CN111473049B - Control method for solid stator magnetic suspension exciting current - Google Patents
Control method for solid stator magnetic suspension exciting current Download PDFInfo
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- CN111473049B CN111473049B CN202010306367.1A CN202010306367A CN111473049B CN 111473049 B CN111473049 B CN 111473049B CN 202010306367 A CN202010306367 A CN 202010306367A CN 111473049 B CN111473049 B CN 111473049B
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C32/00—Bearings not otherwise provided for
- F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
- F16C32/0406—Magnetic bearings
- F16C32/044—Active magnetic bearings
- F16C32/0444—Details of devices to control the actuation of the electromagnets
- F16C32/0457—Details of the power supply to the electromagnets
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- Electromagnetism (AREA)
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- General Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Magnetic Bearings And Hydrostatic Bearings (AREA)
Abstract
A control method of magnetic suspension exciting current of a solid stator comprises the following steps: (1) using FO [ PI ] as core controller to build exciting current control system; (2) deriving a mathematical model of the controlled object; (3) according to the fractional calculus theory, further deducing the amplitude-phase characteristics of the controlled object; (4) deducing the amplitude-phase characteristics of other parts of the control system; (5) the amplitude-phase characteristics of each link in the control system are obtained through the steps, and the amplitude-phase characteristics of the open-loop transfer function of the whole control system can be comprehensively obtained; (6) a simultaneous equation set is used for solving three control parameters of Kp, Ki and lambda in the controller, so that ideal current control performance can be obtained; the controller coefficient is solved according to three conditions that the designed cutoff frequency, stability margin and phase angle transformation rate of the cutoff frequency are zero, and the obtained control system has better control performance compared with the traditional PI controller and is more suitable for magnetic suspension system current control of a solid stator structure.
Description
Technical Field
The invention belongs to the technical field of magnetic suspension bearings, and particularly relates to a control method of magnetic suspension exciting current of a solid stator.
Background
The magnetic suspension bearing (active magnetic suspension bearing) is a new type of bearing which suspends the rotor in a non-contact manner through the magnetic field force between the stator core and the rotor core. It combines the knowledge of many subjects such as rotor dynamics, mechanical design, control theory, power electronics, electromagnetism, computer test technology and signal processing technology, and is a typical electromechanical integrated product. Due to the absence of mechanical contact, it has the following significant advantages over conventional mechanical bearings: the requirement on the working environment is not high; the rotor is free from contact and mechanical friction, and the magnetic suspension bearing does not need a lubricating and sealing system; the service life is longer; because of no mechanical friction, the mechanical contact stress fatigue life of the magnetic suspension bearing is much longer than that of a mechanical bearing; the running speed is high; the rotor and the stator are not in contact, the theoretically highest rotating speed of the magnetic suspension bearing depends on the strength of a rotor material, and therefore the circumferential linear speed of the rotor is much higher than that of the rotor supported by a mechanical bearing; the operation efficiency is high; compared with a mechanical bearing, the power consumption of the magnetic suspension bearing is reduced to 1/10-1/100.
The stator structure of the magnetic suspension bearing adopts a pair of differential electromagnets to control the movement of a rotor in a certain direction, the principle is that a displacement sensor is used for detecting the offset of the magnetic suspension rotor relative to a balance position, and a controller controls a magnetic suspension power amplifier according to the detected offset to generate exciting current so as to generate electromagnetic force, so that the rotor always floats at the balance position. The key for ensuring the stable suspension of the magnetic suspension rotor is to control the electromagnet to accurately generate control current.
The control of the magnetic suspension current can be equivalent to the control of the exciting current of the magnetic suspension electromagnet through a power amplifier, the essence is that the electromagnet is equivalent to a resistance-inductance load to carry out closed-loop control on the current, and the principle and the related technology are mature. In actual industrial products, the stator of the magnetic suspension electromagnet generally adopts a lamination process to reduce eddy current loss, but the lamination process is complicated in procedure, and in addition, because the magnetic suspension bearing has extremely high precision requirement, the laminated stator generally needs to be subjected to secondary processing, so that the production efficiency is reduced, and the magnetic suspension equipment is difficult to produce in quantity. The solid structure can generate a larger eddy current effect, the effect enables the magnetic resistance of the ferromagnetic material to change along with the frequency, and for a current control loop, the load inductance is changed into a time-varying parameter, so that the performance of the original current control loop is greatly influenced.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a method for controlling a solid stator magnetic levitation exciting current, which is used for realizing high performance control of the exciting current of the solid stator structure, aiming at the above defects of the prior art.
The invention aims to complete the technical scheme that a method for controlling the magnetic suspension exciting current of a solid stator comprises the following steps:
(1) establishing an excitation current control system by taking FO [ PI ] as a core controller, wherein the current control system comprises an FO [ PI ] controller, a PWM (pulse-width modulation) modulator, a power amplifier mathematical model and an electromagnet model which are sequentially connected in a signal manner and form a main circuit, and a current transformer and a low-pass filter which are arranged on the main circuit and realize current feedback;
(2) deriving a mathematical model of the controlled object as follows:
in each coefficient in the formula, N is the number of turns of the coil, R is the winding resistance, the two values can be directly measured, and R is0And RtTwo coefficients, representing the reluctance of the magnetic circuit, can be calculated by the following equation:
in the formula, mu 0 is vacuum magnetic conductivity, mu r is relative magnetic conductivity using ferromagnetic materials, lm is effective length of a magnetic circuit, A is area of a magnetic pole, and b is width of the magnetic pole, and a solid stator electromagnet mathematical model considering eddy current effect can be calculated through the coefficients;
(3) according to the fractional calculus theory, s in the formula (1)1/2Equivalent is the following form:
the controlled object amplitude-phase characteristics | G2(j ω) | and Arg [ G2(j ω) ] can be further deduced by taking the formula (4) into the formula (1);
(4) deducing the amplitude-phase characteristics of other parts of the control system, wherein the mathematical models of the PWM modulator and the power amplifier can be equivalent to a voltage amplification coefficient Kv, the current transformer can be equivalent to a gain amplification coefficient Ks, and the equivalent transfer function of the low-pass filtering link is as follows:
wherein T is the time constant of the low-pass filter;
(5) the transfer function of FO [ PI ] is as follows:
the expression of the amplitude-phase characteristics can be derived as follows:
obtaining the amplitude-phase characteristics of each link in the control system through the steps, and comprehensively obtaining the amplitude-phase characteristics | GH (j omega) | and Arg [ GH (j omega) ] of the open-loop transfer function of the whole control system;
(6) designing cut-off frequency ω c and phase angle margin of control system
Designing an optimization target:
|GH(jωc)|＝0
Arg[GH(jω)]＝-π+φm
the three equations are combined, and the three control parameters Kp, Ki and lambda in the controller are solved, so that the ideal current control performance can be obtained.
The invention has the beneficial technical effects that: the invention provides a fractional order-based current control strategy aiming at the structure of the solid stator and provides a parameter design principle thereof, the addition of a fractional order control coefficient lambda ensures that a controller can provide more ideal frequency characteristics, and better current control performance can be obtained aiming at a fractional order controlled object.
Drawings
Fig. 1 is a schematic diagram of a magnetic suspension bearing exciting current control system according to the invention.
In the figure: 1. FO [ PI ] controller for current control, 2, PWM modulator, 3, power amplifier mathematical model, 4, electromagnet model, 5, current transformer, 6, low pass filter.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clearly understood by those skilled in the art, the present invention is further described with reference to the accompanying drawings and examples.
When the stator of the magnetic suspension bearing adopts a laminated structure, the electromagnet can be equivalent to a simple resistance-inductance load, and the transfer function of the electromagnet can be expressed by a first-order inertia link as follows:
in the formula, L is an equivalent inductance of the electromagnet, R is a winding resistance, and s is a laplace operator (s ═ j ω). The controlled object can be corrected by a PI (proportional integral) controller, so that the output current can obtain better precision and dynamic performance.
However, when a solid stator structure is used, the eddy current effect in the magnetic circuit cannot be ignored, and the equivalent transfer function can be derived as follows:
where N is the number of winding turns, R is the winding resistance, s is the Laplace operator, R0 is the static reluctance of the electromagnet circuit (depending primarily on the air gap size), and Rt · s1/2 is the dynamic reluctance, which is frequency dependent. It can be seen that considering that the transfer function of the solid stator becomes a fractional order system under the influence of the eddy current effect, the general PI controller is difficult to achieve a good control effect.
Referring to FIG. 1: the invention relates to a control method of magnetic suspension exciting current of a solid stator, which comprises the following steps:
(1) the method comprises the steps that an excitation current control system is established by taking FO [ PI ] as a core controller, and the current control system comprises an FO [ PI ] controller 1, a PWM (pulse-width modulation) 2, a power amplifier mathematical model 3, an electromagnet model 4, a current transformer 5 and a low-pass filter 6 which are arranged on a main circuit and used for realizing current feedback, wherein the FO [ PI ] controller 1, the PWM 2, the power amplifier mathematical model 3 and the electromagnet model 4 are sequentially in signal connection and form the main circuit;
the current control system uses a fractional order FO [ PI ] controller to achieve the purpose of controlling the excitation current, the mathematical form of FO [ PI ] controller 1 is as follows:
in the formula, Kp is a proportional coefficient of the controller, Ki is an integral coefficient, and lambda belongs to [0,2] as any real number.
A closed-loop control system is constructed based on the FO [ PI ], as shown in figure 1, the input of the system is a given value of magnetic suspension control current, the given value is different from a feedback value, and an error is obtained through an amplifying structure of the FO [ PI ] controller through PWM modulation to obtain a switch control signal to control the on-off of a main circuit of a power amplifier to realize current feedback control, so that the output current tracks the given value of the current.
(2) Deriving a mathematical model of the controlled object as follows:
in each coefficient in the formula, N is the number of turns of the coil, R is the winding resistance, the two values can be directly measured, and R is0And RtTwo coefficients, representing the reluctance of the magnetic circuit, can be calculated by the following equation:
in the formula, mu 0 is vacuum magnetic conductivity, mu r is relative magnetic conductivity using ferromagnetic materials, lm is effective length of a magnetic circuit, A is area of a magnetic pole, and b is width of the magnetic pole, and a solid stator electromagnet mathematical model considering eddy current effect can be calculated through the coefficients;
(3) according to the fractional calculus theory, s in the formula (1)1/2Equivalent is the following form:
the controlled object amplitude-phase characteristics | G2(j ω) | and Arg [ G2(j ω) ] can be further deduced by taking the formula (4) into the formula (1);
(4) deducing the amplitude-phase characteristics of other parts of the control system, wherein the PWM modulator 2 and the power amplifier mathematical model 3 can be equivalent to a voltage amplification coefficient Kv, the current transformer 5 can be equivalent to a gain amplification coefficient Ks, and the low-pass filtering link equivalent transfer function is as follows:
wherein T is the time constant of the low-pass filter 6;
(5) the transfer function of FO [ PI ] is as follows:
the expression of the amplitude-phase characteristics can be derived as follows:
obtaining the amplitude-phase characteristics of each link in the control system through the steps, and comprehensively obtaining the amplitude-phase characteristics | GH (j omega) | and Arg [ GH (j omega) ] of the open-loop transfer function of the whole control system;
(6) designing cut-off frequency ω c and phase angle margin of control system
Designing an optimization target:
|GH(jωc)|＝0
Arg[GH(jω)]＝-π+φm
the three equations are combined, and the three control parameters Kp, Ki and lambda in the controller are solved, so that the ideal current control performance can be obtained. The control method of the invention aims at the characteristic that the eddy current effect of the solid stator structure causes the load inductance to change along with the frequency, the FO [ PI ] controller is used as the core to construct the closed-loop current control system, the controller parameter is designed to deduce the amplitude-phase characteristic of the whole open-loop system according to the fractional order model of the controlled object, and the controller coefficient is solved according to the three conditions that the designed cut-off frequency, stability margin and phase angle transformation rate of the cut-off frequency are zero, the obtained control system has better control performance than the traditional PI controller, and is more suitable for the current control of the magnetic suspension system of the solid stator structure.
The specific embodiments described herein are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.
Claims (1)
1. A control method of magnetic suspension exciting current of a solid stator is characterized in that: the method comprises the following steps:
(1) establishing an excitation current control system by taking FO [ PI ] as a core controller, wherein the current control system comprises an FO [ PI ] controller, a PWM (pulse-width modulation) modulator, a power amplifier mathematical model and an electromagnet model which are sequentially connected in a signal manner and form a main circuit, and a current transformer and a low-pass filter which are arranged on the main circuit and realize current feedback;
(2) deriving a mathematical model of the controlled object as follows:
in each coefficient in the formula, N is the number of turns of the coil, R is the winding resistance, the two values are directly measured, and R is measured0And RtTwo coefficients represent the reluctance of the magnetic circuit, where R0Is static magnetoresistance, RtFor dynamic magnetoresistance, s is the laplace operator; can be calculated by the following formula:
where μ 0 is a vacuum permeability, μ r is a relative permeability using a ferromagnetic material, lm is an effective length of a magnetic path, A is a magnetic pole area, b is a half of an iron core width, and δ0As regards the length of the air gap,
wherein σ represents the electrical conductivity of the core material; calculating a solid stator electromagnet mathematical model considering the eddy current effect according to the coefficients;
(3) according to the fractional calculus theory, s in the formula (1)1/2Equivalent is the following form:
s ═ j ω is a correspondence relationship between laplace transform and fourier transform, s is a complex frequency, and ω frequency is a real number; carrying out formula (4) into formula (1) to further derive controlled object amplitude-phase characteristics | G2(j ω) | and Arg [ G2(j ω) ];
(4) deducing the amplitude-phase characteristics of other parts of the control system, wherein the mathematical models of the PWM modulator and the power amplifier are equivalent to a voltage amplification coefficient Kv, the current transformer is equivalent to a gain amplification coefficient Ks, and the equivalent transfer function of the low-pass filtering link is as follows:
wherein T is the time constant of the low-pass filter;
(5) the transfer function of FO [ PI ] is as follows:
the expression of the amplitude-phase characteristics is derived as follows:
in the formula, Kp、KiIs a proportional coefficient and an integral coefficient in the controller; λ is the order of the fractional order; the amplitude-phase characteristics of each link in the control system are obtained through the steps, and the amplitude-phase characteristics | GH (j omega) | and Arg [ GH (j omega) of the open-loop transfer function of the whole control system are comprehensively obtained]；
(6) Designing cut-off frequency ω c and phase angle margin φ of control systemmDesigning an optimization target:
|GH(jωc)|＝0
Arg[GH(jω)]＝-π+φm
the three equations are combined, and the three control parameters Kp, Ki and lambda in the controller are solved, so that the ideal current control performance can be obtained.
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