Weapon drive control system tracking differentiator based on hyperbolic tangent function

Abstract

The invention belongs to the field of signal processing and weapon driving control, and particularly relates to a weapon driving control system tracking differentiator based on a hyperbolic tangent function, which comprises the following steps of: adopting a hyperbolic tangent function form including an amplitude factor, a speed factor and an exponential factor; the amplitude of the hyperbolic tangent function and the slope near the original point are adjusted by adjusting parameters, and the purpose of improving the convergence speed and the convergence stability is achieved; then designing a nonlinear tracking differentiator based on a hyperbolic tangent function, better filtering the input signals according to the input signals which have different frequencies and are interfered by noise, and simultaneously obtaining differential signals of the input signals for subsequent control links to use. The tracking differentiator is simple in form and high in adaptability to different signals, and has certain engineering practical value.

Description

Technical Field

[0001] The invention belongs to the field of signal processing and weapon drive control, and in particular relates to a weapon drive control system tracking differentiator based on a hyperbolic tangent function. Background Art

[0002] Differential signals are the key to control engineering, and obtaining the future behavior of process variables is a crucial step in formulating control strategies. Tracking differentiators are an important component of the anti-disturbance controller. They are a method that does not rely on the control system model to track input signals and obtain differential signals. In feedback control systems, the control quantity is usually designed based on the input error value, that is, u=f(e), and the error e is the error between the given input and the actual feedback value. However, in actual engineering applications, the given input signal has the characteristic of mutation. The engineering system has limited acceleration capacity based on actual characteristics (such as inertia), and the feedback signal cannot perfectly track the given input signal. The design of the tracking differentiator has the "bridge" effect of "softening" the input signal according to the actual system capacity and obtaining the differential signal at the same time. On the one hand, according to the actual maximum capacity of the system, the tracking differentiator "softens" the input signal into an intermediate input signal, so that the actual system tracks the intermediate signal and fully utilizes the maximum capacity of the system; on the other hand, the use of detection equipment such as speed sensors will not only increase costs but also cause noise interference problems. The tracking differentiator can obtain the input differential signal based on the intermediate input signal, saving costs and reducing noise interference problems. For example Figure 1a As shown, principle ① uses a differential tracker, which can not only save the use of speed sensors and reduce costs, but also improve the anti-noise effect.

[0003] Extracting differential signals from measurement signals submerged in noise was first solved by Han Jingqing through linear and nonlinear tracking differentiators. However, the contradiction between the sensitivity of tracking differentiators to noise and the accuracy of differentiation has not been completely resolved. Therefore, improvements need to be made on this basis. Obtaining a tracking differentiator with more perfect performance has become a current research hotspot. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] The technical problem to be solved by the present invention is: how to design a tracking differentiator for a weapon drive control system based on the hyperbolic tangent function. By adding the hyperbolic tangent function, it mainly solves the contradiction between ensuring the convergence speed in the dynamic stage and the stability performance in the steady stage of the system state quantity. At the same time, to a certain extent, it improves the adaptability of the parameters of the tracking differentiator to different frequency signals. The differential tracker adopts the form of the hyperbolic tangent function, which includes an amplitude factor, a speed factor, and an exponential factor. By adjusting the parameters, the amplitude of the hyperbolic tangent function and the slope near the origin are adjusted to achieve the purpose of improving the convergence speed and convergence stability. Then, a non-linear tracking differentiator is designed based on the hyperbolic tangent function. According to input signals with different frequencies and affected by noise, it can better filter the input signals and obtain the differential signals of the input signals for subsequent control links. The form of this tracking differentiator is simple, has strong adaptability to different signals, and has certain engineering practical value.

[0006] (II) Technical Solution

[0007] To solve the above technical problem, the present invention provides a tracking differentiator for a weapon drive control system based on the hyperbolic tangent function. The tracking differentiator for the weapon drive control system based on the hyperbolic tangent function is a non-linear tracking differentiator designed on the basis of a linear tracking differentiator; it adopts the hyperbolic tangent function, that is, the tanh function, for improvement, and the function form is as follows:

[0008] y(k) = f(x(k), a, b, c) = sign(x(k)) * |atanh(bx(k))| c

[0009] Among them, x(k) is the independent variable, sign(·) is the sign function, which is used to ensure that the function is an odd function; a, b, and c are the three parameters of the hyperbolic tangent function. The parameter a > 0 is the amplitude factor, which affects the amplitude of the function; the parameter b > 0 is the speed factor, which affects the slope of the function near the origin; the parameter c is the exponential factor. When 0 < c < 1, the slope of the function at the origin is the largest; when c > 1, the slope of the function at the origin is the smallest. Taking the value of c > 1 is used to weaken the oscillation problem of the system state quantity near the origin; therefore, both the parameter b and the parameter c play a role in adjusting the slope of the function at the origin.

[0010] The expression of the tracking differentiator for the weapon drive control system based on the hyperbolic tangent function is as follows:

[0011]

[0012] In the expression, x1(k) represents the tracking signal of the input signal r(k), k represents the signal number, x2(k) represents the differential signal of the input signal r(k), T represents the sampling time, and R>0 represents the gain coefficient, which is related to the system bandwidth. The larger R is, the stronger the tracking ability of the system is. However, when there is interference in the input signal, the larger R is, the lower the anti-interference ability of the system is. Therefore, R should take an appropriate value.

[0013] in,

[0014] The expressions of f1(s(k),a,b,c) and f2(x2(k),R,a,b,c) are as follows:

[0015] f1(s(k),a,b,c)=sign(s(k))*|atanh(bs(k))| c

[0016]

[0017] Where sign(·) is the sign function, parameter a is the amplitude factor, which adjusts the amplitude of the nonlinear function; speed factor b and exponential factor c adjust the convergence speed of the nonlinear function at the origin.

[0018] (III) Beneficial effects

[0019] Compared with the prior art, the present invention introduces a nonlinear function, namely, a hyperbolic tangent function, into a linear tracking differentiator, adjusts the amplitude of the function and the slope near the origin, and changes the characteristics of the nonlinear function, thereby improving the convergence speed of the tracking differentiator when far away from the origin and the stability near the origin, and improving the performance of the tracking differentiator. The present invention has three advantages: first, by adjusting the parameters R and a, the tracking speed of the tracking differentiator can be improved; second, by adjusting the parameters b and c, the slope or concave-convexity of the nonlinear function near the origin can be changed, so that the tracking differentiator has stronger stability near the origin; third, the tracking differentiator based on the hyperbolic tangent function proposed by the present invention can improve the adaptability to input signals of different frequencies, and to a certain extent avoids the interference effect that causes poor or even divergent system tracking effect, and the parameters of the tracking differentiator are easy to adjust, which is practical. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1a and Figure 1b This is a schematic diagram of the technical solution of the present invention.

[0021] Figure 2 Schematic diagram of the influence of parameters in the hyperbolic tangent function and nonlinear function.

[0022] Figure 3 It is a schematic diagram for simulation comparison between the DTOC-TD method and the method of the present invention. Detailed implementation manners

[0023] To make the objectives, contents, and advantages of the present invention clearer, the following further describes in detail the specific implementation manners of the present invention with reference to the accompanying drawings and embodiments.

[0024] To solve the above technical problems, the present invention provides a tracking differentiator for a weapon drive control system based on the hyperbolic tangent function. The tracking differentiator for the weapon drive control system based on the hyperbolic tangent function is a non-linear tracking differentiator designed on the basis of a linear tracking differentiator; it uses the hyperbolic tangent function, that is, the tanh function, for improvement, and the function form is as follows:

[0025] y(k) = f(x(k), a, b, c) = sign(x(k)) * |atanh(bx(k))| c

[0026] Wherein, x(k) is the independent variable, sign(·) is the sign function, which is used to ensure that the function is an odd function; a, b, and c are the three parameters of the hyperbolic tangent function. The parameter a>0 is the amplitude factor, which affects the amplitude of the function; the parameter b>0 is the speed factor, which affects the slope of the function near the origin; the parameter c is the exponential factor. When 0<c<1, the slope of the function at the origin is the largest; when c>1, the slope of the function at the origin is the smallest. Take the value of c>1 to weaken the oscillation problem of the system state quantity near the origin; therefore, both the parameter b and the parameter c play a role in adjusting the slope of the function at the origin.

[0027] As Figure 1b shown, the expression of the tracking differentiator for the weapon drive control system based on the hyperbolic tangent function in the linear tracking differentiator is as follows:

[0028]

[0029] In the expression, x1(k) represents the tracking signal of the input signal r(k), k represents the signal sequence number, x2(k) represents the differential signal of the input signal r(k), T is the sampling time, R>0 is the gain coefficient, which is related to the system bandwidth. The larger R is, the stronger the tracking ability of the system. However, when there is interference in the input signal, the larger R is, the weaker the anti-interference ability of the system. Therefore, R should be taken as an appropriate value;

[0030] Wherein,

[0031] The expressions of f1(s(k), a, n, c) and f2(x2(k), R, a, b, c) are as follows:

[0032] f1(s(k), a, b, c) = sign(s(k)) * |atanh(bs(k))| c

[0033]

[0034] Where sign(·) is the sign function, parameter a is the amplitude factor, which adjusts the amplitude of the nonlinear function; speed factor b and exponential factor c adjust the convergence speed of the nonlinear function at the origin.

[0035] The effects of parameters a, b, c on nonlinear functions and the graph of y = tanh (x) are shown in Figure 2 .

[0036] Example 1

[0037] In order to more intuitively illustrate the advantages of the present invention, a specific example is compared with the following. The form of the discrete time optimal control tracking differentiator (DTOC-TD) is as follows:

[0038]

[0039] The expression of fh is as follows:

[0040]

[0041] The present invention tracks micro 3

[0042] Table 1 Tracking differentiator parameter values

[0043] Tracking Differentiator Parameter Value DTOC-TD r=50,h=T Method of the present invention R=50, a=0.5, b=8, c=5 / 3

[0044] Input signal with noise:

[0045]

[0046] Noise n(k)=0.001*randn(1,1) is added, and input signals of different frequencies (0.25Hz, 0.5Hz, 1Hz, 2Hz) are used respectively to observe the tracking speed and convergence stability of the two methods for the input signal and the differential signal of the input signal.

[0047] Depend on Figure 2It can be seen that when the input signal is 0.25Hz, both the DTOC-TD method and the method of the present invention can track the input signal very well and obtain the differential signal, but the method of the present invention is less affected by noise; when the input signal is 0.5Hz, the differential signal obtained by DTOC-TD begins to have a slight lag phenomenon, which is particularly obvious when the input signal frequency increases, and the tracking effect of the input signal becomes worse, while the tracking and differential effects of the method of the present invention are stable; when the input signal frequency continues to increase to 2Hz, the DTOC-TD method can no longer track the input signal and obtain the differential signal, while the method of the present invention can.

[0048] According to the comparison of the two differentiator methods at different frequencies, it can be seen that both tracking differentiators have the functions of tracking input signals, obtaining differential signals and suppressing noise in signals. However, the method of the present invention has better tracking, differentiation and interference suppression effects, and is applicable to a wider frequency range.

[0049] The tracking differentiator based on the hyperbolic tangent function proposed in the present invention adds a nonlinear function without changing the form of the line tracking differentiator, which can not only ensure the tracking of the input signal and the acquisition of the differential signal, but also expand the applicability of the input signal frequency to a certain extent. The parameter setting is simple, and the parameter (R, a, b, c) values ​​can be flexibly adjusted according to different system characteristics to obtain the desired tracking differentiator performance.

[0050] In summary, the present invention belongs to the field of signal processing and weapon drive control, and specifically relates to a tracking differentiator of a weapon drive control system based on a hyperbolic tangent function. The description method is as follows: a hyperbolic tangent function form is adopted, which contains an amplitude factor, a speed factor and an exponential factor. The parameters are adjusted to adjust the amplitude of the hyperbolic tangent function and the slope near the origin to achieve the purpose of improving the convergence speed and convergence stability; then a nonlinear tracking differentiator is designed based on the hyperbolic tangent function, and according to input signals of different frequencies and subject to noise interference, the input signal can be better filtered, and the differential signal of the input signal can be obtained at the same time for use in subsequent control links. The tracking differentiator is simple in form, has strong adaptability to different signals, and has certain engineering practical value.

[0051] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A tracking differentiator for a weapon drive control system based on a hyperbolic tangent function, characterized in that: The tracking differentiator of the weapon drive control system based on the hyperbolic tangent function is a non-linear tracking differentiator designed on the basis of a linear tracking differentiator; it uses the hyperbolic tangent function, i.e., the tanh function, for improvement, and the function form is as follows: y(k)=f(x(k),a,b,c)=sign(x(k))*|atanh(bx(k))| c where x(k) is the independent variable, sign(·) is the sign function, which is used to ensure that the function is an odd function; a, b, and c are the three parameters of the hyperbolic tangent function. The parameter a>0 is the amplitude factor, which affects the amplitude of the function; the parameter b>0 is the speed factor, which affects the slope of the function near the origin; the parameter c is the exponential factor. When 0<c<1, the slope of the function at the origin is the largest; when c>1, the slope of the function at the origin is the smallest. Taking the value of c>1 is used to weaken the oscillation problem of the system state quantity near the origin; therefore, both the parameter b and the parameter c play a role in adjusting the slope of the function at the origin.

2. The weapon drive control system tracking differentiator based on the hyperbolic tangent function as claimed in claim 1, characterized in that: The expression of the tracking differentiator of the weapon drive control system based on the hyperbolic tangent function is as follows: In the expression, x1(k) represents the tracking signal of the input signal r(k), k represents the signal sequence number, x2(k) represents the differential signal of the input signal r(k), T is the sampling time, R>0 is the gain coefficient, which is related to the system bandwidth. The larger R is, the stronger the tracking ability of the system. However, when there is interference in the input signal, the larger R is, the lower the anti-interference ability of the system. Therefore, R should be taken as an appropriate value; where, The expressions of f1(s(k), a, b, c) and f2(x2(k), R, a, b, c) are as follows: f1(s(k),a,b,c)=sign(s(k))*|atanh(bs(k))| c where sign(·) is the sign function, the parameter a is the amplitude factor, which adjusts the amplitude of the non-linear function; the speed factor b and the exponential factor c adjust the convergence speed of the non-linear function at the origin.

3. The weapon drive control system tracking differentiator based on the hyperbolic tangent function as claimed in claim 2, characterized in that: The parameter a>0 is the amplitude factor, which affects the amplitude of the function.

4. The weapon drive control system tracking differentiator based on the hyperbolic tangent function as claimed in claim 3, characterized in that: The parameter b>0 is the speed factor, which affects the slope of the function near the origin.

5. The weapon drive control system tracking differentiator based on the hyperbolic tangent function as claimed in claim 4, characterized in that: The parameter c is the exponential factor.

6. The weapon drive control system tracking differentiator based on the hyperbolic tangent function as claimed in claim 5, characterized in that: When 0<c<1, the slope of the function at the origin is the largest.

7. The weapon drive control system tracking differentiator based on the hyperbolic tangent function as claimed in claim 6, characterized in that: When c>1, the slope of the function at the origin is the smallest. Taking the value of c>1 is used to weaken the oscillation problem of the system state quantity near the origin.

8. The weapon drive control system tracking differentiator based on the hyperbolic tangent function as claimed in claim 7, characterized in that: Both the parameter b and the parameter c play a role in adjusting the slope of the function at the origin.

9. The weapon drive control system tracking differentiator based on the hyperbolic tangent function as claimed in claim 2, characterized in that: x1(k) represents the tracking signal of the input signal r(k), k represents the signal sequence number, x2(k) represents the differential signal of the input signal r(k), and T is the sampling time.

10. The weapon drive control system tracking differentiator based on hyperbolic tangent function as claimed in claim 2, characterized in that: R>0 is the gain coefficient, which is related to the system bandwidth. The larger R is, the stronger the tracking ability of the system. However, when there is interference in the input signal, the larger R is, the lower the anti-interference ability of the system. Therefore, R should be taken as an appropriate value.

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