CN113489404B - Robust bounded control method for permanent magnet linear motor with inequality constraint - Google Patents
Robust bounded control method for permanent magnet linear motor with inequality constraint Download PDFInfo
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- CN113489404B CN113489404B CN202110776420.9A CN202110776420A CN113489404B CN 113489404 B CN113489404 B CN 113489404B CN 202110776420 A CN202110776420 A CN 202110776420A CN 113489404 B CN113489404 B CN 113489404B
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- 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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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- 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
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/06—Linear motors
- H02P25/064—Linear motors of the synchronous type
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- 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
- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
Abstract
The invention provides a robust bounded control method of a permanent magnet linear motor with inequality constraint, which comprises the following specific steps: acquiring the running position of a permanent magnet linear motor to be controlled in real time, and acquiring the speed and the acceleration of the permanent magnet linear motor by utilizing differential operation to acquire acquired data; establishing dynamic modeling of the permanent magnet linear motor system according to the acquired data; setting bounded control conditions of a permanent magnet linear motor system according to dynamic modeling of the permanent magnet linear motor system; performing state conversion on the position, the speed and the acceleration of the permanent magnet linear motor to obtain a dynamic model after the conversion of a permanent magnet linear motor system; and controlling the converted system by adopting a robust bounded controller to obtain required control input, and inputting the required control input into the original permanent magnet linear motor system to control the permanent magnet linear motor. The control method can ensure that the displacement of the permanent magnet linear motor does not exceed a specified range, and the position tracking error is small.
Description
Technical Field
The invention relates to a motor robust bounded control method, in particular to a permanent magnet linear motor robust bounded control method with inequality constraint.
Background
A Permanent Magnet Linear Motor (PMLM) is a device that converts electrical energy directly into mechanical energy for linear motion without any intermediate conversion mechanism. Because the permanent magnet linear motor has the characteristics of high speed, large thrust, high precision and the like, the permanent magnet linear motor is widely applied to various industrial equipment.
The permanent magnet linear motor is a typical nonlinear multivariable system, and the control performance can be influenced by various nonlinear factors such as nonlinear friction, uncertainty of a model and external interference. In order to solve these control problems, various control methods such as adaptive compensation control, adaptive robust control, neural network, and the like have been proposed.
The operation range of the permanent magnet linear motor is not unlimited, the permanent magnet linear motor must operate within a certain stroke to prevent the linear motor from operating beyond the range to damage people and equipment, the conventional physical limit cannot ensure that the linear motor does not collide, and few documents solve the control problem that the linear motor does not exceed the specified movement range in an algorithm.
Disclosure of Invention
The invention aims to provide a robust bounded control method of a permanent magnet linear motor with inequality constraints, which can be used for controlling the permanent magnet linear motor.
The invention is realized by the technical scheme, and the method comprises the following specific steps:
1) Data acquisition: the position x of the permanent magnet linear motor to be controlled in operation is collected in real time, and the speed of the permanent magnet linear motor is obtained by utilizing differential operation
And acceleration
Acquiring collected data;
2) Constructing a dynamic model: establishing a dynamic modeling of the permanent magnet linear motor system according to the acquired data in the step 1);
3) Setting bounded control conditions: setting bounded control conditions of the permanent magnet linear motor system according to the dynamic modeling of the permanent magnet linear motor system in the step 2);
4) And (3) dynamic conversion of the model: position x and speed of permanent magnet linear motor
Acceleration of a vehicle
Performing state conversion to obtain a dynamic model after the permanent magnet linear motor system is converted;
5) Constructing a robust controller: and 4) controlling the system converted in the step 4) by adopting a robust bounded controller to obtain required control input, and inputting the control input into the original permanent magnet linear motor system to control the permanent magnet linear motor.
Further, the specific method for establishing the dynamic modeling of the permanent magnet linear motor system in the step 2) comprises the following steps:
establishing a dynamic model of the permanent magnet linear motor:
in the formula (1), the acid-base catalyst,
is the speed of the linear motor or motors,
acceleration of the linear motor, μ being the control input, K e Is the back electromotive force of the linear motor, M is the inertial load and the mass of the coil assembly, F e Representing the uncertainty factor of the system, F e By a load F load Corrugation force F ripple Frictional force F fric External disturbance F d Consists of the following components:
F e ＝F load +F ripple +F fric +F d (3)
in the formula (2), m is the mass of the motion thrust block, R is the resistance between any two phases of the permanent magnet linear motor, and K f Representing the force generated by the motor;
in the formula (3), frictional force F fric Is a non-linear function related to velocity, which can be modeled as:
in the formula (4), B is an equivalent viscous friction parameter,
comprises the following steps:
in the formula (5), f s Is the coefficient of static friction, f v Is a viscous friction coefficient, f c For a given coefficient of coulomb friction,
is a lubricant parameter;
the dynamic model of the permanent magnet linear motor can also be written as:
F e ＝F load +F ripple +F fricn +F d (7)。
further, the specific method for setting the bounded control condition of the permanent magnet linear motor in the step 3) comprises the following steps:
setting a limiting condition:
|F load +F ripple +F d |<f lm (9)
in the formulae (8) and (9),
f fM 、f lm are all preset upper limit values, f fM For defining a friction force bound, f lm For determining F load 、F ripple 、F d Bounded by a sum;
and (8) obtaining the uncertainty bound of the permanent magnet linear motor through (8) and (9).
Further, the specific method for dynamically converting the kinetic model in the step 4) is as follows:
the constraint of the stroke of the motor is x m <x<x M The control variable of the motor is y, wherein ∞<y<Infinity, then there are:
in the formula (10), x m Is the lower bound, x, of the displacement of the permanent magnet linear motor M The displacement of the permanent magnet linear motor is an upper bound;
the formula (10) is reversely solved to respectively obtain the position x and the speed of the linear motor
Acceleration of a vehicle
The position x and the speed are measured
Acceleration of a vehicle
Substituting into a kinetic equation to obtain the kinetic equation with y as a control variable:
further, the specific method for constructing the robust controller by the dynamically converted dynamic model in the step 5) comprises the following steps:
calculating position tracking error e (t) and speed error of permanent magnet linear motor
e(t)＝y(t)-y d (t) (15)
In equations (15) and (16), y (t) is the actual position of the linear motor in the converted system, y d (t) is the desired position of the linear motor in the converted system;
order to
Then its robust controller is:
in the formula (15), the reaction mixture is,
comprises the following steps:
in the formulae (18) and (19),
for processing robust termsThe uncertainty of the permanent magnet linear motor system,
for a given bounded function, S is a robust term control parameter, and epsilon is a real number determined by actual conditions;
define φ (e, e, t) as a function describing the system uncertainty as a result of the system uncertainty being bounded, i.e.
Due to the adoption of the technical scheme, the invention has the following advantages:
1. the control method can ensure that the displacement of the linear motor does not exceed the specified range, and the position tracking error is small.
2. The application constructs inequality constraint through the determination factor to the permanent magnet linear motor, so that the permanent magnet linear motor operates in a certain stroke, and the permanent magnet linear motor is effectively prevented from operating beyond the range to cause damage to people and equipment.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof.
Drawings
The drawings of the present invention are described below.
Fig. 1 is a control schematic of the present invention.
FIG. 2 is a graph of linear motor position for tracking sinusoidal signals with and without inequality constraints in a comparative experiment of the present invention.
FIG. 3 is a linear motor position error curve for tracking sinusoidal signals in a comparative experiment of the present invention with and without inequality constraints.
FIG. 4 is a linear motor position and error curve for tracking step signals with and without inequality constraints in a comparative experiment of the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the drawings.
A robust bounded control method for a permanent magnet linear motor with inequality constraints comprises the following specific steps:
1) Data acquisition: the position x of the permanent magnet linear motor to be controlled in operation is collected in real time, and the speed of the permanent magnet linear motor is obtained by utilizing differential operation
And acceleration
Acquiring collected data;
2) Constructing a dynamic model: establishing a dynamic modeling of the permanent magnet linear motor system according to the acquired data in the step 1);
3) Setting bounded control conditions: setting bounded control conditions of the permanent magnet linear motor system according to the dynamic modeling of the permanent magnet linear motor system in the step 2);
4) And (3) dynamic conversion of the model: for position x and speed of permanent magnet linear motor
Acceleration of a vehicle
Performing state conversion to obtain a dynamic model after the permanent magnet linear motor system is converted;
5) Constructing a robust controller: and 4) controlling the system converted in the step 4) by adopting a robust bounded controller to obtain required control input, and inputting the control input into the original permanent magnet linear motor system to control the permanent magnet linear motor.
The specific method for establishing the dynamic modeling of the permanent magnet linear motor system in the step 2) comprises the following steps:
establishing a dynamic model of the permanent magnet linear motor:
in the formula (21), the compound represented by the formula,
is the speed of the linear motor or motors,
acceleration of the linear motor, μ being the control input, K e Is the back electromotive force of the linear motor, M is the inertial load and the mass of the coil assembly, F e Representing the uncertainty factor of the system, F e By a load F load Ripple force F ripple Frictional force F fric External disturbance F d Consists of the following components:
F e ＝F load +F ripple +F fric +F d (23)
in the formula (22), m is the mass of the motion thrust block, R is the resistance between any two phases of the permanent magnet linear motor, and K f Representing the force generated by the motor;
in the formula (23), frictional force F fric Is a non-linear function related to velocity, which can be modeled as:
in the formula (24), B is an equivalent viscous friction parameter,
comprises the following steps:
in the formula (25), f s Is a coefficient of static friction, f ν Is a viscous friction coefficient, f c For a given coulomb friction coefficient of the polymer,
is a lubricant parameter;
the dynamic model of the permanent magnet linear motor can also be written as:
F e ＝F load +F ripple +F fricn +F d (27)。
the specific method for setting the bounded control condition of the permanent magnet linear motor in the step 3) comprises the following steps:
setting a limiting condition:
|F load +F ripple +F d |<f lm (29)
in the formulae (28) and (29),
f fM 、f lm are all preset upper limit values, f fM For defining a friction force bounded, f lm For determining F load 、F ripple 、F d Bounded by a sum;
the bound of the uncertainty of the permanent magnet linear motor is obtained by (28), (29).
The specific method for dynamically converting the dynamic model in the step 4) comprises the following steps:
the constraint of the stroke of the motor is x m <x<x M The control variable of the motor is y, where ∞<y<Infinity, then there are:
in the formula (30), x m Lower bound of the displacement of the permanent magnet linear motor, x M The displacement of the permanent magnet linear motor is an upper bound;
the equation (30) is inversely solved to determine the position x and the speed of the linear motor, respectively
Acceleration of a vehicle
The position x and the speed are measured
Acceleration of a vehicle
And substituting the kinetic equation into the kinetic equation to obtain the kinetic equation with y as a control variable:
the specific method for constructing the robust controller by the dynamically converted dynamic model in the step 5) comprises the following steps:
calculating permanent magnet linear electricityPosition tracking error e (t) and speed error of machine
e(t)＝y(t)-y d (t) (35)
In equations (35) and (36), y (t) is the actual position of the linear motor in the converted system, y d (t) is the desired position of the linear motor in the converted system;
order to
Then its robust controller is:
in the formula (38), the reaction mixture is,
comprises the following steps:
in the formulae (38), (39),
to make the robust term for dealing with the uncertainty of the permanent magnet linear motor system,
for a given bounded function, S is a robust termControl parameters, epsilon is a real number determined by actual conditions;
define φ (e, e, t) as a function describing the system uncertainty, since it is bounded, i.e.:
proving the stability of the robust controller type proposed in step 5):
constructing a positive definite Lyapunov function:
derivative it with respect to time t:
if it is
Then:
if it is
Then:
from the formulas (39) and (40):
if it is
The controller is stable.
If it is
λ 1 ＝min{K ν ，SK P } (48)
By choosing the appropriate e, the
The controller is now stable.
And (3) comparison test:
the values of the parameters are as follows:
m＝0.9kg，R＝9.4ohms，K f ＝31N/Amp，K e ＝25V/m/s，f s ＝6V，f ν ＝2V，f c ＝2V；
F ripple (x)＝c 1 sin(wx)+c 2 sin(3wx)+c 3 sin(5wx) (50)
in the formula (50), c 1 ＝3，c 2 ＝2，c 3 ＝1，w＝314rad/s；
Comparing the operation effect of the linear motor under the consideration of inequality constraint and the consideration of inequality constraint, when tracking sinusoidal signals, the amplitude of the selected sinusoidal signals is 0.1m, and the frequency is
The upper and lower limits of the constraint are +/-0.1 m, and the parameter K in the robust controller is considered when the inequality constraint is considered p ＝0.1，K ν =0.5, parameter K in robust controller without taking inequality constraints into account p ＝1， K ν =2; as shown in fig. 2, for tracking the linear motor position curve of the sinusoidal signal in consideration of the inequality constraint and in consideration of the inequality constraint, as shown in fig. 3, for tracking the linear motor position error curve of the sinusoidal signal in consideration of the inequality constraint and in consideration of the inequality constraint, as shown in fig. 4, for tracking the linear motor position and error curve of the step signal in consideration of the inequality constraint and in consideration of the inequality constraint. Experimental results show that when inequality constraints are considered, the control scheme can ensure that the displacement of the linear motor does not exceed a specified range, and errors are small. Regardless of the inequality constraints, the linear motor displacement may be outside of a specified range.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (5)
1. A robust bounded control method for a permanent magnet linear motor with inequality constraints is characterized by comprising the following specific steps:
1) Data acquisition: the position x of the permanent magnet linear motor to be controlled in operation is collected in real time, and the speed of the permanent magnet linear motor is obtained by utilizing differential operation
And acceleration
Acquiring collected data;
2) Constructing a dynamic model: establishing a dynamic modeling of the permanent magnet linear motor system according to the acquired data in the step 1);
3) Setting bounded control conditions: setting bounded control conditions of the permanent magnet linear motor system according to the dynamic modeling of the permanent magnet linear motor system in the step 2);
4) And (3) model state conversion: for position x and speed of permanent magnet linear motor
Acceleration of a vehicle
Performing state conversion to obtain a dynamic model after the permanent magnet linear motor system is converted;
5) Constructing a robust controller: and 4) controlling the system converted in the step 4) by adopting a robust bounded controller to obtain required control input, and inputting the control input into the original permanent magnet linear motor system to control the permanent magnet linear motor.
2. The robust bounded control method for the permanent magnet linear motor with the inequality constraints as recited in claim 1, wherein the specific method for establishing the dynamic modeling of the permanent magnet linear motor system in the step 2) is as follows:
establishing a dynamic model of the permanent magnet linear motor:
in the formula (1), the reaction mixture is,
is the speed of the linear motor or motors,
acceleration of the linear motor, μ being the control input, K e Is the back electromotive force of the linear motor, M is the inertial load and the mass of the coil assembly, F e Representing the uncertainty factor of the system, F e By a load F load Corrugation force F ripple Frictional force F fric External disturbance F d Comprises the following components:
F e ＝F load +F ripple +F fric +F d (3)
in the formula (2), m is the mass of the motion thrust block, R is the resistance between any two phases of the permanent magnet linear motor, and K f Representing the force generated by the motor;
in the formula (3), frictional force F fric Is a nonlinear function related to velocity, which can be modeled as:
in the formula (4), B is an equivalent viscous friction parameter,
comprises the following steps:
in the formula (5), f s Is the coefficient of static friction, f v Is a viscous friction coefficient, f c For a given coefficient of coulomb friction,
is a lubricant parameter;
the dynamic model of the permanent magnet linear motor can also be written as:
F e ＝F load +F ripple +F fricn +F d (7) 。
3. the robust bounded control method for the permanent magnet linear motor with inequality constraints as claimed in claim 2, wherein the specific method for setting the bounded control conditions for the permanent magnet linear motor in the step 3) is as follows:
setting a limiting condition:
|F load +F ripple +F d |<f lm (9)
in the formulae (8) and (9),
f fM 、f lm are all preset upper limit values, f fM For defining a friction force bound, f lm For determining F load 、F ripple 、F d Bounded by a sum;
and (8) obtaining the bound of the uncertainty of the permanent magnet linear motor through (8) and (9).
4. The robust bounded control method for the permanent magnet linear motor with the inequality constraints as recited in claim 3, wherein the specific method for dynamically converting the dynamic model in the step 4) is as follows:
the constraint of the stroke of the motor is x m <x<x M The control variable of the motor is y, wherein ∞<y<Infinity, then there are:
in formula (10), x m Is the lower bound, x, of the displacement of the permanent magnet linear motor M The displacement of the permanent magnet linear motor is an upper bound;
the formula (10) is reversely solved to respectively obtain the position x and the speed of the linear motor
Acceleration of a vehicle
The position x and the speed are measured
Acceleration of a vehicle
And substituting the kinetic equation into the kinetic equation to obtain the kinetic equation with y as a control variable:
5. the robust bounded control method of the permanent magnet linear motor with inequality constraints as claimed in claim 4, wherein the specific method for constructing the robust controller by the dynamically converted dynamic model in the step 5) is as follows:
calculating position tracking error e (t) and speed error of permanent magnet linear motor
e(t)＝y(t)-y d (t) (15)
In equations (15) and (16), y (t) is the actual position of the linear motor in the converted system, y d (t) is the desired position of the linear motor in the system after transformation;
order to
Then its robust controller is:
in the formula (15), the reaction mixture is,
comprises the following steps:
in the formulae (18) and (19),
to make the robust term for dealing with the uncertainty of a permanent magnet linear motor system,
for a given bounded function, S is a robust term control parameter, and epsilon is a real number determined by actual conditions;
define φ (e, e, t) as a function describing the system uncertainty, since it is bounded, i.e.
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| JP2000112528A (en) * | 1998-08-07 | 2000-04-21 | Yaskawa Electric Corp | Method for controlling position and speed of electric motor |
| CN105790661A (en) * | 2016-04-22 | 2016-07-20 | 江苏大学 | Linear permanent magnet vernier motor decoupling control method based on improved regression support vector machine generalized inverse |
| CN108123648A (en) * | 2017-11-30 | 2018-06-05 | 沈阳工业大学 | Linear servo Position Tracking Control based on linear matrix inequality and sliding formwork control |
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