CN114002953A - Adaptive notch sliding mode differentiator method for maglev train signal processing - Google Patents
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Abstract
The invention relates to a self-adaptive notch sliding mode differentiator method for maglev train signal processing. The method comprises the following steps: s1, designing a new adaptive trap to input signal
Amplitude of
Sum frequency
Performing robust real-time estimation; s2, inputting the estimated result into a differentiator parameter setting formula, and determining the adjusting parameter of the sliding mode differentiator through the differentiator parameter setting formula; and the obtained adjustment parameters of the sliding mode differentiator are fed back to the sliding mode differentiator in real time, so that the parameters of the sliding mode differentiator can be adjusted on line in real time according to the change of the input signal, and the method adapts to the real-time changeA signal. The invention provides a novel sliding mode differentiator signal processing framework and algorithm based on a novel self-adaptive notch filter, which are used for acquiring effective gap tracking filtering signals and vertical speed signals, are applied to an actual running line of a magnetic suspension train and can effectively improve the stability of a train suspension system.
Description
Technical Field
The invention relates to a self-adaptive notch sliding mode differentiator method for maglev train signal processing.
Background
The magnetic suspension train suspends the train on the track through the electromagnetic module, changes traditional wheel rail operation mode, possesses advantages such as fast, later stage operation maintenance cost is low, green, and has become a neotype track traffic mode. The suspension system of the magnetic suspension train is a key subsystem for realizing stable suspension of the train. The system adopts gap signals, vertical speed signals between a track and an electromagnet and current signals to realize closed-loop feedback control, and the feedback signals are respectively provided by a gap sensor, integral of signals of an acceleration sensor and a current transformer. There are two ways in which vertical velocity signals can be acquired: one is that an acceleration sensor is loaded on a train and is obtained through an integral circuit or a software integral algorithm; the other is to use the acquired gap signal to be acquired by a differentiator. The acceleration sensor is expensive, large in size and bad in position and working condition of installation and transportation, and most importantly, the acceleration sensor is used for processing low-frequency signals with a certain frequency band, so that the speed signals integrated by the signals have a large phase lag phenomenon, and the stability of the suspension control system at low frequency is influenced. In particular, the integration of the accelerometer signal does not correctly extract an effective vertical velocity signal when the maglev train is passing a track seam, loading, climbing and turning. Therefore, the second approach is adopted, namely, a differentiator algorithm is used for acquiring the speed signal from the gap sensor signal, so that the method not only saves the cost of purchasing sensor equipment by the train, but also reduces the risks that the acceleration sensor is in failure and cannot effectively acquire the speed signal corresponding to the low-frequency signal.
Since a pure differentiator is physically impossible to realize, researchers try to find various ways to approximate a differentiated signal, and improper processing may generate oscillation and even annihilation phenomena, which affect the stability of the system. A differentiator with superior performance needs to be able to obtain an effective filtered and differentiated signal under two conditions, first, when the frequency bandwidth of a given signal changes; second, when random noise interference of different strengths is present for a given signal. The effective filtering and differential signal mainly shows two aspects, firstly, the tracking error of the tracking filtering and differential signal meets the requirement of an actual system; second, the tracking filter has as little phase lag as possible from the differentiated signal compared to the given signal.
Differentiator algorithms can be roughly divided into two categories: a linear differentiator and a non-linear differentiator. Compared with a linear differentiator, the nonlinear differentiator has high parameter utilization rate and better solves the contradiction between rapidity and overshoot. For non-linear differentiators, there are mainly two more well-recognized methods: a robust accurate differentiator based on sliding mode control and a tracking differentiator algorithm based on time optimal control.
Levant (1993) provides a sliding mode differentiator which can effectively extract the differentiation of a signal and is applied to sliding mode control, so that a system can realize robust and stable tracking control under the conditions of disturbance and uncertainty. The differentiator is a double sliding mode algorithm and a continuous differential algorithm, but has no corresponding boundary strategy in a discrete form, and has great defects in differential signal extraction in the presence of noise when the frequency band of an input signal changes, slow dynamic process and overshoot phenomenon. Then, Utkin et al deeply researches a Levant differentiator, and applies the sliding mode differentiator to the sliding mode controller design and the sliding mode observer design of a multivariable control system. However, the sliding mode differentiator has a serious problem that the dynamic process is slow and the flutter phenomenon is very prominent, the control quantity requires high-frequency adjustment, which is unacceptable for an actual control system, the high-frequency change means large energy consumption, the high-frequency micro-amplitude oscillation of the tracking signal means serious abrasion of a mechanical device, and the like.
In order to overcome the problem of high-frequency flutter of the traditional differentiator, Korean Kyoto is based on the thought of bang-bang control, and the concept of boundary layer transformation is provided from the problem of minimum time in optimal control, and a nonlinear tracking differentiator algorithm is introduced. On the basis, some scholars intensively study the closed-loop state feedback problem in a discrete time optimal control system, and point out that a linear boundary layer obtained by the algorithm mode of a Hanjing clear tracking differentiator can replace bang-bang control, and the tracking differentiator can enable a control quantity to change according to a linear rule in the bounded region instead of jumping between two extreme quantities, so that the flutter problem can be overcome. However, because of the boundary layer, when there is a certain noise in the signal, the differentiator will have a large phase lag in processing the signal.
The gap and acceleration signals of the sensor group collection system of the magnetic suspension train participate in the design of a feedback controller of the suspension system. The closed loop feedback control scheme employs a PID controller, wherein velocity signal feedback plays an important role in suppressing overshoot. However, the speed signal obtained by re-integrating the signal measured by the acceleration sensor is severely delayed in phase, sometimes even because the speed signal is invalid due to a change in the operating condition. Therefore, it is important to design an effective differentiator to obtain an effective gap signal and its velocity signal. The signal of the magnetic suspension train gap sensor shows the following characteristics along with the change of the train running process: 1) the frequency bandwidth of the signal is large and may vary from 2Hz to 300 Hz; 2) the signal is doped with random noise of varying intensity. In order to better process a gap signal of a magnetic suspension system, namely the signal frequency has a certain frequency band and is doped with high-frequency random noise, and finally stable suspension of a magnetic suspension train is realized, the invention provides a novel sliding mode differentiator signal processing framework and algorithm based on a self-adaptive notch filter, which are used for acquiring an effective gap tracking filtering signal and a vertical speed signal.
Disclosure of Invention
The invention aims to provide a self-adaptive notch sliding mode differentiator method for maglev train signal processing, aiming at a self-adaptive notch filter, firstly introducing integral feedback of system errors into a cost function structure, constructing a novel self-adaptive notch filter through an optimization method, and estimating the frequency and amplitude of signals in real time; and then, the estimated signal characteristics are used as the input of the sliding mode differentiator algorithm to carry out the adaptive setting of the parameters of the algorithm, and a novel sliding mode differentiator based on an adaptive notch filter is provided.
In order to achieve the purpose, the technical scheme of the invention is as follows: a self-adaptive notch sliding mode differentiator method for maglev train signal processing comprises the following steps:
step S1, designing a novel adaptive notch filter to perform robust real-time estimation on the amplitude A (t) and the frequency w (t) of the input signal f (t);
step S2, inputting the estimated result into a differentiator parameter setting formula, wherein the differentiator parameter setting formula gives the quantity relation between the sliding mode differentiator parameter and the amplitude and frequency of the signal, and the adjusting parameter of the sliding mode differentiator is determined through the differentiator parameter setting formula; and feeding back the obtained adjusting parameters of the sliding mode differentiator to the sliding mode differentiator in real time, so that the parameters of the sliding mode differentiator can be adjusted on line in real time according to the change of the input signal, and the signal which changes in real time is adapted.
In an embodiment of the present invention, the step S1 is specifically implemented as follows:
signal f (t) ═ f of the frequency conversion amplitude for any given noise η (t) doping0(t) + η (t), where the base signal is f0(t)＝A0sin(w0t+δ0) Amplitude A in this base signal0Frequency w0And phase delta0Are all unknown parameters, and have an amplitude A0And frequency w0Is time-varying;
now design a new adaptive notch filter to estimate the fundamental signal f0(t) making its estimation signal y (t) a (t) sin (phi (t)), wherein
Then, an error is obtained of
e(t)＝f(t)-y(t)＝f(t)-A(t)sin(φ(t))
In order to better eliminate the static error of the signal estimation and obtain a more accurate estimation value, an integral term of an error is introduced into the construction of the cost function, namely the newly constructed cost function has the following form:
wherein Θ is [ a (t), w (t), δ (t)]TIs a state quantity, k1Not less than 0 and k2More than or equal to 0 is two adjustable constants; according to the gradient descent method, a novel adaptive trap is obtained, and the structure of the adaptive trap is as follows:
y(t)＝A(t)sin(φ(t))
wherein A (t), w (t) and phi (t) are base signals f0(t) estimated values of amplitude, frequency and phase angle, mu1，μ2，μ3，k1And k2Is a tunable parameter, in which
In the form of
In an embodiment of the present invention, the step S2 is specifically implemented as follows:
the outputs a (t) and w (t) of the novel adaptive notch filter of step S1 are used to update the parameters of the sliding mode differentiator in real time, that is, the structure of the sliding mode differentiator based on the adaptive notch filter is designed as follows:
wherein f (t) is an input signal which is unknown time-varying and doped with random noise, and output y (t) is a basic signal f0(t) estimation of the state variable y1(t) and y2(t) the expected trajectory of the input and its derivative, respectively, sign (·) is a sign function, μ1，μ2，μ3，k1And k2Is an adjustable parameter, and λ (t) and α (t) are adaptive parameters.
The invention also provides an adaptive notch sliding mode differentiator device for maglev train signal processing, which comprises a memory, a processor and computer program instructions stored on the memory and capable of being operated by the processor, wherein when the computer program instructions are operated by the processor, the method steps can be realized.
Compared with the prior art, the invention has the following beneficial effects: the invention provides a novel sliding mode differentiator signal processing framework and algorithm based on a novel self-adaptive notch filter, which are used for acquiring effective gap tracking filtering signals and vertical speed signals, are applied to an actual running line of a magnetic suspension train and can effectively improve the stability of a train suspension system.
Drawings
Fig. 1 shows an algorithm structure of a sliding mode differentiator based on an adaptive notch filter.
Fig. 2 is a comparison of signal tracking filtering of the present invention ANF-SMD with a conventional differentiator.
Fig. 3 is a comparison of signal differential acquisition of the ANF-SMD proposed by the present invention and a conventional differentiator.
FIG. 4 is a diagram illustrating the adaptive adjustment process of parameters λ (t) and α (t) of ANF-SMD according to the present invention.
Fig. 5 shows the result of the tracking filter of the signal processing of the magnetic levitation system.
Fig. 6 shows the differential acquisition result of the signal processing of the magnetic levitation system.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
As shown in fig. 1, the adaptive notch sliding mode differentiator method for magnetic-levitation train signal processing of the present invention comprises the following steps:
step S1, designing a novel adaptive notch filter to perform robust real-time estimation on the amplitude A (t) and the frequency w (t) of the input signal f (t);
step S2, inputting the estimated result into a differentiator parameter setting formula, wherein the differentiator parameter setting formula gives the quantity relation between the sliding mode differentiator parameter and the amplitude and frequency of the signal, and the adjusting parameter of the sliding mode differentiator is determined through the differentiator parameter setting formula; and feeding back the obtained adjusting parameters of the sliding mode differentiator to the sliding mode differentiator in real time, so that the parameters of the sliding mode differentiator can be adjusted on line in real time according to the change of the input signal, and the signal which changes in real time is adapted.
The following is a specific implementation process of the present invention.
Fig. 1 shows an algorithm framework of a sliding mode differentiator based on an adaptive notch filter. The input signal f (t) to be processed has the characteristics of large frequency bandwidth, doping random noise with different intensities and the like. The algorithm structure of the sliding mode differentiator based on the adaptive notch filter is described as follows: a novel self-adaptive wave trap is designed to carry out robust real-time estimation on the amplitude A (t) and the frequency w (t) of an input signal f (t), and then the estimated result is input into a parameter setting formula of a differentiator, wherein the parameter setting formula gives the quantity relation between the parameter of the sliding mode differentiator and the amplitude and the frequency of the signal. Therefore, the adjusting parameters of the sliding mode differentiator can be directly determined through the frame. And then feeding back the obtained parameters to the sliding mode differentiator in real time, so that the parameters of the sliding mode differentiator can be adjusted on line in real time according to the change of the input signal, thereby adapting to the signal changing in real time.
Specifically, the present invention adopts an algorithm structure as follows:
the method comprises the following steps: designing adaptive notch filter
Signal f (t) ═ f of the frequency conversion amplitude for any given noise η (t) doping0(t) + η (t), where the base signal is f0(t)＝A0sin(w0t+δ0) Amplitude A in this base signal0Frequency w0And phase delta0Are all unknown parameters, and have an amplitude A0And frequency w0Is time-varying.
An adaptive notch filter is now designed to estimate the base signal f0(t) the estimated signal is not set to y (t) ═ a (t) sin (phi (t)), where
Then, an error of
e(t)＝f(t)-y(t)＝f(t)-A(t)sin(φ(t)).
When a traditional wave trap is used for estimating signals, the static error cannot be avoided, in order to better eliminate the static error estimated by the signals and obtain a more accurate estimated value, the patent firstly introduces an integral term of an error into the construction of a cost function of an optimization method, namely, the newly constructed cost function has the following form:
wherein Θ is [ a (t), w (t), δ (t)]TIs a state quantity, k1Not less than 0 and k2≧ 0 is two tunable constants. According to the gradient descent method, a novel adaptive notch filter can be obtained, and the structure of the adaptive notch filter is as follows:
y(t)＝A(t)sin(φ(t))
wherein A (t), w (t) and phi (t) are base signals f0(t) estimated values of amplitude, frequency and phase angle, mu1，μ2，μ3，k1And k2Is a tunable parameter, in which
In the form of
Step two: sliding mode differentiator based on adaptive notch filter
Based on the adaptive notch filter proposed above, an adaptive sliding mode differentiator capable of processing an unknown time-varying and doped random noise signal f (t) is designed. The outputs a (t) and w (t) of the proposed adaptive notch filter are used to update the parameters of the sliding mode differentiator in real time. Based on the idea, the structure of the sliding mode differentiator based on the adaptive notch filter is as follows:
wherein f (t) is an input signal which is unknown time-varying and doped with random noise, and output y (t) is a basic signal f0(t) estimation of the state variable y1(t) and y2(t) is the desired trajectory of the input and its derivative, respectively. sign () is a common sign function in mathematics. Mu.s1，μ2，μ3，k1And k2Is an adjustable parameter, and λ (t) and α (t) are adaptive parameters.
An example of a simulation.
1. Numerical simulation
In order to verify the advantages of the sliding mode differentiator algorithm based on the adaptive notch filter in signal tracking filtering and differential signal acquisition, particularly the performance advantage in phase quality. This section performs a simulation comparison study with the following three common differentiator algorithms. Firstly, the sliding mode differentiator algorithm based on the adaptive notch filter designed by the invention is recorded as: ANF-SMD; secondly, the algorithm of the tracking differentiator designed by the scholars in China, Han Jingqing, is written as: DTOC-TD; third, the sliding mode differentiator based on the super-distortion algorithm proposed by Levant is written as: STA-SMD.
The input signal is a time-varying and random noise-doped signal of the form f (t) awgn (f)0(t, 60) wherein the base signal is a time-varying signal, i.e. the amplitude and frequency vary with time
The function awgn is used to add a noise signal with a signal-to-noise ratio of 60dB to the base signal. For STA-SMD, the parameter is λ0140 and α0450. The DTOC-TD has the parameters of r-3000 and c 010. For the proposed ANF-SMD, the parameter μ is chosen1＝80，μ2＝10000，μ3＝600，k 11, and k20.05. In all simulation processes, the sampling time h of the system is 0.001 s. The results of the comparison of the signal tracking filtering and the differential estimation of the ANF-SMD are shown in fig. 2 and 3. The adjustment process of the parameters λ and α is shown in fig. 4.
As can be seen from fig. 2 and 3, both STA-SMD and DTOC-TD have a larger phase delay compared to the proposed ANF-SMD. Meanwhile, for such varying input signals, the STA-SMD algorithm and DTOC-TD perform poorly in acquiring signal tracking filtering and differential acquisition, and even cannot estimate an effective differential signal. Compared with STA-SMD and DTOC-TD, ANF-SMD has higher precision in signal filtering and differential acquisition. Therefore, the ANF-SMD designed by the invention is very effective for obtaining filtering and differential signals of variable input signals. In addition, as can be seen from fig. 4, the parameters λ (t) and α (t) can be adaptively adjusted as the input signal changes to adapt to the signal changing in real time.
2. Analysis of test data
The given data is derived from the signal of the magnetic levitation control system. Wherein the sampling frequency of the signal is 1000Hz and the signal-to-noise ratio of the noise is 50 dB. The sliding mode differentiator (ANF-SMD) based on the self-adaptive notch filter is compared with a tracking differentiator algorithm (DTOC-TD) designed by Korean Kyork clear in common use in a test, and in the test process, the parameters are selected as follows: the DTOC-TD has the parameters of r-3000 and c 010; proposed ANF-SMD, selecting parameter μ1＝80，μ2＝10000，μ3＝600，k 11, and k20.05. The result of the signal processing is shown in fig. 5 and 6.
As can be seen from fig. 5 and 6, the newly proposed sliding mode differentiator based on adaptive notch can effectively adapt to the changes of the frequency and amplitude of the signal, can better suppress the high-frequency noise doped in the signal, and has more accurate signal processing result and smaller phase lag. The processing result meets the actual engineering requirements of the suspension system of the magnetic suspension train.
Aiming at the difficulty of processing random noise with large signal frequency bandwidth and different doped intensities in a gap signal in a magnetic suspension system, the invention provides a novel high-efficiency sliding mode differentiator based on an adaptive notch filter from the design angle of the differentiator, and the differentiator has the advantages of robustness, rapidness, real time, self-adaptation and the like. The invention firstly feeds back the integral of the system error to the construction of the cost function, designs a high-precision self-adaptive trap by using a gradient descent method, can effectively estimate the amplitude and the frequency of a signal to be processed in real time, and can effectively inhibit high-frequency random noise. Then, a novel sliding mode differentiator, namely the sliding mode differentiator based on the adaptive notch filter, is provided by combining a parameter setting formula on the basis of the adaptive notch filter. Simulation comparison with other commonly used differentiators shows that the designed sliding mode differentiator based on the adaptive notch filter can better process signals changing in real time, and is particularly characterized by smaller phase lag and smaller tracking filtering and differential estimation errors. Finally, the sliding mode differentiator based on the self-adaptive notch filter is used for processing a gap system of a magnetic suspension system, and test results show that the differentiator can obtain effective gap signals and vertical acceleration signals. The method has great significance for quickly and accurately completing the control target of the magnetic suspension system.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (4)
1. A self-adaptive notch sliding mode differentiator method for maglev train signal processing is characterized by comprising the following steps of:
step S1, designing a novel adaptive notch filter to perform robust real-time estimation on the amplitude A (t) and the frequency w (t) of the input signal f (t);
step S2, inputting the estimated result into a differentiator parameter setting formula, wherein the differentiator parameter setting formula gives the quantity relation between the sliding mode differentiator parameter and the amplitude and frequency of the signal, and the adjusting parameter of the sliding mode differentiator is determined through the differentiator parameter setting formula; and feeding back the obtained adjusting parameters of the sliding mode differentiator to the sliding mode differentiator in real time, so that the parameters of the sliding mode differentiator can be adjusted on line in real time according to the change of the input signal, and the signal which changes in real time is adapted.
2. The adaptive notch slipform differentiator method for magnetic-levitation train signal processing as recited in claim 1, wherein the step S1 is implemented as follows:
signal f (t) ═ f of the frequency conversion amplitude for any given noise η (t) doping0(t) + η (t), where the base signal is f0(t)＝A0sin(w0t+δ0) Amplitude A in this base signal0Frequency w0And phase delta0Are all unknown parameters, and have an amplitude A0And frequency w0Is time-varying;
now design a new adaptive notch filter to estimate the fundamental signal f0(t) making its estimation signal y (t) a (t) sin (phi (t)), wherein
Then, an error is obtained of
e(t)＝f(t)-y(t)＝f(t)-A(t)sin(φ(t))
In order to better eliminate the static error of the signal estimation and obtain a more accurate estimation value, an integral term of an error is introduced into the construction of the cost function, namely the newly constructed cost function has the following form:
wherein Θ is [ a (t), w (t), δ (t)]TIs a state quantity, k1Not less than 0 and k2More than or equal to 0 is two adjustable constants; according to the gradient descent method, a novel adaptive trap is obtained, and the structure of the adaptive trap is as follows:
y(t)＝A(t)sin(φ(t))
wherein A (t), w (t) and phi (t) are base signals f0(t) estimated values of amplitude, frequency and phase angle, mu1，μ2，μ3，k1And k2Is a tunable parameter, in which
In the form of
3. The adaptive notch slipform differentiator method for magnetic-levitation train signal processing as recited in claim 2, wherein the step S2 is implemented as follows:
the outputs a (t) and w (t) of the novel adaptive notch filter of step S1 are used to update the parameters of the sliding mode differentiator in real time, that is, the structure of the sliding mode differentiator based on the adaptive notch filter is designed as follows:
wherein f (t) is an input signal which is unknown time-varying and doped with random noise, and output y (t) is a basic signal f0(t) estimation of the state variable y1(t) and y2(t) the expected trajectory of the input and its derivative, respectively, sign (·) is a sign function, μ1，μ2，μ3，k1And k2Is an adjustable parameter, and λ (t) and α (t) are adaptive parameters.
4. An adaptive notch sliding mode differentiator device for magnetic levitation train signal processing, comprising a memory, a processor and computer program instructions stored on the memory and executable by the processor, wherein the computer program instructions when executed by the processor enable the method steps according to claims 1-3 to be carried out.
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