A method and system for determining a second-order universal fast-saturation-avoiding controller

Abstract

The application discloses a kind of second-order general type fast desaturation controller determination method and system, it is related to engineering system control field, this method includes: determining the saturation gain of actuator in target industrial control system;Using the input-output deviation of actuator, second-order general type fast integral desaturation compensator is constructed;Based on saturation gain, second-order general type fast integral desaturation compensator is equivalent into the desaturation structure of series compensation, and the compensation link and desaturation channel in desaturation structure are determined;Using the linkage relationship of bandwidth PID controller and desaturation bandwidth, the value of desaturation bandwidth in compensation link and desaturation channel is determined, to obtain the second-order general type fast desaturation controller of target industrial control system.The application can realize control while selecting less parameters, and improve the stability of control.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of engineering system control, in particular to a determination method and system of a second-order general fast desaturation controller. BACKGROUND

[0002] With the continuous advancement of industry, the development of high-end manufacturing industry puts forward higher requirements for control system. For example, the industrial servo system pursues high response bandwidth and anti-interference ability of automatic control under the premise of stability and reliability. Since the actual physical system is generally subject to input amplitude constraint, it is difficult to fully exert the anti-interference ability of the control system. Saturation constraint belongs to hard nonlinearity, and its non-smooth characteristics cannot be ignored or linearized, which increases the difficulty of analysis and design. At the same time, saturation amplitude will destroy the stability of the control system and cause serious harm. At present, the desaturation problem is generally studied for linear time-invariant systems, and the stability and design problem of linear time-invariant systems under saturation constraint are discussed. According to the different design concepts and processing strategies, the existing methods can be divided into three categories. The first method is the classic "two-step method", that is, for a linear time-invariant system, first ignore the saturation factor, and design a linear controller that meets the control requirements. The second method is to consider both linear and nonlinear modes of the system, and to design a closed-loop control system using nonlinear system theory. The third method is a low-gain design, that is, by reducing the loop gain of the control system, the control system is prevented from entering the saturation state. Although the working principle of the anti-saturation control is very intuitive, the adjustment mechanism between the controller parameters and the control performance is still not clear enough, so that the controller design has to rely on the mathematical model of the object and various complex stability conditions. The existing desaturation method is relatively complex, and the control stability needs to be improved. SUMMARY

[0003] Based on this, the embodiment of the present application provides a determination method and system of a second-order general fast desaturation controller, which can realize control while improving the stability of control by selecting fewer parameters.

[0004] To achieve the above object, the present application provides the following scheme:

[0005] A determination method of a second-order general fast desaturation controller, comprising:

[0006] determining the saturation gain of the actuator in the target industrial control system;

[0007] using the input-output deviation of the actuator to construct a second-order general fast integral desaturation compensator;

[0008] determine a saturation gain of the target industrial control system based on the saturation of the actuator of the target industrial control system;

[0009] determine a bandwidthed PID controller of the target industrial control system;

[0010] determine a value of the saturation bandwidth in the compensation link and the saturation channel based on a linkage relationship between the bandwidthed PID controller and the saturation bandwidth;

[0011] determine a second-order general fast saturation compensator of the target industrial control system based on the compensation link after the value of the saturation bandwidth is determined and the saturation channel after the value of the saturation bandwidth is determined.

[0012] Optionally, the expression of the saturation gain is:

[0013]

[0014] wherein, ρ represents the saturation gain; u * is an input of the actuator; u is a saturated output of the actuator; sat(.) is a saturation nonlinear function, u max is an upper limit of the input of the actuator; u min is a lower limit of the input of the actuator; u max = -u min = 1.

[0015] Optionally, the second-order general fast integral saturation compensator is:

[0016]

[0017] G0(s) is a second-order general fast integral saturation compensator; ω s is a saturation bandwidth; τ1 and τ2 are both time constants, τ1, τ2 > 0; n is an order; s is a differential operator after Laplace transformation.

[0018] Optionally, the saturation structure is:

[0019]

[0020] wherein, u(s) is a saturated output of the actuator expressed by a differential operator; u * (s) is an input of the actuator expressed by a differential operator; ρ represents a saturation gain; u(s) is an input of a pre-saturation actuator expressed by a differential operator; s is a differential operator after Laplace transformation; Δ(s) is a saturation channel.

[0021] Optionally, the compensation element is:

[0022]

[0023] wherein M(s) is the compensation element; p represents a saturation gain; s is a differential operator after Laplace transformation; t1 and t2 are both time constants, t1, t2>0; n is an order; w s is a desaturation bandwidth;

[0024] The desaturation channel is:

[0025]

[0026] wherein D(s) is the desaturation channel.

[0027] Optionally, the bandwidthed PID controller is:

[0028]

[0029] wherein C(s) represents the bandwidthed PID controller; s is a differential operator after Laplace transformation; w c is a desired closed-loop bandwidth parameter; a is a phase lead compensation factor; K p is a controller gain, K p >0.

[0030] Optionally, when n=1 or t1=t2, the compensation element after determining the value of the desaturation bandwidth and the desaturation channel after determining the value of the desaturation bandwidth are:

[0031]

[0032] wherein M(s) is the compensation element; D(s) is the desaturation channel; p represents a saturation gain; s is a differential operator after Laplace transformation; t1 and t2 are both time constants, t1, t2>0; n is an order; w s is a desaturation bandwidth; for any p e [0 + ,1], w s satisfies: w s >0, b>1; b is an amplification coefficient;

[0033] When n=2 and t1≠t2, the compensation element after determining the value of the desaturation bandwidth and the desaturation channel after determining the value of the desaturation bandwidth are:

[0034]

[0035] for any p e [0 + ,1], and t1, t2 are both positive, ws Satisfy: ω s >0, ω s (1-ρ)τ²≤1; for ρ=0 + ω s Satisfy: 4ω s τ2≤1; for any ρ∈[0 + ,1], and τ2>τ1>0, ω s satisfy:

[0036] The present invention also provides a system for determining a second-order universal fast desaturation controller, comprising:

[0037] The saturation gain determination module is used to determine the saturation gain of actuators in the target industrial control system.

[0038] The compensator construction module is used to construct a second-order general-purpose fast integral desaturation compensator using the input-output deviation of the actuator;

[0039] The compensator equivalent module is used to convert the second-order general-purpose fast integral desaturation compensator into a series-compensated desaturation structure based on the saturation gain, and to determine the compensation stage and desaturation channel in the desaturation structure; both the compensation stage and the desaturation channel include a desaturation bandwidth to be determined.

[0040] A bandwidth-optimized PID controller determination module is used to determine the bandwidth-optimized PID controller of the target industrial control system.

[0041] The desaturation bandwidth determination module is used to determine the value of the desaturation bandwidth in the compensation circuit and the desaturation channel by using the linkage relationship between the bandwidth-optimized PID controller and the desaturation bandwidth.

[0042] The desaturation controller determination module is used to determine the second-order general-purpose fast desaturation controller of the target industrial control system based on the compensation link after determining the value of the desaturation bandwidth and the desaturation channel after determining the value of the desaturation bandwidth.

[0043] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0044] The embodiment of the present application provides a determination method and system of a second-order general fast desaturation controller, introduces saturation gain, adopts input-output deviation of an actuator to construct a second-order general fast integral desaturation compensator, equivalently converts the second-order general fast integral desaturation compensator into a desaturation structure of series compensation based on the saturation gain, and determines compensation links and desaturation channels in the desaturation structure; adopts a linkage relationship between a bandwidth PID controller and a desaturation bandwidth, determines the value of the desaturation bandwidth in the compensation links and the desaturation channels, and thus obtains the second-order general fast desaturation controller of the target industrial control system. The present application only needs to determine the value of the desaturation bandwidth to obtain the controller, and can improve the stability of control, so that the present application meets stability regulation, has less parameter selection, clear physical meaning and excellent control effect. BRIEF DESCRIPTION OF DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced below. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0046] Figure 1 The flow chart of the determination method of the second-order general fast desaturation controller provided by the embodiment of the present application;

[0047] Figure 2 The schematic diagram of the anti-saturation compensator added in the PID system;

[0048] Figure 3 The schematic diagram of the desaturation compensator equivalent to a desaturation series compensation structure;

[0049] Figure 4 The schematic diagram of the DC motor bandwidth PID non-saturation compensation speed position control;

[0050] Figure 5 The schematic diagram of the DC motor bandwidth PID ω s =5 saturation compensation speed position control;

[0051] Figure 6 The schematic diagram of the DC motor bandwidth PID ω s =10 saturation compensation speed position control;

[0052] Figure 7 The schematic diagram of the DC motor bandwidth PID ω s =20 saturation compensation speed position control;

[0053] Figure 8Different ω for equivalent series compensation bandwidth design of first-order fast desaturation controller in second-order system s Step response time schematic diagram

[0054] Figure 9 Different ω for equivalent series compensation bandwidth design of first-order fast desaturation controller in second-order system s Saturation input schematic diagram

[0055] Figure 10 Different ω for equivalent series compensation bandwidth design of second-order fast desaturation controller in second-order system s Step response time schematic diagram

[0056] Figure 11 Different ω for equivalent series compensation bandwidth design of second-order fast desaturation controller in second-order system s Saturation input schematic diagram

[0057] Figure 12 The structure diagram of the determination system of the second-order universal fast desaturation controller is provided in the embodiment of the present application. DETAILED DESCRIPTION

[0058] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0059] At present, the adjustment mechanism between the controller parameters and the control performance is still not clear enough, so that the controller design has to rely on the mathematical model of the object and various complex stability conditions. Correspondingly, if the feedback adjustment mechanism of each loop can be fully utilized, a simple and clear mapping relationship between the controller parameters and the control performance is established, even if the system model cannot be accurately obtained, engineering application can still be carried out based on the parameter adjustment mapping relationship of the feedback control. The present application introduces a desaturation compensator in a kind of control structure, deeply studies the adjustment mechanism of desaturation control under the bandwidth design concept, and proposes the frequency domain condition and design method of critical desaturation control.

[0060] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0061] Referring to Figure 1 The determination method of the second-order universal fast desaturation controller of the present embodiment comprises:

[0062] Step 101: Determine the saturation gain of the actuators in the target industrial control system.

[0063] Step 102: Using the input-output deviation of the actuator, construct a second-order general-purpose fast integral desaturation compensator.

[0064] Step 103: Based on the saturation gain, the second-order general-purpose fast integral desaturation compensator is equivalent to a series-compensated desaturation structure, and the compensation element and desaturation channel in the desaturation structure are determined; both the compensation element and the desaturation channel include the desaturation bandwidth to be determined.

[0065] Step 104: Determine the bandwidth-optimized PID controller for the target industrial control system.

[0066] Step 105: Using the linkage relationship between the bandwidth-optimized PID controller and the desaturation bandwidth, determine the value of the desaturation bandwidth in the compensation circuit and the desaturation channel.

[0067] Step 106: Based on the compensation circuit after determining the value of the desaturation bandwidth and the desaturation channel after determining the value of the desaturation bandwidth, determine the second-order general-purpose fast desaturation controller of the target industrial control system.

[0068] In one example, in step 101, the saturation gain ρ = u / u is defined. * ∈(0,1], the expression for the saturation gain is:

[0069]

[0070] Where ρ represents the saturation gain, and ρ can be used to measure the degree of system saturation; u * u is the input of the actuator; u is the saturation output of the actuator; sat(.) is a saturated nonlinear function, u max u is the upper bound of the actuator's input; min u is the lower bound of the actuator input; max =-u min =1. When ρ = 1, it is a non-saturated linear state; when ρ: 1→1 - When ρ≈0, it is in the critical saturation state; + At this point, it is in a state of deep saturation. 0 + Represents a number that is close to 0 but greater than 0, 1 - Represents a number that is close to 1 but less than 1, 0 + 1 - It is a commonly used form of expression in mathematics.

[0071] In one example, in step 102, the second-order general-purpose fast integral desaturation compensator is:

[0072]

[0073] G0(s) is a second order general type of fast integral anti-windup compensator; ω s is the anti-windup bandwidth, as the gain of G0(s); τ1 and τ2 are both time constants, τ1, τ2 > 0; n is the order; s is the differential operator after Laplace transform.

[0074] G0(s) contains the widely used integral anti-windup ω s / s in engineering, and also contains other dynamic compensation links to improve the dynamic performance of anti-windup compensation.

[0075] In one example, in step 103, the anti-windup structure is:

[0076]

[0077] wherein u(s) is the saturated output of the actuator expressed in differential operator; u * (s) is the input of the actuator expressed in differential operator; ρ represents the saturation gain; is the input of the anti-windup front actuator expressed in differential operator; s is the differential operator after Laplace transform; Δ(s) is the anti-windup channel. When saturation occurs, ρ: 1 → 1 - , plays an anti-windup role, achieves the effect of weakening u * (s), and forces u * (s) to change towards u(s).

[0078] In one example, in step 103, the compensation link is:

[0079]

[0080] wherein M(s) is the compensation link; ρ represents the saturation gain; s is the differential operator after Laplace transform; τ1 and τ2 are both time constants, τ1, τ2 > 0; n is the order; ω s is the anti-windup bandwidth.

[0081] The anti-windup channel is:

[0082]

[0083] wherein Δ(s) is the anti-windup channel.

[0084] The compensation link M(s) contains the saturation gain ρ and the anti-windup gain [1-Δ(s)], wherein Δ(s) is essentially a low-pass filter, which constitutes the anti-windup channel. ω sω s The greater the ω s , the faster the desaturation speed. c The ω p is the desaturation bandwidth, which determines the desaturation speed.

[0085] In one example, in step 104, the bandwidthed PID controller is:

[0086]

[0087] where C(s) represents the bandwidthed PID controller, s is the differential operator after Laplace transformation, ω c is the expected closed-loop bandwidth parameter, which is determined by the fast and slow characteristics of the system, α is the phase lead compensation factor, and K p is the controller gain, K p > 0.

[0088] In one example, in step 105, when n = 1 or τ1 = τ2, it is a special case of the second order, that is, the conventional integral desaturation is represented as G0(s) = ω s / s, the compensation element after determining the value of the desaturation bandwidth and the desaturation channel after determining the value of the desaturation bandwidth are:

[0089]

[0090] where M(s) is the compensation element, Δ(s) is the desaturation channel, ρ represents the saturation gain, s is the differential operator after Laplace transformation, τ1 and τ2 are both time constants, τ1, τ2 > 0, n is the order, and ω s is the desaturation bandwidth. For any ρ ∈ [0 + , 1], ω s satisfies: ω s > 0, β > 1; β is the amplification coefficient.

[0091] That is, for any ρ ∈ [0 + , 1], ω s > 0 all satisfy the desaturation necessary condition, at this time Δ(s) is a first-order inertial element, and the greater the ω s , the faster the desaturation speed. It can be seen that the conventional integral desaturation compensator has simple structure, easy implementation, and good frequency characteristics, which is the reason why integral desaturation is widely used. At the same time, it is not difficult to find from the above analysis that when the system enters critical saturation, ρ: 1 → 1 - , under the condition that a small amount of ω s (1-ρ) → 0 + , Δ(s) mainly relies on integration to weaken u * (s). Therefore, the faster the desaturation speed is not necessarily better, ωs Too large, will affect the system performance. When ω s > 0, the linkage relationship with ω c is, β> 1.

[0092] When n = 2 and τ1≠ τ2, the compensation link after determining the value of the desaturation bandwidth and the desaturation channel after determining the value of the desaturation bandwidth are:

[0093]

[0094] For any ρ∈ [0 + ,1] and τ1, τ2 are positive, ω s satisfies: ω s > 0, ω s (1-ρ)τ2≤1; for ρ = 0 + , ω s satisfies: 4ω s τ2≤1; for any ρ∈ [0 + ,1] and τ2> τ1> 0, ω s satisfies:

[0095] That is, in order to avoid the oscillation of the desaturation process, it is required that the characteristic polynomial of Δ (s) contains two negative real roots, and the condition is When ω s , τ1, τ2 are positive, if ω s (1-ρ)τ2≤1, then for any ρ∈ [0 + ,1], holds.

[0096] In order to cope with the deep saturation situation, that is, ρ = 0 + , a relatively conservative condition 4ω s τ2≤1 can be established, so that holds.

[0097] Consider a class of extreme cases τ1→ 0, τ2→ ∞, τ2> τ1> 0, in the case of small ω s (1-ρ)→ 0 + , Δ (s) is approximately double integration, and the desaturation speed will be faster than n = 1.

[0098] Therefore, n = 2 generally has τ2> τ1> 0. For high-order cases of n > 2 in G0 (s), the method given by the present application can still be used for analysis and design.

[0099] When the parameters ω s > 0, τ2> τ1> 0, the parameter linkage relationship with ω c is:

[0100]

[0101] In practical applications, one determination method of the above-mentioned second-order general type fast desaturation controller is as follows:

[0102] The general idea is to express the actuator saturation as a variable gain coefficient to measure the saturation degree; in a PID feedback control system, a second-order general type fast integral desaturation compensation is constructed by using the deviation of the actuator input and output; the desaturation compensator is equivalent to a series compensation desaturation structure, wherein the desaturation compensator has a clear filter bandwidth characteristic, and the second-order structure can be compatible with the first-order integral desaturation scheme; the parameter bandwidth form of the PID controller is adopted, and the bandwidth design adjustment of the filter parameters is given, while the stability adjustment is satisfied.

[0103] Specifically as follows:

[0104] Step 1: The actuator saturation is expressed as a variable gain coefficient, and the saturation gain is defined to measure the saturation degree.

[0105] Step 2: For a PID control system, a second-order general type fast integral desaturation compensator G0(s) is constructed by using the deviation of the actuator input and output.

[0106] Step 3: The desaturation compensator is equivalent to a type of desaturation series compensation structure, and the bandwidth characteristic of the compensator parameters is described; as shown in Figure 3 , the desaturation structure can be obtained.

[0107] The desaturation structure is arranged to obtain the compensation link M(s) and the desaturation channel Δ(s), and M(s) is the compensation link containing the saturation gain ρ and the desaturation gain [1-Δ(s)], which is transformed into the structure shown in Figure 3 .

[0108] Step 4: The bandwidth form of the PID controller is adopted to establish the association between the desaturation parameters and the bandwidth of the PID controller, and the fast desaturation parameters are designed under the conditions of stability and non-oscillation.

[0109] As shown in Figure 2 , G(s) is a stable object; G0(s) is a desaturation compensator; C(s) is a bandwidth PID; sat(.) is a saturation nonlinear function; ρ represents a saturation gain; G0(s) is a second-order general type fast integral desaturation compensator; M(s) is a compensation link; G(s) is a controlled object; F r (s) is a pre-filter; C(s) is a bandwidth PID controller; u * is the input of the actuator; u is the saturated output of the actuator; Controller output; r is the set input; y is the system output; d is the external disturbance.

[0110] For further details, a specific example is given below.

[0111] Example 1

[0112] The experimental controlled object is a high-precision DC motor with a photoelectric encoder provided by Dongguan Micro Macro Intelligence Technology Co., Ltd. (15000P / R after reduction), rated voltage 12V, rated current 0.36A, no-load speed 366±rpm, and rated torque 1kg.cm. The motor system transfer function obtained by least squares method system parameter identification is: The saturation input of the object is the duty cycle The no-load, full-load, and half-load experiments are performed on the speed inner loop and position outer loop control.

[0113] Step 1: Define the saturation gain ρ, and given the motor duty cycle saturation input, we have ρ = u / u * ∈(0,1], input is u * , saturation output is u

[0114]

[0115] Step 2: Use n = 1 or (τ1 = τ2), i.e. regular integral desaturation ω s motor control system, the speed loop output duty cycle u is controlled, so G0(s) is added to the speed loop for saturation compensation.

[0116] Step 3: The motor control system desaturation compensator is equivalent to a series compensation structure, M(s) is the compensation link which can be transformed as:

[0117]

[0118] where M(s) is the compensation link containing saturation gain ρ and desaturation [1-Δ(s)] gain, which is transformed as Figure 3 structure. Where Δ(s) is a low-pass filter, which constitutes a desaturation channel, i.e. using filtered signal to weaken , achieve desaturation effect, ω s is the bandwidth related parameter of desaturation channel Δ(s).

[0119] Step 4: Construct C(s) as a bandwidth PID speed inner loop and position outer loop:

[0120]

[0121] The output of the double closed loop control system without saturation compensator is shown in Fig. 1 when the motor is in no-load state. The position curve of the motor is slightly overshooted. The control variable curve shows that the overshoot is caused by the saturation of the controller. Figure 4

[0122] Adjust ω s , ω s The linkage is β>1, ω s >5 is the recommended value range. The bandwidth of the conventional integral saturation compensator is ω s =5, 10, 20, and ω s is gradually increased. The results are shown in Fig. 2. s Figures 5-7 .

[0123] The overshoot of the double closed loop control system without saturation compensator is suppressed by adding the saturation compensator.

[0124] Since the motor is a fast-response system, the anti-disturbance ability of the system is weakened when the bandwidth of the compensator is increased at half load and full load. Therefore, ω s =5 is a reasonable value to meet the control requirements in this embodiment.

[0125] Example 2

[0126] When the controlled object is a second-order system, the saturation input of the object is

[0127] Step 1: Define the saturation gain ρ, ρ = u * ∈(0, 1], the input is u * , and the saturated output is u

[0128]

[0129] Scheme 1:

[0130] Step 2: n = 1 or (τ1 = τ2) is used, that is, the conventional integral saturation compensator is used. The second-order system is added to the saturation compensator.

[0131] Step 3: The second-order system saturation compensator is equivalent to a series saturation compensator structure, and M(s) is the compensation link. It can be transformed as:

[0132]

[0133]

[0134] wherein ​​​M(s) is the compensation stage, which includes the saturation gain ρ and the desaturation gain [1-Δ(s)], and is transformed into... Figure 3 Structure. Where Δ(s) is a low-pass filter, forming a desaturation channel, i.e., using... Attenuation of filtered signal To achieve desaturation effect, ω s The bandwidth-related parameters for the desaturated channel Δ(s) are given.

[0135] Step 4: Construct C(s) as a bandwidth-optimized PID:

[0136]

[0137] ω c The desired closed-loop bandwidth parameter is determined by the system's speed characteristics; α represents the phase lead compensation factor.

[0138] The bandwidth-optimized PI controller used is C(s) = 6(1 + 0.833 / s), where ω c =0.833, α=0. Adjust ω s ω s The linkage relationship is β>1 yields ω s A value greater than 0.417 is the recommended range. The conventional integral desaturation compensator is set to ω... s =0.5, 2, 5, gradually increase ω s Observe its effects, such as Figure 8 , Figure 9 When ω s When the bandwidth ω = 0.5, the system overshoot is quite significant, making it impossible to achieve the desired control effect. Further increasing the desaturation bandwidth ω... s Let its value be ω s =2 or ω s A value of 5 can achieve good control results. A shorter system steady-state time and faster convergence of saturated input can be observed.

[0139] Option 2:

[0140] Step 2: Use a second-order general-purpose fast desaturation controller with n=2 or (τ1≠τ2). A second-order system is added for saturation compensation.

[0141] Step 3: The second-order system desaturation compensator can be equivalently transformed into a desaturation series compensation structure M(s) as the compensation element, which can be reorganized as follows:

[0142]

[0143] in τ1,τ2>0 are time constants, M(s) is the compensation stage containing saturation gain ρ and desaturation gain [1-Δ(s)], which is transformed into Figure 3 Structure. Where Δ(s) is a low-pass filter, forming a desaturation channel, i.e., using... Attenuation of filtered signal To achieve desaturation effect, ω s The bandwidth-related parameters for the desaturated channel Δ(s) are given.

[0144] Step 4: Construct C(s) as a bandwidth-optimized PID:

[0145]

[0146] ω c The desired closed-loop bandwidth parameter is determined by the system's speed characteristics; α represents the phase lead compensation factor.

[0147] The bandwidth-optimized PI controller used is C(s) = 6(1 + 0.833 / s), where ω c =0.833, α=0. According to the parameter value requirements, ω s >0, τ2>τ1>0,

[0148] Given ω c =0.833, ω is gradually increased according to the parameter value requirements. s Take three sets of parameters: Set 1: β = 2, ω s =2, τ2 = 0.2, τ1 = 0.166; Group 2: β = 3, ω s =3, τ2 = 0.1, τ1 = 0.083; Group 3: β = 3, ω s =5, τ2=0.05, τ1=0.02499; gradually increase ω s Observe its effects, such as Figure 10 , Figure 11 When the amplification factor β and the desaturation bandwidth ω s The value changes from the first group to the second group, ω s As β increases, the system's steady-state time shortens, and saturated input convergence accelerates; when the desaturation bandwidth ω... s The value ω changes from the second group to the third group. s Increasing the input speed results in a shorter time for the system to reach steady state and faster convergence of saturated input.

[0149] This invention also provides a determination system for a second-order universal fast desaturation controller, see [link to relevant documentation]. Figure 12 The system includes:

[0150] The saturation gain determination module 201 is configured to determine a saturation gain of an actuator in the target industrial control system.

[0151] The compensator construction module 202 is configured to construct a second-order general type fast integral anti-windup compensator by using an input-output deviation of the actuator.

[0152] The compensator equivalence module 203 is configured to, based on the saturation gain, equivalently transform the second-order general type fast integral anti-windup compensator into a series-compensated anti-windup structure, and determine a compensation link and an anti-windup channel in the anti-windup structure; the compensation link and the anti-windup channel both include an anti-windup bandwidth to be determined.

[0153] The bandwidth PID controller determination module 204 is configured to determine a bandwidth PID controller of the target industrial control system.

[0154] The anti-windup bandwidth determination module 205 is configured to, by using a linkage relationship between the bandwidth PID controller and the anti-windup bandwidth, determine a value of the anti-windup bandwidth in the compensation link and the anti-windup channel.

[0155] The anti-windup controller determination module 206 is configured to determine a second-order general type fast anti-windup controller of the target industrial control system according to the compensation link after the value of the anti-windup bandwidth is determined and the anti-windup channel after the value of the anti-windup bandwidth is determined.

[0156] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments, and the same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the related parts can be referred to the method part.

[0157] The principles and implementation manners of the present application are described by using specific examples in the present application, and the above embodiment description is only used to help understand the method of the present application and its core idea; meanwhile, for the general technical personnel in the art, according to the idea of the present application, the specific implementation manner and application range will be changed. In conclusion, the content of the specification should not be understood as the limitation of the present application.

Claims

1. A method for determining a second-order universal fast desaturation controller, characterized in that, include: Determine the saturation gain of the actuators in the target industrial control system; A second-order general-purpose fast integral desaturation compensator is constructed using the input-output deviation of the actuator. Based on the saturation gain, the second-order general-purpose fast integral desaturation compensator is equivalent to a series-compensated desaturation structure, and the compensation element and desaturation channel in the desaturation structure are determined; both the compensation element and the desaturation channel include a desaturation bandwidth to be determined. Determine the bandwidth-optimized PID controller for the target industrial control system; The value of the desaturation bandwidth in the compensation stage and the desaturation channel is determined by using the linkage relationship between the bandwidth-optimized PID controller and the desaturation bandwidth. Based on the compensation circuit after determining the value of the desaturation bandwidth and the desaturation channel after determining the value of the desaturation bandwidth, the second-order general-purpose fast desaturation controller of the target industrial control system is determined.

2. The method for determining a second-order universal fast desaturation controller according to claim 1, characterized in that, The expression for the saturation gain is: Where ρ represents the saturation gain; u * u is the input of the actuator; u is the saturation output of the actuator; sat(.) is a saturated nonlinear function, u max u is the upper bound of the actuator's input; min u is the lower bound of the actuator input; max =-u min =1.

3. The method for determining a second-order universal fast desaturation controller according to claim 1, characterized in that, The second-order universal fast integral desaturation compensator is: G0(s) is a second-order general-purpose fast integral desaturation compensator; ω s τ is the desaturation bandwidth; τ1 and τ2 are time constants, τ1, τ2 > 0; n is the order; s is the differential operator after Laplace transform.

4. The method for determining a second-order universal fast desaturation controller according to claim 1, characterized in that, The desaturation structure is: Where u(s) is the saturated output of the actuator expressed in terms of the differential operator; u * (s) represents the input of the actuator in terms of differential operators; ρ represents the saturation gain; s is the input of the actuator before antisaturation, expressed in terms of differential operators; s is the differential operator after Laplace transform; Δ(s) is the desaturation channel.

5. The method for determining a second-order universal fast desaturation controller according to claim 1, characterized in that, The compensation process is as follows: Where M(s) is the compensation element; ρ represents the saturation gain; s is the differential operator after Laplace transform; τ1 and τ2 are time constants, τ1,τ2>0; n is the order; ω s For desaturation bandwidth; The desaturation channel is: Where Δ(s) is the desaturation channel.

6. The method for determining a second-order universal fast desaturation controller according to claim 1, characterized in that, The bandwidth-optimized PID controller is: Where C(s) represents the bandwidth-optimized PID controller; s is the differential operator after Laplace transform; ω c K represents the desired closed-loop bandwidth parameter; α is the phase lead compensation factor; K p For controller gain, K p >0.

7. The method for determining a second-order universal fast desaturation controller according to claim 6, characterized in that, When n = 1 or τ1 = τ2, the compensation stage and the desaturation channel after determining the desaturation bandwidth are as follows: Where M(s) is the compensation stage; Δ(s) is the desaturation channel; ρ represents the saturation gain; s is the differential operator after Laplace transform; τ1 and τ2 are time constants, τ1,τ2>0; n is the order; ω s The desaturation bandwidth; for any ρ∈[0] + ,1],ω s Satisfy: ω s >0, β > 1; β is the amplification factor; When n = 2 and τ1 ≠ τ2, the compensation stage and the desaturation channel after determining the desaturation bandwidth are as follows: For any ρ∈[0] + ,1], and τ1 and τ2 are both positive, ω s Satisfy: ω s >0, ω s (1-ρ)τ²≤1; for ρ=0 + ω s Satisfy: 4ω s τ2≤1; for any ρ∈[0] + ,1], and τ2>τ1>0, ω s satisfy:

8. A determination system for a second-order universal fast desaturation controller, characterized in that, include: The saturation gain determination module is used to determine the saturation gain of actuators in the target industrial control system. The compensator construction module is used to construct a second-order general-purpose fast integral desaturation compensator using the input-output deviation of the actuator; The compensator equivalent module is used to convert the second-order general-purpose fast integral desaturation compensator into a series-compensated desaturation structure based on the saturation gain, and to determine the compensation stage and desaturation channel in the desaturation structure; both the compensation stage and the desaturation channel include a desaturation bandwidth to be determined. A bandwidth-optimized PID controller determination module is used to determine the bandwidth-optimized PID controller of the target industrial control system. The desaturation bandwidth determination module is used to determine the value of the desaturation bandwidth in the compensation circuit and the desaturation channel by using the linkage relationship between the bandwidth-optimized PID controller and the desaturation bandwidth. The desaturation controller determination module is used to determine the second-order general-purpose fast desaturation controller of the target industrial control system based on the compensation link after determining the value of the desaturation bandwidth and the desaturation channel after determining the value of the desaturation bandwidth.

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