Linear active disturbance rejection control parameter initial value calculation method for photoelectric platform

Abstract

The invention provides a linear active disturbance rejection control parameter initial value calculation method for a photoelectric platform. The method comprises the steps of establishing an equivalent two-degree-of-freedom control model of an LADRC controller, calculating a transfer function of an in-loop controller C (s), calculating an observer bandwidth of the LADRC controller, calculating a control gain of the LADRC controller, and calculating a time constant of a low-pass filter. According to the method, the proportional-integral controller parameters are converted into the linear active-disturbance-rejection control parameters, it can be ensured that when the LADRC replaces a PI controller, approximate control performance is obtained, smooth transition is achieved, and a foundation is laid for practical application of the linear active-disturbance-rejection controller in photoelectric platform control.

Description

Technical Field

[0001] The invention belongs to the technical field of guidance control, and in particular relates to a method for calculating initial values ​​of linear auto-disturbance rejection control parameters for an optoelectronic platform. Background Art

[0002] Most optoelectronic platform servo control systems adopt a dual closed-loop series control method. The outer loop is a position loop or a tracking loop, and the inner loop is a velocity loop. The velocity loop control determines the stability of the line of sight, which is a basic prerequisite for high-precision tracking. In the velocity loop, if the MEMS gyro noise is large, the differential control of the traditional PID controller will further amplify the noise, so the proportional integral (PI) controller is often used in the velocity loop. The PI controller has a simple structure and easy parameters to adjust. However, when tracking the target, the optoelectronic platform is affected by uncertain factors such as load characteristic changes and external disturbances. In a complex battlefield environment, the PI controller cannot guarantee the stability of the line of sight. Based on this problem, some researchers have proposed a method of using a linear active disturbance rejection control (LADRC) instead of a PI controller. Because the linear active disturbance rejection control is based on the working principle of the classic PID, it considers friction disturbances, carrier motion disturbances, and gyro noise as "total disturbances", uses an observer to estimate the "total disturbance" online, and compensates in real time in the controller, thereby improving the anti-interference ability of the velocity loop. However, the method of replacing PI controller with LADRC still has the following disadvantages: (1) The method of adjusting the control parameters of LADRC is mostly the "frequency method", which mainly relies on the experience of the debugger, which is not conducive to the application of LADRC by inexperienced personnel. (2) When converting from PI to LADRC, the problem of selecting the initial value is not solved, and whether LADRC can approach the performance of the existing PI controller is not considered. Therefore, in order to ensure a smooth transition when converting from PI controller to LADRC, it is necessary to propose a method for calculating the initial value of linear anti-disturbance control parameters for optoelectronic platforms. Summary of the invention

[0003] 1. Technical issues to be resolved

[0004] The present invention proposes a method for calculating initial values ​​of linear auto-disturbance rejection control parameters for an optoelectronic platform, so as to solve the technical problem that it is difficult to quickly and effectively give a set of suitable initial values ​​of auto-disturbance rejection control parameters when an auto-disturbance rejection controller is used instead of a PI controller, thereby ensuring that the auto-disturbance rejection controller and the PI controller have similar control performance.

[0005] (II) Technical solution

[0006] In order to solve the above technical problems, the present invention proposes a method for calculating the initial value of a linear active disturbance rejection control parameter for an optoelectronic platform. The method comprises the following steps:

[0007] S1. Establish the equivalent two-degree-of-freedom control model of LADRC controller

[0008] The equivalent two-degree-of-freedom control model has two control degrees of freedom, consisting of a front controller F(s) and an in-loop controller C(s);

[0009] S2. Calculate the transfer function of the in-loop controller C(s)

[0010] The transfer function of the in-loop controller C(s) is calculated using the superposition theorem of linear systems:

[0011]

[0012] Assume that the control parameter of the PI controller is k′ p =1, k′ i =10; derive the parameters of the LADRC controller, including β1, β2, k p , b0, τ; β1, β2 are two adjustable observer gains, k p is the controller gain, b0 is the actual control gain, and τ is the time constant of the low-pass filter;

[0013] S3. Calculate the observer bandwidth of the LADRC controller

[0014] The observer bandwidth ω0 of the LADRC controller is calculated according to the following formula:

[0015] ω0=2k′ i / k′ p

[0016] S4. Calculate the control gain of the LADRC controller

[0017] The control gain b0 of the LADRC controller is calculated according to the following formula:

[0018]

[0019] S5. Calculate the time constant of the low-pass filter

[0020] The time constant τ of the low-pass filter is calculated according to the following formula:

[0021]

[0022] In the formula, ω τIt is the frequency corresponding to the point where the amplitude of the in-loop controller is less than the set value L(ω) of the PI controller found on the Bode diagram.

[0023] Furthermore, in step S1, according to the first-order LADRC model:

[0024]

[0025] In the formula, f = g + (b-b0)u; y is the output of the control model; u is the control quantity of the system; g is the external disturbance; b is the real control gain; b0 is the actual control gain; f is the total disturbance of the system, including the external disturbance of the system and the unknown disturbance of the system;

[0026] Take f as the expanded state of the system, introduce state variables x1 and x2, let x1 = y, x2 = f, Design a linear expansion observer as follows:

[0027]

[0028] In the formula, z1 and z2 are the state variables of the observer, z1 is the output of the estimation system, and z2 is the total disturbance of the estimation system; β1 and β2 are two adjustable observer gains. From the frequency method, we can know that in LADRC, there is:

[0029]

[0030] Where ω0 is the bandwidth of the LADRC observer;

[0031] The total disturbance z2 of the observer estimated system is compensated to the control quantity in real time, and the linear state error feedback control law is adopted as follows:

[0032]

[0033] In the formula, k p is the gain of the controller, r is the reference input of the system;

[0034] Substitute equation (4) into equation (2), and then use Laplace transform to get the expression of control quantity U(s), input R(s) and output Y(s), such as:

[0035]

[0036] In formula (5), let Y(s) = 0, and we get:

[0037]

[0038] In formula (5), let R(s) = 0, and we get:

[0039]

[0040] From (6) and (7), we can obtain the equivalent two-degree-of-freedom control model of the LADRC controller.

[0041] Furthermore, in step S3, to ensure that the zero points of the LADRC controller and the PI controller are equal, let:

[0042]

[0043] In the formula, λ is a multiple.

[0044] Further, in step S5, according to the characteristics of the low-pass filter, when ω=1 / τ, L(ω)=-3dB; in the high-frequency stage, a point is found on the Bode diagram where the amplitude of the in-loop controller is 3dB smaller than that of the PI controller.

[0045] (III) Beneficial effects

[0046] The present invention proposes a method for calculating the initial value of linear active disturbance rejection control parameters for an optoelectronic platform, including establishing an equivalent two-degree-of-freedom control model of a LADRC controller, calculating the transfer function of an in-loop controller C(s), calculating the observer bandwidth of the LADRC controller, calculating the control gain of the LADRC controller, and calculating the time constant of a low-pass filter. The present invention converts proportional-integral controller parameters into linear active disturbance rejection control parameters, which can ensure that when the LADRC controller replaces the PI controller, approximate control performance is obtained, and a smooth transition is achieved, laying a foundation for the practical application of the linear active disturbance rejection controller in the control of an optoelectronic platform.

[0047] The present invention uses existing PI parameters to calculate the initial values ​​of LADRC parameters, and the obtained LADRC control performance is similar to the original PI system, thereby reducing the workload during replacement. The main features of this method are: establishing an equivalent two-degree-of-freedom control model of LADRC, using the transfer function of the in-loop controller C(s) and the transfer function of the PI controller to have equal zero points and equal low-order gains, to calculate the observer bandwidth and control gain of LADRC; using the amplitude-frequency characteristics of the in-loop controller and the PI controller, to calculate the time constant of the low-pass filter. A method for calculating the initial values ​​of parameters for converting a PI controller into an anti-disturbance control controller is proposed, thereby laying the foundation for the application of linear anti-disturbance control in the control process of optoelectronic platforms. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is the two-degree-of-freedom control model of the present invention;

[0049] Figure 2 The image of f(ω) when λ takes different values ​​in the present invention;

[0050] Figure 3It is a schematic diagram of the frequency characteristics of the in-loop controller and the PI controller in the present invention;

[0051] Figure 4 It is a comparison diagram of the frequency characteristics of the in-loop controller and the PIF controller in the present invention. DETAILED DESCRIPTION

[0052] In order to make the purpose, content and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below in conjunction with the drawings and examples.

[0053] This embodiment proposes a method for calculating initial values ​​of linear active disturbance rejection control parameters for an optoelectronic platform, which specifically includes the following steps:

[0054] S1. Establish the equivalent two-degree-of-freedom control model of LADRC controller

[0055] According to the first-order LADRC model:

[0056]

[0057] In the formula, f = g + (b-b0) u, y is the output of the control model, u is the control quantity of the system, g is the external disturbance, b is the real control gain (unknown quantity), b0 is the actual control gain (b0 is the estimated value of b), and f is the total disturbance of the system (including the external disturbance of the system and the unknown disturbance of the system). Take f as the expanded state of the system, introduce state variables x1 and x2, let x1 = y, x2 = f, In order to estimate the total disturbance f of the system, a linear extended state observer (LESO) is designed as follows:

[0058]

[0059] In the formula, z1 and z2 are the state variables of the observer, z1 is the output of the estimation system, z2 is the total disturbance of the estimation system; β1 and β2 are two adjustable observer gains. From the frequency method, we can know that in LADRC, we have:

[0060]

[0061] Where ω0 is the bandwidth of the LADRC observer.

[0062] The total disturbance z2 of the observer estimated system is compensated to the control quantity in real time, and the linear state error feedback control law is adopted as follows:

[0063]

[0064] In the formula, k p is the gain of the controller, r is the reference input of the system;

[0065] Substitute equation (4) into equation (2), and then use Laplace transform to get the expression of control quantity U(s), input R(s) and output Y(s), such as:

[0066]

[0067] In formula (5), let Y(s) = 0, and we get:

[0068]

[0069] In formula (5), let R(s) = 0, and we get:

[0070]

[0071] From (6) and (7), we can see that LADRC control can be equivalent to Figure 1 The two-degree-of-freedom control model is shown in Figure 1 In the control model, there are two control degrees of freedom, namely, the front controller F(s) and the in-loop controller C(s), which can be designed independently. In the two-degree-of-freedom control model, the front controller F(s) is similar to a filter, which only meets the system's tracking characteristics for the input value and lacks anti-interference function. However, the in-loop controller C(s) can meet the system's anti-interference requirements. In view of the problem that the optoelectronic platform is susceptible to external disturbances when tracking the target, the in-loop controller C(s) becomes the key to LADRC control.

[0072] S2. Calculate the transfer function of the in-loop controller C(s)

[0073] Based on step S1, the transfer function of the in-loop controller C(s) is calculated using the superposition theorem of linear systems:

[0074]

[0075] It can be seen from equation (8) that the in-loop controller C(s) is equivalent to a PI controller connected in series with a low-pass filter (PIF), that is:

[0076]

[0077] Next, given the known PI controller parameter k′ p , k′ i Under the condition of p , b0, τ, τ is the time constant of the low-pass filter. From equation (3), we can see that the unknown parameters are ω0, k p , b0, τ. For the convenience of analysis, assume that the control parameter of the PI controller is k′ p=1, k′ i =10.

[0078] S3. Calculate the observer bandwidth ω0 of the LADRC controller

[0079] In order to ensure that the zero points of the LADRC controller and the PI controller are equal, the numerator in equation (9) is made into a multiple relationship, that is:

[0080]

[0081] In the formula, λ is a multiple;

[0082] Substituting formula (3) into formula (10), we get:

[0083]

[0084] To solve equation (11) for real roots when ω>0, let f(ω)=ω 3 -λk′ p ω+2λk′ i ; Taking the derivative of f(ω), we get:

[0085] f′(ω)=3ω 2 -λk′ p (12)

[0086] That is, f(ω) is There are two poles. In order for equation (11) to have real roots greater than zero, When f(ω)<0, we can calculate:

[0087]

[0088] The parameter of the PI controller, k′ p =1, k′ i = 10, substitute into formula (13), λ≥2700, let λ0=2700. When λ takes different values, the graph of f(ω) is as follows Figure 2 As shown. Figure 2 It can be seen that as λ continues to increase, the root of f(ω) will converge to 20 for the following reasons:

[0089] In formula (11), when λ>>ω0, we get:

[0090] -k′ p ω0+2k′ i =0 (14)

[0091] That is, ω0=2k′ i / k′ p =20. Therefore, as λ continues to increase, the root of f(ω) will converge to 20.

[0092] After the above analysis, the real roots of f(ω) are and as λ increases, it quickly converges to 2k′ i / k′ p Therefore, when solving equation (11), we can use equation (14) to calculate: ω0 = 2k′ i / k′ p .

[0093] S4. Calculate the control gain b0 of the LADRC controller

[0094] Using the fact that the low-frequency gains of the LADRC controller and the PI controller are equal, calculate b0 and set it in equation (10):

[0095]

[0096] When λ>>ω0, the simplification yields:

[0097]

[0098] S5. Calculate the time constant τ of the low-pass filter

[0099] The above steps can ensure that the Bode diagrams of the in-loop controller and the PI controller overlap at low frequencies, such as Figure 3 As shown, but from Figure 3 It can be seen that the in-loop controller and the PI controller do not overlap in the high-frequency stage. This is because the in-loop controller is similar to a low-pass filter in the high-frequency stage. In step S5, the time constant τ of the low-pass filter is calculated.

[0100] According to the characteristics of the low-pass filter in equation (9), when ω = 1 / τ, L(ω) = -3dB. In the high-frequency stage, find the point on the Bode diagram where the amplitude of the in-loop controller is 3dB smaller than that of the PI controller. Figure 3 As shown in point P, the frequency corresponding to point P is ω τ ,so:

[0101]

[0102] S6. Frequency characteristics verification of the in-loop controller and PIF controller

[0103] Through the above analysis, all the parameters of ADRC controller β1, β2, k are obtained. p The calculation formula of b0 and τ is:

[0104]

[0105] Among them, λ needs to satisfy formula (14) and be as large as possible.

[0106] The parameter of the PI controller, k′ p =1, k′ i =10, substituting into equation (9) and equation (18), the transfer function of PIF is calculated as:

[0107]

[0108] The parameter of the PI controller, k′ p =1, k′ i =10, and substituting it into equation (9) and equation (18), we get the transfer function of the in-loop controller C(s) as follows:

[0109]

[0110] Among them, take λ = 10 5 .

[0111] Use MATLAB to draw the Bode diagram of the loop controller and PIF controller as shown below: Figure 4 In the whole frequency range, the Bode diagrams of the in-loop controller and the PIF controller completely overlap, which verifies the correctness of the method proposed in this paper.

[0112] 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 method for calculating the initial value of linear active disturbance rejection control parameters for an optoelectronic platform, characterized in that: The linear active disturbance rejection control parameter initial value calculation method comprises the following steps: S1. Establish the equivalent two-degree-of-freedom control model of LADRC controller The equivalent two-degree-of-freedom control model has two control degrees of freedom, consisting of a front controller F(s) and an in-loop controller C(s); S2. Calculate the transfer function of the in-loop controller C(s) The transfer function of the in-loop controller C(s) is calculated using the superposition theorem of linear systems: Assume that the control parameter of the PI controller is k′ p =1, k i ′=10; derive the parameters of the LADRC controller, including β1, β2, k p , b0, τ; β1, β2 are two adjustable observer gains, k p is the controller gain, b0 is the actual control gain, and τ is the time constant of the low-pass filter; S3. Calculate the observer bandwidth of the LADRC controller The observer bandwidth ω0 of the LADRC controller is calculated according to the following formula: ω0=2k i ′ / k p ′ S4. Calculate the control gain of the LADRC controller The control gain b0 of the LADRC controller is calculated according to the following formula: S5. Calculate the time constant of the low-pass filter The time constant τ of the low-pass filter is calculated according to the following formula: In the formula, ω τ It is the frequency corresponding to the point where the amplitude of the in-loop controller is less than the set value L(ω) of the PI controller found on the Bode diagram.

2. The method for calculating initial values ​​of linear active disturbance rejection control parameters for an optoelectronic platform according to claim 1, characterized in that: In step S1, according to the first-order LADRC model: In the formula, f = g + (b-b0)u; y is the output of the control model; u is the control quantity of the system; g is the external disturbance; b is the real control gain; b0 is the actual control gain; f is the total disturbance of the system, including the external disturbance of the system and the unknown disturbance of the system; Take f as the expanded state of the system, introduce state variables x1 and x2, let x1 = y, x2 = f, Design a linear expansion observer as follows: In the formula, z1 and z2 are the state variables of the observer, z1 is the output of the estimation system, and z2 is the total disturbance of the estimation system; β1 and β2 are two adjustable observer gains. From the frequency method, we can know that in LADRC, there is: Where ω0 is the bandwidth of the LADRC observer; The total disturbance z2 of the observer estimated system is compensated to the control quantity in real time, and the linear state error feedback control law is adopted as follows: In the formula, k p is the gain of the controller, r is the reference input of the system; Substitute equation (4) into equation (2), and then use Laplace transform to get the expression of control quantity U(s), input R(s) and output Y(s), such as: In formula (5), let Y(s) = 0, and we get: In formula (5), let R(s) = 0, and we get: From (6) and (7), we get the equivalent two-degree-of-freedom control model of the LADRC controller.

3. The method for calculating initial values ​​of linear active disturbance rejection control parameters for an optoelectronic platform according to claim 2, characterized in that: In step S3, to ensure that the zero points of the LADRC controller and the PI controller are equal, set: In the formula, λ is a multiple.

4. The method for calculating initial values ​​of linear active disturbance rejection control parameters for an optoelectronic platform according to claim 1, characterized in that: In step S5, according to the characteristics of the low-pass filter, when ω=1 / τ, L(ω)=-3dB; in the high-frequency stage, find the point on the Bode diagram where the amplitude of the in-loop controller is 3dB smaller than that of the PI controller.

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