A variable parameter tracking differentiator for arranging transition process

Abstract

The present invention relates to the field of signal processing, and in particular to a variable parameter tracking differentiator for arranging a transition process. The variable parameter tracking differentiator takes into account a physical system in which the speed and acceleration of a system feedback signal response have physical boundaries, designs a fast factor r as a time-varying function, and associates the parameter values ​​in the function with the maximum speed of the system feedback signal and the maximum acceleration of the system feedback signal; matches the arranged transition process with the feedback capability of the physical system, adds a speed saturation design to the second output of the tracking differentiator, so as to ensure that the transition process given by the designed tracking differentiator can truly play the role of a transition bridge, fully considers the maximum tracking capability of the system feedback signal, makes up for the deficiency of a linear tracking differentiator in arranging the transition process, and is simple in calculation, low in algorithm complexity, and is conducive to implementation in engineering applications.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, in particular to a variable parameter tracking differentiator for arranging a transition process. Background Art

[0002] In the feedback control system, the control quantity is designed based on the control deviation, that is, the error e=pm between the reference signal p and the feedback signal m is used as the main factor in the controller design. Since the reference signal inevitably has a large step change, and the feedback signal in the actual physical system generally does not produce a jump change, for example, the position signal changes according to a certain speed and acceleration, and the speed and acceleration of the physical system have an upper limit, so when the reference signal has a large step, there will be a relatively large control error in an instant, resulting in controller saturation and the system is prone to overshoot. In order to reconcile the contradiction between rapidity and overshoot, the reference signal can be arranged for a transition process, so that the actual feedback physical signal tracks the transition process signal, and then achieves the purpose of smoothly tracking the reference signal, so that the control error will not have a large jump, and the rapid and stable tracking is guaranteed. It can be seen that the transition process signal is actually a bridge built between the feedback signal and the reference signal, which plays a transition role. If the speed and acceleration of the arranged transition process signal do not match the speed and acceleration of the physical system, then it will not play a transition role.

[0003] Tracking Differentiator (TD) is the main component of Active Disturbance Rejection Control (ADRC). In addition to being a tool for extracting differential signals, its other main function is to arrange the transition process for the reference signal. The simplest linear tracking differentiator (LTD) gives the transition process in the form of solving a second-order linear differential equation, but it has only one constant parameter r called the fast factor, which determines the transition time of the transition process signal, and the transition time is almost inversely proportional to the fast factor r, and has nothing to do with the amplitude of the tracked signal. This makes it possible that when tracking a reference signal with a large step, the transition process speed and acceleration given may far exceed the fastest signal that can be given by the feedback of the physical system, so it cannot play the role of arranging the transition process. Summary of the invention

[0004] The embodiment of the present invention provides a variable parameter tracking differentiator for arranging a transition process, in order to make up for the shortcomings of the existing differentiators in arranging the transition process.

[0005] According to an embodiment of the present invention, a variable parameter tracking differentiator for arranging a transition process is provided, wherein the variable parameter tracking differentiator is configured as follows:

[0006] Considering the physical system with physical boundaries of the speed and acceleration of the system feedback signal response, the fast factor r is designed as a time-varying function, and the parameter values ​​in the function are related to V max and a max Make an association, record V max and a max are the maximum speed and maximum acceleration of the system feedback signal respectively;

[0007] The arranged transition process is matched with the feedback capability of the physical system, and a speed saturation design is added to the second output of the tracking differentiator.

[0008] Furthermore, the calculation formula of the variable parameter tracking differentiator is:

[0009]

[0010] Where x1(t) is the first output of the tracking differentiator, x2(t) is the second output of the tracking differentiator, p(t) is the tracked signal, and r(t) is the fast factor, which is designed to be the following time-varying parameters:

[0011]

[0012] Where min() is the minimum function, σ≥1 is an adjustable parameter, and the maximum acceleration of the transition process given is σ 2 a max , and the larger σ is, the larger the maximum speed of the given transition process will be.

[0013] Furthermore, the variable parameter tracking differentiator is a variable parameter tracking differentiator with speed saturation limit, and its discrete implementation form is as follows:

[0014]

[0015] Where sign() is the sign function, k∈Ν, and h is the sampling step size.

[0016] Furthermore, the fast factor parameter r is adjusted in real time with the tracking error, where the comparison operation is to compare and 1, then take r as follows:

[0017]

[0018] where a max is the maximum acceleration of the system feedback signal, and σ≥1 is an adjustable parameter.

[0019] Furthermore, VLTD_fun is a function written in an m-file to calculate The specific form is as follows:

[0020]

[0021] Furthermore, the speed output signal x2 provided by the variable parameter tracking differentiator is added to the control system as speed feedforward information.

[0022] Furthermore, the variable parameter tracking differentiator is used to track any time-varying signal as long as the maximum velocity and the maximum acceleration of the feedback signal are known in advance.

[0023] Furthermore, in the variable parameter tracking differentiator, the reference signal is recorded as the position signal, the first-order derivative is recorded as the velocity signal, and the second-order derivative is recorded as the acceleration signal.

[0024] A storage medium stores a program file capable of realizing any one of the above-mentioned variable parameter tracking differentiators for arranging a transition process.

[0025] A processor is used to run a program, wherein when the program is run, any one of the above-mentioned variable parameter tracking differentiators for arranging a transition process is executed.

[0026] The variable parameter tracking differentiator for arranging the transition process in the embodiment of the present invention considers the physical system in which the speed and acceleration of the system feedback signal response have physical boundaries, and designs the fast factor r as a time-varying function, and the parameter values ​​in the function are related to V max and a max The transition process is matched with the feedback capability of the physical system, and a speed saturation design is added to the second output of the tracking differentiator to ensure that the transition process given by the designed tracking differentiator can truly serve as a transition bridge. The maximum tracking capability of the system feedback signal is fully considered, which makes up for the shortcomings of the linear tracking differentiator in arranging the transition process. The calculation is simple, the algorithm complexity is low, and it is conducive to implementation in engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0028] Figure 1 A signal flow chart from a reference signal p to an output x1 of the tracking differentiator in a variable parameter tracking differentiator for arranging a transition process according to the present invention;

[0029] Figure 2A schematic diagram of component connections for realizing a discrete variable parameter tracking differentiator with velocity saturation in MATLAB / Simulink of the present invention;

[0030] Figure 3 The position, velocity and acceleration diagrams when the present invention uses the given tracking differentiator to track the constant signal p=10;

[0031] Figure 4 The position, velocity and acceleration diagrams when the present invention uses the given tracking differentiator to track the constant signal p=50;

[0032] Figure 5 The position, velocity and acceleration diagrams for tracking a constant signal p=100 using the given tracking differentiator are shown for the present invention. DETAILED DESCRIPTION

[0033] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0034] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0035] The present invention provides a variable parameter tracking differentiator for arranging a transition process, which fully considers the maximum tracking capability of a system feedback signal, makes up for the deficiency of a linear tracking differentiator in arranging a transition process, and has simple calculation and low algorithm complexity, which is conducive to implementation in engineering applications.

[0036] The present invention is proposed to arrange the reference signal of the feedback control system in a transition process that is more in line with the law of physical change of the signal. Depending on the controlled object being studied, the reference signal of the system can be position, angle, temperature, etc. In short, it is a physical signal, and the speed and acceleration mentioned in the present invention actually refer to the first-order derivative and second-order derivative of the reference signal. The most common is that the reference signal is position, then the first-order derivative and the second-order derivative correspond to the speed and acceleration respectively. The present invention only considers the physical system in which the speed and acceleration of the system feedback signal response have physical boundaries, denoted by V max and a max are the maximum velocity and maximum acceleration of the physical signal respectively.

[0037] The variable parameter tracking differentiator with speed saturation is to design the fast factor r of the differentiator as a time-varying function, and the parameter value in the function is related to V max and a max In order to make the arranged transition process match the feedback capability of the physical system, a speed saturation design is added to the second output of the tracking differentiator to ensure that the transition process given by the designed tracking differentiator can truly serve as a transition bridge.

[0038] The variable parameter tracking differentiator designed by the present invention for arranging the transition process is as follows:

[0039]

[0040] The fast factor r(t) is designed as the following time-varying parameter:

[0041]

[0042] Where x1(t) is the first output of the tracking differentiator, x2(t) is the second output of the tracking differentiator, p(t) is the tracked signal, r(t) is the fast factor, min() is the minimum function, σ≥1 is an adjustable parameter, and the maximum acceleration of the transition process given is σ 2 a max , and the larger σ is, the larger the maximum speed of the given transition process will be. Therefore, in the actual application of the tracking differentiator, the parameter σ can be appropriately greater than 1, that is, the arranged maximum acceleration of the transition process can be appropriately slightly greater than the maximum feedback acceleration of the system, as long as it does not last too long, it will not cause the feedback signal and the transition process signal to deviate too much.

[0043] On the other hand, the maximum speed and maximum acceleration of the feedback signal of the physical system are not necessarily matched. That is, if the transition process signal given by the above tracking differentiator can exert the maximum acceleration capability, the given transition process speed signal may far exceed the maximum tracking capability of the feedback signal of the physical system. Therefore, the speed saturation limit is imposed on the above variable parameter tracking differentiator to obtain the design of a variable parameter tracking differentiator with speed saturation limit.

[0044] The discrete implementation of the variable parameter tracking differentiator with speed saturation limit is as follows:

[0045]

[0046] Where min() is the minimum function, sign() is the sign function, k∈Ν, and h is the sampling step size.

[0047] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0048] Figure 1 The signal flow chart from the reference signal p to the output x1 of the tracking differentiator is given. The biggest difference from the traditional linear TD is that the fast factor parameter r is adjusted in real time with the tracking error. The comparison operation is and 1, then take r as follows:

[0049]

[0050] where a max is the maximum acceleration of the feedback signal of the physical system, and σ≥1 is an adjustable parameter.

[0051] Figure 2 This is a schematic diagram of the components used to implement a discrete variable parameter tracking differentiator with velocity saturation in MATLAB / Simulink. VLTD_fun is a function written in an m-file to calculate The specific form is as follows:

[0052]

[0053] Take a set of parameters as an example to illustrate the design process of the variable parameter tracking differentiator. max is 15, a max is 10, h is 0.002, σ is 2, Figure 3 The position, velocity and acceleration diagrams are given when the given tracking differentiator is used to track the constant signal p = 10. It can be seen that when tracking p = 10, the velocity output does not enter the saturation state. At this time, although the acceleration output is greater than a for 0.31s maxThe situation may cause a slightly larger feedback error during this period (because the maximum acceleration of the feedback signal is a max ), but since this is only the initial stage of the transition process, even if the controller is saturated for a short time, it will not cause overshoot in the final steady state, and the absolute value of the acceleration of the whole process after 0.31s is less than a max Therefore, the system feedback signal will quickly track the upper transition process signal, thereby ensuring that the feedback error is within a relatively small range before the system enters a steady state.

[0054] Figure 4 and Figure 5 The position, velocity and acceleration diagrams are given for p = 50 and 100 respectively. It can be seen that at this time, the velocity signal of the transition process enters the saturated nonlinear interval. At this time, although the acceleration signal output of the transition process is greater than a for 0.63s and 0.51s respectively, max However, since there is a relatively long period of time when the acceleration signal of the transition process is 0, this stage is sufficient to ensure that the feedback signal of the physical system can accelerate and quickly approach the position signal given by the transition process. Therefore, the tracking differentiator can still serve as a transition bridge between the reference signal and the feedback signal.

[0055] The tracking differentiator provided by the present invention can be used as a signal arrangement transition process for an actual physical system with clear limits on both velocity and acceleration, and the velocity output signal x2 provided by the tracking differentiator can be added to the control system as velocity feedforward information. In addition, Figures 3 to 5 Only the case of tracking a constant signal is given. In fact, the given tracking differentiator can be used to track any time-varying signal as long as the maximum velocity and maximum acceleration of the feedback signal are known in advance.

[0056] A storage medium stores a program file capable of realizing any one of the above-mentioned variable parameter tracking differentiators for arranging a transition process.

[0057] A processor is used to run a program, wherein when the program is run, any one of the above-mentioned variable parameter tracking differentiators for arranging a transition process is executed.

[0058] 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 principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A variable parameter tracking differentiator for arranging a transient process, characterized in that: The variable parameter tracking differentiator is configured as: Considering the physical system with physical boundaries of the speed and acceleration of the system feedback signal response, the fast factor r is designed as a time-varying function, and the parameter values ​​in the function are related to V max and a max Make an association, record V max and a max are the maximum speed and maximum acceleration of the system feedback signal respectively; Match the arranged transition process with the feedback capability of the physical system, and add a speed saturation design to the second output of the tracking differentiator; The calculation formula of the variable parameter tracking differentiator is: Where x1(t) is the first output of the tracking differentiator, x2(t) is the second output of the tracking differentiator, p(t) is the tracked signal, and r(t) is the fast factor, which is designed to be the following time-varying parameters: Where min() is the minimum function, σ≥1 is an adjustable parameter, and the maximum acceleration of the transition process given is σ 2 a max , and the larger σ is, the larger the maximum speed of the given transition process will be.

2. The variable parameter tracking differentiator for arranging a transition process according to claim 1, characterized in that: The variable parameter tracking differentiator is a variable parameter tracking differentiator with speed saturation limit, and its discrete implementation form is as follows: Where sign() is the sign function, k∈Ν, and h is the sampling step size.

3. The variable parameter tracking differentiator for arranging a transition process according to claim 1, characterized in that: The fast factor parameter r is adjusted in real time with the tracking error, and the comparison operation is and 1, then take r as follows: where a max is the maximum acceleration of the system feedback signal, and σ≥1 is an adjustable parameter.

4. The variable parameter tracking differentiator for arranging a transition process according to claim 2, characterized in that: VLTD_fun is a function written in an m file to calculate The specific form is as follows:

5. The variable parameter tracking differentiator for arranging a transition process according to claim 1, characterized in that: The speed output signal x2 given by the variable parameter tracking differentiator is added to the control system as speed feedforward information.

6. The variable parameter tracking differentiator for arranging a transient process according to claim 1, characterized in that: The variable parameter tracking differentiator is used to track any time-varying signal as long as the maximum velocity and maximum acceleration of the feedback signal are known in advance.

7. The variable parameter tracking differentiator for arranging a transient process according to claim 1, characterized in that: In the variable parameter tracking differentiator, the reference signal is recorded as the position signal, the first-order derivative is recorded as the velocity signal, and the second-order derivative is recorded as the acceleration signal.

8. A storage medium, characterized in that: The storage medium stores a program file capable of implementing the variable parameter tracking differentiator for arranging a transition process as described in any one of claims 1 to 7.

9. A processor, characterized in that: The processor is used to run a program, wherein the program, when running, executes the variable parameter tracking differentiator for arranging a transition process as claimed in any one of claims 1 to 7.

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