CN116909137B - Closed-loop control method and device for lifting system with dynamic compensation of position error - Google Patents
Closed-loop control method and device for lifting system with dynamic compensation of position error Download PDFInfo
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Abstract
The invention provides a closed-loop control method and a closed-loop control device for a lifting system with dynamic compensation of position errors, wherein the method comprises the following steps: constructing a mathematical model of the lifting system; a controller for dynamically compensating the position error is designed by utilizing the mathematical model; and verifying the controller. Based on the traditional robustness control method, the invention integrates the self-adaptive control thought, designs the controller gain self-adaptive law to carry out on-line adjustment on the integral robust gain value of the controller, effectively solves the problems of randomness, conservation, limitation and potential high gain feedback of the gain adjustment in the traditional method, obtains better tracking performance, and improves the accuracy and stability of the lifting process.
Description
Technical Field
The invention relates to the technical field of control, in particular to a closed-loop control method and device for a lifting system with dynamic compensation of position errors.
Background
The lifting mechanism has wide application in engineering machinery and other fields, and the lifting time is as short as possible and the in-position angle meets certain precision. The electrohydraulic servo system has the advantages of high power density, quick dynamic response, small volume and convenient layout, and is widely applied to lifting motion mechanisms. However, an electromechanical hydraulic system composed of a lifting mechanism and an electrohydraulic servo system is a highly nonlinear system, and is mainly represented by a nonlinear relationship between linear motion of a hydraulic cylinder piston and rotational motion of a lifting frame, nonlinearity caused by switching of an opening direction of a servo valve, and the like. In addition, the lifting system has a plurality of model uncertainties, which can be divided into parameter uncertainties and uncertainty nonlinearities. With the increasing control performance requirements of the lifting system, the nonlinear characteristics and the uncertainty of the model become decisive factors for limiting the servo performance improvement of the lifting system, so that the advanced nonlinear control method is explored, and the tracking performance improvement of the servo system is still an urgent requirement in the field of practical engineering application.
Aiming at the nonlinear control problem of the lifting system, the self-adaptive control method is a very effective method for processing the uncertainty problem of parameters, and can obtain the steady-state performance of asymptotic tracking. However, uncertainty nonlinearity such as strong interference of external load is not attractive, and the system can be unstable in severe cases; because of the uncertainty of system modeling, the gain value of the error sign function in the integral robust term can only be as large as possible to obtain better performance. However, due to the existence of interference noise, the excessive gain value can lead to high gain feedback, thereby causing vibration of the system, and even instability of the lifting system can be caused in severe cases. Therefore, a gain value capable of reducing vibration and obtaining a certain control performance is often required to be determined through repeated tests, so that a test process is complex, the method is only suitable for a specific lifting working condition, and when the working condition/environment/system parameters change, the gain obtained through the previous test may not be suitable, so that the traditional control method has a great limitation.
Disclosure of Invention
The present invention has been made in view of the above problems, and it is an object of the present invention to provide a closed loop control method and apparatus for a lifting system that overcomes or at least partially solves the above problems.
In one aspect of the invention, a closed loop control method for a lifting system for dynamically compensating position errors is provided, and the method comprises the following steps:
constructing a mathematical model of the lifting system;
a controller for dynamically compensating the position error is designed by utilizing the mathematical model;
and verifying the controller.
Further, the constructing a mathematical model of the lifting system includes:
the moment balance equation of the lifting system is as follows:
wherein J is the equivalent moment of inertia of the load relative to the rotary trunnion; q is the load lifting angle;lifting angular acceleration for a load; f is the driving force of the hydraulic cylinder acting on the lifting mechanism; l (L) 3 The distance between the upper pivot of the hydraulic cylinder and the rotary trunnion; l (L) 4 Distance of load mass center relative to the rotary trunnion; alpha is the included angle between the load and the hydraulic cylinder; beta 0 The included angle of the mass center relative to the horizontal plane is the initial horizontal state of the load; m is the total mass of the lifting load;
according to the cosine law:
wherein L is the total length of the hydraulic cylinder; l (L) 1 The distance between the lower pivot of the hydraulic cylinder and the rotary trunnion; q 0 For L in initial horizontal state of load 1 And L is equal to 3 An included angle between the two;
according to the sine theorem, the following is obtained:
the thrust of the hydraulic cylinder is as follows:
according to Newton's second law, the lift system load dynamics equation is:
wherein A is 1 The piston action area of the rodless cavity of the hydraulic cylinder; a is that 2 The piston is provided with a rod cavity for the hydraulic cylinder; p (P) 1 Is the pressure of the rodless cavity; p (P) 2 Is the pressure of the rod cavity; b is the viscous friction coefficient; a is that f S f For coulomb friction moment, A f For the magnitude of coulomb friction, S f Is a continuous approximate coulomb friction shape function; d (t) is an unmodeled interference term of the lifting system; x is x p For displacement of piston of hydraulic cylinderLifting an angular velocity for a load;
state variable x= [ x ] 1 ,x 2 ,x 3 ,x 4 ] T ＝[q,q,P 1 ,P 2 ] T The state space equation of the lifting system is obtained as follows:
unmodeled interference
Wherein k is t Is the flow coefficient beta e For the elastic modulus of hydraulic oil, R 1 The pressure loss function of the rodless cavity of the hydraulic cylinder is achieved; r is R 2 As a pressure loss function of a rod cavity of the hydraulic cylinder, V 1 Is the volume of a rodless cavity of the hydraulic cylinder; v (V) 2 The volume of the rod cavity of the hydraulic cylinder is u is the control item and C of the controller t Is the leakage coefficient in the hydraulic cylinder;
unknown parameter vector θ= [ θ ] 1 ,θ 2 ,θ 3 ,θ 4 ,θ 5 ] T ＝[B,A f ,β e k t ,β e ,β e C t ] T ，Is an estimated value of the parameter θ; the size range of the unknown parameter theta of the preset lifting system is as follows:
θ∈Ω θ {θ:θ min ≤θ≤θ max }；
in θ max ＝[θ 1max ,…,θ 5max ] T Is a known upper bound for vector θ; θ min ＝[θ 1min ,…,θ 5min ] T Is a known lower bound for vector θ;
error for parameter estimation +.>The parameter estimation value is between the upper and lower boundaries of theta, and the following discontinuous mapping function is defined:
where i=1,..5, the following parameter adaptation law was used:
where Γ is a positive definite diagonal matrix, representing the adaptive gain and τ as an adaptive function.
Further, the controller for dynamically compensating the position error by using the mathematical model comprises:
setting z 1 ＝x 1 -x 1d X is the tracking error of the system 1d Is a pre-programmed position instruction according to the equationSelecting x 2 For virtual control, equation->Reaching a stable state; let x 2eq Is the expected value of virtual control, x 2eq And true state x 2 Error of z 2 ＝x 2 -x 2eq For z 1 And (3) deriving to obtain:
in the method, in the process of the invention,a speed command is represented by differentiation of a position command planned in advance;
virtual control law:
wherein k is 1 Is a first adjustable gain, and k 1 > 0, then
Error signal r:
wherein k is 2 Is a second adjustable gain, and k 2 ＞0；
The error signal r is expanded as:
wherein x is 3 For the first virtual control input, x 4 For a second virtual control input, load pressureAnd->
α 2 As virtual control function, the error is z 3 ＝P L -α 2 Virtual control function alpha 2 The method comprises the following steps:
α 2 ＝α 2a +α 2s
α 2s ＝α 2s1 +α 2s2
α 2s1 ＝-k r z 2 ；
wherein alpha is 2a Alpha is a feedforward compensation term based on a mathematical model 2s For a robust control law, α 2s1 Is a linear robust feedback term, alpha 2s2 K is a nonlinear robust term for suppressing disturbance terms r A first feedback gain that is positive;
and deriving r to obtain:
the controller is designed as follows:
u＝u a +u s
wherein k is 3 A second feedback gain of positive, u a For feedforward compensation term sum u based on mathematical model s Is a robust control term.
Further, the verifying the controller includes:
based on the Lyapunov stability proving process, the method obtainsOn-line parameter adaptive error symbology of (c):
in the method, in the process of the invention,as the estimated value of the robust gain beta, gamma is the positive adaptive error symbol law gain;
auxiliary function:
wherein z is 2 (0) Is z 2 Initial value sum of (t)Is->Is set to an initial value of (1);
when (when)When P (t) is equal to or greater than 0, the Lyapunov function is as follows:
in the method, in the process of the invention,is the estimation error of beta;
the controller is subjected to stability demonstration by utilizing Lyapunov stability theory, a global stable result of the lifting system is obtained, and the gain k is adjusted 1 、k 2 、k r And Γ, tracking error of the lifting systemAnd the zero is reached under the condition that the time is towards infinity.
In a second aspect of the present invention, there is provided a closed loop control device for a lifting system for dynamic compensation of position errors, the device comprising:
the construction module is used for constructing a mathematical model of the lifting system;
the design module is used for designing a controller for dynamically compensating the position error by utilizing the mathematical model;
and the verification module is used for verifying the controller.
Further, the moment balance equation of the building module for the lifting system is:
wherein J is the equivalent moment of inertia of the load relative to the rotary trunnion; q is the load lifting angle;lifting angular acceleration for a load; f is the driving force of the hydraulic cylinder acting on the lifting mechanism; l (L) 3 The distance between the upper pivot of the hydraulic cylinder and the rotary trunnion; l (L) 4 Distance of load mass center relative to the rotary trunnion; alpha is the included angle between the load and the hydraulic cylinder; beta 0 The included angle of the mass center relative to the horizontal plane is the initial horizontal state of the load; m is the total mass of the lifting load;
according to the cosine law:
wherein L is the total length of the hydraulic cylinder; l (L) 1 The distance between the lower pivot of the hydraulic cylinder and the rotary trunnion; q 0 For L in initial horizontal state of load 1 And L is equal to 3 An included angle between the two;
according to the sine theorem, the following is obtained:
the thrust of the hydraulic cylinder is as follows:
according to Newton's second law, the lift system load dynamics equation is:
wherein A is 1 The piston action area of the rodless cavity of the hydraulic cylinder; a is that 2 The piston is provided with a rod cavity for the hydraulic cylinder; p (P) 1 Is the pressure of the rodless cavity; p (P) 2 Is the pressure of the rod cavity; b is the viscous friction coefficient; a is that f S f For coulomb friction moment, A f For the magnitude of coulomb friction, S f Is a continuous approximate coulomb friction shape function; d (t) is an unmodeled interference term of the lifting system; x is x p For displacement of piston of hydraulic cylinderLifting an angular velocity for a load;
state variable x= [ x ] 1 ,x 2 ,x 3 ,x 4 ] T ＝[q,q,P 1 ,P 2 ] T The state space equation of the lifting system is obtained as follows:
unmodeled interference
Wherein k is t Is the flow coefficient beta e For the elastic modulus of hydraulic oil, R 1 The pressure loss function of the rodless cavity of the hydraulic cylinder is achieved; r is R 2 As a pressure loss function of a rod cavity of the hydraulic cylinder, V 1 Is the volume of a rodless cavity of the hydraulic cylinder; v (V) 2 The volume of the rod cavity of the hydraulic cylinder is u is the control item and C of the controller t Is the leakage coefficient in the hydraulic cylinder;
unknown parameter vector θ= [ θ ] 1 ,θ 2 ,θ 3 ,θ 4 ,θ 5 ] T ＝[B,A f ,β e k t ,β e ,β e C t ] T ，Is an estimated value of the parameter θ; the size range of the unknown parameter theta of the preset lifting system is as follows:
θ∈Ω θ {θ:θ min ≤θ≤θ max }；
in θ max ＝[θ 1max ,…,θ 5max ] T Is a known upper bound for vector θ; θ min ＝[θ 1min ,…,θ 5min ] T Is a known lower bound for vector θ;
error for parameter estimation +.>The parameter estimation value is between the upper and lower boundaries of theta, and the following discontinuous mapping function is defined:
where i=1,..5, the following parameter adaptation law was used:
where Γ is a positive definite diagonal matrix, representing the adaptive gain and τ as an adaptive function.
Further, the design module is used for setting z 1 ＝x 1 -x 1d X is the tracking error of the system 1d Is a pre-programmed position instruction according to the equationSelecting x 2 For virtual control, equation->Reaching a stable state; let x 2eq Is the expected value of virtual control, x 2eq And true state x 2 Error of z 2 ＝x 2 -x 2eq For z 1 And (3) deriving to obtain:
in the method, in the process of the invention,a speed command is represented by differentiation of a position command planned in advance;
virtual control law:
wherein k is 1 Is a first adjustable gain, and k 1 > 0, then
Error signal r:
wherein k is 2 Is a second adjustable gain, and k 2 ＞0；
The error signal r is expanded as:
wherein x is 3 For the first virtual control input, x 4 For a second virtual control input, load pressureAnd->
α 2 As virtual control function, the error is z 3 ＝P L -α 2 Virtual control function alpha 2 The method comprises the following steps:
α 2 ＝α 2a +α 2s
α 2s ＝α 2s1 +α 2s2
α 2s1 ＝-k r z 2 ；
wherein alpha is 2a Alpha is a feedforward compensation term based on a mathematical model 2s For a robust control law, α 2s1 Is a linear robust feedback term, alpha 2s2 K is a nonlinear robust term for suppressing disturbance terms r A first feedback gain that is positive;
and deriving r to obtain:
the controller is designed as follows:
u＝u a +u s
wherein k is 3 A second feedback gain of positive, u a For feedforward compensation term sum u based on mathematical model s Is a robust control term.
Further, the verification module is configured to obtain based on a lyapunov stability proving processOn-line parameter adaptive error symbology of (c):
in the method, in the process of the invention,as the estimated value of the robust gain beta, gamma is the positive adaptive error symbol law gain;
auxiliary function:
wherein z is 2 (0) Is z 2 Initial value sum of (t)Is->Is set to an initial value of (1);
when (when)When P (t) is equal to or greater than 0, the Lyapunov function is as follows:
in the method, in the process of the invention,is the estimation error of beta;
the controller is subjected to stability demonstration by utilizing Lyapunov stability theory, a global stable result of the lifting system is obtained, and the gain k is adjusted 1 、k 2 、k r And Γ, the tracking error of the lifting system tends to infinity in timeAnd under the condition of zero.
In another aspect of the invention, a computer readable storage medium is provided having stored thereon a computer program which, when executed by a processor, performs the steps of the lift system closed loop control method of dynamic compensation of position errors as described above.
In yet another aspect of the present invention, there is also provided an electronic device comprising a storage controller including a memory, a processor and a computer program stored on the memory and executable on the processor, the processor executing the computer program to perform the steps of the lifting system closed loop control method of dynamic compensation of position errors as described above.
According to the closed-loop control method and device for the lifting system with the dynamic compensation of the position error, provided by the embodiment of the invention, the problems of randomness, conservation, limitation and potential high-gain feedback of gain adjustment in the traditional method are solved, better tracking performance is obtained, and the accuracy and stability of the lifting process are improved.
The foregoing description is only an overview of the present invention, and is intended to be implemented in accordance with the teachings of the present invention in order that the same may be more clearly understood and to make the same and other objects, features and advantages of the present invention more readily apparent.
Drawings
Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to designate like parts throughout the figures. In the drawings:
FIG. 1 is a flow chart of a closed-loop control method of a lifting system for dynamic compensation of position errors according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a lifting system according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a closed-loop control strategy of a lifting system for dynamic compensation of position errors according to an embodiment of the present invention;
FIG. 4 is a graph of the desired lift angle command signal and the first and second differential results provided by an embodiment of the present invention;
FIG. 5 is a graph showing the tracking error of a lift system over time under the control strategy with an interference condition according to an embodiment of the present invention;
FIG. 6 is a graph comparing tracking errors of a lifting system under the control strategy, the conventional RISE control strategy and the conventional PID control strategy under the interference condition provided by the embodiment of the invention;
FIG. 7 is a graph showing the pressure of two cavities of a hydraulic cylinder with time under the control strategy under the interference condition provided by the embodiment of the invention;
FIG. 8 is a graph of piston displacement versus piston velocity of a hydraulic cylinder of a lifting system over time under control strategy under disturbance conditions provided by an embodiment of the present invention;
fig. 9 is a schematic structural diagram of a closed-loop control device of a lifting system for dynamically compensating position errors according to an embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless expressly stated otherwise, as understood by those skilled in the art. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It will be understood by those skilled in the art that all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs unless defined otherwise. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
FIG. 1 schematically illustrates a flow chart of a method of closed loop control of a lift system for dynamic compensation of position errors in accordance with one embodiment of the present invention. Referring to fig. 1, the closed-loop control method of a lifting system for dynamically compensating position errors according to an embodiment of the present invention specifically includes the following steps:
s11, constructing a mathematical model of the lifting system;
s12, designing a controller for dynamically compensating the position error by utilizing the mathematical model;
s13, verifying the controller.
In this embodiment, the principle of the lifting system is schematically shown in fig. 2.
Further, the constructing a mathematical model of the lifting system includes:
the moment balance equation of the lifting system is as follows:
wherein J is the equivalent moment of inertia of the load relative to the rotary trunnion; q is the load lifting angle;lifting angular acceleration for a load; f is the driving force of the hydraulic cylinder acting on the lifting mechanism; l (L) 3 The distance between the upper pivot of the hydraulic cylinder and the rotary trunnion; l (L) 4 Distance of load mass center relative to the rotary trunnion; alpha is the included angle between the load and the hydraulic cylinder; beta 0 The included angle of the mass center relative to the horizontal plane is the initial horizontal state of the load; m is the total mass of the lifting load;
according to the cosine law:
wherein L is the total length of the hydraulic cylinder; l (L) 1 The distance between the lower pivot of the hydraulic cylinder and the rotary trunnion; q 0 For L in initial horizontal state of load 1 And L is equal to 3 An included angle between the two;
according to the sine theorem, the following is obtained:
the thrust of the hydraulic cylinder is as follows:
according to Newton's second law, the lift system load dynamics equation is:
wherein A is 1 The piston action area of the rodless cavity of the hydraulic cylinder; a is that 2 The piston is provided with a rod cavity for the hydraulic cylinder; p (P) 1 Is the pressure of the rodless cavity; p (P) 2 Is the pressure of the rod cavity; b is the viscous friction coefficient; a is that f S f For coulomb friction moment, A f For the magnitude of coulomb friction, S f Is a continuous approximate coulomb friction shape function; d (t) is an unmodeled interference term of the lifting system; x is x p For displacement of piston of hydraulic cylinderLifting an angular velocity for a load;
state variable x= [ x ] 1 ,x 2 ,x 3 ,x 4 ] T ＝[q,q,P 1 ,P 2 ] T The state space equation of the lifting system is obtained as follows:
unmodeled interference/>
Wherein k is t Is the flow coefficient beta e For the elastic modulus of hydraulic oil, R 1 The pressure loss function of the rodless cavity of the hydraulic cylinder is achieved; r is R 2 As a pressure loss function of a rod cavity of the hydraulic cylinder, V 1 Is the volume of a rodless cavity of the hydraulic cylinder; v (V) 2 The volume of the rod cavity of the hydraulic cylinder is u is the control item and C of the controller t Is the leakage coefficient in the hydraulic cylinder;
unknown parameter vector θ= [ θ ] 1 ,θ 2 ,θ 3 ,θ 4 ,θ 5 ] T ＝[B,A f ,β e k t ,β e ,β e C t ] T ，Is an estimated value of the parameter θ; the size range of the unknown parameter theta of the preset lifting system is as follows:
θ∈Ω θ {θ:θ min ≤θ≤θ max }；
in θ max ＝[θ 1max ,…,θ 5max ] T Is a known upper bound for vector θ; θ min ＝[θ 1min ,…,θ 5min ] T Is a known lower bound for vector θ;
error for parameter estimation +.>The parameter estimation value is between the upper and lower boundaries of theta, and the following discontinuous mapping function is defined:
where i=1,..5, the following parameter adaptation law was used:
where Γ is a positive definite diagonal matrix, representing the adaptive gain and τ as an adaptive function.
Further, the controller for dynamically compensating the position error by using the mathematical model comprises:
setting z 1 ＝x 1 -x 1d X is the tracking error of the system 1d Is a pre-programmed position instruction according to the equationSelecting x 2 For virtual control, equation->Reaching a stable state; let x 2eq Is the expected value of virtual control, x 2eq And true state x 2 Error of z 2 ＝x 2 -x 2eq For z 1 And (3) deriving to obtain:
in the method, in the process of the invention,a speed command is represented by differentiation of a position command planned in advance;
virtual control law:
wherein k is 1 Is a first adjustable gain, and k 1 > 0, then
Error signal r:
wherein k is 2 Is a second adjustable gain, and k 2 ＞0；
The error signal r is expanded as:
wherein x is 3 For the first virtual control input, x 4 For a second virtual control input, load pressureAnd->
α 2 As virtual control function, the error is z 3 ＝P L -α 2 Virtual control function alpha 2 The method comprises the following steps:
α 2 ＝α 2a +α 2s
α 2s ＝α 2s1 +α 2s2
α 2s1 ＝-k r z 2 ；
wherein alpha is 2a Alpha is a feedforward compensation term based on a mathematical model 2s For a robust control law, α 2s1 Is a linear robust feedback term, alpha 2s2 K is a nonlinear robust term for suppressing disturbance terms r A first feedback gain that is positive;
and deriving r to obtain:
the controller is designed as follows:
u＝u a +u s
wherein k is 3 A second feedback gain of positive, u a For feedforward compensation term sum u based on mathematical model s Is a robust control term.
In the present embodiment of the present invention,for the first intermediate variable and +.>Is a second intermediate variable.
Further, the verifying the controller includes:
based on the Lyapunov stability proving process, the method obtainsOn-line parameter adaptive error symbology of (c):
in the method, in the process of the invention,as the estimated value of the robust gain beta, gamma is the positive adaptive error symbol law gain;
auxiliary function:
/>
wherein z is 2 (0) Is z 2 (t)Initial value and initial valueIs->Is set to an initial value of (1);
when (when)When P (t) is equal to or greater than 0, the Lyapunov function is as follows:
in the method, in the process of the invention,is the estimation error of beta;
the controller is subjected to stability demonstration by utilizing Lyapunov stability theory, a global stable result of the lifting system is obtained, and the gain k is adjusted 1 、k 2 、k r And Γ, the tracking error of the lifting system tends to zero under the condition that the time tends to infinity.
In this embodiment, a schematic diagram of a closed-loop control strategy of a lifting system for dynamic compensation of position errors, as shown in fig. 3, will expect x 1d The controller is input and outputs u to the lifting system, and the lifting system outputs a speed signal x 2 First virtual control input x 3 And a second virtual control input x 4 Giving the controller; the lifting system outputs a position signal x 1 Position signal x output by lifting system 1 And desired x 1d Subtracting to obtain tracking error z 1 The method comprises the steps of carrying out a first treatment on the surface of the Will track the error z 1 The tracking error z is fed back to the controller through the self-adaptive law of the parameter theta and the self-adaptive law of the gain beta respectively 1 Performance evaluation was performed.
In this embodiment, the lifting system is modeled in a simulation system, and the desired lifting angle command signal and the first and second differential results are shown in fig. 4.
In this embodiment, there is a graph of tracking error of the lifting system with time under the action of the disturbance condition control strategy, as shown in fig. 5; under the action of the controller, the position instruction tracking precision of the lifting system is higher, and the steady-state tracking error amplitude is about 9.023 multiplied by 10 -4 。
In this embodiment, under the interference condition, the control strategy, the conventional RISE control strategy and the tracking error comparison graph of the lifting system under the effect of the conventional PID control strategy are shown in fig. 6; compared with the traditional RISE controller and the traditional PID controller, the tracking error of the controller is much smaller, the tracking performance of the traditional PID controller in the acceleration section and the deceleration section of the position instruction is worst, and in the whole process, as with the RISE controller, steady tracking performance cannot be obtained within a limited time, while for the controller disclosed by the invention, due to the effect of on-line real-time error dynamic compensation, the estimated value of the gain beta can be correspondingly increased to enhance the robustness of the nonlinear robust term of the controller to interference, the transient tracking performance of the controller is superior to that of the traditional RISE controller, the tracking result of the whole lifting process is synthesized, and the controller disclosed by the invention can meet the lifting requirements of lifting mechanism, stability and high precision.
In this embodiment, under the interference condition, the pressure of two cavities of the hydraulic cylinder changes with time under the action of the control strategy, as shown in fig. 7.
In this embodiment, under the interference condition, the graph of the piston displacement and the piston speed of the hydraulic cylinder of the lifting system with time under the action of the control strategy is shown in fig. 8.
According to the closed-loop control method for the lifting system with the dynamic compensation of the position error, which is provided by the embodiment of the invention, the problems of randomness, conservation, limitation and potential high-gain feedback of gain adjustment exist in the traditional method, so that better tracking performance is obtained, and the accuracy and stability of the lifting process are improved.
For the purposes of simplicity of explanation, the methodologies are shown and described as a series of acts, it is to be understood and appreciated by one of ordinary skill in the art that the methodologies are not limited by the order of acts, as some acts may, in accordance with the methodologies, take place in other order or concurrently. Further, those skilled in the art will appreciate that the embodiments described in the specification are presently preferred embodiments, and that the acts are not necessarily required by the embodiments of the invention.
FIG. 9 schematically illustrates a schematic structural diagram of a closed-loop control device for a lift system with dynamic compensation of position errors in accordance with one embodiment of the present invention. Referring to fig. 9, a closed loop control device for a lifting system for dynamically compensating a position error according to an embodiment of the present invention specifically includes:
the construction module 901 is used for constructing a mathematical model of the lifting system;
a design module 902, configured to design a controller for dynamically compensating for a position error using the mathematical model;
and the verification module 903 is configured to verify the controller.
Further, the building module 901 is configured to set a moment balance equation of the lifting system as follows:
wherein J is the equivalent moment of inertia of the load relative to the rotary trunnion; q is the load lifting angle;lifting angular acceleration for a load; f is the driving force of the hydraulic cylinder acting on the lifting mechanism; l (L) 3 The distance between the upper pivot of the hydraulic cylinder and the rotary trunnion; l (L) 4 Distance of load mass center relative to the rotary trunnion; alpha is the included angle between the load and the hydraulic cylinder; beta 0 The included angle of the mass center relative to the horizontal plane is the initial horizontal state of the load; m is the total mass of the lifting load;
according to the cosine law:
wherein L is the total length of the hydraulic cylinder; l (L) 1 The distance between the lower pivot of the hydraulic cylinder and the rotary trunnion; q 0 For L in initial horizontal state of load 1 And L is equal to 3 An included angle between the two;
according to the sine theorem, the following is obtained:
the thrust of the hydraulic cylinder is as follows:
according to Newton's second law, the lift system load dynamics equation is:
wherein A is 1 The piston action area of the rodless cavity of the hydraulic cylinder; a is that 2 The piston is provided with a rod cavity for the hydraulic cylinder; p (P) 1 Is the pressure of the rodless cavity; p (P) 2 Is the pressure of the rod cavity; b is the viscous friction coefficient; a is that f S f For coulomb friction moment, A f For the magnitude of coulomb friction, S f Is a continuous approximate coulomb friction shape function; d (t) is an unmodeled interference term of the lifting system; x is x p For displacement of piston of hydraulic cylinderLifting an angular velocity for a load;
state variable x= [ x ] 1 ,x 2 ,x 3 ,x 4 ] T ＝[q,q,P 1 ,P 2 ] T The state space equation of the lifting system is obtained as follows:
/>
unmodeled interference
Wherein k is t Is the flow coefficient beta e For the elastic modulus of hydraulic oil, R 1 The pressure loss function of the rodless cavity of the hydraulic cylinder is achieved; r is R 2 As a pressure loss function of a rod cavity of the hydraulic cylinder, V 1 Is the volume of a rodless cavity of the hydraulic cylinder; v (V) 2 The volume of the rod cavity of the hydraulic cylinder is u is the control item and C of the controller t Is the leakage coefficient in the hydraulic cylinder;
unknown parameter vector θ= [ θ ] 1 ,θ 2 ,θ 3 ,θ 4 ,θ 5 ] T ＝[B,A f ,β e k t ,β e ,β e C t ] T ，Is an estimated value of the parameter θ; the size range of the unknown parameter theta of the preset lifting system is as follows:
θ∈Ω θ {θ:θ min ≤θ≤θ max }；
in θ max ＝[θ 1max ,…,θ 5max ] T Is a known upper bound for vector θ; θ min ＝[θ 1min ,…,θ 5min ] T Is a known lower bound for vector θ;
error for parameter estimation +.>The parameter estimation value is between the upper and lower boundaries of theta, and the following discontinuous mapping function is defined:
where i=1,..5, the following parameter adaptation law was used:
where Γ is a positive definite diagonal matrix, representing the adaptive gain and τ as an adaptive function.
Further, the design module 902 is configured to set z 1 ＝x 1 -x 1d X is the tracking error of the system 1d Is a pre-programmed position instruction according to the equationSelecting x 2 For virtual control, equation->Reaching a stable state; let x 2eq Is the expected value of virtual control, x 2eq And true state x 2 Error of z 2 ＝x 2 -x 2eq For z 1 And (3) deriving to obtain:
in the method, in the process of the invention,a speed command is represented by differentiation of a position command planned in advance;
virtual control law:
/>
wherein k is 1 Is a first adjustable gain, and k 1 > 0, then
Error signal r:
wherein k is 2 Is a second adjustable gain, and k 2 ＞0；
The error signal r is expanded as:
wherein x is 3 For virtual control input, load pressureAnd->
α 2 As virtual control function, the error is z 3 ＝P L -α 2 Virtual control function alpha 2 The method comprises the following steps:
α 2 ＝α 2a +α 2s
α 2s ＝α 2s1 +α 2s2
α 2s1 ＝-k r z 2 ；
wherein alpha is 2a Alpha is a feedforward compensation term based on a mathematical model 2s For a robust control law, α 2s1 Is a linear robust feedback term, alpha 2s2 K is a nonlinear robust term for suppressing disturbance terms r A first feedback gain that is positive;
and deriving r to obtain:
the controller is designed as follows:
u＝u a +u s
wherein k is 3 A second feedback gain of positive, u a For feedforward compensation term sum u based on mathematical model s Is a robust control term.
Further, the verification module 903 is configured to obtain, based on the lyapunov stability proving processOn-line parameter adaptive error symbology of (c):
in the method, in the process of the invention,as the estimated value of the robust gain beta, gamma is the positive adaptive error symbol law gain;
auxiliary function:
wherein z is 2 (0) Is z 2 Initial value sum of (t)Is->Is set to an initial value of (1);
when (when)When P (t) is equal to or greater than 0, the Lyapunov function is as follows:
in the method, in the process of the invention,is the estimation error of beta;
the controller is subjected to stability demonstration by utilizing Lyapunov stability theory, a global stable result of the lifting system is obtained, and the gain k is adjusted 1 、k 2 、k r And Γ, the tracking error of the lifting system tends to zero under the condition that the time tends to infinity.
According to the closed-loop control device for the lifting system with the position error dynamic compensation, provided by the embodiment of the invention, the problems of randomness, conservation, limitation and potential high-gain feedback of gain adjustment exist in the traditional method, so that better tracking performance is obtained, and the accuracy and stability of a lifting process are improved.
For the device embodiments, since they are substantially similar to the method embodiments, the description is relatively simple, and reference is made to the description of the method embodiments for relevant points.
In addition, the embodiment of the invention also provides a computer readable storage medium, wherein a computer program is stored on the computer readable storage medium, and the program is executed by a processor to realize the steps of the lifting system closed-loop control method for dynamically compensating the position error.
In this embodiment, the module/unit integrated with the closed loop control device of the lifting system for dynamically compensating the position error may be stored in a computer readable storage medium if implemented as a software functional unit and sold or used as a separate product. Based on such understanding, the present invention may implement all or part of the flow of the method of the above embodiment, or may be implemented by a computer program to instruct related hardware, where the computer program may be stored in a computer readable storage medium, and when the computer program is executed by a processor, the computer program may implement the steps of each of the method embodiments described above. Wherein the computer program comprises computer program code which may be in source code form, object code form, executable file or some intermediate form etc. The computer readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer Memory, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), an electrical carrier signal, a telecommunications signal, a software distribution medium, and so forth. It should be noted that the computer readable medium contains content that can be appropriately scaled according to the requirements of jurisdictions in which such content is subject to legislation and patent practice, such as in certain jurisdictions in which such content is subject to legislation and patent practice, the computer readable medium does not include electrical carrier signals and telecommunication signals.
In addition, the embodiment of the invention also provides an electronic device, which comprises a storage controller, wherein the storage controller comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, and the processor realizes the steps of the lifting system closed-loop control method for dynamically compensating the position error when executing the program. For example, steps S11 to S13 shown in fig. 1. Alternatively, the processor, when executing the computer program, implements the functions of each module/unit in the embodiment of the closed loop control device of the lifting system for dynamically compensating the position error, such as the building module 901, the design module 902 and the verification module 903 shown in fig. 9.
According to the closed-loop control method and device for the lifting system with the dynamic compensation of the position error, provided by the embodiment of the invention, the problems of randomness, conservation, limitation and potential high-gain feedback of gain adjustment in the traditional method are solved, better tracking performance is obtained, and the accuracy and stability of the lifting process are improved.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
Furthermore, those skilled in the art will appreciate that while some embodiments herein include some features but not others included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention and form different embodiments. For example, any of the claimed embodiments can be used in any combination.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (4)
1. A closed loop control method for a lifting system for dynamic compensation of position errors, the method comprising:
constructing a mathematical model of the lifting system;
a controller for dynamically compensating the position error is designed by utilizing the mathematical model;
verifying the controller;
the construction of the mathematical model of the lifting system comprises the following steps:
the moment balance equation of the lifting system is as follows:
wherein J is the equivalent moment of inertia of the load relative to the rotary trunnion; q is the load lifting angle;lifting angular acceleration for a load; f is the driving force of the hydraulic cylinder acting on the lifting mechanism; l (L) 3 The distance between the upper pivot of the hydraulic cylinder and the rotary trunnion; l (L) 4 Distance of load mass center relative to the rotary trunnion; alpha is the included angle between the load and the hydraulic cylinder; beta 0 The included angle of the mass center relative to the horizontal plane is the initial horizontal state of the load; m is the total mass of the lifting load;
according to the cosine law:
wherein L is the total length of the hydraulic cylinder; l (L) 1 The distance between the lower pivot of the hydraulic cylinder and the rotary trunnion; q 0 For L in initial horizontal state of load 1 And L is equal to 3 An included angle between the two;
according to the sine theorem, the following is obtained:
the thrust of the hydraulic cylinder is as follows:
according to Newton's second law, the lift system load dynamics equation is:
wherein A is 1 The piston action area of the rodless cavity of the hydraulic cylinder; a is that 2 The piston is provided with a rod cavity for the hydraulic cylinder; p (P) 1 Is the pressure of the rodless cavity; p (P) 2 Is the pressure of the rod cavity; b is the viscous friction coefficient; a is that f S f For coulomb friction moment, A f For the magnitude of coulomb friction, S f Is a continuous approximate coulomb friction shape function; d (t) is an unmodeled interference term of the lifting system; x is x p For displacement of piston of hydraulic cylinderLifting an angular velocity for a load;
state variable x= [ x ] 1 ,x 2 ,x 3 ,x 4 ] T ＝[q,q,P 1 ,P 2 ] T The state space equation of the lifting system is obtained as follows:
unmodeled interference
Wherein k is t Is the flow coefficient beta e For the elastic modulus of hydraulic oil, R 1 The pressure loss function of the rodless cavity of the hydraulic cylinder is achieved; r is R 2 As a pressure loss function of a rod cavity of the hydraulic cylinder, V 1 Is the volume of a rodless cavity of the hydraulic cylinder; v (V) 2 The volume of the rod cavity of the hydraulic cylinder is u is the control item and C of the controller t Is the leakage coefficient in the hydraulic cylinder;
unknown parameter vector θ= [ θ ] 1 ,θ 2 ,θ 3 ,θ 4 ,θ 5 ] T ＝[B,A f ,β e k t ,β e ,β e C t ] T ，Is an estimated value of the parameter θ; the size range of the unknown parameter theta of the preset lifting system is as follows:
θ∈Ω θ {θ：θ min ≤θ≤θ max }；
in θ max ＝[θ 1max ,…,θ 5max ] T Is a known upper bound for vector θ; θ min ＝[θ 1min ,…,θ 5min ] T Is a known lower bound for vector θ;
error for parameter estimation +.>The parameter estimation value is between the upper and lower boundaries of theta, and the following discontinuous mapping function is defined:
where i=1,..5, the following parameter adaptation law was used:
wherein Γ is a positive definite diagonal matrix, representing that the adaptive gain sum τ is an adaptive function;
the controller for dynamically compensating the position error by utilizing the mathematical model comprises:
setting z 1 ＝x 1 -x 1d X is the tracking error of the system 1d Is a pre-programmed position instruction according to the equationSelecting x 2 For virtual control, equation->Reaching a stable state; let x 2eq Is the expected value of virtual control, x 2eq And true state x 2 Error of z 2 ＝x 2 -x 2eq For z 1 And (3) deriving to obtain:
in the method, in the process of the invention,a speed command is represented by differentiation of a position command planned in advance;
virtual control law:
wherein k is 1 Is a first adjustable gain, and k 1 > 0, then
Error signal r:
wherein k is 2 Is a second adjustable gain, and k 2 ＞0；
The error signal r is expanded as:
wherein x is 3 For the first virtual control input, x 4 For a second virtual control input, load pressureAnd->
α 2 As virtual control function, the error is z 3 ＝P L -α 2 Virtual control function alpha 2 The method comprises the following steps:
α 2 ＝α 2a +α 2s
α 2s ＝α 2s1 +α 2s2
α 2s1 ＝-k r z 2 ；
wherein alpha is 2a Alpha is a feedforward compensation term based on a mathematical model 2s For a robust control law, α 2s1 Is a linear robust feedback term, alpha 2s2 K is a nonlinear robust term for suppressing disturbance terms r A first feedback gain that is positive;
and deriving r to obtain:
the controller is designed as follows:
u＝u a +u s
wherein k is 3 A second feedback gain of positive, u a For feedforward compensation term sum u based on mathematical model s Is a robust control term;
the verifying the controller includes:
based on the Lyapunov stability proving process, the method obtainsOn-line parameter adaptive error symbology of (c):
in the method, in the process of the invention,as the estimated value of the robust gain beta, gamma is the positive adaptive error symbol law gain;
auxiliary function:
wherein z is 2 (0) Is z 2 Initial value sum of (t)Is->Is set to an initial value of (1);
when (when)When P (t) is equal to or greater than 0, the Lyapunov function is as follows:
in the method, in the process of the invention,is the estimation error of beta;
stabilization with LyapunovThe stability of the controller is proved by the sexual theory, the global stable result of the lifting system is obtained, and the gain k is adjusted 1 、k 2 、k r And Γ, the tracking error of the lifting system tends to zero under the condition that the time tends to infinity.
2. A closed loop control device for a lifting system for dynamic compensation of position errors, the device comprising:
the construction module is used for constructing a mathematical model of the lifting system;
the design module is used for designing a controller for dynamically compensating the position error by utilizing the mathematical model;
the verification module is used for verifying the controller;
the construction module is used for a moment balance equation of the lifting system, and the moment balance equation is as follows:
wherein J is the equivalent moment of inertia of the load relative to the rotary trunnion; q is the load lifting angle;lifting angular acceleration for a load; f is the driving force of the hydraulic cylinder acting on the lifting mechanism; l (L) 3 The distance between the upper pivot of the hydraulic cylinder and the rotary trunnion; l (L) 4 Distance of load mass center relative to the rotary trunnion; alpha is the included angle between the load and the hydraulic cylinder; gamma ray 0 The included angle of the mass center relative to the horizontal plane is the initial horizontal state of the load; m is the total mass of the lifting load;
according to the cosine law:
wherein L is the total length of the hydraulic cylinder; l (L) 1 The distance between the lower pivot of the hydraulic cylinder and the rotary trunnion; q0 is the included angle between L1 and L3 in the initial horizontal state of the load;
according to the sine theorem, the following is obtained:
the thrust of the hydraulic cylinder is as follows:
according to Newton's second law, the lift system load dynamics equation is:
wherein A is 1 The piston action area of the rodless cavity of the hydraulic cylinder; a is that 2 The piston is provided with a rod cavity for the hydraulic cylinder; p (P) 1 Is the pressure of the rodless cavity; p (P) 2 Is the pressure of the rod cavity; b is the viscous friction coefficient; a is that f S f For coulomb friction moment, A f For the magnitude of coulomb friction, S f Is a continuous approximate coulomb friction shape function; d (t) is an unmodeled interference term of the lifting system; x is x p For displacement of piston of hydraulic cylinderLifting an angular velocity for a load;
state variable x= [ x ] 1 ,x 2 ,x 3 ,x 4 ] T ＝[q,q,P 1 ,P 2 ] T The state space equation of the lifting system is obtained as follows:
unmodeled interference
Wherein k is t Is the flow coefficient beta e For the elastic modulus of hydraulic oil, R 1 The pressure loss function of the rodless cavity of the hydraulic cylinder is achieved; r is R 2 As a pressure loss function of a rod cavity of the hydraulic cylinder, V 1 Is the volume of a rodless cavity of the hydraulic cylinder; v (V) 2 The volume of the rod cavity of the hydraulic cylinder is u is the control item and C of the controller t Is the leakage coefficient in the hydraulic cylinder;
unknown parameter vector θ= [ θ ] 1 ,θ 2 ,θ 3 ,θ 4 ,θ 5 ] T ＝[B,A f ,β e k t ,β e ,β e C t ] T ，Is an estimated value of the parameter θ; the size range of the unknown parameter theta of the preset lifting system is as follows:
θ∈Ω θ {θ：θ min ≤θ≤θ max }；
in θ max ＝[θ 1max ,…,θ 5max ] T Is a known upper bound for vector θ; θ min ＝[θ 1min ,…,θ 5min ] T Is a known lower bound for vector θ;
error for parameter estimation +.>The parameter estimation value is between the upper and lower boundaries of theta, and the following discontinuous mapping function is defined:
where i=1,..5, the following parameter adaptation law was used:
wherein Γ is a positive definite diagonal matrix, representing that the adaptive gain sum τ is an adaptive function;
the design module is used for setting z 1 ＝x 1 -x 1d X is the tracking error of the system 1d Is a pre-programmed position instruction according to the equationSelecting x 2 For virtual control, equation->Reach toA steady state; let x 2eq Is the expected value of virtual control, x 2eq And true state x 2 Error of z 2 ＝x 2 -x 2eq For z 1 And (3) deriving to obtain:
in the method, in the process of the invention,a speed command is represented by differentiation of a position command planned in advance;
virtual control law:
wherein k is 1 Is a first adjustable gain, and k 1 > 0, then
Error signal r:
wherein k is 2 Is a second adjustable gain, and k 2 ＞0；
The error signal r is expanded as:
wherein x is 3 For the first virtual control input, x 4 For a second virtual control input, load pressureAnd->
α 2 As virtual control function, the error is z 3 ＝P L -α 2 Virtual control function alpha 2 The method comprises the following steps:
α 2 ＝α 2a +α 2s
α 2s ＝α 2s1 +α 2s2
α 2s1 ＝-k r z 2 ；
wherein alpha is 2a Alpha is a feedforward compensation term based on a mathematical model 2s For a robust control law, α 2s1 Is a linear robust feedback term, alpha 2s2 K is a nonlinear robust term for suppressing disturbance terms r A first feedback gain that is positive;
and deriving r to obtain:
the controller is designed as follows:
u＝u a +u s
wherein k is 3 A second feedback gain of positive, u a For feedforward compensation term sum u based on mathematical model s Is a robust control term;
the verification module is used for obtaining based on the Lyapunov stability proving processOn-line parameter adaptive error symbology of (c):
in the method, in the process of the invention,as the estimated value of the robust gain beta, gamma is the positive adaptive error symbol law gain;
auxiliary function:
wherein z is 2 (0) Is z 2 Initial value sum of (t)Is->Is set to an initial value of (1);
when (when)When P (t) is equal to or greater than 0, the Lyapunov function is as follows:
in the method, in the process of the invention,is the estimation error of beta;
the controller is subjected to stability demonstration by utilizing Lyapunov stability theory, a global stable result of the lifting system is obtained, and the gain k is adjusted 1 、k 2 、k r And Γ, the tracking error of the lifting system tends to zero under the condition that the time tends to infinity.
3. A computer readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to claim 1.
4. An electronic device comprising a memory controller, the memory controller comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the method of claim 1 when the computer program is executed.
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| 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 |
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| 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 |
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