CN111062147A - Fixed time control and structure combined optimization method and system for four-motor linkage system - Google Patents
Fixed time control and structure combined optimization method and system for four-motor linkage system Download PDFInfo
- Publication number
- CN111062147A CN111062147A CN201911412866.2A CN201911412866A CN111062147A CN 111062147 A CN111062147 A CN 111062147A CN 201911412866 A CN201911412866 A CN 201911412866A CN 111062147 A CN111062147 A CN 111062147A
- Authority
- CN
- China
- Prior art keywords
- motor
- optimization
- load
- linkage system
- coefficient
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P5/00—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors
- H02P5/46—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors for speed regulation of two or more dynamo-electric motors in relation to one another
Abstract
The invention relates to a fixed time control and structure joint optimization method and a system of a four-motor linkage system, which are characterized in that the structural coefficient and the performance coefficient of the four-motor linkage system are obtained; according to the structural coefficient and the performance coefficient, an integrated performance index model is constructed by taking the rotational inertia of the motor as an optimization target and taking the difference between the upper bound of the rotational inertia of the motor, the lower bound of the rotational inertia of the motor, the transmission torque and the fixed time control and structure joint optimization input quantity of the four-motor linkage system as constraint conditions; determining the minimum value of the rotational inertia of the motor in the integrated performance index model by adopting a bacterial foraging optimization algorithm; and driving and controlling the motors in the four-motor linkage system by adopting the minimum value of the rotational inertia of the motors. The method and the system for fixed time control and structure joint optimization of the four-motor linkage system can efficiently and reliably obtain the global optimal parameters of the four-motor linkage system so as to realize accurate control of the four-motor linkage system.
Description
Technical Field
The invention relates to the technical field of electromechanical control, in particular to a fixed time control and structure combined optimization method and system for a four-motor linkage system.
Background
The multi-motor driving system is characterized in that the number of driving motors is increased on the basis of a single-motor driving structure, the driving motors are connected with a load through gear boxes, and a plurality of motors drive a common load together. The integrated design is used as a pre-design process of the system, and can provide basis and reference for selection of relevant elements of the system. Such as the selection of the motor model, the rigidity of the transmission device and the like. In a multi-motor system, the magnitude of the load directly reflects the driving capability of the system. The larger the load is, the larger the driving torque which needs to be provided by the driving motor is; conversely, the smaller the inertia of the drive motor is selected, the smaller the load that can be driven. Through parameter optimization design, the direct relation between the load size and the control input can be reflected, and a basis is provided for structure and control design of other aspects such as motor selection, system driving capability design and the like. The structure/control integrated design method can process the coupling between the structure design and the control design, and simultaneously design the structure parameters and the controller parameters, thereby improving the control performance of the system. Perez and the like apply the integrated design method to the flexible mechanism design of the spacecraft to obtain the global optimal solution of the control system. Shirazi et al use a linear matrix inequality iteration method to integrally design the wind turbine, improving the performance of the closed loop system. Chiang and the like combine robust control with an integrated design method, design a control system of a large-scale space mechanism, and improve the robustness of the system.
Because the integrated optimization problem is composed of structural optimization and controller optimization, the objective function of the integrated optimization problem is often non-convex. This creates difficulties in solving the integration problem. In order to reduce the difficulty in solving the integration problem and efficiently and reliably obtain the global optimal solution of the system, two optimization strategies, namely integral optimization and nested optimization, are often used. The Alyaqout and the like compare the advantages and disadvantages of a plurality of optimization strategies, indicate that the nested optimization strategy can better solve the optimization problem of the integrated design, simultaneously has small calculated amount and clear physical significance, and can efficiently obtain the optimal solution of the integrated design. A Bacterial Foraging algorithm (BFO) proposed by Passiono simulates chemotaxis, colony propagation, elimination and diffusion processes of escherichia coli and consists of 3 circulation processes of chemotaxis, propagation and migration. The bacterial foraging algorithm is applied to image compression by glume storage and the like, and the defect that the BP neural network is easy to fall into local optimum is overcome by combining the BP neural network and the bacterial foraging algorithm. Wang proposes a feature selection algorithm based on bacterial colony optimization, combines a bacterial foraging algorithm with a weighted feature selection strategy, classifies features according to two matrixes, and reduces feature dimensions in classification. And selecting performance indexes such as the minimum feature quantity, the minimum calculation cost and the like, testing the performance of the algorithm, and experiments show that the proposed BCO algorithm can effectively select the features. Aiming at the problems of travelers, Wang Yong Zhen and the like, a discrete bacterial foraging algorithm is provided, chemotactic operators capable of processing discrete variables are designed, and the bacterial foraging algorithm is developed from continuous optimization to the solution of the discrete optimization problem. The Subudhi aims at the parameter extraction problem of Photovoltaic (PV) modules, tests are carried out on PV modules of different types by adopting a bacterial foraging algorithm, the experimental result shows the global search capability of the bacterial foraging algorithm, and the obtained optimization result is more accurate than a particle swarm algorithm and an enhanced simulated annealing method. The bacterial foraging algorithm with the self-adaptive step length is provided by the quiescence and the like, and the solving efficiency of the algorithm is improved by introducing the self-adaptive step length and a differential evolution operator aiming at the problem that the traditional algorithm is easy to fall into the local optimum in the process of solving the high-dimensional optimization problem. Ramyachhtra aims at the problem of protein structure prediction, is based on a face-centered cubic lattice and a hydrophobic/polar (HP) energy model, and is combined with a bacterial foraging algorithm, so that the performance of the algorithm is improved. The research result proves that the algorithm can be successfully applied to protein structure prediction.
The fixed time stabilization is a special form of a finite time stabilization theory, and can obtain an upper bound of convergence time which is irrelevant to the initial state of the system, so that the convergence performance of the system can be analyzed in advance. On the other hand, the fixed time controller can calculate the upper bound of the convergence time of the system in advance, can preset the convergence time and provides a basis for the parameter adjustment of the controller. Zhang et al have designed the guidance law that can actually fix the time convergence to the guidance problem of the mars soft landing power descent phase. Chen et al designed an adaptive fixed time parameter estimation and synchronization controller. Defoort et al designed a fixed time controller for multi-agent systems with unknown nonlinear dynamics. Zuo et al achieve fixed time consistent tracking control of multi-agent systems. Aiming at the design problem of the nonsingular fixed time controller, Jiang and the like also design a sliding mode replacement method, so that the nonsingular fixed time controller is obtained and is applied to the design of the spacecraft attitude controller. The method is widely applied to the fields of multi-agent control, mechanical arm control, spacecraft attitude control and the like.
However, in the prior art, there is no method for efficiently and reliably obtaining the global optimal parameters of the four-motor linkage system, and therefore, the problem of low control accuracy of the four-motor linkage system in the prior art cannot be really solved.
Disclosure of Invention
The invention aims to provide a method and a system for fixed time control and structure joint optimization of a four-motor linkage system, which can efficiently and reliably obtain global optimal parameters of the four-motor linkage system so as to realize accurate control of the four-motor linkage system.
In order to achieve the purpose, the invention provides the following scheme:
a fixed time control and structure combined optimization method for a four-motor linkage system comprises the following steps:
acquiring a structural coefficient and a performance coefficient of a four-motor linkage system; the structural coefficients include: the motor rotational inertia, the transmission torque and the control input quantity of the four-motor linkage system; the coefficient of performance includes: performance index and structural design performance index of the controller;
according to the structural coefficient and the performance coefficient, constructing an integrated performance index model by taking the motor rotational inertia as an optimization target and taking the difference value between the upper bound of the motor rotational inertia, the lower bound of the motor rotational inertia, the transmission torque and the control input quantity of the four-motor linkage system as a constraint condition;
determining an optimal solution of the integrated performance index model by adopting a bacterial foraging optimization algorithm; the optimal solution is the minimum value of the rotational inertia of the motor;
and driving and controlling the motors in the four-motor linkage system by adopting the minimum value of the rotational inertia of the motors.
Optionally, the integrated performance index model is as follows:
wherein, wpDesigning a weight coefficient, w, of a performance index for a structurecTo control the weight coefficient of the performance index, s.t. is a constraint condition, fpDesign of the Performance index for the Structure, fp＝(umax-umin)2，umaxIs the maximum value of the control input of the controller, uminIs the minimum value of the control input of the controller, fcIn order to control the performance index,
x1is the position of the load, ydFor the desired position of the load, t is the convergence time of the four-motor linkage system, JmIs the moment of inertia of the motor, JlowIs the lower bound of the moment of inertia, JhighIs the upper bound of the moment of inertia,
is the angular acceleration of the motor i and,
is the angular velocity of the motor i and,
is the angular acceleration of the load and,
angular velocity of the load, JLIs the moment of inertia of the load, bmIs the viscous friction coefficient at the motor end, bLIs the viscous friction coefficient at the load side, u is the control input to the controller,
is the driving torque of the motor i.
Optionally, determining an optimal solution of the integrated performance index model by using a bacterial foraging optimization algorithm specifically includes:
respectively determining an outer optimization ring and an inner optimization ring according to the integrated performance index model by adopting a nested optimization algorithm;
respectively determining the optimal solution of the outer optimization ring and the optimal solution of the inner optimization ring by adopting a bacterial foraging optimization algorithm;
and obtaining the optimal solution of the integrated performance index model according to the optimal solution of the outer optimization ring and the optimal solution of the inner optimization ring.
Optionally, the outer optimization ring is:
the inner optimization ring is:
wherein the content of the first and second substances,
for outer optimization of the ring result, wpAnd wcAre all weight coefficients, s.t. is a constraint condition, uminIs the minimum value of the control input of the controller, umaxIs the maximum value of the control input of the controller, JlowIs the lower bound of the moment of inertia, JhighIs an upper bound of moment of inertia, JmIs the moment of inertia of the motor, JmIs the rotational inertia of the motor and is,
for internal optimization of the ring result, JmIs the moment of inertia of the motor, x1Is the position of the load, ydFor the desired position of the load, t is the convergence time of the four-motor linkage system, JLIs the moment of inertia of the load, bmIs the viscous friction coefficient at the motor end, bLIn order to be the viscous friction coefficient at the load end,
is the angular acceleration of the motor i and,
is the angular velocity of the motor i and,
is the angular acceleration of the load and,
is the angular velocity of the load, u is the control input to the controller,
is the transmission torque of the motor i,
k is the torsion coefficient, c is the damping coefficient, ΔiIs the difference in position, Δ, between motor i and the loadi＝θi-θL，θiIs the position of motor i, θLF (-) is a non-linear function caused by backlash, being the position of the load,
δ is the tooth gap width.
Optionally, before the structural coefficient and the controller coefficient of the four-motor linkage system are respectively obtained, the method further includes:
acquiring structural parameters of the four-motor linkage system; the structural parameters include: the method comprises the following steps of (1) enabling the rotational inertia of a motor, a tracking error, a synchronization error, a viscous friction coefficient at the motor end and the rotational inertia of a load to be in a synchronous mode;
according to the structural parameters, a structural model in the four-motor linkage system is constructed; the structural model includes: a drive motor synchronous controller and a load tracking controller;
constructing a controller model of the four-motor linkage system according to the structural model; the controller model is as follows:
wherein xisIn order to synchronize the control parameters with each other,
psi is normal number, sigma1For synchronization error, usiFor synchronous control of drive motors utIs a load tracking controller.
Optionally, the drive motor synchronous controller usiComprises the following steps:
load tracking controller utComprises the following steps:
wherein, JmIs the rotational inertia of the motor, ms1And ms2Are all proportionality coefficients, and ms1≥1，ms2≥1，σ2、φs2、φs1、s2And phi1Are all the intermediate variables of the series of the Chinese characters,
s1in order to track the error, the tracking error is,
is s is1The approach rate of (a) to (b),
σ1for synchronization error, ξs2Is an exponential coefficient, and
is the drive torque of motor i, bmAs a viscous friction coefficient at the motor end,
is the angular velocity of the motor i and,
is an estimate of the load speed, n is the transmission ratio coefficient,
as second derivative of the reference signal, m1For the parameters of the controller to be optimized,
m2for tracking controller index coefficients, m2≥1，ξ2In order for the tracking controller to be informed,
a four-motor linkage system fixed time control and structure combined optimization system comprises:
the coefficient acquisition module is used for acquiring the structural coefficient and the performance coefficient of the four-motor linkage system; the structural coefficients include: the motor rotational inertia, the transmission torque and the control input quantity of the four-motor linkage system; the coefficient of performance includes: performance index and structural design performance index of the controller;
the integrated performance index model building module is used for building an integrated performance index model by taking the rotational inertia of the motor as an optimization target and taking the difference between the upper limit of the rotational inertia of the motor, the lower limit of the rotational inertia of the motor, the transmission torque and the control input quantity of the four-motor linkage system as a constraint condition according to the structural coefficient and the performance coefficient;
the optimal solution determining module is used for determining the optimal solution of the integrated performance index model by adopting a bacterial foraging optimization algorithm; the optimal solution is the minimum value of the rotational inertia of the motor;
and the driving control module is used for driving and controlling the motors in the four-motor linkage system by adopting the minimum value of the rotational inertia of the motors.
Optionally, the optimal solution determining module specifically includes:
the internal and external optimization ring determination unit is used for respectively determining an external optimization ring and an internal optimization ring according to the integrated performance index model by adopting a nested optimization algorithm;
the internal and external optimization ring optimal solution determination unit is used for respectively determining the optimal solution of the external optimization ring and the optimal solution of the internal optimization ring by adopting a bacterial foraging optimization algorithm; the optimal solution of the inner optimization ring is the minimum value of the position error of the load; the optimal solution for the outer optimization loop is the minimum of the sum of the position error of the load and the control input error;
and the optimal solution determining unit is used for obtaining the optimal solution of the integrated performance index model according to the optimal solution of the outer optimization ring and the optimal solution of the inner optimization ring.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: according to the fixed time control and structure combined optimization method and system for the four-motor linkage system, the motor rotational inertia is taken as an optimization target according to the obtained structural coefficient and performance coefficient, an integrated performance index model is constructed by taking the upper bound of the motor rotational inertia, the lower bound of the motor rotational inertia and the difference value between the transmission torque, the transmission torque and the control input quantity of the four-motor linkage system as constraint conditions, the optimal solution of the integrated performance index model is determined by adopting a bacterial foraging optimization algorithm, the minimum value of the motor rotational inertia of the four-motor linkage system is obtained efficiently and reliably, and then the minimum value of the motor rotational inertia of the four-motor linkage system is adopted, so that the accurate control of the motor in the four-motor linkage system is realized.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a block diagram of a four motor linkage system upon which the present invention is based;
FIG. 2 is a flowchart of a four-motor linkage system control method according to an embodiment of the present invention;
FIG. 3 is a load tracking effect diagram of the motor linkage system in an embodiment of the present invention;
FIG. 4 is a diagram of a load tracking error of a motor linkage system in accordance with an exemplary embodiment;
FIG. 5 is a load following control input diagram for a motor linkage system in accordance with an exemplary embodiment;
fig. 6 is a schematic structural diagram of a four-motor linkage system control system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for fixed time control and structure joint optimization of a four-motor linkage system, which can efficiently and reliably obtain global optimal parameters of the four-motor linkage system so as to realize accurate control of the four-motor linkage system.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a block diagram of a four-motor linkage system based on the present invention, and as shown in fig. 1, the four-motor linkage system based on the present invention includes a tracking controller, a synchronous controller, and a state observer. In fig. 1, the tracking controller 1 indicates a tracking controller No. 1, the synchronization controller 1 indicates a synchronization controller No. 1, and so on. u. of1Denotes the control input of tracking controller No. 1, u2Indicating the control input of tracking controller No. 2, and so on. Theta1Indicates the output of No. 1 motor (motor 1), theta2And the output of the No. 2 motor (the motor 2) is shown, and the like.
In order to enable the system to achieve optimal control, the invention simultaneously considers structure optimization and controller optimization, thereby enabling the control system to achieve global optimization.
Based on the purpose, the invention provides a fixed time control and structure combined optimization method for a four-motor linkage system, as shown in fig. 2, the method comprises the following steps:
s100, obtaining the structural coefficient and the performance coefficient of the four-motor linkage system. The structural coefficients include: the motor moment of inertia, the driving moment and the control input quantity of the four-motor linkage system. The coefficient of performance includes: performance index of the controller and structural design performance index.
S101, according to the structural coefficient and the performance coefficient, an integrated performance index model is constructed by taking the motor rotational inertia as an optimization target and taking the difference between the upper bound of the motor rotational inertia, the lower bound of the motor rotational inertia, the transmission torque and the control input quantity of the four-motor linkage system as constraint conditions. The integrated performance index model is as follows:
wherein, wpDesigning a weight coefficient, w, of a performance index for a structurecTo control the weight coefficient of the performance index, s.t. is a constraint condition, fpDesign of the Performance index for the Structure, fp＝(umax-umin)2，umaxIs the maximum value of the control input of the controller, uminIs the minimum value of the control input of the controller, fcIn order to control the performance index,
x1is the position of the load, ydFor the desired position of the load, t is the convergence time of the four-motor linkage system, JmIs the moment of inertia of the motor, JlowIs the lower bound of the moment of inertia, JhighIs the upper bound of the moment of inertia,
is the angular acceleration of the motor i and,
is the angular velocity of the motor i and,
is the angular acceleration of the load and,
angular velocity of the load, JLIs the moment of inertia of the load, bmIs the viscous friction coefficient at the motor end, bLIs the viscous friction coefficient at the load side, u is the control input to the controller,
is the driving torque of the motor i.
S102, determining an optimal solution of the integrated performance index model by adopting a bacterial foraging optimization algorithm. The optimal solution is the minimum value of the rotational inertia of the motor, and specifically includes:
and respectively determining an outer optimization ring and an inner optimization ring according to the integrated performance index model by adopting a nested optimization algorithm.
And respectively determining the optimal solution of the outer optimization ring and the optimal solution of the inner optimization ring by adopting a bacterial foraging optimization algorithm.
And obtaining the optimal solution of the integrated performance index model according to the optimal solution of the outer optimization ring and the optimal solution of the inner optimization ring.
Wherein the outer optimization ring is:
the inner optimization ring is:
wherein the content of the first and second substances,
for outer optimization of the ring result, wpAnd wcAre all weight coefficients, s.t. is a constraint condition, uminIs the minimum value of the control input of the controller, umaxIs the maximum value of the control input of the controller, JlowIs the lower bound of the moment of inertia, JhighIs an upper bound of moment of inertia, JmIs the moment of inertia of the motor, JmIs the rotational inertia of the motor and is,
for internal optimization of the ring result, JmIs the moment of inertia of the motor, x1Is the position of the load, ydFor the desired position of the load, t is the convergence time of the four-motor linkage system, JLIs the moment of inertia of the load, bmIs the viscous friction coefficient at the motor end, bLIn order to be the viscous friction coefficient at the load end,
is the angular acceleration of the motor i and,
is the angular velocity of the motor i and,
is the angular acceleration of the load and,
is the angular velocity of the load, u is the control input to the controller,
is the transmission torque of the motor i,
k is the torsion coefficient, c is the damping coefficient, ΔiIs the difference in position, Δ, between motor i and the loadi＝θi-θL，θiIs the position of motor i, θLF (-) is a non-linear function caused by backlash, being the position of the load,
δ is the tooth gap width.
The optimization of the inner optimization ring and the outer optimization ring is respectively carried out by adopting a bacterial foraging optimization algorithm, so that an optimal solution of an integrated design, namely the optimal motor rotational inertia and controller observer parameters, is obtained. In the process, the ith bacterium v in the bacterial foraging optimization algorithmiThe position after j tropism manipulations, γ replications and l migrations is expressed as:
νi(j+1,γ,l)＝νi(j,γ,l)+C(i)Λi
wherein
For the adaptive step size adjustment factor, κ is a congestion factor between (0,1),
for the step size adjustment factor, δ (i) is [ -1,1 [ ]]Random direction vector between c is crowdedness, B is search interval length, ΛiIs a unit length direction vector.
And S103, driving and controlling the motors in the four-motor linkage system by adopting the minimum value of the rotational inertia of the motors.
In order to accurately describe the four-motor linkage system based on the present invention, before S100 disclosed by the present invention, the method further includes:
1) and establishing a multi-motor driving system model and a simplified model thereof.
The established four-motor linkage system model is as follows:
wherein theta isiIs the position of motor i, i is 1,2,3,4, θLAs the loaded position, JmIs the moment of inertia of the motor, JLIs the moment of inertia of the load, bmIs a viscous friction coefficient ofLIs the viscous friction coefficient at the load side, u is the control input to the system,
in order to transmit the torque,
k is the torsion coefficient, c is the damping coefficient, Δi＝θi-θL. f (-) is the backlash induced nonlinearity,
δ is the tooth gap width.
Because the moments at the two ends of the gear box are in a linear relation, the established four-motor linkage system model can be simplified into a simplified model of a motor driving system:
wherein n is a transmission ratio coefficient.
2) Fixed time state observer design
A fixed time state observer is designed to estimate the speed information of the load subsystem. Selecting the state variables of the load subsystem:
the following model can be obtained:
then further obtaining a fixed time state observer of the motor drive system as:
wherein z is1Is the intermediate variable(s) of the variable,
for the estimation error of the position of the load,
is an estimate of the angular velocity of the load,
is x1Derivative of the estimated value, x1Position of load, μ1And mu2Are parameters of a fixed time state observer, p and q are exponential coefficients, p is more than 0 and less than 1, q is more than 1, mu1> 0 and mu2＞0，p、q、μ1And mu2Are all constants.
3) Fixed time controller design
Considering a multi-motor driving structure, a tracking controller and a driving motor synchronous controller are respectively designed in the step.
Defining a tracking error:
s1＝x1-yd。
and designing an approach law:
wherein the content of the first and second substances,
the load tracking controller is designed as follows:
wherein the content of the first and second substances,
m2≥1，
according to the tracking controller of the present invention, the system convergence time t can be calculated by the following formula:
wherein xi ═ max { ξ1,ξ2And ξ min (ξ)1,ξ2}。
Defining a synchronization error:
designing a synchronous controller of a driving motor:
wherein, JmIs the rotational inertia of the motor, ms1And ms2Are all proportionality coefficients, and ms1≥1，ms2≥1，σ2、φs2、φs1、s2And phi1Are all the intermediate variables of the series of the Chinese characters,
s1in order to track the error, the tracking error is,
is s is1The approach rate of (a) to (b),
σ1for synchronization error, ξs2Is an exponential coefficient, and
is the drive torque of motor i, bmAs a viscous friction coefficient at the motor end,
is the angular velocity of the motor i and,
is an estimate of the load speed, n is the transmission ratio coefficient,
as second derivative of the reference signal, m1For the parameters of the controller to be optimized,
m2for tracking controller index coefficients, m2≥1，ξ2In order for the tracking controller to be informed,
in summary, the overall controller of the multi-motor drive system is:
wherein the content of the first and second substances,
for the synchronization control parameter psi is a normal number.
The fixed time control and structure combined optimization method based on the four-motor linkage system specifically has the following advantages:
1) aiming at the control problem of a multi-motor driving system, a fixed time tracking and synchronous controller is designed. The controller of the invention can make the tracking and synchronization error convergence time irrelevant to the initial state, and can be obtained by calculation in advance according to the controller parameters, thereby improving the dynamic performance of the motor driving system.
2) Aiming at the problem that the system state is not measurable, a fixed time state observer is designed. The designed observer can finish convergence in fixed time, so that the observation performance is guaranteed, and the load speed information is estimated and used in the controller.
3) A structure/control integrated design method of a multi-motor driving system is provided by considering the coupling existing between the structure design and the controller design in the system. Meanwhile, the optimization of the rotational inertia of the motor and the parameters of the controller is considered, and the integrated performance index is designed. By solving the proposed performance index, the optimal motor moment of inertia can be obtained on the premise of meeting the control performance requirement.
4) The integrated performance index is solved by combining a bacterial foraging optimization algorithm and a nested optimization strategy, so that the solving difficulty of the optimization problem is reduced, and the integration problem has more definite physical significance: the outer optimization ring optimizes the structural parameters, and the inner optimization ring optimizes the controller parameters.
As another embodiment of the invention, the method for jointly optimizing the fixed time control and the structure of the four-motor linkage system is adopted to carry out structure and control integrated optimization on the radar servo system.
The known radar servo system consists of a driving motor, a transmission gear box, a load, a sensor and the like. The industrial personal computer is Pentium 2.8GHz, adopts PCI bus to carry out data transmission between the host computer and the encoder, and carries out signal amplification by a pulse width modulation method ware to realize the control to the motor. The system sampling time was 0.001 seconds. A tracking controller of the motor driving system is designed by using a fixed time convergence theory, so that the convergence of a tracking error is not influenced by the initial state of the system. A structure/control integrated design method based on a nested optimization scheme is adopted, the structural design and the controller design of the system are optimized simultaneously, and the global optimal design of the motor driving system is obtained by combining an intelligent optimization algorithm.
Parameters shown in the table 1 are selected, and a simulation experiment is carried out by adopting the fixed time control and structure joint optimization method of the four-motor linkage system provided by the invention.
TABLE 1 System simulation parameters
Wherein, the load tracking effect of the motor driving system obtained in the simulation experiment is shown in figure 3, and the load tracking error curve of the motor driving system is shown in figure 4 (y in figure 4 represents the actual position error of the load, y represents the actual position error of the loaddRepresenting the load position error in the control method), the motor drive system load tracking error curve is shown in fig. 5. From FIGS. 3-5Therefore, the method provided by the invention can quickly converge under the condition of larger initial error and obtain better dynamic performance.
In addition, aiming at the control method, the invention also correspondingly provides a system for controlling fixed time and optimizing structure of the four-motor linkage system, as shown in fig. 6, the system comprises: the system comprises a coefficient acquisition module 1, an integrated performance index model construction module 2, an optimal solution determination module 3 and a drive control module 4.
The coefficient acquisition module 1 is used for acquiring the structural coefficient and the performance coefficient of the four-motor linkage system. The structural coefficients include: the motor moment of inertia, the driving moment and the control input quantity of the four-motor linkage system. The coefficient of performance includes: performance index of the controller and structural design performance index.
And the integrated performance index model building module 2 is used for building an integrated performance index model by taking the rotational inertia of the motor as an optimization target and taking the difference between the upper bound of the rotational inertia of the motor, the lower bound of the rotational inertia of the motor, the transmission torque and the control input quantity of the four-motor linkage system as constraint conditions according to the structural coefficient and the performance coefficient.
And the optimal solution determination module 3 is used for determining the optimal solution of the integrated performance index model by adopting a bacterial foraging optimization algorithm. The optimal solution is the minimum value of the rotational inertia of the motor.
And the driving control module 4 is used for driving and controlling the motors in the four-motor linkage system by adopting the minimum value of the rotational inertia of the motors.
The optimal solution determining module 3 specifically includes: the device comprises an internal and external optimization ring determining unit, an internal and external optimization ring optimal solution determining unit and an optimal solution determining unit.
The internal and external optimization ring determination unit is used for determining an external optimization ring and an internal optimization ring respectively according to the integrated performance index model by adopting a nested optimization algorithm.
The internal and external optimization ring optimal solution determination unit is used for respectively determining the optimal solution of the external optimization ring and the optimal solution of the internal optimization ring by adopting a bacterial foraging optimization algorithm. The optimal solution for the inner optimization loop is the minimum of the position error of the load. The optimal solution for the outer optimization loop is the minimum of the sum of the position error of the load and the control input error.
The optimal solution determining unit is used for obtaining the optimal solution of the integrated performance index model according to the optimal solution of the outer optimization ring and the optimal solution of the inner optimization ring.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A fixed time control and structure combined optimization method for a four-motor linkage system is characterized by comprising the following steps:
acquiring a structural coefficient and a performance coefficient of a four-motor linkage system; the structural coefficients include: the motor rotational inertia, the transmission torque and the control input quantity of the four-motor linkage system; the coefficient of performance includes: performance index and structural design performance index of the controller;
according to the structural coefficient and the performance coefficient, constructing an integrated performance index model by taking the motor rotational inertia as an optimization target and taking the difference between the upper bound of the motor rotational inertia, the lower bound of the motor rotational inertia, the transmission torque and the control input quantity of the four-motor linkage system as constraint conditions;
determining an optimal solution of the integrated performance index model by adopting a bacterial foraging optimization algorithm; the optimal solution is the minimum value of the rotational inertia of the motor;
and driving and controlling the motors in the four-motor linkage system by adopting the minimum value of the rotational inertia of the motors.
2. The fixed time control and structure joint optimization method of the four-motor linkage system according to claim 1, wherein the integrated performance index model is as follows:
wherein, wpDesigning a weight coefficient, w, of a performance index for a structurecTo control the weight coefficient of the performance index, s.t. is a constraint condition, fpDesign of the Performance index for the Structure, fp＝(umax-umin)2，umaxIs the maximum value of the control input of the controller, uminIs the minimum value of the control input of the controller, fcIn order to control the performance index,
x1is the position of the load, ydFor the desired position of the load, t is the convergence time of the four-motor linkage system, JmIs the moment of inertia of the motor, JlowIs the lower bound of the moment of inertia, JhighIs the upper bound of the moment of inertia,
is the angular acceleration of the motor i and,
is the angular velocity of the motor i and,
is the angular acceleration of the load and,
angular velocity of the load, JLIs the moment of inertia of the load, bmIs the viscous friction coefficient at the motor end, bLIs the viscous friction coefficient at the load side, u is the control input to the controller,
is the driving torque of the motor i.
3. The fixed time control and structure joint optimization method of the four-motor linkage system according to claim 1, wherein the optimal solution of the integrated performance index model is determined by using a bacterial foraging optimization algorithm, and specifically comprises:
respectively determining an outer optimization ring and an inner optimization ring according to the integrated performance index model by adopting a nested optimization algorithm;
respectively determining the optimal solution of the outer optimization ring and the optimal solution of the inner optimization ring by adopting a bacterial foraging optimization algorithm;
and obtaining the optimal solution of the integrated performance index model according to the optimal solution of the outer optimization ring and the optimal solution of the inner optimization ring.
4. The fixed time control and structure joint optimization method of the four-motor linkage system according to claim 3, wherein the outer optimization ring is:
the inner optimization ring is:
wherein the content of the first and second substances,
optimizing ring results for external use，wpAnd wcAre all weight coefficients, s.t. is a constraint condition, uminIs the minimum value of the control input of the controller, umaxIs the maximum value of the control input of the controller, JlowIs the lower bound of the moment of inertia, JhighIs an upper bound of moment of inertia, JmIs the rotational inertia of the motor and is,
for internal optimization of the ring result, JmIs the moment of inertia of the motor, x1Is the position of the load, ydFor the desired position of the load, t is the convergence time of the four-motor linkage system, JLIs the moment of inertia of the load, bmIs the viscous friction coefficient at the motor end, bLIn order to be the viscous friction coefficient at the load end,
is the angular acceleration of the motor i and,
is the angular velocity of the motor i and,
is the angular acceleration of the load and,
is the angular velocity of the load, u is the control input to the controller,
is the transmission torque of the motor i,
k is the torsion coefficient, c is the damping coefficient, ΔiIs the difference in position, Δ, between motor i and the loadi＝θi-θL，θiIs the position of motor i, θLF (-) is a non-linear function caused by backlash, being the position of the load,
δ is the tooth gap width.
5. The method for fixed time control and structure joint optimization of the four-motor linkage system according to claim 1, further comprising, before the obtaining of the structural coefficients and the controller coefficients of the four-motor linkage system, respectively:
acquiring structural parameters of the four-motor linkage system; the structural parameters include: the method comprises the following steps of (1) enabling the rotational inertia of a motor, a tracking error, a synchronization error, a viscous friction coefficient at the motor end and the rotational inertia of a load to be in a synchronous mode;
according to the structural parameters, a structural model in the four-motor linkage system is constructed; the structural model includes: a drive motor synchronous controller and a load tracking controller;
constructing a controller model of the four-motor linkage system according to the structural model; the controller model is as follows:
wherein xisIn order to synchronize the control parameters with each other,
psi is normal number, sigma1For synchronization error, usiFor synchronous control of drive motors utIs a load tracking controller.
6. The method for fixed time control and structure joint optimization of a four-motor linkage system according to claim 5, wherein the synchronous controller u of the driving motorsiComprises the following steps:
load trackingController utComprises the following steps:
wherein, JmIs the rotational inertia of the motor, ms1And ms2Are all proportionality coefficients, and ms1≥1，ms2≥1，σ2、φs2、φs1、s2And phi1Are all the intermediate variables of the series of the Chinese characters,
s1in order to track the error, the tracking error is,
is s is1The approach rate of (a) to (b),
σ1for synchronization error, ξs2Is an exponential coefficient, and
is the drive torque of motor i, bmAs a viscous friction coefficient at the motor end,
is the angular velocity of the motor i and,
is an estimate of the load speed, n is the transmission ratio coefficient,
as second derivative of the reference signal, m1For the parameters of the controller to be optimized,
m2for tracking controller index coefficients, m2≥1，ξ2In order for the tracking controller to be informed,
7. the utility model provides a four motor linked systems fixed time control and structure are united optimization system which characterized in that includes:
the coefficient acquisition module is used for acquiring the structural coefficient and the performance coefficient of the four-motor linkage system; the structural coefficients include: the motor rotational inertia, the transmission torque and the control input quantity of the four-motor driving system; the coefficient of performance includes: performance index and structural design performance index of the controller;
the integrated performance index model building module is used for building an integrated performance index model by taking the rotational inertia of the motor as an optimization target and taking the difference between the upper limit of the rotational inertia of the motor, the lower limit of the rotational inertia of the motor, the transmission torque and the control input quantity of the four-motor linkage system as a constraint condition according to the structural coefficient and the performance coefficient;
the optimal solution determining module is used for determining the optimal solution of the integrated performance index model by adopting a bacterial foraging optimization algorithm; the optimal solution is the minimum value of the rotational inertia of the motor;
and the driving control module is used for driving and controlling the motors in the four-motor linkage system by adopting the minimum value of the rotational inertia of the motors.
8. The system for fixed time control and structure joint optimization of a four-motor linkage system according to claim 7, wherein the optimal solution determination module specifically comprises:
the internal and external optimization ring determination unit is used for respectively determining an external optimization ring and an internal optimization ring according to the integrated performance index model by adopting a nested optimization algorithm;
the internal and external optimization ring optimal solution determination unit is used for respectively determining the optimal solution of the external optimization ring and the optimal solution of the internal optimization ring by adopting a bacterial foraging optimization algorithm; the optimal solution of the inner optimization ring is the minimum value of the position error of the load; the optimal solution for the outer optimization loop is the minimum of the sum of the position error of the load and the control input error;
and the optimal solution determining unit is used for obtaining the optimal solution of the integrated performance index model according to the optimal solution of the outer optimization ring and the optimal solution of the inner optimization ring.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911412866.2A CN111062147B (en) | 2019-12-31 | 2019-12-31 | Fixed time control and structure combined optimization method and system for four-motor linkage system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911412866.2A CN111062147B (en) | 2019-12-31 | 2019-12-31 | Fixed time control and structure combined optimization method and system for four-motor linkage system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111062147A true CN111062147A (en) | 2020-04-24 |
| CN111062147B CN111062147B (en) | 2022-02-01 |
Family
ID=70305801
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911412866.2A Active CN111062147B (en) | 2019-12-31 | 2019-12-31 | Fixed time control and structure combined optimization method and system for four-motor linkage system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111062147B (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111880483A (en) * | 2020-08-11 | 2020-11-03 | 青岛大学 | Method for controlling preset performance of four-motor drive servo system of radar antenna |
| CN113093547A (en) * | 2021-04-06 | 2021-07-09 | 北京理工大学 | Space robot control method based on self-adaptive sliding mode and differential evolution |
| CN117544033A (en) * | 2023-11-14 | 2024-02-09 | 江南大学 | BDOA-based PMSM prediction control system parameter compensation method |
| CN117544033B (en) * | 2023-11-14 | 2024-05-14 | 江南大学 | BFOA-based PMSM prediction control system parameter compensation method |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1862054A (en) * | 2005-05-10 | 2006-11-15 | 福特环球技术公司 | Inertial torque reaction management with selectively engageable counter rotating component |
| CN107738691A (en) * | 2017-09-28 | 2018-02-27 | 南京航空航天大学 | A kind of 4 wheel driven composite turning system and its Multipurpose Optimal Method in good time |
| CN107947646A (en) * | 2017-12-22 | 2018-04-20 | 中国矿业大学 | It is a kind of to coordinate control optimization method based on the double permanent magnet synchronous motors for having mechanical attachment |
| CN109080427A (en) * | 2018-09-21 | 2018-12-25 | 广州市新域动力技术有限公司 | Bi-motor hybrid engine multimode dynamical system and its driving method |
| CN109905067A (en) * | 2019-04-12 | 2019-06-18 | 北京理工大学 | Motor driven systems structure and the integrated optimization method of control |
-
2019
- 2019-12-31 CN CN201911412866.2A patent/CN111062147B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1862054A (en) * | 2005-05-10 | 2006-11-15 | 福特环球技术公司 | Inertial torque reaction management with selectively engageable counter rotating component |
| CN107738691A (en) * | 2017-09-28 | 2018-02-27 | 南京航空航天大学 | A kind of 4 wheel driven composite turning system and its Multipurpose Optimal Method in good time |
| CN107947646A (en) * | 2017-12-22 | 2018-04-20 | 中国矿业大学 | It is a kind of to coordinate control optimization method based on the double permanent magnet synchronous motors for having mechanical attachment |
| CN109080427A (en) * | 2018-09-21 | 2018-12-25 | 广州市新域动力技术有限公司 | Bi-motor hybrid engine multimode dynamical system and its driving method |
| CN109905067A (en) * | 2019-04-12 | 2019-06-18 | 北京理工大学 | Motor driven systems structure and the integrated optimization method of control |
Non-Patent Citations (5)
| Title |
|---|
| TIANYI ZENG, ETC: "Structure/controller Co-design of Multi-motor Driving System with Fixed-time Dynamic Surface Backstepping Control", 《PROCEEDINGS OF THE 38TH CHINESE CONTROL CONFERENCE》 * |
| WEILI,LI，ETC: "Continuous quantum ant colony optimization and its application to optimization and analysis of induction motor structure", 《2010 IEEE FIFTH INTERNATIONAL CONFERENCE ON BIO-INSPIRED COMPUTING:THEORIES AND APPLICATIONS》 * |
| 刘天虬: "基于多目标优化的多电机伺服系统的结构/控制一体化设计", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
| 曾添一，任雪梅: "基于有限时间滤波控制的电机驱动系统结构/控制一体化设计", 《工程科学学报》 * |
| 路君勇: "CK518数控立式车床进给系统的优化设计分析", 《安阳工学院学报》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111880483A (en) * | 2020-08-11 | 2020-11-03 | 青岛大学 | Method for controlling preset performance of four-motor drive servo system of radar antenna |
| CN111880483B (en) * | 2020-08-11 | 2024-01-26 | 青岛大学 | Method for controlling preset performance of four-motor driving servo system of radar antenna |
| CN113093547A (en) * | 2021-04-06 | 2021-07-09 | 北京理工大学 | Space robot control method based on self-adaptive sliding mode and differential evolution |
| CN113093547B (en) * | 2021-04-06 | 2022-03-01 | 北京理工大学 | Space robot control method based on self-adaptive sliding mode and differential evolution |
| CN117544033A (en) * | 2023-11-14 | 2024-02-09 | 江南大学 | BDOA-based PMSM prediction control system parameter compensation method |
| CN117544033B (en) * | 2023-11-14 | 2024-05-14 | 江南大学 | BFOA-based PMSM prediction control system parameter compensation method |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111062147B (en) | 2022-02-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109581868B (en) | Reconfigurable robot decentralized nerve optimal control method based on judgment and identification structure | |
| CN102385342B (en) | Self-adaptation dynamic sliding mode controlling method controlled by virtual axis lathe parallel connection mechanism motion | |
| CN111062147B (en) | Fixed time control and structure combined optimization method and system for four-motor linkage system | |
| CN110877333A (en) | Flexible joint mechanical arm control method | |
| CN111273544B (en) | Radar pitching motion control method based on prediction RBF feedforward compensation type fuzzy PID | |
| CN108555914B (en) | DNN neural network self-adaptive control method based on tendon-driven dexterous hand | |
| CN113093538A (en) | Non-zero and game neural-optimal control method of modular robot system | |
| Yang et al. | A CMAC-PD compound torque controller with fast learning capacity and improved output smoothness for electric load simulator | |
| CN116991068A (en) | Motor control method and system based on distributed preset time gradient descent method | |
| CN109905067B (en) | Motor driving system structure and control integrated optimization method | |
| CN112947083B (en) | Nonlinear model predictive control optimization method based on magnetic suspension control system | |
| CN116079741B (en) | Self-adaptive control method for motor-driven single-link mechanical arm | |
| Vasak et al. | State estimation of an electronic throttle body | |
| He et al. | Synthetic robust model predictive control with input mapping for constrained visual servoing | |
| CN108267970B (en) | Time-lag rotor active balance control system and method based on Smith model and single neuron PID | |
| CN113283090B (en) | Friction compensation method for electric servo system of airplane steering engine based on bee colony algorithm | |
| CN116088299A (en) | Neural network backstepping control method for satellite antenna series-parallel motor mechanism | |
| Supriyono et al. | Control of a single-link flexible manipulator using improved bacterial foraging algorithm | |
| Lukichev et al. | Application of fuzzy cooperative coevolution adaptive control for damping of torsional vibrations in multi-mass drive system | |
| CN111399377A (en) | Control method of electric load simulator based on negative feedback correction | |
| CN110932609A (en) | Self-adaptive recursion control method and system for multi-motor servo system | |
| Tran | Nonlinear flight control design using backstepping methodology | |
| CN110685310A (en) | Engine extreme load control method and system based on neural network and engineering vehicle | |
| CN116149262B (en) | Tracking control method and system of servo system | |
| Abd-Alrahem et al. | Fully symbolic-based technique for solving complex state-space control systems |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |