First-order linear active disturbance rejection controller parameter setting method based on phase margin method

Abstract

The invention discloses a first-order linear active disturbance rejection controller parameter setting method based on a phase margin method, and the method comprises the following steps: S1, obtaining simplified first-order inertia delay object parameters through an open-loop step response curve on site, and the simplified first-order inertia delay object parameters comprise the steady-state gain K, the inertia time constant T and the delay time tau of a controlled object; and S2, discussing and setting parameters of the controller according to conditions according to the ratio theta of the delay time tau of the controlled object to the inertia constant T. According to the first-order linear active-disturbance-rejection controller parameter setting method based on the phase angle margin method, the phase angle margin of the first-order linear active-disturbance-rejection controller is subjected to theoretical analysis, and the phase angle margin of the first-order linear active-disturbance-rejection controller and a closed-loop stable system of a controlled object is directly configured; and therefore, the problem of overshoot in parameter setting of the linear active disturbance rejection controller can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial process automation, and in particular to a first-order linear active disturbance rejection controller parameter tuning method based on a phase margin method. Background Art

[0002] With the rapid advancement of industrial automation technology, control systems are facing increasing demands for improved disturbance immunity and dynamic response performance. Active disturbance rejection control (ADRC) has become an important control strategy due to its ability to estimate system states in real time and effectively suppress disturbances. However, despite significant progress in theory and practice, ADRC still faces challenges in practical industrial applications, particularly in parameter tuning.

[0003] Traditional ADRC system parameter tuning typically relies on empirical trial-and-error methods, requiring extensive on-site debugging and repeated experimentation. This approach is not only inefficient but also susceptible to human influence, resulting in unstable and non-repeatable tuning results. Especially in complex industrial systems, parameter tuning often struggles to strike a balance between overshoot, response speed, and interference rejection. Overly fast system responses can lead to excessive overshoot, while overly slow responses can compromise control accuracy. As control system requirements increase, trial-and-error-based parameter tuning methods are becoming increasingly limited. More scientific and systematic tuning methods are urgently needed to improve control system performance and applicability.

[0004] Therefore, how to overcome the various problems brought about by the trial-and-error method and accurately and efficiently adjust the controller parameters has become the key to improving the ADRC control performance and promoting its widespread application in industry. Summary of the Invention

[0005] The purpose of the present invention is to provide a first-order linear active disturbance rejection controller parameter tuning method based on the phase margin method, which solves the problem of easy overshoot of the system closed-loop step response in the parameter tuning process of the standard first-order linear active disturbance rejection controller.

[0006] To achieve the above object, the present invention provides a first-order linear active disturbance rejection controller parameter tuning method based on a phase margin method, comprising the following steps:

[0007] S1. Obtain simplified first-order inertia delay object parameters on site through the open-loop step response curve, including the steady-state gain K, inertia time constant T and delay time τ of the controlled object;

[0008] S2. Based on the ratio θ of the controlled object delay time τ to the inertia constant T, the controller parameters are discussed and adjusted according to different situations.

[0009] Preferably, the specific process of S1 is:

[0010] The linear ADRC controller is simplified to the following transfer function form:

[0011] u=G v (s)v0-G y (s)y;

[0012] Where s is the complex frequency domain variable in the Laplace transform used to represent the dynamic characteristics of the system, v0 is the input of the tracking differentiator, and y is the output of the controlled object.

[0013]

[0014] Among them, ω o is the bandwidth of the extended state observer, ω c is the bandwidth of the linear error feedback control law, b0 is the initial value of the control gain of the active disturbance rejection control system;

[0015] make Then we have:

[0016]

[0017] The transfer function of the controlled object is:

[0018]

[0019] Where K is the steady-state gain of the controlled object, T is the inertia time constant and τ is the delay time;

[0020] Then the closed-loop transfer function is:

[0021] The open-loop transfer function is:

[0022] The cutoff frequency ω of the open-loop transfer function satisfies:

[0023]

[0024] The phase margin γ should be no less than That is, it satisfies:

[0025]

[0026] Preferably, the value range of λ is 0<λ≤1.

[0027] Preferably, in S2, the controlled object The ratio of the delay time τ to the inertia time constant T When 0<θ≤0.04, the following rules are used for parameter tuning:

[0028] Set the relevant parameters of the controller to:

[0029]

[0030] Preferably, in S2, when the controlled object When there is a delay and 0.04<θ≤2, use the following rules for parameter tuning:

[0031] Set the relevant parameters of the controller to:

[0032]

[0033] Preferably, in S2, when λ=0.1, The value range of k is 1.948≤k≤3.638;

[0034] like This season

[0035] When λ=0.1, k=2, the bandwidth ω of the linear error feedback law is obtained. c , bandwidth ω of the extended state observer o , the initial value of the control quantity gain b0 of the active disturbance rejection control system, and then adjust the k value according to the closed-loop response curve under the initial parameter state until the closed-loop response curve meets the overshoot of no more than 5%.

[0036] Preferably, in S2, when the controlled object When there is a delay and θ>2, use the following rules for parameter tuning:

[0037] According to the constant term of the controlled object, the expression is normalized into unitary form:

[0038]

[0039] Let the controller steady-state gain And take 0.25≤K c K≤0.3.

[0040] Preferably, let At this point we get:

[0041]

[0042] Preferably, set λ = 0.1, then The value of n is determined by n = f(θ) = (1 + θ) / 3, and the bandwidth ω of the linear error feedback law is obtained. c , bandwidth ω of the extended state observer o , the control quantity gain b0 of the active disturbance rejection control system.

[0043] Therefore, the present invention adopts the above-mentioned first-order linear active disturbance rejection controller parameter tuning method based on the phase margin method, and the beneficial effects are as follows:

[0044] (1) The present invention proposes a parameter tuning method for a first-order linear active disturbance rejection controller based on the phase margin method, which has a clear theoretical basis and simple operability. It overcomes the subjectivity and ambiguity of traditional empirical parameter tuning methods. In the parameter tuning process, the phase margin is followed, which greatly reduces the complexity of trial and error in traditional methods and greatly adapts to the needs of rapid on-site debugging.

[0045] (2) The tuning method proposed in the present invention effectively improves the dynamic performance and robustness of the control system through precise adjustment of the phase margin, and has significant technical innovation and broad application potential.

[0046] (3) The present invention has wide applicability in the field of industrial control, especially in dynamic and complex environments such as energy and power, and automation equipment, and has significant application advantages.

[0047] (4) The present invention not only improves the debugging efficiency of the control system, but also provides reliable guarantee for precise control in industrial processes, showing important technical value and practical significance.

[0048] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 1 is a control system structure diagram of an embodiment of a first-order linear active disturbance rejection controller parameter tuning method based on a phase margin method according to the present invention;

[0050] Figure 2 This is an n-θ fitting curve diagram of a first-order controlled object with θ>2 according to an embodiment of a first-order linear active disturbance rejection controller parameter tuning method based on a phase margin method of the present invention;

[0051] Figure 3 This is a closed-loop response curve effect diagram of a first-order controlled object with a value of 0<θ≤0.04 according to an embodiment of a first-order linear active disturbance rejection controller parameter tuning method based on a phase margin method of the present invention;

[0052] Figure 4 This is a closed-loop response curve effect diagram of a first-order controlled object with a value of 0.04<θ≤2 according to an embodiment of a first-order linear active disturbance rejection controller parameter tuning method based on a phase margin method of the present invention;

[0053] Figure 5 This is a closed-loop response curve effect diagram of an embodiment of a first-order linear active disturbance rejection controller parameter tuning method based on a phase margin method of the present invention for a first-order controlled object with θ>2;

[0054] Figure 6It is an effect diagram of the closed-loop response curve of the main steam temperature control system (sixth-order controlled object) of a thermal power plant according to an embodiment of the first-order linear active disturbance rejection controller parameter tuning method based on the phase margin method of the present invention. DETAILED DESCRIPTION

[0055] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0056] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0057] The control system in the first-order linear active disturbance rejection controller parameter tuning method based on the phase margin method is as follows Figure 1 As shown, including a controlled object and an active disturbance rejection controller, a first-order linear active disturbance rejection controller parameter tuning method based on phase margin includes the following steps:

[0058] S1. Obtain the simplified first-order inertia delay object parameters through the open-loop step response curve on site, including the steady-state gain K, inertia time constant T and delay time τ of the controlled object. The specific process is as follows:

[0059] The linear ADRC controller can be simplified into the following transfer function form:

[0060] u=G v (s)v0-G y (s)y;

[0061] Where s is the complex frequency domain variable in the Laplace transform used to represent the dynamic characteristics of the system, v0 is the input of the tracking differentiator, and y is the output of the controlled object.

[0062]

[0063] Among them, ω o is the bandwidth of the extended state observer, ω c is the bandwidth of the linear error feedback control law, b0 is the initial value of the control gain of the active disturbance rejection control system;

[0064] make Then we have:

[0065]

[0066] Then the transfer function of the controlled object (the simplified standard form of the first-order inertia delay object) is:

[0067]

[0068] Where K is the steady-state gain of the controlled object, T is the inertia time constant and τ is the delay time;

[0069] The following steps are usually taken to obtain these parameters through the open-loop step response curve:

[0070] 1. Estimation of gain K

[0071] The gain K can be estimated by observing the output changes in steady state. When the system inputs a step signal, the final output value is the product of the gain K and the input amplitude. Specifically, assuming the step input amplitude is A, the steady-state output value is Y ss , then the gain K is approximately:

[0072]

[0073] 2. Estimation of time constant T

[0074] The time constant, T, describes the dynamic characteristics of a system's response. It represents the time required for the system to reach 63% of its steady-state value. Specifically, by observing the step response curve, we can find the time required for the response curve to reach 63% of its steady-state value. This time difference is the time constant, T.

[0075] 3. Estimation of time lag τ

[0076] Time lag τ is the system's delay, representing the time from the start of a step input signal to the beginning of the output's response. This is typically done by observing the step response curve to find the moment when the output signal first noticeably responds (e.g., the response value deviates from zero). This time delay is then estimated, giving us the value of time lag τ.

[0077] Then the closed-loop transfer function is:

[0078] The open-loop transfer function is:

[0079] The cutoff frequency ω of the open-loop transfer function satisfies:

[0080]

[0081] The parameter tuning method of the first-order linear active disturbance rejection controller based on the phase margin method should make the phase margin γ not less than That is, it satisfies:

[0082]

[0083] The value range of λ is 0<λ≤1, preferably λ=0.1.

[0084] S2. Based on the ratio θ of the controlled object delay time τ to the inertia constant T, the controller parameters are discussed and adjusted according to different situations.

[0085] Order the accused The ratio of the delay time τ to the inertia time constant T When 0<θ≤0.04, the following rules are used for parameter tuning:

[0086] Set the relevant parameters of the controller to:

[0087]

[0088] When the accused When there is a delay and 0.04<θ≤2, use the following rules for parameter tuning:

[0089] Set the relevant parameters of the controller to:

[0090]

[0091] When λ=0.1, The value range of k is 1.948≤k≤3.638, and k=2 is preferred;

[0092] like This season

[0093] When λ=0.1, k=2, the bandwidth ω of the linear error feedback law is obtained. c , the bandwidth of the extended state observer ω o , the initial value of the control quantity gain b0 of the active disturbance rejection control system, and then adjust the k value according to the closed-loop response curve under the initial parameter state until the closed-loop response curve meets the overshoot of no more than 5%.

[0094] When the accused When there is a delay and θ>2, use the following rules for parameter tuning:

[0095] According to the constant term of the controlled object, the expression is normalized into unitary form:

[0096]

[0097] Let the controller steady-state gain And take 0.25≤K c K≤0.3, preferably K c K=0.25.

[0098] make At this point we get:

[0099]

[0100] If λ=0.1, then The value of n is determined by n = f(θ) = (1 + θ) / 3, and the bandwidth ω of the linear error feedback law is obtained. c, the bandwidth of the extended state observer ω o , the control quantity gain b0 of the active disturbance rejection control system.

[0101] Example 1:

[0102] First-order linear ADRC, we have:

[0103] D1=(s+ω o ) 2 , D2=s+ω c

[0104]

[0105] D3=s+(2ω o +ω c ),

[0106] then: Again but The transfer function of the controlled object is:

[0107]

[0108] Then the closed-loop transfer function is:

[0109] Open-loop transfer function:

[0110] First find the cutoff frequency:

[0111]

[0112] Then calculate the phase margin (this phase margin method is to make ):

[0113]

[0114] According to the above analysis, there are two equations for cutoff frequency and phase margin, but there are three unknowns (ω, ω c , b0), so one of the ADRC parameters must be known, so the following will be based on the ratio of the delay time of the controlled object to the inertia time constant The parameter adjustment is discussed in three cases.

[0115] 1) When the accused When the ratio of the delay time to the inertia time constant is small, that is, 0≤θ≤0.04, the controller parameters are directly configured as

[0116] First find the cutoff frequency:

[0117]

[0118] As a special case, when λ = 0.1, Tω = 6.631, and the phase margin is:

[0119]

[0120] Therefore, when the controller parameters are directly configured as When θ is less than 0.04, it can be deduced from the phase margin method that the maximum ratio of the delay time of the controlled object to the inertia time constant cannot exceed 0.04, that is, θ≤0.04.

[0121] 2) When the accused When the ratio of the delay time to the inertia time constant satisfies 0.04<θ≤2, the following rules are used for parameter tuning:

[0122] make Using the cutoff frequency formula:

[0123]

[0124] Obtain:

[0125]

[0126] Unitize the constant term in the above formula to get:

[0127]

[0128] make but

[0129] Then use the phase margin formula have to:

[0130]

[0131] Special case: when λ=0.1, is known, then according to the phase margin formula, we have Solve for τω. The following table shows the corresponding values ​​of k and b0 for different values ​​of θ.

[0132] Table 1 Obtain the corresponding values ​​of k and b0 according to different values ​​of θ

[0133]

[0134]

[0135] Therefore, when the ratio of the delay time of the controlled object to the inertia time constant satisfies 0.04<θ≤2, according to the phase margin method, the value range of the controller parameter k must satisfy 1.948≤k≤3.638.

[0136] 3) When the accused When the ratio of the delay time to the inertia time constant satisfies θ>2, the following rules are used for parameter tuning:

[0137] The open-loop transfer function at this time is:

[0138] If zero-pole cancellation is not performed, then the definition is:

[0139] Again

[0140] The open-loop transfer function is then organized as:

[0141]

[0142] Then use the cutoff frequency formula:

[0143]

[0144] Let x = Tω, the above formula can be rearranged as follows:

[0145]

[0146] Still taking λ=0.1 as an example, the above formula can be derived as follows:

[0147]

[0148] There are two unknowns, And x=Tω. According to the phase margin formula, we can get:

[0149]

[0150] Then we get:

[0151]

[0152] At this point, the ratio of the controlled object's delay time to its inertia time constant, θ, is known and satisfies θ>2. Theoretically, the value of n should be solved by combining equations (1) and (2). However, the solution is cumbersome and not applicable to engineering sites. Therefore, we consider fitting the n=f(θ) curve.

[0153] Substitute the value of n into formula (1) to obtain x, and substitute x into formula (2) to obtain the relationship between n and θ as shown in the table below.

[0154] Table 2 The relationship between n and θ according to different values ​​of n

[0155] n 1 1.5 2 2.5 3 3.5 4 4.5 5 x 0.25 0.169 0.128 0.103 0.0857 0.0736 0.0644 0.0573 0.0516 θ 2.055 3.507 4.975 6.450 7.928 9.407 10.887 12.368 13.850

[0156] According to the results in the table, draw the n-θ fitting curve as shown in the following figure: Figure 2 The results show that the relationship between n and θ satisfies n = f(θ) = (1 + θ) / 3. Using the phase margin method and the n-θ fitting curve, the value of θ is obtained from the parameters of the controlled object, and the controller parameter n is then obtained using the n-θ fitting curve.

[0157] Example 2:

[0158] For the first-order model with 0<θ≤0.04 The first-order linear active disturbance rejection controller parameter tuning method based on the phase margin method proposed in the present invention is used for simulation verification.

[0159] The simulation uses the fixed-step Euler method to solve the problem, with a step size of 0.01. Determine the system parameters T = 1, K = 1, and take τ = 0, τ = 0.02 and τ = 0.04 respectively, that is, θ = 0, θ = 0.02 and θ = 0.04. Since 0 < θ ≤ 0.04, according to the tuning method, take Let λ = 01. Then we get The step response curve obtained by running is as follows Figure 3 As shown, the first-order linear active disturbance rejection controller maintains The results prove the necessity of the present invention, that is, when 0<θ≤0.04, the overshoot-free parameter tuning of the linear active disturbance rejection controller is achieved.

[0160] Example 3:

[0161] First-order model for small delays The first-order linear active disturbance rejection controller parameter tuning method based on the phase margin method proposed in the present invention is used for simulation verification.

[0162] The simulation is solved by the fixed-step Euler method with a step size of 0.01. The system parameters T = 1, K = 1, and the values ​​of τ are 0.05, 0.1, 0.5, 1 and 2 respectively. According to the above tuning method, let λ = 0.1, and then we get At this time, k is preferably 2, and the initial value is They are 0.686, 1.371, 6.857, 13.714 and 27.429 respectively.

[0163] Note that when τ = 0.05, k = 2 is preferred, and according to Calculated Therefore, according to the parameter setting method, when τ = 0.05,

[0164] The step response curve obtained by running is as follows Figure 4As shown, the values ​​of τ are 0.05, 0.1, 0.5, 1 and 2, and the overshoot of the closed-loop response curve is 0.00%, 0.00%, 0.00%, 1.59% and 3.79% respectively. The results show that the parameter tuning method described in this patent can effectively control the overshoot within 5%.

[0165] Example 4:

[0166] First-order model for large delays The first-order linear active disturbance rejection controller parameter tuning method based on the phase margin method proposed in the present invention is used for simulation verification.

[0167] The simulation is solved by the fixed-step Euler method with a step size of 0.01. The system parameters T = 1, K = 1, and the values ​​of τ are 29, 119 and 299 respectively. They are 29, 119 and 299 respectively, and the values ​​of θ are all greater than 2. Let λ = 0.1 and according to the above tuning method, the corresponding relationship of n-θ n = f(θ) = (1+θ) / 3 determines that n is 10, 40 and 100 respectively, and then we get Take 2.743, 0.686 and 0.274 respectively.

[0168] And according to Get ω c The values ​​of are 0.120, 0.030 and 0.012 respectively, ω o The values ​​of are 1.200, 0.300 and 0.120 respectively. According to the above parameters, the step response curve is as follows Figure 5 As shown, the overshoot of the closed-loop response curve is 4.43% at this time. The results show that the parameter tuning method described in this patent can effectively control the overshoot within 5%.

[0169] Embodiment 5:

[0170] For a main steam temperature system model, is the leading zone model (℃ / %), is the inert zone model (℃ / ℃). This model can be simplified to a first-order model

[0171] The simulation uses the fixed-step Euler method to solve the problem, with a step size of 0.01. Determine the system parameters T = 80, K = -2.51, τ = 84.2, and set λ = 0.1. Since 0 < θ < 2, according to the tuning method, k is preferably 2 at this time, and the initial value is obtained. Let λ = 1.0, and then we get Draw the closed-loop response curve under the initial value state; to reduce the adjustment time, adjust the value of k according to the closed-loop response curve until the closed-loop response curve meets the overshoot of no more than 5%, at this time b0 = -0.383.

[0172] The step response curve obtained by running is as follows Figure 6 As shown, the first-order linear active disturbance rejection controller maintains Under the premise of increasing the value of controller parameter b0 from -0.453 to -0.383, the overshoot of the response curve increases from 0.10% to 4.89%, and the adjustment time of the response curve decreases from 376.52s to 320.44s. The results show that the parameter tuning method of the present invention can effectively control the overshoot within 5% and minimize the adjustment time.

[0173] Therefore, the present invention adopts the above-mentioned first-order linear active disturbance rejection controller parameter tuning method based on the phase margin method. The debugging rules are reasonable, more suitable for the debugging site, and the theoretical guidance is specific, avoiding the problem of vague parameter adjustment process brought about by the empirical tuning method.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments,

[0175] It should be understood by those skilled in the art that the technical solution of the present invention can still be modified.

[0176] Modification or equivalent replacement, and these modifications or equivalent replacements cannot make the modified technology

[0177] The solution deviates from the spirit and scope of the technical solution of the present invention.

Claims

1. A first-order linear active disturbance rejection controller parameter tuning method based on the phase margin method is characterized by: The following steps are involved: S1. Obtain simplified first-order inertia delay object parameters on site through the open-loop step response curve, including the steady-state gain K, inertia time constant T and delay time τ of the controlled object; S2. Based on the ratio θ of the controlled object delay time τ to the inertia constant T, the controller parameters are discussed and adjusted according to different situations.

2. The method for parameter tuning of a first-order linear active disturbance rejection controller based on the phase margin method according to claim 1, characterized in that: The specific process of S1 is as follows: The linear ADRC controller is simplified to the following transfer function form: u=G v (s)v0-G y (s)y; Where s is the complex frequency domain variable in the Laplace transform used to represent the dynamic characteristics of the system, v0 is the input of the tracking differentiator, and y is the output of the controlled object. Among them, ω o is the bandwidth of the extended state observer, ω c is the bandwidth of the linear error feedback control law, b0 is the initial value of the control gain of the active disturbance rejection control system; make Then we have: The transfer function of the controlled object is: Where K is the steady-state gain of the controlled object, T is the inertia time constant and τ is the delay time; Then the closed-loop transfer function is: The open-loop transfer function is: The cutoff frequency ω of the open-loop transfer function satisfies: The phase margin γ should be no less than That is, it satisfies:

3. The method for parameter tuning of a first-order linear active disturbance rejection controller based on the phase margin method according to claim 2, characterized in that: The value range of λ is 0<λ≤1.

4. The method for parameter tuning of a first-order linear active disturbance rejection controller based on the phase margin method according to claim 3, characterized in that: In S2, let the controlled object The ratio of the delay time τ to the inertia time constant T When 0<θ≤0.04, the following rules are used for parameter tuning: Set the relevant parameters of the controller to:

5. The method for parameter tuning of a first-order linear active disturbance rejection controller based on the phase margin method according to claim 4, characterized in that: In S2, when the controlled object When there is a delay and 0.04<θ≤2, use the following rules for parameter tuning: Set the relevant parameters of the controller to:

6. The method for parameter tuning of a first-order linear active disturbance rejection controller based on the phase margin method according to claim 5, characterized in that: In S2, when λ=0.1, The value range of k is 1.948≤k≤3.638; like This season When λ=0.1, k=2, the bandwidth ω of the linear error feedback law is obtained. c , bandwidth ω of the extended state observer o , the initial value of the control quantity gain b0 of the active disturbance rejection control system, and then adjust the k value according to the closed-loop response curve under the initial parameter state until the closed-loop response curve meets the overshoot of no more than 5%.

7. The method for parameter tuning of a first-order linear active disturbance rejection controller based on the phase margin method according to claim 6, characterized in that: In S2, when the controlled object When there is a delay and θ>2, use the following rules for parameter tuning: According to the constant term of the controlled object, the expression is normalized into unitary form: Let the controller steady-state gain And take 0.25≤K c K≤0.

3.

8. The method for parameter tuning of a first-order linear active disturbance rejection controller based on the phase margin method according to claim 7, characterized in that: make At this point we get:

9. The method for parameter tuning of a first-order linear active disturbance rejection controller based on the phase margin method according to claim 8, characterized in that: If λ=0.1, then The value of n is determined by n = f(θ) = (1 + θ) / 3, and the bandwidth ω of the linear error feedback law is obtained. c , bandwidth ω of the extended state observer o , the control quantity gain b0 of the active disturbance rejection control system.

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