CN116696735A - Linear compressor frequency control method and system based on terminal sliding mode observer - Google Patents
Linear compressor frequency control method and system based on terminal sliding mode observer Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04B—POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
- F04B49/00—Control, e.g. of pump delivery, or pump pressure of, or safety measures for, machines, pumps, or pumping installations, not otherwise provided for, or of interest apart from, groups F04B1/00 - F04B47/00
- F04B49/06—Control using electricity
- F04B49/065—Control using electricity and making use of computers
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- Compressors, Vaccum Pumps And Other Relevant Systems (AREA)
Abstract
The invention discloses a linear compressor frequency control method and a linear compressor frequency control system based on a terminal sliding mode observer, which belong to the technical field of linear compressor resonant frequency tracking control, and the method is characterized in that according to the characteristic that the piston stroke and current phase difference is 90 degrees when a linear compressor works at a system resonant frequency point, a stroke current product value filtering method is provided, stroke-current phase difference information is obtained by using stroke and current product calculation and a second-order low-pass filter, and is controlled to be 90 degrees, so that resonant frequency tracking control is realized; combining a second-order nonsingular terminal sliding mode and a variable index approach law, constructing a hybrid terminal sliding mode observer, and acquiring a travel estimation signal by adopting a second-order generalized integrator; the method can realize the piston stroke control without a position sensor and the resonant frequency tracking control, and has the advantages of small calculated amount, high tracking precision and the like.
Description
Technical Field
The invention belongs to the technical field of linear compressor resonant frequency tracking control, and particularly relates to a linear compressor frequency control method and system based on a terminal sliding mode observer.
Background
The linear compressor is a novel compressor driven by a linear oscillating motor, and can directly convert electric energy into linear motion without a mechanical conversion device. Compared with the traditional rotary compressor, the linear compressor has the advantages of simple structure, large thrust, high efficiency and the like, and is suitable for occasions needing reciprocating linear oscillation, such as artificial hearts, pumps, air compressors, refrigeration of refrigerators and the like.
The linear compressor is structurally characterized in that the linear compressor comprises a mechanical resonant spring, when the spring compresses gas force load in a cylinder, the whole system has a resonant frequency point, and the maximum output efficiency can be obtained when the motor operates at the frequency. To optimize motor operating efficiency, it is necessary to implement a high performance resonant frequency tracking control strategy for linear compressors. Based on the characteristic that the ratio of travel to current amplitude is the largest when the linear compressor operates at the resonance point, a scholars propose a maximum power point searching method, and resonance frequency tracking control under different working conditions can be realized. Still the scholars further combine the search method with fuzzy control, put forward a kind of input current or power minimum frequency tracking fuzzy control algorithm, this method simple in construction is easy to implement, but because the search process is constantly going on, easy to cause the running frequency to oscillate near the resonance point.
Since most of the resonant frequency tracking control methods are designed based on the characteristic relation between the travel and the current, the travel signal is critical to the resonant frequency tracking control, and the accuracy of the travel signal directly affects the tracking accuracy of the resonant frequency. In addition, the closed-loop control of the piston stroke requires a stroke signal, and the safe and reliable operation of the whole system is ensured by controlling the stroke. It is known that a mechanical sensor can be installed to obtain an accurate stroke signal, but the mechanical sensor is difficult to install and maintain, and has the problems of large system volume, high cost, reduced system reliability and the like. For this reason, researchers have studied the sensorless control of the linear compressor, and the back electromotive force integration method is one of the most widely used stroke estimation methods. However, the method is an open loop calculation method, and does not contain an error correction link, so that when the motor parameter changes, the estimation accuracy is greatly affected.
In conclusion, the existing method for tracking and controlling the resonance frequency of the linear compressor without the position sensor has the problems of low frequency tracking precision, easiness in stroke estimation affected by parameters, poor overall control performance of the system and the like.
Disclosure of Invention
Aiming at the defects and improvement demands of the prior art, the invention provides a linear compressor frequency control method and a linear compressor frequency control system based on a terminal sliding mode observer, which aim to acquire accurate piston stroke signals, accurately track the resonant frequency of a system and realize the resonant frequency tracking control without a position sensor.
In order to achieve the above object, according to one aspect of the present invention, there is provided a linear compressor frequency control method based on a terminal sliding mode observer, comprising the steps of:
s1, deforming a voltage equation of a linear oscillation motor to obtain a current state equation, observing the counter electromotive force of the motor by adopting a hybrid terminal sliding mode observer, wherein a sliding mode control law of the observer is constructed by adopting a second-order nonsingular terminal sliding mode surface and a variation index approach law;
s2, calculating a piston speed signal by utilizing the observed counter electromotive force according to the proportional relation between the counter electromotive force and the speed of the linear oscillation motor, and filtering the speed signal by adopting a second-order generalized integrator so as to obtain a stroke estimation signal;
s3, performing product calculation on the stroke estimation signal and the current signal acquired by the current sensor, and obtaining a direct current component existing in a product value by adopting a second-order low-pass filter;
s4, adjusting the direct current component to 0 by adopting a P controller, ensuring that the phase difference between the travel and the current is 90 degrees at the moment, accumulating the frequency variation in the adjustment process to the original operating frequency of the motor, and realizing the tracking control of the resonant frequency;
s5, the estimated stroke of the piston is also used for closed-loop control of the stroke, so that resonance frequency tracking control of the whole system without a position sensor is realized.
Further, the method of step S1 includes:
the linear compressor voltage equation is:
wherein R is a stator resistor, L is a stator inductance, u is a motor terminal voltage, i is a current, and e is a motor back electromotive force.
Further, the voltage equation is rewritten as a current state equation:
further, based on a current state equation, the constructed hybrid terminal sliding mode observer is as follows:
wherein ,to observe the current, u smo Is a sliding mode control law.
When the observed current is consistent with the actual current, the method can obtainThus, a hybrid terminal sliding mode observer is used to obtain the motor back emf signal.
Further, the second-order nonsingular terminal sliding mode surface is as follows:
the exponential approach law of variability is:
s＝-(λ+γ)|s| α sgn(s)-μs
the constructed higher order sliding mode control law is
u smo ＝u eq +u n
And, in addition, the method comprises the steps of,
wherein p, q, λ, γ, α, β, μ are design parameters;γ＞0，μ＞0，α∈(0,1)；s＝-(λ+γ)s α sgn(s) - μs is the exponential approach law of variability.
Further, the method of step S2 includes:
the relationship between back emf and speed is:
e＝K i v
wherein ,Ki Is the thrust coefficient.
Further, the velocity signal estimated by the hybrid terminal sliding mode observer can be obtained as
Further, an estimated travel signal can be obtained by filtering the estimated speed signal with a second-order generalized integratorThe transfer function expression is:
wherein a is an independent variable of G (a), v is an input signal, v' is a filtering signal, and ω c Is the cut-off frequency of the second order generalized integrator, and delta is the filter constant.
Further, the method of step S3 includes:
the linear compressor current signal expression is:
i(t)＝I p sin(ωt+θ)
wherein ,Ip Is the current peak.
The estimated piston travel signal expression is:
for convenience, the estimated travel signal is analyzed as a system real travel signal, namely:
x(t)＝X p sin(ωt)
wherein ,Xp Is the amplitude of the piston stroke.
Further, according to the expression of the stroke and the current, the product of the stroke-current signal is obtained as:
further, the alternating current component can be filtered out by using a low-pass filter, and the direct current component only containing the stroke current phase difference theta is reserved. The filter employed herein is a second order low pass filter whose transfer function is:
wherein ,ωh For cut-off filtering, ζ is the filter constant.
Further, the method of step S4 includes:
the direct current component is adjusted to 0 by a P controller, namely:
at this point, the piston travel is exactly 90 out of phase with the current signal.
Further, the frequency variation controlled by the P controller is accumulated to the original operating frequency of the motor, so that the system resonant frequency can be obtained, and the resonant frequency tracking control is realized.
Further, the piston stroke estimated in step S5 is also used for stroke closed-loop control. Thus, the method provided herein can achieve linear compressor sensorless resonant frequency tracking control.
The invention also provides a linear compressor frequency control system based on the terminal sliding mode observer, which comprises: a computer readable storage medium and a processor;
the computer-readable storage medium is for storing executable instructions;
the processor is used for reading executable instructions stored in the computer readable storage medium and executing the linear compressor frequency control method based on the terminal sliding mode observer.
In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:
(1) Compared with the prior art, the method for tracking and controlling the resonant frequency of the linear compressor has the advantages that the stroke estimation precision is greatly improved due to the fact that the piston stroke is estimated by the high-performance terminal sliding mode observer, the phase difference information between two signals can be directly obtained due to the fact that the second-order low-pass filter is adopted for filtering the stroke current product, and therefore tracking and controlling of the resonant frequency of the linear compressor are achieved, and the advantages of being small in calculated amount and high in tracking precision are achieved.
(2) Compared with the traditional sliding mode observer, the mixed sliding mode observer is adopted for observing the piston stroke signal, so that sliding mode buffeting can be greatly weakened, and stroke estimation accuracy is remarkably improved.
(3) Compared with the existing resonant frequency tracking method, the stroke current product value filtering method ensures the tracking precision, greatly reduces the calculated amount of the algorithm, and has simpler structure and easy realization.
(4) The hybrid terminal sliding mode observer is combined with the resonance frequency tracking method, so that the resonance frequency tracking control of the linear compressor without the position sensor with high performance can be realized.
Drawings
FIG. 1 is a block diagram of linear compressor frequency control based on a terminal sliding mode observer;
FIG. 2 is a piston travel estimation result based on a hybrid terminal sliding mode observer and a second-order generalized integrator;
fig. 3 is a graph showing the result of tracking the resonant frequency based on the travel current product value filtering method.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The invention provides a linear compressor frequency control method based on a terminal sliding mode observer, wherein a control system structure block diagram is shown in figure 1, and the method comprises the following steps:
s1, deforming a voltage equation of a linear oscillation motor to obtain a current state equation, designing a hybrid terminal sliding mode observer to observe back electromotive force information of the motor, wherein a second-order nonsingular terminal sliding mode surface and a variation index approach law are adopted to construct a high-order sliding mode observer;
specifically, the voltage equation of the linear oscillating motor is
The voltage equation is rewritten as the current equation
Based on a current state equation, the constructed sliding mode observer of the hybrid terminal is as follows
The adopted second-order nonsingular terminal sliding mode surface is
Change the index approach law to
s＝-(λ+γ)s α sgn(s)-μs
The constructed higher order sliding mode control law is
u smo ＝u eq +u n
And, in addition, the method comprises the steps of,
s2, calculating a piston speed signal by utilizing the observed electromotive force according to the proportional relation between the counter electromotive force and the speed of the linear oscillation motor, and filtering the speed signal by adopting a second-order generalized integrator so as to obtain a stroke estimation signal;
specifically, the relationship between back emf and speed is:
e＝K i v
the speed signal estimated by the hybrid terminal sliding mode observer is
The transfer function of the adopted second-order generalized integrator is
S3, performing product calculation on the estimated travel signal and the current signal acquired by the current sensor, and obtaining a direct current component existing in a product value by adopting a second-order low-pass filter;
specifically, the linear compressor current signal expression is:
i(t)＝I p sin(ωt+θ)
the estimated piston travel signal expression is:
conveniently, the estimated travel signal is analyzed as a system true travel signal, i.e
x(t)＝X p sin(ωt)
From the expression of the stroke and the current, the product of the stroke-current signal can be obtained as
The transfer function of the adopted second-order low-pass filter is
S4, adjusting the direct current component to 0 by adopting a P controller, ensuring that the phase difference between the travel and the current is 90 degrees at the moment, and accumulating the frequency variation in the adjustment process to the original operating frequency of the motor to obtain the tracking control of the resonant frequency;
specifically, the P controller is used to adjust the dc component to 0, namely:
at this point, the piston travel is exactly 90 out of phase with the current signal. The frequency variation controlled by the P controller is accumulated to the original operating frequency of the motor, so that the system resonant frequency can be obtained, and the resonant frequency tracking control is realized.
S5, the estimated piston stroke is also used for stroke closed-loop control, so that resonance frequency tracking control of the whole system without a position sensor is realized;
s6, using the estimated piston stroke signal for product calculation and piston stroke closed-loop control of a resonant frequency tracking method, thereby realizing the resonant frequency tracking control without a position sensor.
Examples:
in the embodiment, the linear compressor driven by the linear oscillation motor is taken as an example, the simulation verification is carried out on the method, the rated power is set to be 120W, the system resonant frequency is 23Hz, the stator resistance is 18.4Ω, the stator inductance is 0.755H, the thrust coefficient is 30N/A, and the mass of the rotor piston is 1.03kg.
The piston stroke reference amplitude was set at 5mm and the initial operating frequency was 20.5Hz. As shown in fig. 2, the proposed hybrid terminal sliding mode observer is able to accurately estimate the piston stroke signal. As shown in fig. 3, the proposed resonant frequency tracking method can accurately track the resonant frequency of the system.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (9)
1. The linear compressor frequency control method based on the terminal sliding mode observer is characterized by comprising the following steps of:
s1, deforming a voltage equation of a linear oscillation motor to obtain a current state equation, observing the counter electromotive force of the motor by adopting a hybrid terminal sliding mode observer, wherein a sliding mode control law of the observer is constructed by adopting a second-order nonsingular terminal sliding mode surface and a variation index approach law;
s2, calculating a piston speed signal by utilizing the observed electromotive force according to the proportional relation between the counter electromotive force and the speed of the linear oscillation motor, and filtering the speed signal by adopting a second-order generalized integrator so as to obtain a stroke estimation signal;
s3, performing product calculation on the travel estimation signal and the current signal acquired by the current sensor to obtain a direct current component in a product value;
s4, adjusting the direct current component to 0 by adopting a P controller, ensuring that the phase difference between the travel and the current is 90 degrees at the moment, accumulating the frequency variation in the adjustment process to the original operating frequency of the motor, and realizing the tracking control of the resonant frequency.
2. The control method according to claim 1, wherein the motor voltage equation in step S1 is:
wherein R is a stator resistor, L is a stator inductor, u is a motor terminal voltage, i is a current, and e is a motor back electromotive force;
the voltage equation is rewritten as a current equation:
based on a current state equation, the constructed hybrid terminal sliding mode observer is as follows:
wherein ,to observe the current, u smo Is a sliding mode control law;
the second-order nonsingular terminal sliding mode surface is as follows:
the exponential approach law of variability is:
s＝-(λ+γ)|s| α sgn(s)-μs
the constructed high-order sliding mode control law is as follows:
u smo ＝u eq +u n
and, in addition, the method comprises the steps of,
wherein p, q, λ, γ, α, β, μ are design parameters;γ＞0，μ＞0，α∈(0,1)；s＝-(λ+γ)|s| α sgn(s) - μs is the exponential approach law of variability.
3. The control method according to claim 2, wherein the piston speed signal in step S2 is:
wherein ,Ki Is the thrust coefficient.
4. A control method according to claim 3, characterized in that the estimated speed signal is filtered using a second-order generalized integrator, the transfer function of which is expressed as:
wherein a is an independent variable of G (a), v is an input signal, and v' is a filtering signalNumber, omega c Is the cut-off frequency of the second order generalized integrator, and delta is the filter constant.
5. The control method according to claim 1, characterized in that the step S3 includes:
the linear compressor current signal expression is:
i(t)＝I p sin(ωt+θ)
wherein ,Ip Is the current peak;
the piston estimated stroke signal expression of (2) is:
analyzing the travel estimation signal as a system true travel signal, i.e
x(t)＝X p sin(ωt)
According to the expression of the stroke and the current, the product of the stroke-current signal can be obtained as follows:
wherein ,Xp Is the amplitude of the piston stroke.
6. The control method according to claim 5, wherein a second-order low-pass filter is used to obtain a direct current component present in the product value, and the transfer function is:
wherein ,ωh For cut-off filtering, ζ is the filter constant.
7. The control method according to claim 5, characterized in that said step S4 includes:
the direct current component is adjusted to 0 by a P controller, namely:
at the moment, the phase difference between the piston stroke and the current signal is exactly 90 degrees, the frequency variation controlled by the P controller is accumulated to the original operating frequency of the motor, the system resonant frequency can be obtained, and the resonant frequency tracking control is realized.
8. The control method according to claim 1, wherein the stroke estimation signal is also used for a stroke closed-loop control, thereby realizing a sensorless resonant frequency tracking control of the entire system.
9. A linear compressor frequency control system based on a terminal sliding mode observer, comprising: a computer readable storage medium and a processor;
the computer-readable storage medium is for storing executable instructions;
the processor is configured to read executable instructions stored in the computer readable storage medium and execute the linear compressor frequency control method based on the terminal sliding mode observer according to any one of claims 1 to 8.
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