CN108777556B - Model-free adaptive robust decoupling control method for two-motor speed regulation system - Google Patents
Model-free adaptive robust decoupling control method for two-motor speed regulation system Download PDFInfo
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Abstract
The invention discloses a model-free adaptive robust decoupling control method of a two-motor speed regulating system based on a neural network inverse model, which comprises the following steps of: analyzing the mathematical model of the two-motor speed regulating system to obtain an input-output relational expression about an inverse system of an original system; acquiring dynamic and static data samples of two motor speed regulating systems under different input excitations, training a big data sample to approach an inverse system model and constructing a pseudo linear composite system; a tracking differentiator is added to arrange a transition signal, the output of the model-free control compensator for compensating nonlinear feedback is designed according to a dynamic linearization method, the influence caused by uncertain disturbance in a multi-motor speed regulation system is restrained, and the tension overshoot caused by a step signal is reduced. The invention obviously inhibits the torque disturbance error caused by nonlinearity and variable structure, improves the problem of tension step overshoot and improves the robust decoupling capability of the system aiming at the characteristics of nonlinearity and strong coupling of a multi-motor speed regulating system.
Description
Technical Field
The invention designs a neural network inverse model-free compensation implementation method for a multi-motor speed regulation system, which is suitable for the multi-motor speed regulation system taking Siemens PLC as a controller and can also be used in other electromechanical control occasions with nonlinearity, strong coupling and poor robustness.
Background
At present, the control of a multi-motor speed regulating system still has at least two problems: 1) in engineering application, most accurate mathematical models of nonlinear strong coupling systems are difficult to obtain, so that various nonlinear control difficulties are increased; 2) the coexistence of accidental disturbance and continuous mechanical abrasion in the multi-motor speed regulation system causes numerous system operation conditions and more complex control target constraint relation, and greatly reduces the robustness and adaptability of the system. With the development of control theory, it is desirable to directly utilize the input and output data of the controlled object to get rid of the "data-driven" concept that depends on mathematical models.
The model mismatch is caused by factors such as load disturbance and motor parameter perturbation, so that the control precision and reliability of system control are influenced, the system is directly subjected to robust control, and a multivariable nonlinear system with strong coupling does not have a decoupling effect, so that the ideal effect in simulation is often not achieved in practical engineering application although a plurality of advanced control algorithms appear in recent years.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a two-motor neural network inverse model-free compensation control method based on PLC (programmable logic controller), which improves the decoupling performance of a two-motor speed regulating system and inhibits torque fluctuation interference caused by nonlinearity and variable structure, thereby enhancing the overall robustness performance of a multi-motor speed regulating system.
The technical scheme adopted by the invention is as follows: a model-free adaptive robust decoupling control method of a two-motor speed regulation system based on a neural network inverse model comprises the following steps:
firstly, two sets of rollers are respectively driven by two alternating current asynchronous motors, the rotating shafts of the motors are rigidly connected with the rollers, and a PLC (programmable logic controller) transmits a rotating speed signal u through a bus2、u4Transmitting the signals to a frequency converter for vector control, thereby forming a two-motor speed regulating system;
and secondly, reversibility verification is carried out on the two motor speed regulating systems, and an inverse system relational expression is deduced:
wherein u ═ u2,u4]T＝[ω1,ω2]T，ω1、ω2For input speed, y, of two-motor speed regulation systems2、y4The output rotating speed and the actual tension of the two motor speed regulating systems are respectively;
thirdly, selecting proper excitation signals to fully excite the coupling relation among the state quantities in the system, and collecting omega according to the inverse system relation expression1、ω2、y2、y4Carrying out numerical differentiation and normalization on data by MATLAB (matrix laboratory) on variable data samples, approximating an inverse system of a two-motor speed regulation system by adopting a neural network, optimizing a weight threshold of the neural network by utilizing a particle swarm optimization, and establishing a pseudo-linearized two-motor speed regulation system and the inverse system thereof in series to form the two-motor speed regulation systemA machine discrete system;
fourthly, performing dynamic linearization processing on the two motor discrete systems subjected to pseudo linearization, estimating pseudo partial derivatives of the two motor discrete systems on line through input and output data, and designing a model-free compensation controller; arranging a transition process for signal input, designing a nonlinear control law and reducing the overshoot of tension;
and fifthly, operating the two motor speed regulating systems on a PLC platform: the upper computer gives input square waves related to the rotating speed and the tension, the rotating speed signals of the two asynchronous motors are transmitted to the frequency converter to work through a PLC control algorithm by a bus, the current of the magnetic powder brake is adjusted to simulate the torque fluctuation caused by unknown interference, and the input value of the system and the data block corresponding to the weight threshold value of the neural network can be updated by utilizing the OPC technology.
And further, in the second step, reversibility verification is carried out on the two motor speed regulating systems.
In a two-motor speed regulating system, torque fluctuation interference is considered, and when a frequency converter adopts a vector mode, a mathematical model is
y＝h(x)＝[y1,y2,y3,y4]T＝[x2,x1,x4,x5]T
In the formula: u ═ u1,u2,u3,u4]T＝[isd1,ω1,isd2,ω2]T,x＝[x1,x2,x3,x4,x5]T＝[ωr1,ψr1,ωr2,ψr2,F]TControl variables and state variables; f is belt tension; k is a transmission coefficient; t is a tension change time constant; p is a radical ofni、Ji、ωi、ωri、Tri、Lri、Lmi、ψri、TLi、ΔTLi、ri、ki、isdi(i＝1,2) The number of pole pairs of an ith motor, the inertia of a rotor, the rotating speed of a stator, the rotating speed of the rotor, an electromagnetic time constant, the self-inductance of the rotor, the mutual inductance, the flux linkage of the rotor, the load torque, the torque fluctuation interference, the radius of a belt wheel, the speed ratio and the d-axis stator current are respectively set;
considering the constancy of the rotor flux linkage, the above equation can be simplified to
y＝h(x)＝[y2,y4]T＝[x1,x5]T＝[ωr1,F]T
When psir1≠0，ψr2Not equal to 0, A (x, u) is not singular, the relative order of the system is (1,2), the system is reversible, according to the implicit theorem, the inverse system can be represented as
Further, the fourth step model-free compensation controller estimates the pseudo partial derivative of the system on line by the input and output of the two-motor speed regulating system so as to compensate the nonlinear feedback law.
Arranging a transition link for a pseudo-linear discrete system to obtain a tracking signal v of an original input signal1And its differential signal v2
Wherein
Defining a function for the interval, h an integration step, v the original input signal, fhan () a control synthesis function, r0、h0Respectively a speed factor and a filtering factor.
The two-motor speed regulating system can obtain a linearized mathematical model of the two-motor speed regulating system by a dynamic linearization method
y(k+1)＝y(k)+φ(k)Δu(k)
Δu(k)＝u(k)-u(k-1)
Based on the linearized model, defining a control input criterion function as
In the formula: y (k) is [ v1，v2]TU (k) is [ u (k) ]1，u2]TV matrix of1、v2The system output and its differential, u1、u2Respectively, the input quantity and its differential, | y*(k+1)-y(k+1)|2The output is guaranteed to accurately track the expected input value; lambada | u (k) -u (k-1) & gtdoes not smoke2Is a softening process performed to prevent abrupt change of input signals, wherein lambda >0 is a weight coefficient.
The extreme value of u (k) can be obtained by the formula
Wherein rho and alpha are constant coefficients, and T is a sampling time constant;
since the partial derivative φ (k) is unknown as described above, it can be estimated by inputting output data, taking into account the estimation criterion function of the partial derivative as follows
An estimate of the partial derivative phi (k) can be obtained
Is composed of
Wherein eta and mu are constant coefficients;
thus, the input-output relationship of the calculated model-free compensated controller can be expressed as
Designing the nonlinear feedback control rate to
Wherein λ is1、λ2Respectively taking 0.75 and 1.25,
respectively a given input value and its differential.
The final input of the system is known as
u＝β1fal(e1,λ1,δ)+β2fal(e2,λ2,δ)+u1+u2
Wherein, 0 < lambda1＜1＜λ2，β1、β2Is a constant.
The invention has the following beneficial effects:
1) the control method based on data driving does not depend on a mathematical model, has self-adaptive capacity, solves the problem that simulation is not matched with practical application due to inaccuracy of the mathematical model, has better control effect of a nonlinear system compared with the traditional PID control, effectively solves the problems of poor load disturbance resistance and tension step overshoot in the neural network inverse decoupling control of the two-motor speed regulation system, and improves the robustness of the two-motor system.
2) The invention converts the nonlinear system into the pseudo linear system in the form of the neural network inverse system series integrator, provides conditions for the linear discrete system without model control, and thus improves the estimation precision of the pseudo partial derivative of the multi-motor speed regulation system.
3) The invention optimizes the weight threshold of the neural network by using the particle swarm algorithm, avoids the problem that the training process falls into a local minimum value, and greatly shortens the training time.
4) The invention is based on Siemens S7300PLC to carry out experiments, and the characteristics of modularization, integration, portability and expandability enable the system performance to be more reliable and the application to be more extensive.
5) The invention adopts OPC technology to carry out data interaction of the upper computer and WINCC, PLC and Matlab training, is more suitable for actual field operation and is convenient to debug.
Drawings
FIG. 1 is a control schematic diagram of a two-motor speed regulating system
FIG. 2 is a schematic view of the connection of the apparatus
FIG. 3 is a logic flow diagram of particle swarm optimization
FIG. 4 is a block diagram of model-free compensation control
FIG. 5 is a block diagram of the overall control of a two-motor speed control system
FIG. 6 is a logic flow diagram for PLC operation
FIG. 7 is a logic flow diagram of a neural network
FIG. 8 is the upper computer WINCC interface
FIG. 9 is a PID, MFAC-NNI decoupled control comparison; (a) a PID control curve; (b) an NNI-based MFA robust control curve;
FIG. 10 is a PID, PID-NNI and MFAC-NNI robust control comparison; (a) a PID control curve; (b) NNI-based PID control curves; (c) an NNI-based MFA robust control curve;
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
Step 1: two sets of rollers are respectively driven by two squirrel-cage AC asynchronous motors, the rotating shafts of the motors are rigidly connected with the rollers, and a rotating speed signal u is transmitted by a Siemens S7-300PLC through a Profibus bus2、u4Transmitting the signals to a frequency converter for vector control, thereby forming a two-motor speed regulating system; the driving part of the two-motor speed regulation experiment system mainly comprises two MMV440 frequency converters and two 2.2KW three-phase cage-type asynchronous motors, and respectively controls a driving roller shaft to enable a belt to be transmitted as shown in figure 1; the control part mainly comprises a porphyry industrial personal computer and a Siemens PLC300, and a PLC control unit comprises a power supply module (PS 30710A), a CPU module (315-2DP), a digital quantity input/output module (SM321), an analog quantity input/output module (SM335) and a high-speed counter (FM 350); the detection part mainly comprises a tension sensor and a photoelectric encoder, and experiments and process monitoring are carried out through an upper computer Siemens WinCC6.0 as shown in figure 2.
Step 2: the invention adopts a master-slave control mode, wherein the No. 1 motor is a master motor, the No. 2 motor is a slave motor, the rotating speed of the No. 2 motor is determined by the actual rotating speed of the No. 1 motor and the tension between the No. 1 motor and the No. 2 motor, the PLC outputs a rotating speed value to the frequency converter so as to act on the corresponding motor, and the rotating speed is adjusted to stabilize the floating roller, namely the tension between the two motors is stable. Reversibility verification of the two-motor speed regulation system provides a theoretical basis for an inverse system method.
Reversibility verification is carried out on the two motor speed regulating systems, and an inverse system relational expression can be deduced:
wherein u ═ u2,u4]T＝[ω1,ω2]T，ω1、ω2For input speed, y, of two-motor speed regulation systems2、y4The output rotating speed and the actual tension of the two motor speed regulating systems are respectively.
And step 3: and collecting data samples. Selecting proper excitation signals to fully excite the coupling relation among the state quantities in the system, and collecting omega according to an inverse system relational expression1、ω2、y2、y4A variable data sample is subjected to 5-point value differentiation and normalization processing on data through MATLAB 2014b, a weight threshold of a neural network is optimized by utilizing a particle swarm algorithm, the situation that the neural network training is trapped in a local minimum value is reduced, two motor speed regulation systems and an inverse system of the two motor speed regulation systems are connected in series to construct a pseudo-linearized two-motor discrete system, the neural network has 5 inputs, 22 hidden nodes and 2 outputs, and the inputs are y respectively2、
y4、
The outputs are respectively omega1、ω2。
In order to fully embody the dynamic and static characteristics of the system and have enough training samples at the same time, and in consideration of the parameter range of system hardware, a given signal of the system adopts random square waves. The given rotation speed range is (200-1000) r/min, and the given tension range is (200-720) N. Sampling to obtain 10 groups of 20000 data sample points, pinching and removing the head and the tail of the data, and normalizing the data to [ -1,1] so as to facilitate network convergence, wherein a normalization formula is as follows:
wherein the sampling signal comprises ω1、ω2、y2、y4，
Is y2、y4The 5 point values of (1) can be differentiated and can be processed by off-line calculation.
The weight threshold value optimization of data network training is carried out by a particle swarm algorithm, a logic flow chart is shown in figure 3, a three-layer BP neural network is sampled, 5 neurons are input into the layer, 22 hidden nodes are arranged in the middle layer, 2 neurons are output from the layer, and the input is y2、
y4、
The outputs are respectively omega1、ω2。
And 4, step 4: the two motor discrete systems after pseudo-linearization are subjected to dynamic linearization processing, pseudo partial derivatives of the two motor discrete systems are estimated online through input and output data, a model-free compensation controller is designed, and the anti-interference performance of the system is enhanced; and arranging a transition process for signal input, designing a nonlinear control law and reducing the overshoot of tension.
After the original two motor speed regulation systems are decoupled into a pseudo-linear discrete system by a neural network inverse system, a model-free compensation controller is constructed for the pseudo-linear discrete system, and a schematic block diagram is shown in fig. 4.
The pseudo linear discrete system can be known through a dynamic linearization method
y(k+1)＝y(k)+φ(k)Δu(k)
Δu(k)＝u(k)-u(k-1)
Based on the linearized model, defining a control input criterion function as
In the formula: y (k) is [ v1，v2]TU (k) is [ u (k) ]1，u2]TV matrix of1、v2The system output and its differential, u1、u2Respectively, input quantity and differential thereof, wherein lambda is more than 0 and is a weight coefficient;
the extreme value of u (k) can be obtained by the formula
Wherein rho epsilon (0, 1) is a step-size factor used for penalizing a constraint factor of a related item, and lambda >0 can prevent a singular phenomenon that a denominator is zero.
Since phi (k) is unknown, an estimate thereof is introduced
And (k) is estimated on line through input and output data of the controlled system.
Estimation criterion function taking into account partial derivatives
Wherein μ >0 is a weight coefficient.
The minimum value of phi (k) can be obtained
Wherein: eta.e (0, 2) is the sequence of step sizes.
From the above analysis, the pseudo-partial derivative estimation value of the MFA control based on the pseudo-linear system can be obtained as
If it is
Or | delta u (k) | < epsilon,
wherein,
is that
Is a small positive number. δ is a constant used to determine the piecewise function.
Given the control law
In order to improve the response speed of the MFAC controller, the penalty related term of the above formula is improved, so that
The deformation is obtained to the final control law of
Wherein k is1>0 is a proportionality coefficient, and u (k) is a control input of the two-motor speed regulating system.
The modeless controller output is compensated to the pseudo linear system, as shown in fig. 5, which is an overall block diagram of the system.
And 5: the two-motor speed regulating system operates on a Siemens S7-300PLC platform: an upper computer gives input square waves related to rotating speed and tension, rotating speed signals of two asynchronous motors are transmitted to a frequency converter to work through a PLC control algorithm by a Profibus bus, and the current of a magnetic powder brake is adjusted to simulate torque fluctuation caused by unknown interference. And the OPC technology can be used for updating the input value of the system and the data block corresponding to the weight threshold value of the neural network.
And writing an OPC client program by using VB (visual basic), and establishing OPC group and OPC Item. In VB, the objects that trigger events are called event sources, and the variables of the object class are declared by WithEvents, and the events are triggered when the properties of the group subscribe. The weight threshold values input to given variables and neural network are loaded into the PLC by OPC technique, and the initialization and release procedures are as follows
Const ServerName＝"OPCServer.WinCC"
Dim WithEvents MyOPCServer As OPCServer
Dim MyOPCGroupColl As OPCGroups
Dim WithEvents MyOPCGroup As OPCGroup
Dim MyOPCItemColl As OPCItems
Dim MyOPCItem As OPCItem
Dim ClientHandles(4000)As Long
Dim ServerHandles()As Long
Dim Values(4000)As Variant
Dim Errors()As Long
Dim STSP_ItemIDs(4000)As String
Dim GroupName As String
Dim NodeName As String
Dim STSP_Itemv(4000)As Variant
Dim i As Integer
Closing the link release group and the server object after the processing is finished
MyOPCGroupColl.RemoveAll
MyOPCServer.Disconnect
Set MyOPCItemColl＝Nothing
Set MyOPCGroup＝Nothing
Set MyOPCGroupColl＝Nothing
Set MyOPCServer＝Nothing
FIG. 6 is a logic flow diagram of the neural network in the FB module in the PLC experiment process, which realizes the effect that the 3-layer BP neural network approaches the inverse model of the system
FIG. 7 is a logic flow diagram of OB100, OB1, OB35 and main program in PLC
FIG. 8 is a hardware configuration block diagram of the upper computer
FIG. 9 is a comparison of the decoupling effect of PID control and the algorithm of the present invention. The coupling influence between the rotating speed and the tension is greatly reduced, the neural network inverse control achieves a good decoupling effect, and the tension overshoot is restrained. As can be seen, the MFA robust control based on the NNI can achieve a good system decoupling effect compared with the traditional PID control.
FIG. 10 is a PID, PID-NNI, and MFAC-NNI robust control comparison. The currents of the magnetic powder brake are set, load disturbance is added at 80s and 150s respectively, and the graph shows that the MFA robust control based on the NNI can effectively reduce the deviation of the rotating speed and the tension caused by the load disturbance and effectively shorten the time for the system to recover to be stable.
It is to be understood that the above examples are intended to illustrate and not to limit the scope of the invention, which is defined by the claims appended hereto, and that various equivalent modifications of the invention will occur to those skilled in the art upon reading the present disclosure.
Claims (5)
1. A model-free adaptive robust decoupling control method of a two-motor speed regulation system based on a neural network inverse model is characterized by comprising the following steps:
firstly, two sets of rollers are respectively driven by two alternating current asynchronous motors, the rotating shafts of the motors are rigidly connected with the rollers, and a PLC (programmable logic controller) transmits a rotating speed signal u through a bus2、u4Transmitting the signals to a frequency converter for vector control, thereby forming a two-motor speed regulating system;
and secondly, reversibility verification is carried out on the two motor speed regulating systems, and an inverse system relational expression is deduced:
wherein u ═ u2,u4]T＝[ω1,ω2]T，ω1、ω2For input speed, y, of two-motor speed regulation systems2、y4The output rotating speed and the actual tension of the two motor speed regulating systems are respectively;
thirdly, selecting proper excitation signals to fully excite the coupling relation among the state quantities in the system, and collecting omega according to the inverse system relation expression1、ω2、y2、y4Carrying out numerical differentiation and normalization on data by MATLAB (matrix laboratory) on a variable data sample, approximating an inverse system of two motor speed regulation systems by adopting a neural network, optimizing a weight threshold of the neural network by utilizing a particle swarm algorithm, and connecting the two motor speed regulation systems and the inverse system in series to construct a pseudo-linearized two motor discrete system;
the third step is to perform numerical differentiation and normalization on the data, and the specific process is as follows:
for y2、y4Performs a 5 point value differentiation at time tiThe sampled value of (i ═ 0,1 …, N) is yi＝y(ti) The sampling step length is ts＝ti-ti-1The first and second order calculation formulas are
Normalizing the data to [ -1,1] to facilitate network convergence, the normalization formula is as follows:
wherein D isiIn order to sample the data, the data is sampled,
is normalized data，DmaxAnd DminMaximum and minimum values of the data samples respectively;
fourthly, performing dynamic linearization processing on the two motor discrete systems subjected to pseudo linearization, estimating pseudo partial derivatives of the two motor discrete systems on line through input and output data, and designing a model-free compensation controller; arranging a transition process for signal input, designing a nonlinear control law and reducing the overshoot of tension;
the model-free compensation controller of the fourth step:
the two-motor speed regulating system can obtain a linearized mathematical model of the two-motor speed regulating system by a dynamic linearization method
y(k+1)＝y(k)+φ(k)Δu(k)
Δu(k)＝u(k)-u(k-1)
Based on the linearized model, defining a control input criterion function as
In the formula: y (k) is [ v1，v2]TU (k) is [ u (k) ]1，u2]TV matrix of1、v2The system output and its differential, u1、u2Respectively, input quantity and differential thereof, wherein lambda is more than 0 and is a weight coefficient;
the extreme value of u (k) can be obtained by the formula
Wherein rho and alpha are constant coefficients, and T is a sampling time constant;
since the partial derivative φ (k) is unknown as described above, but can be estimated by inputting and outputting data, an estimated value of the partial derivative φ (k) can be obtained
Is composed of
Wherein eta and mu are constant coefficients;
thus, the input-output relationship of the calculated model-free compensated controller can be expressed as
Wherein k is1Is a constant coefficient;
designing the nonlinear feedback control rate to
Wherein,
respectively the tracking value of a given input and its differential, beta1、β2Is a control parameter; δ is a constant used to determine the piecewise function, λ1、λ2Is a constant;
the final input of the system is known as
u＝β1fal(e1,λ1,δ)+β2fal(e2,λ2,δ)+u1+u2；
And fifthly, operating the two motor speed regulating systems on a PLC platform: an upper computer gives input square waves related to rotating speed and tension, rotating speed signals of two asynchronous motors are transmitted to a frequency converter to work through a PLC control algorithm and a bus, the current of a magnetic powder brake is adjusted to simulate torque fluctuation caused by unknown interference, and an input value of a system and a data block corresponding to a weight threshold value of a neural network can be updated by utilizing an OPC technology;
in the third step, the neural network has 5 inputs, 22 hidden nodes and 2 outputs, and the inputs are respectively y2、
y4、
The outputs are respectively omega1、ω2。
2. The model-free adaptive robust decoupling control method for the two-motor speed regulation system based on the neural network inverse model as claimed in claim 1, wherein in the second step, the reversibility certification specific process of the two-motor speed regulation system is as follows:
in a two-motor speed regulating system, torque fluctuation interference is considered, and when a frequency converter adopts a vector mode, a mathematical model is
y＝h(x)＝[y1,y2,y3,y4]T＝[x2,x1,x4,x5]T
In the formula: u ═ u1,u2,u3,u4]T＝[isd1,ω1,isd2,ω2]T,x＝[x1,x2,x3,x4,x5]T＝[ωr1,ψr1,ωr2,ψr2,F]TControl variables and state variables; f is belt tension; k is a transmission coefficient; t is a tension change time constant; p is a radical ofni、Ji、ωi、ωri、Tri、Lri、Lmi、ψri、TLi、ΔTLi、ri、ki、isdi(i is 1,2) is the pole pair number of the ith motor, the rotor inertia, the stator rotating speed, the rotor rotating speed, the electromagnetic time constant, the rotor self-inductance, the mutual inductance, the rotor flux linkage, the load torque, the torque fluctuation interference, the belt pulley radius, the speed ratio and the d-axis stator current respectively;
considering the constancy of the rotor flux linkage, the above equation can be simplified to
y＝h(x)＝[y2,y4]T＝[x1,x5]T＝[ωr1,F]T
When psir1≠0，ψr2Not equal to 0, A (x, u) is not singular, the relative order of the system is α, the system is reversible, and the inverse system can be represented as
3. The model-free adaptive robust decoupling control method for the two-motor speed regulating system based on the neural network inverse model is characterized in that the relative order of the system is alpha (1, 2).
4. The model-free adaptive robust decoupling control method for the two-motor speed regulation system based on the neural network inverse model as claimed in claim 1, characterized in that λ1、λ2Respectively taking 0.75 and 1.25.
5. The model-free adaptive robust decoupling control method for the two-motor speed regulating system based on the neural network inverse model as claimed in claim 1, wherein the fifth step is a specific process:
writing an OPC client program by VB, establishing OPC group and OPC Item, declaring variables of an object class by WithEvents, triggering an event after the attribute of the group is subscribed, and loading a weight threshold value for inputting a given variable and a neural network into a PLC (programmable logic controller) through OPC technology.
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