Transition process arrangement method based on band speed saturation limit tracking differentiator

Abstract

The invention relates to a transition process arrangement method based on a tracking differentiator with speed saturation limitation, which relates to the technical field of position control and comprises the following steps of: constructing the tracking differentiator with speed saturation limitation according to the maximum speed and the maximum acceleration of a feedback system; searching two time points in the data; intercepting the data between the time intervals and recording; and designing a position loop piecewise control function based on the tracking error. According to the transition process arrangement method based on the tracking differentiator with the speed saturation limitation, an exponential function fitted based on the maximum speed and the maximum acceleration of a feedback system is adopted to replace a traditional arrangement transition process of the tracking differentiator, and the arranged transition process not only can exert the maximum feedback capability of the system, but also can exert the maximum acceleration of the tracking differentiator. The response efficiency of the system is improved, and higher robustness is achieved for unknown internal and external interference of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of position control, and in particular to a transition process arrangement method based on a tracking differentiator with speed saturation limitation. Background Art

[0002] When designing a control system, if there is a relatively large step in the control target value, it is generally necessary to arrange a transition process for the control target value to achieve a fast, high-precision response without overshoot of the control system. The transition process serves as a bridge between the target value and the feedback value to ensure that when a large step occurs in the target value, the control error of the control system will not have a large step.

[0003] Traditional methods for arranging transition processes include tracking differentiators (TDs), S-curves, and trapezoidal curves. These existing technologies generally fail to consider tracking error when arranging transition processes, specifically whether the feedback system is truly keeping up with the planned transition process. This can result in the planned transition process not truly functioning in certain application scenarios. For example, in some applications, the driver and control modules of a tracking control system are enabled separately. If only the control module is enabled, but the driver module is not, the transition process has already begun, but the feedback system has not responded. Consequently, when the driver module is enabled, the previously planned transition process will not truly function. Furthermore, when the control system is subject to unknown internal and external disturbances, the feedback system may deviate from the transition process. In summary, the aforementioned methods for arranging transition processes are essentially open-loop planning methods that do not consider the dynamic feedback of the actual tracking error.

[0004] In addition, the position loop segmented control method actually used in engineering is actually a transition process arrangement method based on control error. However, the speed function it arranges is a discontinuous piecewise constant function, and the design value mainly depends on empirical values ​​and experimental debugging to determine. Moreover, when the maximum speed and maximum acceleration of the controlled object change, the previously arranged piecewise function may not match the system feedback capability. It may be too slow to maximize the energy efficiency of the system; or too fast, and the feedback value cannot keep up with the changes in the transition process. Therefore, the program's portability and universality are not good. Summary of the Invention

[0005] The present invention aims to solve the technical problem in the prior art that the speed function design value mainly depends on experience and experimental debugging, resulting in poor transplantation and universality, and provides a transition process arrangement method based on a speed saturation limit tracking differentiator.

[0006] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0007] A method for arranging a transient process based on a tracking differentiator with a speed saturation limit comprises the following steps:

[0008] Step 1: According to the maximum speed V of the feedback system max and the maximum acceleration a max Construct a tracking differentiator with speed saturation limit, and record data length to record the entire transition process;

[0009] Step 2: Find the following two time points in the data:

[0010] Time point t0: The absolute value of the state variable x2 reaches the velocity saturation value V max The initial time point of the subsequent decline;

[0011] Time point t end : The initial time point when the absolute value of the state variable x2 decreases to 0;

[0012] Among them, x2 is the speed signal of the transition process;

[0013] Step 3: Intercept the time interval [t0,t end ] between the record data, record I =p0-x1, The data combination [I,O] is fitted using the following exponential formula:

[0014] O=aI b

[0015] Get the fitting coefficient

[0016] Among them, x1 is the position signal of the transition process;

[0017] Step 4: Design the position loop segmented control function based on tracking error:

[0018]

[0019] Among them, P out (e) represents the output of the position loop, is the coefficient fitted in the third step, e is the error between the target value and the system feedback value, e0 is the threshold of the position segment, and sign() is the sign function.

[0020] In the above technical solution, in the fourth step, C p (e) is a function of e, which is either a proportional controller or a proportional-integral controller.

[0021] In the above technical solution, the tracking differentiator with speed saturation limit constructed in the first step is as follows:

[0022]

[0023] Among them, h is the sampling period, sign() is the sign function, min() is the function to find the minimum value, and the function fhan(x1-p0,x2,a max ,h) is of the following form:

[0024]

[0025] Where a1, a2, and a3 are intermediate variables of the function, and fsg() is a function defined as follows:

[0026] fsg(y1,y2)=(sign(y1+y2)-sign(y1-y2)) / 2

[0027] Here, y1 and y2 refer to the two independent variables of the function.

[0028] In the above technical solution, the first step is to discretize the tracking differentiator with speed saturation limit to obtain:

[0029]

[0030] Among them, x1(k) and x2(k) are the k-th discrete sampling values ​​of states x1 and x2, h is the sampling period, sign() is the sign function, min() is the function for finding the minimum value, and the function fhan(x1(k+1)-p0,x2(k+1),a max ,h) is of the following form:

[0031]

[0032] Where a1(k+1), a2(k+1), and a3(k+1) are intermediate variables of the function, and fsg() is a function defined as follows:

[0033] fsg(y1,y2)=(sign(y1+y2)-sign(y1-y2)) / 2

[0034] Among them, y1 and y2 refer to the two independent variables of the function, and k is the number of sampling times;

[0035] Set the target value p0 to be large enough to ensure that |x2| can reach the maximum speed value V max , synchronously record data x1(k) and x2(k) until the state x2(k) tracks the target value p0.

[0036] In the above technical solution, the third step is specifically as follows:

[0037] The valid data is intercepted from the data, where the starting time point of the data t0 = k0·h is selected as |x2(k)| from V max The point where the data starts to decline, the end time point t end =k end h is chosen as the point where |x2(k)| decreases to 0;

[0038] The data involved in parameter fitting are defined as follows:

[0039]

[0040] Among them, x1([k0:k end ]) and x2([k0:k end ]) represent from k0 to k end The x1 and x2 sampling values ​​of the fitting calculation are shown in Figure 2. I represents the input data of the fitting calculation, and O represents the output data of the fitting calculation;

[0041] The following exponential function is used to fit the data I and O:

[0042] O=aI b

[0043] Use the least squares method as a fitting tool to obtain the fitting coefficients

[0044] In the above technical solution, in the fourth step:

[0045] When the control error |p0-p f When |≥e0, the output of the position loop is given according to the arranged transition process;

[0046] When the control error |p0-p f When |<e0, closed-loop control is performed based on the error.

[0047] The present invention has the following beneficial effects:

[0048] The transition process arrangement method based on the tracking differentiator with speed saturation limit of the present invention adopts an exponential function fitted based on the maximum speed and maximum acceleration of the feedback system to replace the traditional tracking differentiator to arrange the transition process. The arranged transition process can not only give full play to the maximum feedback capability of the system and improve the response efficiency of the system, but also has stronger robustness against unknown internal and external interference of the system.

[0049] The transient process arrangement method based on the tracking differentiator with speed saturation limit of the present invention has significantly lower computational complexity than that of the traditional tracking differentiator, which is conducive to online real-time implementation in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] Figure 1 The figure is a flow chart of a method for arranging a transition process based on a tracking differentiator with speed saturation limitation according to the present invention.

[0052] Figure 2 V max =16,a max =6 as an example, the TD collected * Output curve diagram.

[0053] Figure 3 V max =16,a max =6 and the fitting data and fitting function curve diagram.

[0054] Figure 4 This is the block diagram of the position and speed dual control loop based on the fitting function.

[0055] Figure 5 For TD * The speed output x2 and the position loop output P out Schematic diagram of the comparison curve. DETAILED DESCRIPTION

[0056] The inventive concept of the present invention is:

[0057] The present invention discloses a method for arranging a transition process based on a tracking differentiator with a speed saturation limit. The method is a method for fitting a position loop controller using a tracking differentiator with a speed saturation limit. The position loop output of the method matches the maximum speed and maximum acceleration feedback capabilities of the system, thereby maximizing the response capability of the system and arranging the transition process, so that the position loop responds smoothly, quickly and without overshoot.

[0058] The transient process arrangement method based on the velocity saturation limiting tracking differentiator of the present invention can maximize the energy efficiency of the system, allowing it to achieve the maximum speed and maximum acceleration while ensuring that the feedback signal tracks the transient process signal in real time.

[0059] The present invention relates to a method for arranging a transition process based on a tracking differentiator with a velocity saturation limit. A "nonlinear TD with velocity saturation limit" (hereinafter referred to as TD*) is designed based on the maximum velocity and maximum acceleration of the feedback system. By analyzing the relationship between the velocity signal x2 output by TD* and the tracking error p0-x1 (where x1 and x2 are the position and velocity signal outputs of TD*, and p0 is the tracked constant signal), a functional relationship between the velocity signal and the position error of TD* is fitted, namely, x2 = f(x1-p0). The function f() characterizes the relationship between the velocity output of TD* and the position error (the error between the target value and the output position of the transition process). Inspired by this, this function is applied to arranging the transition process, and the output of the position loop (i.e., the reference input of the velocity loop) is designed to be the control error (i.e., the error between the target value and the system feedback value), thereby realizing a method for arranging the transition process based on the control error.

[0060] The fitting part of the method of the present invention can be performed in advance, and only the final function implementation needs to be performed online in real time. Its algorithm complexity is significantly lower than that of TD*, which is more conducive to the online real-time implementation of the algorithm.

[0061] The method for arranging a transition process based on a tracking differentiator with a speed saturation limit of the present invention comprises the following steps:

[0062] Step 1: According to the maximum speed V of the feedback system max and the maximum acceleration a max Construct a tracking differentiator with speed saturation limit, set the initial values ​​of state variables x1 and x2 to 0, and set the target value p0 to a sufficiently large positive number so that the tracking differentiator output state variable x2 can reach the maximum speed saturation value V max The tracking error p0-x1 of the tracking differentiator and the state variable x2 are collected simultaneously at a sufficiently high sampling frequency; the length of the recorded data is based on recording the entire transition process, that is, after the state variable x1 tracks p0, data collection stops;

[0063] Step 2: The change pattern of the state variable x2 is that it first rises to the maximum speed saturation value, maintains for a period of time, and then begins to drop to zero. Therefore, find the following two time points in the data:

[0064] Time point t0: The absolute value of the state variable x2 reaches the velocity saturation value V max The initial time point of the subsequent decline;

[0065] Time point t end : The initial time point when the absolute value of the state variable x2 decreases to 0; where x2 is the speed signal of the transition process;

[0066] Step 3: Intercept the time interval [t0,tend ] between the record data, record I =p0-x1, The data combination [I,O] is fitted using the following exponential formula:

[0067] O=aI b (1)

[0068] Get the fitting coefficient Among them, x1 is the position signal of the transition process;

[0069] Step 4: Design the position loop segmented control function based on tracking error:

[0070]

[0071] Among them, P out (e) represents the output of the position loop and is also the reference input of the speed loop. is the coefficient fitted in the third step, e is the error between the target value and the system feedback value, that is, the control error of the control system, e0 is the threshold of the position segment, and sign() is the sign function.

[0072] According to the above design, when the control system responds to a position step, it can accelerate to the maximum speed of the system at its maximum capacity during the acceleration phase, then continue tracking to a certain position at the maximum speed, and then decelerate at the reverse maximum acceleration until it tracks the target value.

[0073] The method of the present invention is not only applicable to situations where the initial control error is large (that is, the initial target value is far from the feedback value and needs to be accelerated to the maximum speed), but also to situations where the initial control error is small (that is, the situation where the maximum speed cannot be reached during the tracking process). In fact, the above control method realizes the design concept of "large error, small gain, small error, large gain" when designing a control system, and the change pattern of the gain is designed based on the maximum feedback capability of the system (maximum speed and maximum acceleration). It plays a transitional role and gives full play to the maximum feedback capability of the system, achieving the fast, no-overshoot control quality that the control system has always pursued.

[0074] The present invention will be described in detail below with reference to the accompanying drawings.

[0075] Figure 1 A data flow chart for calculating the fitting coefficients using a tracking differentiator with a speed saturation limit is given. The design of the tracking differentiator with a speed saturation limit (the traditional tracking differentiator is abbreviated as TD. For the sake of distinction, TD* will be used here to replace "tracking differentiator with speed saturation limit") is as follows:

[0076]

[0077] Among them, x1 and x2 are TD * The state variables can be defined as x1, x2, and the position signal of the transition process, respectively. max It's TD * The maximum acceleration output, parameter V max It's TD * The maximum speed of the output, h is the sampling period, sign() is the sign function, min() is the function to find the minimum value, the function fhan(x1-p0,x2,a max ,h) is of the following form:

[0078]

[0079] Where a1, a2, and a3 are intermediate variables of the function, and fsg() is a function defined as follows:

[0080] fsg(y1,y2)=(sign(y1+y2)-sign(y1-y2)) / 2

[0081] Where y1 and y2 refer to the two independent variables of the function; discretizing formula (3) yields:

[0082]

[0083] Among them, x1(k) and x2(k) are the k-th discrete sampling values ​​of states x1 and x2, h is the sampling period, sign() is the sign function, min() is the function for finding the minimum value, and the function fhan(x1(k+1)-p0,x2(k+1),a max ,h) is of the following form:

[0084]

[0085] Where a1(k+1), a2(k+1), and a3(k+1) are intermediate variables of the function, and fsg() is a function defined as follows:

[0086] fsg(y1,y2)=(sign(y1+y2)-sign(y1-y2)) / 2

[0087] Among them, y1 and y2 refer to the two independent variables of the function, and k is the number of sampling times;

[0088] Set the target value p0 to be large enough to ensure that |x2| can reach the maximum speed value V max , synchronously record data x1(k) and x2(k) until the state x2(k) tracks the target value p0.

[0089] Valid data (i.e., the data segment required for parameter fitting later) is intercepted from the data, where the starting time point t0 = k0·h of the data is selected as |x2(k)| from V max The point where the data starts to decline, the end time point t end =k end h is selected as the point where |x2(k)| decreases to 0 (or a smaller threshold L0 is preset and t end =k end h is |x2(k)| from V max down to the starting point of L0).

[0090] The data involved in parameter fitting are defined as follows:

[0091]

[0092] Among them, x1([k0:k end ]) and x2([k0:k end ]) represent from k0 to k end The x1 and x2 sample values ​​are shown in Figure 1. I represents the input data for the fitting calculation, and O represents the output data for the fitting calculation. Use any data fitting toolbox to fit the functional relationship between data I and O. After data analysis, it is found that the functional relationship between data I and O is highly consistent with the exponential function. Therefore, the following exponential function is selected to fit data I and O:

[0093] O=aI b (1)

[0094] The least squares method can be used as a fitting tool to obtain the fitting coefficients In fact, the fitting function is to establish the TD * When arranging the transition process, the functional relationship between the speed and position error during the speed drop process provides support for the subsequent transition process arrangement method based on control error.

[0095] V max =16,a max =6 as an example to illustrate the execution process of this method. Take the sampling period h = 0.01, p0 = 100, and the obtained TD * The output curve is as follows Figure 2 As shown, according to the method introduced above, the starting and ending points of the intercepted data are t0=6.25, t end =8.92, so the data extracted for function fitting is as follows Figure 2 As shown in the right figure.

[0096] Assume the fitting function is O = aI b, the least squares method is used to fit the data, and the fitting coefficient is and Figure 3 The fitting results are given. The horizontal axis is the tracking error p0-x1, and the vertical axis is the gain of the output speed x2 relative to the tracking error p0-x1. It can be seen that the exponential function is very effective in fitting the change law, and the two are highly consistent.

[0097] Figure 4 The control block diagram based on the fitting function is given. It is a classic position and speed dual closed-loop control mode. The fitting result is mainly used for the controller design of the position loop. In the figure, p0 is the position target value, p f is the position feedback value, P out is the output value of the position loop controller (i.e. the reference input of the speed loop), e=p0-p f is the control error, and Is in advance based on V max and a max The fitted coefficient, V f is the speed feedback value. The position loop controller is designed as follows:

[0098]

[0099] The position loop controller is designed in two stages. e0 is the threshold of the position stage. When the control error |p0-p f |≥e0, the output of the position loop is given according to the arranged transition process; when the control error |p0-p f |<e0, closed-loop control is performed based on the error; where C p (e) is a function of e and can be designed as a proportional controller or a proportional-integral controller, etc.

[0100] Figure 5 Given TD * The speed output x2 and the position loop output P out The comparison curves show that the two are highly consistent, which means that this design method can obtain the same * The same transition process is used, but the computational complexity is significantly reduced, and the control error is used as feedback. It is not affected by whether the drive module and the control module are enabled at the same time, forming a closed-loop mechanism. It has stronger robustness to uncertain internal and external interference and is easy to implement online in real time in engineering.

[0101] The above-described derivation process of the method of the present invention is performed for the case where the target value p0 is a constant. In fact, this method of arranging the transition process is also applicable to the case where the target value is a time-varying signal. Moreover, the aforementioned "position signal" and "speed signal" are both broad concepts and can be any time signal. The position signal is the time signal itself, while the speed signal represents the differential signal of the time signal, such as the differential signals of position and speed, angular position and angular velocity, and temperature and temperature. It can be applied to various fields of engineering control.

[0102] When the method of the present invention is applied to the angular position control of the main axis of a ground-based large-aperture photoelectric telescope, a high-precision position control effect with fast speed and no overshoot can be achieved under various step lengths.

[0103] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will readily appreciate that other variations or modifications based on the above descriptions are possible. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for arranging a transient process based on a tracking differentiator with a speed saturation limit, characterized in that: The following steps are involved: Step 1: According to the maximum speed V of the feedback system max and the maximum acceleration a max Construct a tracking differentiator with speed saturation limit, and record the data length to record the entire transition process; Step 2: Find the following two time points in the data: Time point t0: The absolute value of the state variable x2 reaches the velocity saturation value V max The initial time point of the subsequent decline; Time point t end : The initial time point when the absolute value of the state variable x2 decreases to 0; Among them, x2 is the speed signal of the transition process; Step 3: Intercept the time interval [t0,t end ] between the recorded data, record I = p0-x1, The data combination [I,O] is fitted using the following exponential formula: O=aI b Get the fitting coefficient Among them, x1 is the position signal of the transition process; Step 4: Design the position loop segmented control function based on tracking error: Among them, P out (e) represents the output of the position loop, is the coefficient fitted in the third step, e is the error between the target value and the system feedback value, e0 is the threshold of the position segment, and sign() is the sign function.

2. The method for arranging a transient process based on a tracking differentiator with speed saturation limit according to claim 1, characterized in that: In the fourth step, C p (e) is a function of e, which is either a proportional controller or a proportional-integral controller.

3. The method for arranging a transient process based on a tracking differentiator with speed saturation limit according to claim 1, characterized in that: The tracking differentiator with speed saturation limit constructed in the first step is as follows: Initial value: x1(0)=0; x2(0)=0 Among them, h is the sampling period, sign() is the sign function, min() is the function to find the minimum value, and the function fhan(x1-p0,x2,a max ,h) is in the following form: Among them, a1, a2 and a3 are intermediate variables of the function, and fsg() is a function defined as follows: fsg(y1,y2)=(sign(y1+y2)-sign(y1-y2)) / 2 Here, y1 and y2 refer to the two independent variables of the function.

4. The method for arranging a transient process based on a tracking differentiator with speed saturation limit according to claim 3, characterized in that: The first step is to discretize the tracking differentiator with speed saturation limit to obtain: Initial value: x1(1)=0; x2(1)=0; Among them, x1(k) and x2(k) are the k-th discrete sampling values ​​of states x1 and x2, h is the sampling period, sign() is the sign function, min() is the function for finding the minimum value, and the function fhan(x1(k+1)-p0,x2(k+1),a max ,h) is in the following form: Where a1(k+1), a2(k+1), and a3(k+1) are intermediate variables of the function, and fsg() is a function defined as follows: fsg(y1,y2)=(sign(y1+y2)-sign(y1-y2)) / 2 Among them, y1 and y2 refer to the two independent variables of the function, and k is the number of sampling times; Set the target value p0 to be large enough to ensure that |x2| can reach the maximum speed value V max , synchronously record data x1(k) and x2(k) until the state x2(k) tracks the target value p0.

5. The method for arranging a transient process based on a tracking differentiator with speed saturation limit according to claim 1, characterized in that: The third step is as follows: The valid data is intercepted from the data, where the starting time point of the data t0 = k0·h is selected as |x2(k)| from V max The point where the data starts to decline, the end time point t end =k end h is chosen as the point where |x2(k)| decreases to 0; The data involved in parameter fitting are defined as follows: I=p0-x1([k0:k end ]), Among them, x1([k0:k end ]) and x2([k0:k end ]) represent from k0 to k end The x1 and x2 sampling values ​​of the fitting calculation are shown in Figure 2. I represents the input data of the fitting calculation, and O represents the output data of the fitting calculation; The following exponential function is used to fit the data I and O: O=aI b Use the least squares method as a fitting tool to obtain the fitting coefficients 6. The method for arranging a transient process based on a tracking differentiator with speed saturation limit according to claim 1, characterized in that: In the fourth step: When the control error |p0-p f When |≥e0, the output of the position loop is given according to the arranged transition process; When the control error |p0-p f When |<e0, closed-loop control is performed based on the error.

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