamic model of the underwater multi-joint hydraulic mechanical arm; the system nonlinear dynamics model is connected with the adaptive robust control law to form an adaptive robust controller of the underwater multi-joint hydraulic manipulator;
3) the tracking error value obtained by the measurement of the sensor is fed back to the adaptive robust controller in real time, the adaptive robust controller realizes self-adaptive iterative updating of self parameters, the adaptive robust controller controls the underwater multi-joint hydraulic mechanical arm in real time to form a complete closed-loop control system of the underwater multi-joint hydraulic mechanical arm, and the adaptive robust controller realizes effective control of the underwater multi-joint hydraulic mechanical arm;
the step 1) is specifically as follows:
establishing a system nonlinear dynamical model of the underwater multi-joint hydraulic mechanical arm, wherein the system nonlinear dynamical model of the underwater multi-joint hydraulic mechanical arm mainly comprises a dynamic relation between a joint angle and a hydraulic cylinder push rod, a nonlinear dynamical model of a connecting rod mechanical arm, a nonlinear dynamical model of a hydraulic system and a dynamic relation between chamber flow and valve core displacement of a hydraulic valve;
1.1) establishing a dynamic relation between a joint angle and a hydraulic cylinder push rod, which specifically comprises the following steps:
each joint angle q of the underwater multi-joint hydraulic mechanical arm satisfies q ═ q1,q2,…,qi,…,qn]TThe extension x of the push rod of each joint hydraulic cylinder meets the condition that x is ═ x1,x2,…,xi,…,xn]TWherein q is1Representing the joint angle, q, of the first joint of an underwater multi-joint hydraulic manipulatoriRepresenting the joint angle, x, of the ith joint of an underwater multi-joint hydraulic manipulator1Shows the extension amount, x, of the push rod of the joint hydraulic actuator of the first joint of the underwater multi-joint hydraulic mechanical armiThe hydraulic actuator push rod elongation of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented, i represents the serial number of the joint, n represents the total number of the joints, i is 1,2,3, …, n, T represents the transposition operation, and each joint angle and the hydraulic actuator push rod elongation of the corresponding joint satisfy the following relations:
wherein the content of the first and second substances,
indicating the length between the i-1 th joint and the ith joint,
represents the length between the ith joint and the (i + 1) th joint;
1.2) establishing a nonlinear dynamics model of the connecting rod mechanical arm, and satisfying the following formula:
wherein, M (q),
and G (q) are an inertia matrix, a Coriolis force and centrifugal force matrix and a gravity matrix of the underwater multi-joint hydraulic mechanical arm respectively;
the angular velocity of each joint of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirements are met
The joint angular velocity of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented,
the angular acceleration of each joint of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirements of the angular acceleration
Representing the joint angular acceleration of the ith joint of the underwater multi-joint hydraulic mechanical arm;
a full differential matrix representing the extension x of the push rod of each joint hydraulic cylinder to each joint angle q, and satisfies
PinIndicating the advance of the hydraulic cylinders of each jointOil pressure in oil cavity to satisfy
The oil pressure of an oil inlet cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; poutThe oil pressure of an oil return cavity of each joint hydraulic cylinder is shown, and the requirement of oil pressure
The oil pressure of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; a. theinThe area of the oil inlet cavity of each joint hydraulic cylinder is shown, and the requirement is met
The area of an oil inlet cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; a. theoutThe area of an oil return cavity of each joint hydraulic cylinder is shown, and the requirement is met
The area of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; d represents an interference item in the motion of the underwater multi-joint hydraulic mechanical arm, wherein the interference item comprises mechanical arm interference factors influenced by mechanical friction, hydraulic oil resistance and wave flow;
1.3) establishing a hydraulic system nonlinear dynamics model, and satisfying the following formula:
wherein, VinThe volume of the oil inlet cavity of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirements of the oil inlet cavity volume of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm
VoutThe volume of an oil return cavity of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirement of the volume of the oil return cavity of each joint hydraulic cylinder of the underwater multi-joint hydraulic mechanical arm is met
And
respectively representing the volume of an oil inlet cavity and the volume of an oil return cavity of each joint hydraulic cylinder under the initial condition; diag [ 2 ]]Representing a matrix diagonalization operation; beta is aeThe volume modulus of the hydraulic oil is shown; qinThe flow of the oil inlet cavity of each joint hydraulic cylinder is expressed, and the requirement of the flow
The flow of an oil inlet cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented; qoutThe flow of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is expressed, and the requirement of the flow of the oil return cavity of the hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is met
The flow of an oil return cavity of a hydraulic cylinder of the ith joint of the underwater multi-joint hydraulic mechanical arm is represented;
the differential of the oil pressure of the oil inlet cavity of each joint hydraulic cylinder is represented;
the differential of the oil pressure of the oil return cavity of each joint hydraulic cylinder is represented;
1.4) establishing a dynamic relation between the chamber flow and the displacement of the valve core of the hydraulic valve, and satisfying the following formula:
Qin＝kqingin(Pin,xv)xv (5)
Qout＝kqoutgout(Pout,xv)xv (6)
wherein x isvIs the valve core displacement of each joint hydraulic control valve, and meets the requirements
A valve body displacement of a hydraulic control valve of the ith joint; k is a radical ofqinShows the flow gain constant of each joint oil inlet chamber and satisfies
A flow gain constant representing the oil inlet chamber of the ith joint; k is a radical ofqoutShows the flow gain constant of the oil inlet chamber and the oil return chamber, and satisfies
A flow gain constant of an oil return chamber of the i-th joint is represented; gin(Pin,xv) Indicating the spool displacement x of each joint hydraulic control valvevPressure P of oil inlet chamberinValve element displacement transfer function of gout(Pout,xv) Indicating the spool displacement x of each joint hydraulic control valvevAnd return chamber pressure PoutThe spool displacement transfer function of (1) satisfies the following equation:
wherein the content of the first and second substances,
valve element displacement of hydraulic control valve for ith joint
Pressure of oil inlet chamber
The transfer function of the spool displacement of (a),
valve element displacement of hydraulic control valve for ith joint
And pressure of oil return chamber
Valve element displacement transfer function of, PsIs the supply pressure coefficient, P, of the hydraulic pumprIs the reference pressure coefficient of the hydraulic return tank.
2. The adaptive robust based nonlinear control method for the underwater multi-joint hydraulic manipulator according to claim 1, wherein the step 2) is specifically as follows:
2.1) establishing a first adaptive robust control law P based on the system nonlinear dynamics model established in the step 1)LdThe following formula is satisfied:
PLd＝PLda+PLds1+PLds2 (11)
wherein, PLdaRepresenting a compensation parameter of the first adaptive model, PLds1To representFirst linear robust parameter, PLds2Representing a first uncertainty compensation parameter;
a matrix is estimated for parameters in a nonlinear dynamical model of the link arm,
compensating the parameter P for the first adaptive modelLdaIn the parameter estimation matrix
A coefficient regression matrix corresponding to each parameter in (1);
and
respectively an inertia matrix M (q), a Coriolis force matrix and a centrifugal force matrix in the nonlinear dynamics model of the connecting rod mechanical arm
A gravity matrix g (q) and an estimate of an interference matrix D; z is a radical of2Representing the angle conversion error of the underwater hydraulic mechanical arm; k is a radical of2Is a predetermined angle conversion error z2The coefficient feedback gain positive definite matrix; t represents a transpose operation; epsilon2A compensation parameter representing a first adaptive robust control law; compensation parameter epsilon for first adaptive robust control law2Is set to be greater than the first adaptive model compensation parameter PLdaAnd a first linear robust parameter PLds1Is smaller by three or more orders of magnitude;
an error matrix representing uncertainty model parameters satisfying
Theta is a parameter matrix in the nonlinear dynamical model of the connecting rod mechanical arm;
the uncertain nonlinear error parameter of the underwater environment is expressed and satisfied
2.2) based on the first adaptive robust control law PLdEstablishing a second adaptive robust control law QLdThe following formula is satisfied:
QLd＝QLda+QLds1+QLds2 (16)
z3 TβeQLds2≤0 (20)
wherein Q isLdaRepresenting a second adaptive model compensation parameter, QLds1Representing a second linear robust parameter, QLds2Representing a second uncertainty compensation parameter;
the compensation parameter Q is represented in the second adaptive modelLdaIn the parameter estimation matrix
A coefficient regression matrix corresponding to each parameter in (1); z is a radical of3Representing the pressure parameter error, k, of an underwater hydraulic manipulator3Is a preset pressure parameter error z3The coefficient feedback gain positive definite matrix; oil inlet cavity flow Q of each joint hydraulic cylinderinNominal flow Q of the inlet chambers of the hydraulic cylinders of each jointinmAnd the error flow of the oil inlet cavity of each joint hydraulic cylinder
Flow Q of oil return cavity of each joint hydraulic cylinderoutNominal flow Q of the return chambers of the hydraulic cylinders comprising each jointoutmAnd error flow rate of oil return chamber
ε3A compensation parameter representing a second adaptive robust control law, a compensation parameter epsilon of the second adaptive robust control law3Is set to be greater than the second adaptive model compensation parameter QLdaAnd a second linear robust parameter QLds1Is smaller by three or more orders of magnitude;
representing a first adaptive robust control law PLdDifferential of (2)
A non-calculation section;
2.3) based on the tracking error value obtained by the sensor measurement, carrying out self-adaptive iteration on the parameter matrix theta in the nonlinear dynamical model of the system by using a parameter self-adaptive adjusting method to obtain an updated parameter estimation matrix
Thereby updating the first adaptive model compensation parameter PLdaCompensating parameter Q with the second adaptive modelLda(ii) a By a first linear robust parameter PLds1A first uncertainty compensation parameter PLds2And after updatingFirst adaptive model compensation parameter PLdaForming an updated first adaptive robust control law PLdFrom the second linear robust parameter QLds1A second uncertainty compensation parameter QLds2And updated second adaptive model compensation parameter QLdaForming an updated second adaptive robust control law, and obtaining the updated second adaptive robust control law QLdaThe method is used as a self-adaptive robust control law of the underwater multi-joint hydraulic mechanical arm;
2.4) constructing the adaptive robust controller of the hydraulic mechanical arm based on the system nonlinear dynamical model and the adaptive robust control law, specifically, inputting a second adaptive model compensation parameter of the adaptive robust control law into the system nonlinear dynamical model, adding the output of the system nonlinear dynamical model, the second linear robust parameter and the uncertainty compensation parameter, and outputting the sum as the output of the adaptive robust controller, and obtaining the output of the adaptive robust controller by simultaneous equations (6) - (9) and (16), wherein the following relations are satisfied:
xv＝(AinVin -1kqingin(Pin，xv)+AoutVout -1kqoutgout(Pout，xv))-1QLd (21)
and the output of the adaptive robust controller is transmitted to a hydraulic system of the underwater multi-joint hydraulic mechanical arm, so that control is realized.
3. The adaptive robust based nonlinear control method for the underwater multi-joint hydraulic manipulator according to claim 2, wherein the step 2.3) is specifically as follows:
s1: determining the initial value of a parameter matrix theta according to a system nonlinear dynamic model, and recording as a parameter self-adaptive initial matrix
S2: angle of underwater hydraulic mechanical arm obtained based on sensor measurementConversion error z2And the pressure parameter error z of the underwater hydraulic mechanical arm3Adapting the initial matrix to the parameters by using the adaptive parameter adjustment method
Performing nonlinear model parameter adaptive iteration to obtain updated parameter adaptive initial matrix
And a parameter estimation matrix
Specifically, iteration is performed by the following formula:
wherein the content of the first and second substances,
representing a differential of the parameter estimation matrix;
is a function of the discrete projection that is,
is a preset parameter adaptive gain matrix, tauθDenotes the adaptive adjustment quantity, tsIndicating the sampling time of the controller, thetamaxRepresenting the maximum value of a predetermined parameter matrix thetaminRepresenting the minimum value of a preset parameter matrix theta; in the formula (22), the first and second groups,
representing the updated parameter estimation matrix and serving as the parameter adaptive initial matrix of the next iteration
S3: in the process of controlling the motion of the underwater multi-joint hydraulic mechanical arm, the step S2 is continuously repeated, and a parameter estimation matrix is obtained
Performing a non-linear model parameter adaptive iteration to thereby update a parameter estimation matrix
And a second adaptive model compensation parameter QLdaThe second adaptive model compensation parameter Q is obtained while the parameter matrix theta of the model uncertainty is made to approach the actual valueLdaThe method approaches to an ideal control value, thereby overcoming the influence of model uncertainty on the control effect and improving the control precision.
4. The adaptive robust based nonlinear control method for the underwater multi-joint hydraulic manipulator of claim 1, characterized in that: the underwater multi-joint hydraulic mechanical arm is mainly formed by connecting a multi-joint connecting rod mechanical arm and a hydraulic system, sensors are arranged in the multi-joint connecting rod mechanical arm and the hydraulic system, and the sensors measure the state of the underwater hydraulic mechanical arm and transmit the state to the self-adaptive robust controller.
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO1999046731A1 (en) * | 1998-03-13 | 1999-09-16 | The University Of Houston System | Methods for performing daf data filtering and padding |
| US5959861A (en) * | 1996-10-31 | 1999-09-28 | Fujitsu Limited | Adaptive robust control device |
| CN106842954A (en) * | 2017-03-14 | 2017-06-13 | 北京理工大学 | A kind of control method of semi-flexible mechanical arm system |
| CN109062039A (en) * | 2018-07-25 | 2018-12-21 | 长安大学 | A kind of adaptive robust control method of Three Degree Of Freedom Delta parallel robot |
| CN109240086A (en) * | 2018-10-16 | 2019-01-18 | 浙江大学 | A kind of adaptive robust control method of non-linear bilateral teleoperation system |
| CN109421042A (en) * | 2017-08-23 | 2019-03-05 | 中国空气动力研究与发展中心计算空气动力研究所 | Robust self-adaptive sliding mode control method for flexible hinge space station mechanical arm |
| CN111546350A (en) * | 2020-04-30 | 2020-08-18 | 浙江大学 | Multi-joint heavy-load hydraulic robot system and high-precision motion control method |
-
2021
- 2021-06-10 CN CN202110648342.4A patent/CN113219841B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5959861A (en) * | 1996-10-31 | 1999-09-28 | Fujitsu Limited | Adaptive robust control device |
| WO1999046731A1 (en) * | 1998-03-13 | 1999-09-16 | The University Of Houston System | Methods for performing daf data filtering and padding |
| CN106842954A (en) * | 2017-03-14 | 2017-06-13 | 北京理工大学 | A kind of control method of semi-flexible mechanical arm system |
| CN109421042A (en) * | 2017-08-23 | 2019-03-05 | 中国空气动力研究与发展中心计算空气动力研究所 | Robust self-adaptive sliding mode control method for flexible hinge space station mechanical arm |
| CN109062039A (en) * | 2018-07-25 | 2018-12-21 | 长安大学 | A kind of adaptive robust control method of Three Degree Of Freedom Delta parallel robot |
| CN109240086A (en) * | 2018-10-16 | 2019-01-18 | 浙江大学 | A kind of adaptive robust control method of non-linear bilateral teleoperation system |
| CN111546350A (en) * | 2020-04-30 | 2020-08-18 | 浙江大学 | Multi-joint heavy-load hydraulic robot system and high-precision motion control method |
Non-Patent Citations (4)
| Title |
|---|
| Adaptive Robust Cascade Force Control of 1-DOF Hydraulic Exoskeleton for Human Performance Augmentation;Shan Chen;《ASME TRANSACTIONS ON MECHATRONICS》;20170430;全文 * |
| Adaptive Robust Motion Control of a Pump Direct Drive Electro-hydraulic System with Meter-Out Pressure Regulation;陈正;《IFCA》;20201231;全文 * |
| ADAPTIVE-ROBUST CONTROL OF THE STEWART-GOUGH PLATFORM AS A SIX DOF PARALLEL ROBOT;Amir, Ghobakhloo;《 World Automation Congress》;20060726;全文 * |
| An adaptive robust nonsingular fast terminal sliding mode controller based on wavelet neural network for a 2-DOF robotic arm;A.Jouila;《Journal of the Franklin Institute》;20201231;全文 * |
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