CN111824958B - Method for generating bridge crane winch controller, control method and controller generation system - Google Patents
Method for generating bridge crane winch controller, control method and controller generation system Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B66—HOISTING; LIFTING; HAULING
- B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
- B66C13/00—Other constructional features or details
- B66C13/18—Control systems or devices
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B66—HOISTING; LIFTING; HAULING
- B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
- B66C13/00—Other constructional features or details
- B66C13/16—Applications of indicating, registering, or weighing devices
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B66—HOISTING; LIFTING; HAULING
- B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
- B66C13/00—Other constructional features or details
- B66C13/18—Control systems or devices
- B66C13/48—Automatic control of crane drives for producing a single or repeated working cycle; Programme control
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B66—HOISTING; LIFTING; HAULING
- B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
- B66C2700/00—Cranes
- B66C2700/08—Electrical assemblies or electrical control devices for cranes, winches, capstans or electrical hoists
Abstract
The invention relates to a bridge crane hoisting controller generation method, a control method and a controller generation system, relating to the technical field of bridge crane hoisting control, wherein the bridge crane hoisting control system is subjected to dynamics analysis according to the structure of the bridge crane hoisting control system, and a control model to be observed under the dynamics structure of the hoisting system is established; obtaining an estimation model of the optimal feedback full-state observer based on the measurement variable rope pendulum length; performing model conversion based on a control model to be observed, and combining an estimation model and the model conversion to obtain an actual controller; and obtaining a bridge crane control hoisting method by using an actual controller, and further obtaining a control model acquisition module to be observed, an estimation model acquisition module and an actual controller generation module by using the controller generation method so as to generate a control system. Compared with the prior art, the bridge crane has the effect of improving the conveying efficiency of the bridge crane.
Description
Technical Field
The invention relates to the technical field of bridge crane control, in particular to a bridge crane hoisting controller generation method, a bridge crane hoisting controller control method and a bridge crane hoisting controller generation system.
Background
Bridge cranes are typically non-linear mechanical systems that utilize long ropes to connect a load to a crane and move the crane to transport the load to a desired location, and are widely used in ports, warehouses, construction sites, and the like. In recent decades, how to realize accurate full-automatic control on a bridge crane so as to improve the conveying efficiency, the positioning accuracy and the safety coefficient is a research hotspot problem in the current industrial field.
In the traditional bridge crane control method, a concrete mathematical model of a crane system is mostly relied on. However, in the process of the bridge crane operation, due to the coupling characteristics among system variables, load variation among different transportation batches, interference of external uncertain factors such as wind direction, collision and the like, it is difficult to obtain a system accurate parameter model of the bridge crane, that is, the accurate model of the bridge crane hoisting system is unknown, so that the position tracking control effect of the bridge crane hoisting system is poor, and the bridge crane transportation efficiency is low.
With the development of model estimation and data-driven control theory, an intelligent control method represented by fuzzy control and a neural network provides a method and a basis for controlling and designing to get rid of an accurate parameter model. However, fuzzy control requires extensive experience by experts and operators; neural network systems require a large amount of abundant data and lack rigorous reasoning processes and selection bases, and these characteristics cause great dilemma on the problem of online regulation of control systems. The observation error discussion of the linear extended state observer is published in the control and decision by Ganzhou and Dong minister, the linear/nonlinear switching extended state observer is published in the control theory and application by Chengxiang and Ganzhou, and the linear extended state observer and the performance analysis of the high-order form thereof are published in the control and decision by Shaoxing and Wang Honglong, so that the control system forms simple series integral control, and satisfactory effect can be obtained under the condition of reasonable parameter selection. But on the other hand, the integrator series type structure limits the application range of the estimation method and the wide application of the control scheme. Meanwhile, in the design process of the observer, the method only implements feedback design aiming at observation errors, and cannot ensure the running track of each observation variable.
Disclosure of Invention
The invention aims to provide a method for generating a bridge crane winch controller, which has the characteristic of being beneficial to improving the conveying efficiency.
The above object of the present invention is achieved by the following technical solutions:
a bridge crane hoist controller generation method, the generation method comprising:
the observation control model is acquired, dynamic analysis is carried out on the bridge crane hoisting control system according to the bridge crane hoisting control system structure, and the observation control model to be observed under the hoisting system dynamic structure is established:
wherein y (t) represents the length of a rope pendulum controlled by the winch, f (t) represents a model to be observed, which comprises an existing model, unmodeled dynamic and uncertain disturbance information, in the winch system, u (t) represents the control input of the winch system, and b is a known control coefficient;
obtaining an estimation model, namely obtaining an estimation model of the optimal feedback full-state observer based on a measurement variable y (t); and the number of the first and second groups,
and generating an actual controller, performing model conversion based on the control model to be observed, and combining the estimation model and the model conversion to obtain the actual controller.
By adopting the technical scheme, all internal state information of the optimal full feedback state observer is fully utilized through the configured optimal full feedback state observer; through the feedback of the length of the rope pendulum, the length and the speed of the rope pendulum are estimated by combining an estimation model, and the model is controlled and designed to obtain an actual bridge crane hoisting controller, so that the adjustment of the motion state of the next rope pendulum according to the obtained bridge crane hoisting controller is facilitated, and the conveying efficiency of crane hoisting is further facilitated to be improved.
The invention is further configured to: the specific method for obtaining the estimation model comprises the following steps,
carrying out system expansion on the control model to be observed to obtain a system expansion matrix; defining a system observer based on the system expansion matrix;
defining a full-state virtual controller according to the system observer based on a defined performance index JvObtaining a quadratic optimal feedback rate k, and obtaining an optimal feedback full-state observer by combining the quadratic optimal feedback rate k and the virtual controller; and the number of the first and second groups,
based on the optimal feedback full-state observer, obtaining an estimation model which contains f (t) and is suitable for control design
By adopting the technical scheme, the virtual controller has better observation performance based on the whole observability of the self variable in the optimal feedback full-state observer, and the stability and the optimality of the performance index of the system observer of the winch system can be considered by adopting the linear quadratic optimal feedback function Lqry.
The present invention may be further configured to: the estimation model
The specific method for obtaining comprises the following steps:
defining an extended state x (t) ═ x for the control model to be observed1(t),x2(t),x3(t)]TAnd obtaining a system expansion matrix:
y(t)＝Cx(t) (2)
where u (t) represents the control input to the hoist system, h (t) is the derivative of f (t),
n is the order of the dynamic system; n ═ 0(n-1)×1；1]；
The extended state space description is characterized in that AcAnd BcThe form is not unique, and matrix configuration can be carried out according to the order of the system and the structure required by control design, so that a state model form meeting the requirement of actual control design is obtained; for bridge crane hoist control systems, AcAnd BcConfigured as controllable standard types, i.e.
According to AcAnd BcThe spreading matrix constructed for the hoisting system can be expressed as follows:
definition of g (t) ═ f (t) + x1(t)+x2(t), based on equation (2), then h (t) is the derivative of g (t);
therefore, equation (2) is equivalent to
y(t)＝Cx(t)
At this time, x (t) ═ x1(t),x2(t)]T(ii) a Based on the definition of C in formula (2), there is y (t) ═ x1(t) the subsequent part is all put the rope for the length x1(t) directly as a measured variable;
defining the extended state vector as:
z＝[z1,z2,z3]T (4)
wherein z is1Representing a measured variable x1(t) estimate of (z)2Representing a measured variable x1(t) using the estimated value of the derivative, z3Represents an estimate of the system model g (t);
based on equation (4), the system observer of the hoisting system is defined as:
wherein A isvA, v is a virtual controller of the system observer, which is used for designing and configuring parameters of the system observer; the virtual controller fully utilizes all states of the system observer and feedback information of all states to drive the system observer to track the system state, so that estimation of the model g (t) is obtained
The dimension and the form of the virtual controller are flexibly configured according to the tracking requirement; in a hoisting system, v is defined as 3 x 1 dimension, BV＝eye(3)；
By defining the following performance indicators
Obtaining the optimal feedback rate of linear quadratic form
k＝lqry(Av,Bv,Cv,Dv,Qv,Rv) (6)
Wherein, Cv＝eye(3)，Dv＝zeros(3,3)，QvAnd RvIs the coefficient to be adjusted;
designing a virtual controller to be
v＝-kz+kRef (7)
Wherein Ref ═ x1(t)，ref2，ref3]TAnd is provided with
Is composed of
Is estimated from the derivative of (a) the time,
is composed of
Can be obtained by a derivative estimation method;
and finally substituting the virtual controller shown in the formula (7) into the system observer shown in the formula (5) to obtain the optimal feedback full-state observer, and meanwhile, substituting the optimal feedback full-state observer into the system observer shown in the formula (5)Obtaining the estimation model
By adopting the technical scheme, the matrix configuration can be carried out according to the order of the system and the structure required by the control design, so that the state space model form required by the actual control design is obtained. Based on the method, the system observer is arranged, and the feedback information of the length of the rope pendulum and all state information in the system observer are fully utilized to estimate the system states and models such as the length, the speed and the like of the rope pendulum of the hoisting system. In the actual control design, the system module is offset by using the state and the model estimation information to obtain an actual bridge crane hoisting controller, so that the bridge crane hoisting controller is facilitated to adjust the following rope swinging motion state, and the conveying efficiency of the crane hoisting is facilitated to be improved.
The present invention may be further configured to: the specific method for estimating the derivative comprises the following steps:
defining a derivative estimation variable and providing a derivative estimator
Implementing a derivative estimation method;
where r is the derivative estimate variable, r ═ r1,r2,r3]T，
vrIs a virtual controller of the estimator for designing the parameters required for the derivative estimation,
vr＝-krr+krErx1(t) (16)
wherein the content of the first and second substances,
kris to define a performance index JrObtaining quadratic optimum feedback rate
kr＝lqr(Ar,Br,Qr,Rr) (18)
Wherein Q isrAnd RrFor the coefficient to be adjusted, kr＝[kr1,kr2,kr3]。
By adopting the technical scheme, the linear quadratic regulator is utilized to carry out derivative estimation configuration, the stability and optimality of the performance index of the derivative estimation system are considered, the derivative estimation of the measurement signal is obtained, and the derivative tracking error is ensured to be zero. The derivative estimation is combined with the design of a virtual controller of the system observer, and an estimation model of the optimal feedback full-state observer can be obtained.
The present invention may be further configured to: the method for generating the actual controller comprises the following steps:
according to the configuration of the system expansion matrix of formula (2), the kinetic model to be observed is equivalent to formula (3), and can be expressed in the following form
Wherein x (t) ═ x1(t),x2(t)]T，g(t)＝x1(t)+x2(t) + f (t) is the model to be observed;
based on AcAnd BcDefining a performance index JcObtaining the optimal feedback rate k of linear quadratic formc
kc＝lqr(Ac,Bc,Qc,Rc) (12)
Wherein Q iscAnd RcFor the coefficient to be adjusted, kc＝[kc1,kc2,kc3]。
Obtaining an actual controller u (t) by combining the estimation model offset and the linear quadratic optimal feedback rate
Wherein, yd(t) desired hoisting Displacement, yd(t)' is the desired derivative of the displacement, obtained by a derivative estimation method.
By adopting the technical scheme, the estimation model is obtained based on the optimal feedback full-state observer, and is combined with the linear quadratic regulator LQR to obtain the control scheme based on the LQR under the condition that the mathematical model is unknown, so that the control on the hoisting of the bridge crane is realized, and the control effect on the hoisting of the bridge crane is improved to a certain extent.
The invention also aims to provide a bridge crane hoisting control method which has the characteristic of improving the conveying efficiency of the bridge crane.
The above object of the present invention is achieved by the following technical solutions:
a bridge crane hoisting control method is realized based on an actual controller generated by a hoisting controller generation method.
By adopting the technical scheme, the actual controller produced based on the winding controller generation method is used for controlling the winding of the bridge crane, the accurate control of the swing motion of the winding rope of the bridge crane can be realized to a certain extent, and the improvement of the conveying efficiency is facilitated.
The third purpose of the invention is to provide a bridge crane winch controller generating system which has the characteristic of being beneficial to improving the conveying efficiency of a bridge crane.
The above object of the present invention is achieved by the following technical solutions:
a bridge crane hoist controller generation system, the generation system comprising,
the module is obtained to the control model of waiting to observe, according to bridge crane hoist control system structure, carries out the dynamics analysis to bridge crane hoist control system, establishes the control model of waiting to observe under the hoist system dynamics structure:
wherein y (t) represents the length of a rope pendulum controlled by the winch, f (t) represents a model to be observed, which comprises an existing model, unmodeled dynamic and uncertain disturbance information, in the winch system, u (t) represents the control input of the winch system, and b is a known control coefficient;
the estimation model acquisition module is used for acquiring an estimation model of the optimal feedback full-state observer based on the measurement variable y (t); and the number of the first and second groups,
and the actual controller generation module is used for carrying out model conversion based on the control model to be observed and obtaining an actual controller by combining the estimation model and the model conversion.
By adopting the technical scheme, the optimal feedback full-state observer is arranged, and all state information in the system observer is fully utilized; through the feedback of the length of the rope pendulum and the estimation of the length and the speed of the rope pendulum by combining the estimation model, the control model to be observed is controlled and designed to obtain an actual winch controller generating system of the bridge crane, so that the winch motion state of the bridge crane is adjusted, and the conveying efficiency of the bridge crane is improved.
In summary, the invention includes at least one of the following beneficial technical effects:
1. according to the method for generating the bridge crane hoisting controller, all state information in the optimal full feedback state observer is fully utilized through the configured optimal full feedback state observer; through the feedback of the length of the rope pendulum, the length and the speed of the rope pendulum are estimated by combining an estimation model, the control model to be observed is further subjected to control design, and an actual bridge crane hoisting controller is obtained, so that the adjustment of the next hoisting motion state according to the obtained bridge crane hoisting controller is facilitated, and the conveying efficiency of a bridge crane is further facilitated to be improved.
2. The bridge crane hoisting control method gets rid of the dependence on the model, realizes the position tracking control of the bridge crane hoisting system by using the obtained actual controller, and is beneficial to improving the conveying efficiency of the bridge crane;
3. the bridge crane hoisting controller generation system provided by the invention utilizes the controller generation method to obtain the control model acquisition module to be observed, the estimation model acquisition module and the actual controller generation module, so that the hoisting controller system is generated, the tracking control of the hoisting motion state of the bridge crane is favorably realized, and the motion efficiency of the bridge crane is favorably improved.
Drawings
FIG. 1 is a schematic diagram of a bridge crane hoist control system;
FIG. 2 is a flow chart of a method for generating a hoist controller for a bridge crane according to one embodiment of the present invention;
fig. 3 is a control effect diagram of the practical controller of the invention.
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. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Any feature disclosed in this specification (including any accompanying drawings) may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
Referring to fig. 2, a bridge crane on the bridge frame can move along the bridge frame, a hoist control system is positioned on the crane, a hoist is connected with a load through a rope pendulum, and the hoist realizes longitudinal cargo handling by manipulating the length of the rope pendulum. In the working process of the bridge crane, due to the coupling characteristic among system variables, load change among different batches and interference of external uncertainty factors such as wind direction, collision and the like, the accurate parameter model of the system is difficult to obtain.
As an embodiment of the method for generating the hoisting controller of the bridge crane, as shown in fig. 2, the method comprises:
the method comprises the following steps of acquiring 101 a to-be-observed control model, carrying out dynamics analysis on a bridge crane hoisting control system according to a bridge crane hoisting control system structure, and establishing the to-be-observed control model under the hoisting system dynamics structure:
wherein y (t) represents the length of a rope pendulum controlled by the winch, f (t) represents a model to be observed, which comprises an existing model, unmodeled dynamic and uncertain disturbance information, in the winch system, u (t) represents the control input of the winch system, and b is a known control coefficient;
according to analysis, certain deviation exists in a model-based control method due to modeling precision, external disturbance, load change and the like of a bridge crane hoisting control system. Therefore, the model is estimated according to the fact measurement data y (t), and further control design is carried out according to the estimated model, so that the current practical control method is provided.
Obtaining an estimation model 102, namely obtaining an estimation model of the optimal feedback full-state observer based on a measurement variable y (t);
and generating 103 an actual controller, performing model conversion based on the control model to be observed, and combining the estimation model and the model conversion to obtain the actual controller.
As an implementation manner of estimation model acquisition, the specific method includes:
carrying out system expansion on the control model to be observed to obtain a system expansion matrix; defining a system observer based on the system expansion matrix;
according to the system viewThe detector defines a virtual controller of the full state based on defining a performance index JvObtaining a quadratic optimal feedback rate k, and obtaining an optimal feedback full-state observer by combining the quadratic optimal feedback rate k and the virtual controller; and the number of the first and second groups,
based on the optimal feedback full-state observer, obtaining an estimation model which contains f (t) and is suitable for control design
The specific method of system expansion is not definite, and the obtained system expansion matrix is theoretically equivalent representation of the control model to be observed and can be used as a structural reference and an error proof of a system observer of a winch system.
In the embodiment of obtaining the estimation model, the virtual controller has better observation performance based on all observability of the state variables in the system observer, and the stability and optimality of the system performance indexes of the system observer can be considered by adopting a quadratic optimal feedback function.
As an implementation mode of the control model system to be observed, the specific method comprises the following steps:
defining an extended state x (t) ═ x for a control model to be observed1(t),x2(t),x3(t)]TEstablishing a system expansion matrix:
y(t)＝Cx(t) (2)
where u (t) represents the control input to the hoist system, h (t) is the derivative of f (t),
n is the order of the dynamic system; n ═ 0(n-1)×1；1]；
The feature of the extended state space description is thatIn, AcAnd BcThe form is not unique, and matrix configuration is carried out according to the order of the system and the structure required by control design, so that a model form between states which is in line with the actual control design is obtained; for bridge crane hoist control systems, AcAnd BcConfigured as controllable standard types, i.e.
According to AcAnd BcThe spreading matrix constructed for the hoisting system can be expressed as follows:
definition of g (t) ═ f (t) + x1(t)+x2(t), based on equation (2), then h (t) is the derivative of g (t);
therefore, equation (2) is equivalent to
y(t)＝Cx(t)
At this time, x (t) ═ x1(t),x2(t)]T(ii) a Based on the definition of C in formula (2), there is y (t) ═ x1(t) the subsequent part is all put the rope for the length x1(t) directly as a measured variable;
due to the fact that certain deviation exists in the model-based control method due to system modeling precision, external disturbance, load change and the like, the crane hoisting control system needs to be controlled, and the motion state of the crane can be adjusted according to state information of observing the length of the rope pendulum.
For one embodiment of the define system observer, the extended state vector is defined as
z＝[z1,z2,z3]T (4)
Wherein z is1For measuring variable x1(t) estimate of (z)2Representing a measured variable x1(t) estimation of the derivative, z3Is an estimate of the system model g (t);
based on the definition of C in formula (2), there is y (t) ═ x1(t) the subsequent part is all put the rope for the length x1(t) directly as a measured variable. Based on this, as one implementation of obtaining a system observer of the hoisting system, the system observer of the hoisting system is defined as:
wherein A isvA, v is a virtual controller of the system observer for designing and configuring the state feedback observer parameters; the virtual controller fully utilizes all states of the system observer and feedback information of all states to drive the system observer to track the system state, so that estimation of the model g (t) is obtained
The dimension and the form of the virtual controller can be flexibly configured according to the tracking requirement; in a hoisting system, v is defined as 3 x 1 dimension, BV＝eye(3)。
By defining the following performance indicators
Obtaining the optimal feedback rate of linear quadratic form
k＝lqry(Av,Bv,Cv,Dv,Qv,Rv) (6)
Wherein, Cv＝eye(3)，Dv＝zeros(3,3)，QvAnd RvIs the coefficient to be adjusted.
Designing a virtual controller to be
v＝-kz+kRef (7)
Wherein Ref ═ x1(t)，ref2，ref3]TAnd is provided with
Is composed of
Is estimated from the derivative of (a) the time,
is composed of
Can be obtained by a derivative estimation method.
And finally substituting the virtual controller shown in the formula (7) into the system observer shown in the formula (5) to obtain an optimal feedback full-state observer and obtain the estimation model
The obtained estimation model can be substituted into a bridge crane hoisting system through an actual controller to offset the original model, so that the total A is obtainedcAnd BcAn approximately linear model of composition.
The obtained estimation model can estimate the following motion state of the bridge crane hoisting system, thereby realizing the prejudgment of the motion of the hoisting machine.
As an embodiment generated by an actual controller, the specific method is as follows:
according to the configuration of the system expansion matrix of formula (2), the kinetic model to be observed is equivalent to formula (3), and can be expressed in the following form
Wherein x (t) ═ x1(t),x2(t)]T，g(t)＝x1(t)+x2(t) + f (t) is the model to be observed;
if the model g (t) to be observed can be estimated
Offset, the winch control system can be completely controlled by AcAnd BcAn approximately linear model of the composition.
Based on AcAnd BcDefining a performance index JcObtaining the optimal feedback rate k of linear quadratic formc
kc＝lqr(Ac,Bc,Qc,Rc) (12)
Wherein Q iscAnd RcFor the coefficient to be adjusted, kc＝[kc1,kc2,kc3]。
Obtaining an actual controller u (t) by combining the estimation model offset and the linear quadratic optimal feedback rate
Wherein, yd(t)' is the desired derivative of the displacement, obtained by a derivative estimation method, yd(t) as the hoisting displacement expectation,
wherein T belongs to [0, T ], and T is the target running time length.
The actual controller shown in equation (13) will estimate the model
Taking back to equation (9), the matrix shown in equation (10) is obtained, thereby proving that the closed-loop optimal control design formed based on equation (10) is feasible.
In the embodiment generated by the actual controller, the control design is combined with the linear quadratic regulator to form the LQR control method based on the optimal feedback full-state observer, so that the traditional LQR controller gets rid of the dependence on a model, and the efficient position tracking control of the bridge crane hoisting is realized.
For the acquisition of the derivative estimation, a traditional derivation method can be adopted, but in the traditional derivation method, the situation that the derivative error is large exists, the derivative obtained by the traditional derivation method in the virtual controller can influence the result of the estimation model, and in order to reduce the error of the derivative, a new derivative estimation method is provided, which is used in the following steps
Specific embodiments of derivative estimation are described.
In the derivative estimation acquisition, a derivative estimation variable is defined and passes through a derivative estimator
A derivative estimation method is implemented.
Where r is the derivative estimate variable, r ═ r1,r2,r3]T，
vrIs a virtual controller of the estimator for designing the parameters required for the derivative estimation,
vr＝-krr+krErx1(t) (16)
wherein the content of the first and second substances,
kris to define a performance index JrObtaining quadratic optimum feedback rate
kr＝lqr(Ar,Br,Qr,Rr) (18)
Wherein Q isrAnd RrFor the coefficient to be adjusted, kr＝[kr1,kr2,kr3]。
Substituting the formula (16) into the formula (15) to obtain
Further written as
As can be seen from equations (19) and (20), the feedback matrix k is configured by equation (18)rThe pole of the closed-loop system can reach an expected state, and the stability and the optimality of the system performance index of the optimal feedback full-state observer are considered. Thus, based on virtual controllers vrCan ensure that x is obtained1(t) -r is 0, thus obtaining
Is estimated as
And can ensure that the tracking error is zero, thereby ensuring the accuracy of ref.
For proving the stability of the optimal feedback full-state observer, based on an extension matrix (2), an extension model of a bridge crane hoisting system is
The virtual controller (7) is substituted into a system observer (5) of the hoisting system, and the virtual controller comprises the following components:
(21) - (22) and define e ═ x (t) -z ═ 0, since it is defined in formula (7)
Then on the premise that the derivative estimation is accurate,
in combination with the formula (21),
therefore, ref2-z2＝x2(t)-z2＝e2，ref3-z3＝x3(t)-z3＝e3Thus, the formula (22) becomes
Further expressed as:
it follows that the root of the error system characteristic can be determined by the state matrix of the system observer and the feedback control rate k. Thus, under the assumption that the model derivative h (t) is bounded and the derivative estimation error is zero, error system stability can be guaranteed. Thereby having
e→0 (25)
As can be seen from the combination of the formula (3),
as an implementation mode of the bridge crane hoisting control method, the actual controller obtained in the bridge crane hoisting controller generation method is utilized to track the position of the bridge crane hoisting, so as to track the information such as the length of the rope pendulum and the like, and the following motion state of the bridge crane hoisting is pre-judged according to the motion state information obtained by tracking, and the adjustment and control are carried out in time, so that the conveying efficiency of the bridge crane is improved.
As an embodiment of the overhead hoist controller generation system, includes,
the module is obtained to the control model of waiting to observe, according to bridge crane hoist control system structure, carries out the dynamics analysis to bridge crane hoist control system, establishes the control model of waiting to observe under the hoist system dynamics structure:
wherein y (t) represents the length of a rope pendulum controlled by the winch, f (t) represents a model to be observed, which comprises an existing model, unmodeled dynamic and uncertain disturbance information, in the winch system, u (t) represents the control input of the winch system, and b is a known control coefficient;
the estimation model acquisition module is used for acquiring an estimation model of the optimal feedback full-state observer based on the measurement variable y (t); and the number of the first and second groups,
and the actual controller generation module is used for carrying out model conversion based on the control model to be observed and obtaining the actual controller by combining the estimation model and the model conversion.
By utilizing the controller generation method, the control model acquisition module to be observed, the estimation model acquisition module and the actual controller generation module are obtained, so that a controller system is generated, the tracking control of the bridge crane hoisting is facilitated, and the conveying efficiency of the bridge crane is facilitated to be improved.
Referring to fig. 3, the control effect of the overhead traveling crane hoist control using the actual controller is shown in fig. 3, and the target curve yd(t) is a solid black line, and the actual response curve y (t) is x1(t) is a black dotted line. As can be seen from the rope pendulum length response curve y (t), the system output can accurately and quickly track the target.
Claims (5)
1. A bridge crane hoisting controller generation method is characterized by comprising the following steps:
the method comprises the following steps of obtaining (101) a control model to be observed, carrying out dynamics analysis on a bridge crane hoisting control system according to a bridge crane hoisting control system structure, and establishing the control model to be observed under the hoisting system dynamics structure:
wherein y (t) represents the length of a rope pendulum controlled by the winch, f (t) represents a model to be observed, which comprises an existing model, unmodeled dynamic and uncertain disturbance information, in the winch system, u (t) represents the control input of the winch system, and b is a known control coefficient;
obtaining (102) an estimation model of the optimal feedback full-state observer based on the measurement variable y (t); and the number of the first and second groups,
generating (103) an actual controller, performing model conversion based on the control model to be observed, and combining the estimation model and the model conversion to obtain the actual controller;
the specific method for obtaining the estimation model (102) comprises the following steps:
carrying out system expansion on the control model to be observed to obtain a system expansion matrix; defining a system observer based on the system expansion matrix;
defining a full-state virtual controller according to the system observer based on a defined performance index JvObtaining a quadratic optimal feedback rate k, and obtaining an optimal feedback full-state observer by combining the quadratic optimal feedback rate k and the virtual controller; and the number of the first and second groups,
based on the optimal feedback full-state observer, obtaining an estimation model which contains f (t) and is suitable for control design
The estimation model
The specific method for obtaining comprises the following steps:
defining an extended state x (t) ═ x for the control model to be observed1(t),x2(t),x3(t)]TAnd obtaining a system expansion matrix:
y(t)＝Cx(t) (2)
where u (t) represents the control input to the hoist system, h (t) is the derivative of f (t),
n is the order of the dynamic system; n ═ 0(n-1)×1；1]；
The extended state space description is characterized in that AcAnd BcThe form is not unique, and the matrix configuration can be carried out according to the order of the system and the structure required by control design, thereby obtainingObtaining a model form between states which is in accordance with the actual control design; for bridge crane hoist control systems, AcAnd BcConfigured as controllable standard types, i.e.
According to AcAnd BcThe spreading matrix constructed for the hoisting system can be expressed as follows:
definition of g (t) ═ f (t) + x1(t)+x2(t), based on equation (2), then h (t) is the derivative of g (t);
therefore, equation (2) is equivalent to
At this time, x (t) ═ x1(t),x2(t)]T(ii) a Based on the definition of C in formula (2), there is y (t) ═ x1(t) the subsequent part is all put the rope for the length x1(t) directly as a measured variable;
defining the extended state vector as:
z＝[z1,z2,z3]T (4)
wherein z is1Representing a measured variable x1(t) estimate of (z)2Representing a measured variable x1(t) using the estimated value of the derivative, z3Represents an estimate of the system model g (t);
based on equation (4), the system observer of the hoisting system is defined as:
wherein A isvA, v is a virtual controller of the system observer, which is used for designing and configuring parameters of the system observer; the virtual controller fully utilizes all states of the system observer and feedback information of all states to drive the system observer to track the system state, so that estimation of the model g (t) is obtained
The dimension and the form of the virtual controller are flexibly configured according to the tracking requirement; in a hoisting system, v is defined as 3 x 1 dimension, BV＝eye(3)；
By defining the following performance indicators
Obtaining the optimal feedback rate of linear quadratic form
k＝lqry(Av,Bv,Cv,Dv,Qv,Rv) (6)
Wherein, Cv＝eye(3)，Dv＝zeros(3,3)，QvAnd RvIs the coefficient to be adjusted;
designing a virtual controller to be
v＝-kz+kRef (7)
Wherein Ref ═ x1(t),ref2,ref3]TAnd is provided with
Is composed of
Is estimated from the derivative of (a) the time,
is composed of
Can be obtained by a derivative estimation method;
and finally substituting the virtual controller shown in the formula (7) into the system observer shown in the formula (5) to obtain an optimal feedback full-state observer and obtain the estimation model
2. The controller generation method according to claim 1, wherein the specific method of derivative estimation comprises:
defining a derivative estimation variable and providing a derivative estimator
Implementing a derivative estimation method;
where r is the derivative estimate variable, r ═ r1,r2,r3]T，
vrIs a virtual controller of the estimator for designing the parameters required for the derivative estimation,
vr＝-krr+krErx1(t) (16)
wherein the content of the first and second substances,
kris to define a performance index JrObtaining quadratic optimum feedback rate
kr＝lqr(Ar,Br,Qr,Rr) (18)
Wherein Q isrAnd RrFor the coefficient to be adjusted, kr＝[kr1,kr2,kr3]。
3. The controller generation method according to claim 1, characterized in that the method of actual controller generation (103) comprises:
according to the configuration of the system expansion matrix of formula (2), the kinetic model to be observed is equivalent to formula (3), and can be expressed in the following form
Wherein x (t) ═ x1(t),x2(t)]T，g(t)＝x1(t)+x2(t) + f (t) is the model to be observed;
based on AcAnd BcDefining a performance index JcObtaining the optimal feedback rate k of linear quadratic formc
kc＝lqr(Ac,Bc,Qc,Rc) (12)
Wherein Q iscAnd RcFor the coefficient to be adjusted, kc＝[kc1,kc2,kc3]；
Obtaining an actual controller u (t) by combining the estimation model offset and the linear quadratic optimal feedback rate
Wherein, yd(t) desired hoisting Displacement, yd(t)' is the desired derivative of the displacement, obtained by a derivative estimation method.
4. A bridge crane winding control method, characterized in that the control method is implemented based on an actual controller generated by the controller generating method of one of claims 1 to 3.
5. A bridge crane hoist controller generation system, characterized in that the generation system comprises,
the module is obtained to the control model of waiting to observe, according to bridge crane hoist control system structure, carries out the dynamics analysis to bridge crane hoist control system, establishes the control model of waiting to observe under the hoist system dynamics structure:
wherein y (t) represents the length of a rope pendulum controlled by the winch, f (t) represents a model to be observed, which comprises an existing model, unmodeled dynamic and uncertain disturbance information, in the winch system, u (t) represents the control input of the winch system, and b is a known control coefficient;
the estimation model acquisition module is used for acquiring an estimation model of the optimal feedback full-state observer based on the measurement variable y (t); and the number of the first and second groups,
the actual controller generation module is used for carrying out model conversion on the basis of the control model to be observed and obtaining an actual controller by combining the estimation model and the model conversion;
the specific method for obtaining the estimation model comprises the following steps:
carrying out system expansion on the control model to be observed to obtain a system expansion matrix; defining a system observer based on the system expansion matrix;
defining a full-state virtual controller according to the system observer based on a defined performance index JvObtaining a quadratic optimal feedback rate k, and obtaining an optimal feedback full-state observer by combining the quadratic optimal feedback rate k and the virtual controller; and the number of the first and second groups,
based on the optimal feedback full-state observer, obtaining an estimation model which contains f (t) and is suitable for control design
The estimation model
The specific method for obtaining comprises the following steps:
defining an extended state x (t) ═ x for the control model to be observed1(t),x2(t),x3(t)]TAnd obtaining a system expansion matrix:
y(t)＝Cx(t) (2)
where u (t) represents the control input to the hoist system, h (t) is the derivative of f (t),
n is the order of the dynamic system; n ═ 0(n-1)×1；1]；
The extended state space description is characterized in that AcAnd BcThe form is not unique, and matrix configuration can be carried out according to the order of the system and the structure required by control design, so that a state model form meeting the requirement of actual control design is obtained; aiming at the hoisting control system of the bridge crane,Acand BcConfigured as controllable standard types, i.e.
According to AcAnd BcThe spreading matrix constructed for the hoisting system can be expressed as follows:
definition of g (t) ═ f (t) + x1(t)+x2(t), based on equation (2), then h (t) is the derivative of g (t);
therefore, equation (2) is equivalent to
At this time, x (t) ═ x1(t),x2(t)]T(ii) a Based on the definition of C in formula (2), there is y (t) ═ x1(t) the subsequent part is all put the rope for the length x1(t) directly as a measured variable;
defining the extended state vector as:
z＝[z1,z2,z3]T (4)
wherein z is1Representing a measured variable x1(t) estimate of (z)2Representing a measured variable x1(t) using the estimated value of the derivative, z3Represents an estimate of the system model g (t);
based on equation (4), the system observer of the hoisting system is defined as:
wherein A isvA, v is systematic observationA virtual controller of the device for designing and configuring system observer parameters; the virtual controller fully utilizes all states of the system observer and feedback information of all states to drive the system observer to track the system state, so that estimation of the model g (t) is obtained
The dimension and the form of the virtual controller are flexibly configured according to the tracking requirement; in a hoisting system, v is defined as 3 x 1 dimension, BV＝eye(3)；
By defining the following performance indicators
Obtaining the optimal feedback rate of linear quadratic form
k＝lqry(Av,Bv,Cv,Dv,Qv,Rv) (6)
Wherein, Cv＝eye(3)，Dv＝zeros(3,3)，QvAnd RvIs the coefficient to be adjusted;
designing a virtual controller to be
v＝-kz+kRef (7)
Wherein Ref ═ x1(t),ref2,ref3]TAnd is provided with
Is composed of
Is estimated from the derivative of (a) the time,
is composed of
Can be obtained by a derivative estimation method;
and finally substituting the virtual controller shown in the formula (7) into the system observer shown in the formula (5) to obtain an optimal feedback full-state observer and obtain the estimation model
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