A crystallizer liquid level control system and control method with disturbance observer

Abstract

The application discloses a crystallizer liquid level control system and control method with a disturbance observer. An interference observer based on a reverse nominal model is set, and direct compensation for the output of a PID feedback controller is formed based on the observation result; a two-degree-of-freedom crystallizer liquid level control system composed of the PID controller and the interference observer is formed, and the system is set under the constraint of system robust stability. In the corresponding control method, the suppression feedback for the uncertainty disturbance of the system is completed by calculating the stopper adjusting amount based on the PID controller and the compensation amount calculated based on the interference observer observation gain regulator in each sampling period of the system. The crystallizer liquid level control system and control method with a disturbance observer have the advantages of ingenious overall design, strong anti-interference ability, small fluctuation and strong practicability.

Description

Technical Field

[0001] This invention belongs to the field of steelmaking continuous casting, specifically relating to a crystallizer level control system and control method with a disturbance observer. Background Technology

[0002] In continuous casting, molten steel is injected into the crystallizer through an immersion nozzle by adjusting the opening of the stopper rod inside the tundish. Under the action of the cooling water in the crystallizer, the molten steel forms a billet with a certain shell thickness. The continuous casting machine pulls the gradually solidifying billet out of the crystallizer at a speed set by the process. During continuous casting, the crystallizer level must be controlled within a certain range. Excessive level fluctuations can easily cause slag inclusions and cracks on the billet surface, resulting in quality loss, or even steel leakage, leading to serious production accidents. Simultaneously, stable control of the crystallizer level is crucial for safe continuous casting production and ensuring product quality. The performance and quality of products in actual use demand high-precision control of the crystallizer level. However, due to the complexity of the causes of crystallizer level fluctuations—numerous influencing factors and their interaction and superposition—a perfect control method for crystallizer level control has yet to be found. Most existing crystallizer level control methods employ conventional PID control, which cannot effectively suppress the uncertainties of time-delay systems and external interference.

[0003] The invention application with application number CN2008100406857 discloses an "Adaptive and Fuzzy Logic PID Crystallizer Liquid Level Online Control System and Method," comprising: a calculation module that receives the input crystallizer liquid level setpoint and the actual value measured by the liquid level measurement module, and calculates the deviation e between the two values; an online parameter adjustment module; a fuzzy logic module connected to the online parameter adjustment module that receives e, determines abnormal fluctuations in the casting speed, nozzle wear, slagging, and slagging detachment based on e, receives Kp, Tn, and Tv input from the online parameter adjustment module, and outputs adjusted Kp, Tn, and Tv to the PID controller; a PID controller; a P controller; a hydraulic mechanical device; and a liquid level measurement module.

[0004] The invention application with application number CN2009101495693 discloses "a method for controlling the liquid level of a continuous casting crystallizer based on Fuzzy-PID". This control method, under the control of a computer and a PLC, uses a hybrid control of self-tuning parameter PID control and fuzzy control to control the liquid level of the crystallizer, and incorporates a flow deviation compensation module, etc. The specific steps of its control process are as follows: set the initial liquid level y0, and collect the liquid levels y1 and y2 through a liquid level sensor and a liquid level measuring device; input the collected data y1 and y2 into the PLC, process the signal using a hybrid control of self-tuning parameter PID control and fuzzy control, and perform compensation through a compensation module; the output of the PLC is u(k) = u1(k), and the PLC controls the position of the stopper rod through the stopper rod controller, thereby controlling the liquid level of the crystallizer.

[0005] The invention application with application number CN2019109516899 discloses "a method for improving the liquid level control accuracy of the crystallizer in a 400 series stainless steel continuous casting machine". It achieves the stability of the liquid level in the crystallizer of the stainless steel continuous casting machine and improves the control accuracy by formulating a stopper rod motion control algorithm, optimizing the parameters in the formula, and increasing the stopper rod vibration when the liquid level is stable. It solves the problem of crust formation on the liquid surface at the upper end of the stopper rod and stabilizes the liquid level control accuracy of the crystallizer within the range of ±3mm.

[0006] The invention application with application number CN202210647009.6 discloses "a method for controlling the periodic fluctuation of liquid level in a medium and low carbon steel crystallizer", which includes the following steps: acquiring liquid level data of the crystallizer and current data of each drive roller, and performing differential processing on the liquid level data and current data; when the fluctuation value of the liquid level data exceeds a preset fluctuation value, identifying the target drive roller, the fluctuation trend of the current data of the target drive roller is the same as the fluctuation trend of the liquid level data; calculating the correlation coefficient between the current data of each drive roller and the current data of the target drive roller, and determining the drive roller to be adjusted, the correlation coefficient of the current data of the drive roller to be adjusted being ≥ a preset coefficient; reducing the roller gap of the sector segment where the drive roller to be adjusted is located by a preset distance. Summary of the Invention

[0007] This invention provides a crystallizer level control system and control method with a disturbance observer, the purpose of which is to suppress crystallizer level fluctuations caused by sudden disturbances and system uncertainties.

[0008] To achieve the above technical objectives, the present invention adopts the following technical solution:

[0009] A crystallizer level control system with a disturbance observer.

[0010] Set up an interference observer based on the inverse nominal model, and form a direct compensation for the output of the PID feedback controller based on the observation results.

[0011] Based on this, a two-degree-of-freedom crystallizer level control system, consisting of a PID controller and a set disturbance observer, is set up under the constraint of system robust stability.

[0012] Furthermore,

[0013] The low-pass filter in the interference observer is determined according to the following steps:

[0014] S1: Establish the estimated state matrix based on the Luneburg observer;

[0015] S2: Based on the estimated state matrix and the actual state matrix, determine the transfer function from the actual flow disturbance to its estimated flow disturbance;

[0016] S3: Determine the low-pass filter based on the determined transfer function.

[0017] Furthermore,

[0018] The perturbation factor of the system is composed of the flow coefficient Gc and the time delay τ of the crystallizer object. The uncertain system is characterized by the multiplicative perturbation structure, and... For system robust stability constraints,

[0019] Meanwhile, the "direct compensation for the output of the PID feedback controller based on the observation results" is achieved by a gain regulator set between the output of the low-pass filter of the interference observer and the output of the PID feedback controller.

[0020] The disturbance-based uncertain crystallizer level control system is configured by determining the weight function, approximating the pure time delay part in the inverse nominal model, determining the filter poles, and determining the gain coefficient of the gain regulator.

[0021] In the above formula,

[0022] The weight function is an upper bound on the multiplicative uncertainty of the system;

[0023] T(S): Complementary sensitivity function, which refers to the closed-loop transfer function from system input to output.

[0024] Furthermore,

[0025] The gain regulator described herein has the following specific structure:

[0026]

[0027] in,

[0028] d c : Output of the gain regulator;

[0029] K fGain coefficient;

[0030] G c Flow coefficient;

[0031] Estimate traffic disturbances.

[0032] Furthermore,

[0033] Gain coefficient K f ∈[0, 1 / Gc].

[0034] Furthermore,

[0035] Gain coefficient K f ∈[0, 0.35 / Gc].

[0036] Furthermore,

[0037] The flow coefficient Gc is determined empirically or according to the following formula:

[0038] Gc = (V × A) / dr,

[0039] In the formula,

[0040] Gc: Flow coefficient;

[0041] V: Pulling speed; Unit: m / s;

[0042] A: Cross-sectional area of ​​the crystallizer; unit: m² 2 ;

[0043] dr: stopper rod opening, unit: m.

[0044] Furthermore,

[0045] The pure time-delay part of the inverse nominal model is approximated using a linear approximation method;

[0046] By setting the following linear approximation expression and setting B(s) as a linear element with high-gain low-pass characteristics, a linear approximation expression can be achieved.

[0047]

[0048] In the formula,

[0049] L(s): A linear approximation expression used to form an approximate expression for the low-frequency range of the pure time-delay part in the inverse nominal model;

[0050] B(s): A linear element with high-gain low-pass characteristics;

[0051] Tp: Parameter to be determined;

[0052] s: Laplace differential operator.

[0053] Furthermore,

[0054] B(s) in the formula is determined according to the following formula:

[0055]

[0056] In the formula,

[0057] B(S): First-order inertial element;

[0058] K1: Parameter to be determined;

[0059] K2: Parameter to be determined;

[0060] s: Laplace differential operator.

[0061] Furthermore,

[0062] First, the value of K1 is determined. Then, under the constraint that the phase frequency characteristics of the pure time-delay part of the inverse nominal model and the linear approximation expression satisfy the following, K2 and Tp are determined based on the Bode plot of the pure time-delay part of the inverse nominal model and the linear approximation expression. Finally, based on the determined K1, K2, and Tp, an approximate expression of the pure time-delay part of the inverse nominal model is completed.

[0063]

[0064] In the formula,

[0065] ∠e jτω Phase-frequency characteristics of the inverse nominal model;

[0066] ∠L(jω): The phase frequency characteristic of the linear approximation expression;

[0067] ph max The maximum phase difference that can be tolerated;

[0068] f max : Maximum frequency of the main periodic disturbance, unit: Hz;

[0069] ω: angular frequency, unit: rad / s.

[0070] Furthermore,

[0071] By performing a fast Fourier transform on the actual liquid levels of multiple crystallizers over multiple days, the fluctuation frequency range of the main cycle is determined; and based on this, the maximum disturbance frequency and the maximum tolerable phase angle difference are determined.

[0072] Furthermore,

[0073] The weight function is determined based on the following conditions, and is obtained using the Bode plot.

[0074]

[0075] In the formula,

[0076] R: The range of variation of the flow coefficient Gc;

[0077] L1: The range of variation of the time delay τ of the crystallizer object;

[0078] Frequency response of the weighting function.

[0079] Furthermore,

[0080] The low-pass filter determined in step S3 is a second-order low-pass filter. The corresponding two poles, in an uncertain system characterized by a multiplicative perturbation structure, and with... To determine the robust stability of the system under constraints, follow these steps:

[0081] S11: Determine the larger of the two poles based on the maximum frequency of the disturbance in the main period;

[0082] S12: Set the difference between the two to 1, and determine the other one accordingly.

[0083] Furthermore,

[0084] By performing a fast Fourier transform on the actual liquid levels of multiple crystallizers over multiple days, the fluctuation frequency range of the main cycle is determined, and the maximum disturbance frequency is determined accordingly.

[0085] Furthermore,

[0086] The larger of the two poles mentioned in step S11 is determined according to the following formula:

[0087]

[0088] In the formula,

[0089] P i The larger of the two poles;

[0090] f max : Maximum frequency of disturbance.

[0091] A control method for a crystallizer level control system with a disturbance observer.

[0092] In each sampling period of the system, the following steps are performed to achieve suppressive feedback against uncertain disturbances in the system.

[0093] SS1: Obtain the liquid level setpoint and the actual measured value, and calculate the difference between the two;

[0094] SS2: Call the PID controller to calculate the stopcock adjustment amount;

[0095] SS3: Invoke the disturbance observer to calculate and estimate the flow disturbance;

[0096] SS4: Calculate the disturbance control compensation amount based on the estimated flow disturbance;

[0097] SS5: Based on the stopper rod adjustment amount determined in step SS2 and the disturbance control compensation amount determined in step SS4, complete the adjustment control of the stopper rod position.

[0098] The present invention discloses a crystallizer level control system and control method with a disturbance observer. The basic structure of this technical solution is formed by adding a disturbance observer to the original PID feedback control system. Based on this structure, a gain control loop is set to form direct compensation based on disturbance observation within the system. Since the system settings are placed under the classical robust control theory, the specific settings of the system can be completed with the help of robust stability and Bode plot.

[0099] In this classic two-degree-of-freedom controller structure, which consists of an interference observer and a feedback controller based on an inverse nominal model, the design of the filter is crucial. This technical solution completes the filter setting in two steps. First, under state-space observation, the transfer function from the actual flow disturbance to its estimated flow disturbance is determined, and the specific order of the filter is determined accordingly. Then, under the constraint of robust stability, the poles are configured. This process fully leverages the advantages of both methods and demonstrates the ingenuity of the setting. Furthermore, in the process of confirming the poles, the focus is solely on the requirements of system robust stability and mid-frequency band.

[0100] The weighting function is obtained on the Bode plot using an approximation method, combined with constraints designed to match engineering realities. The inverse nominal model is approximated using a notifiable approximation method. However, in the specific approximation process, a minor technical detail is made in the structural design of the high-gain low-pass component. Furthermore, during parameter determination, specific constraints are set on the phase-frequency characteristics of the pure time-delay component in the inverse nominal model and the linear approximation expression. Overall, this technical solution is ingeniously designed, exhibiting strong anti-interference capabilities, low fluctuation, and high practicality. Attached Figure Description

[0101] Figure 1 This is a block diagram of the control system of the present invention;

[0102] Figure 2 A schematic diagram of the steps of the control method of the present invention;

[0103] Figure 3This is a schematic diagram illustrating the filter determination process in this invention;

[0104] Figure 4 This is a schematic diagram illustrating the steps for determining filter poles in this invention;

[0105] Figure 5 This is a block diagram of the control system in an embodiment of the present invention;

[0106] Figure 6 This is a schematic diagram of the phase frequency characteristics (left) and phase frequency-phase angle difference (right) of L(s) under different K2 and Tp in this embodiment of the invention;

[0107] Figure 7 The diagram shows the amplitude-frequency characteristics of the complementary sensitivity function T(s) and 1 / W2 (top) under different Kf values ​​in the embodiments of the present invention; and the step disturbance response (bottom) under different Kf values.

[0108] Figure 8 This is a schematic diagram comparing the system output of PID control under step disturbance in this embodiment of the invention with that of the control solution in this invention;

[0109] Figure 9 This is a schematic diagram comparing the system output of PID control under periodic disturbance conditions and the control method of this technical solution in an embodiment of the present invention. Detailed Implementation

[0110] The following is a further detailed description of a crystallizer level control system and control method with a disturbance observer according to the present invention, based on the accompanying drawings and specific embodiments.

[0111] like Figure 1 The crystallizer level control system shown is implemented using a disturbance observer based on an inverse nominal model, combined with a gain regulator positioned between the output of the low-pass filter and the output of the PID feedback controller. System implementation prioritizes robust stability. Due to the aforementioned structural design, the specific implementation involves five aspects: determining the weight function, the filter, the filter poles, approximating the pure time-delay portion of the inverse nominal model, and determining the gain coefficient of the gain regulator. Furthermore, this technical solution innovatively designs a complete system determination scheme based on practical engineering considerations. The control method for the system determined by this technical solution in actual operation follows the following... Figure 2 The control steps shown are performed. The specific working principle and process of the technical solution are as follows:

[0112] like Figure 1As shown, the core modules of the system include a PID controller module, a disturbance observation controller module, a level actuator, and a level sensor. The disturbance observation controller includes: a time-delay inverse, a filter, a gain coefficient, and a flow coefficient. The corresponding execution steps are as follows: Figure 2 As shown, the process includes: SS1: Obtaining the liquid level setpoint and actual measured value, and calculating the difference between the two; SS2: Calling the PID controller to calculate the stopper rod adjustment amount; SS3: Calling the disturbance observer to calculate the estimated flow disturbance; SS4: Calculating the disturbance control compensation amount based on the estimated flow disturbance; SS5: Completing the adjustment control of the stopper rod position based on the stopper rod adjustment amount determined in step SS2 and the disturbance control compensation amount determined in step SS4. That is:

[0113] (1) Calculate the deviation e(t) = r(t) - y(t) between the set liquid level r(t) and the actual liquid level measurement value y(t), and obtain the liquid level feedback setpoint u for the stopper rod adjustment position through the PID control algorithm. c (t)=e(t)*G PID The algorithm expression for PID is G. PID for:

[0114] G PID =K p +K i / s+K d *s

[0115] Where Kp, Ki, and Kd are PID controller parameters. The initial PID controller parameters can be obtained by using the model tuning method or the empirical manual tuning method through the identified actual system control model. Then, the PID parameters can be further precisely adjusted according to the actual control needs. s in the expression is the Laplace transform operator.

[0116] (2) The actual liquid level measurement value is processed by the inverse model G of the object containing hysteresis. -1 p *e τ*s The difference between the stopper rod inlet flow rate calculated by the model and the stopper rod molten steel flow rate calculated based on the current stopper rod position is given, which is approximately equal to the disturbance. This disturbance is filtered and adjusted by a gain coefficient, and then combined with the PID calculation result from step 1 to obtain the final set control value Rod_ps for the stopper rod position, i.e.:

[0117] Rod_ps = u c -d c

[0118] (3) The inverse model of the object involved in step 2 above consists of a gain element, a differential element, and the inverse of a pure time delay element. The specific expression is: A*s*e τ*s, where A is the cross-sectional area of ​​the crystallizer, τ=t1+t2, where t1 is the time delay of the controlled object, t2 is the time delay of the liquid level sensor, and s is the Laplace differential operator.

[0119] (4) The robust stability criterion of the system: the flow coefficient Gc and the time delay τ of the crystallizer are uncertain. If the controller of the PID+disturbance observer can keep the closed-loop system internally stable within the range of Gc and time delay τ, then the controller is considered to be a robust stable controller and the system has robust stability.

[0120] Uncertain models that determine system model parameters using multiplicative perturbations:

[0121]

[0122] For real-world objects containing uncertainties in Gc and τ;

[0123] P is the nominal object determined by Gc and τ;

[0124] Δ is the scale factor;

[0125] The weight function; weight function The choice is not unique (it only depends on the uncertainty of the object), but the following conditions must be met:

[0126]

[0127] R represents the range of variation of the flow coefficient Gc, i.e., R ∈ [Gc]. min / Gc, Gc max / Gc];

[0128] L1 is the range of time delay τ, i.e., L1∈[τ] min -τ,τ max -τ];

[0129] When the controlled object has uncertainty, the criterion for the robust stability of the system is:

[0130]

[0131] T(s) is the complementary sensitivity function, defined as the closed-loop transfer function from input r(t) to output y(t). It requires selecting appropriate linear approximation element L(s) parameters, filter Q(s) poles, and gain coefficient Kf to ensure that the complementary sensitivity function T(s) always satisfies the above system robustness stability criterion.

[0132] (5) The inverse e of the pure time delay involved in step 3 τ*sSince it is physically impossible to achieve, a linear approximation method is used as an approximation. The goal is to achieve an approximate prediction in the low-frequency range, while having no effect in the high-frequency range (approximately 1). The specific approximation expression is L(s), where B(s) is a linear element with high-gain low-pass characteristics. The following approximation expression demonstrates the mathematical idea of ​​limit approximation in both the low-frequency and high-frequency ranges:

[0133]

[0134] For the sake of simplicity and ease of implementation, B(s) in this technical solution is configured according to the following specific structure.

[0135]

[0136] The principle for choosing the value of K1 is that it should be greater than or equal to 1. When Tp = τ, K1 takes a larger value, and the above approximation expression holds well. However, due to the feedback of the time delay element, a larger K1 may lead to system instability. Therefore, to prevent system instability, K1 can be set to 1. However, in this case, when Tp = τ, no matter what value K2 takes, the above approximation expression may not be approximately equivalent. To solve this problem, different K2 and Tp can be tried to approximate e as closely as possible, under the premise of satisfying the robust stability of the system and within the actual frequency range of the main periodic fluctuation of the liquid level [0, fmax] Hz. τ*s phase frequency characteristics, e τ*s The phase frequency characteristics of L(s) must satisfy the following equation:

[0137] |∠e jτω -∠L(jω)|≤ph max / (2*pi*f max )*ω

[0138] ph max To the maximum tolerable phase angle difference,

[0139] f max The maximum frequency of the main periodic disturbance is Hz.

[0140] ∠e jτω For e τ * s Phase frequency characteristics,

[0141] ∠L(jω) is the phase frequency characteristic of L(s).

[0142] ω is the angular frequency in rad / s.

[0143] The actual frequency range of the main periodic fluctuations in the liquid level mentioned above can be determined by Fast Fourier Transform (FFT) of the actual liquid level data.

[0144] (6) The filter involved in step 2 is a second-order low-pass filter, and its specific expression is:

[0145]

[0146] Where a2, a1, and a0 are the coefficients of the filter, and the poles of the filter are a2·s. 2 The roots P1 and P2 of +a1·s+a0=0. The choice of poles P1 and P2 is extremely important, as it may directly affect the robust stability of the system and the effective bandwidth of the disturbance observer; see [link to relevant documentation]. Figure 4 Several important principles for selecting poles P1 and P2: 1) The robust stability of the system must be satisfied; 2) P1 and P2 should be as close as possible. To ensure that the intermediate frequency band is as short as possible, the difference between their poles P1 and P2 can be assumed to be 1; 3) The corner frequency determined by the largest pole among P1 and P2 should be near the maximum frequency of the main periodic disturbance. This will enable the disturbance observer to estimate the effective liquid level periodic disturbance and avoid overestimation of measurement noise.

[0147] Assuming P1 > P2, P1 can be determined based on condition 3:

[0148] P1≈-2*pi*f max

[0149] Based on condition 2, determine P2:

[0150] P2 = P1-1

[0151] The designation of it as a second-order low-pass filter is achieved using the concept of a state observer, specifically a Romberg observer. (See [link to relevant documentation]). Figure 3 The specific process is as follows:

[0152] right Figure 1 The given system uses a disturbance observer to estimate the flow disturbance d. Assuming the flow disturbance d is a step disturbance, the state space of the controlled object is represented as follows:

[0153]

[0154] For ease of use, we rewrite x in the above equation as u, and in the state equation, we rewrite A as a, y as x1, and d as x2. Therefore, the above equation becomes the following standard form:

[0155]

[0156] The corresponding standard form of the state equation:

[0157]

[0158] And the output equation is:

[0159]

[0160] The state estimated by the Lundberg observer is:

[0161]

[0162] Transformed into:

[0163]

[0164] Therefore, the observer bias is:

[0165]

[0166] Differentiating the above equation (the Romberg observer is one where the limits of the state variables are equal to those of the original system's state variables)

[0167]

[0168] If A-LC converges, then the observer converges.

[0169] In the crystallizer level control system,

[0170]

[0171] but:

[0172]

[0173] Observer estimates state:

[0174]

[0175] Since x1 = y, x2 = d, and u = x have already been defined above, substituting them into the above equation yields:

[0176]

[0177] Where g1 and g2 are the observer gains. and These are the estimated values ​​of the crystallizer liquid level y and the flow disturbance d, respectively. From the flow disturbance d to its estimated value... The derivation of the transfer function is as follows:

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185] Simplifying the above equation, we get:

[0186]

[0187] Taking the Laplace transform on both sides, we get We obtain Q(s):

[0188]

[0189] (7) The gain coefficient Kf involved in step 2 is determined based on offline simulation or online adjustment, and its range is generally [0, 1 / Gc]. Its range is related to the flow coefficient Gc. The selection principle is to maximize the value while ensuring the system's robust stability and preventing oscillations. It can be seen that when the gain Kf... f When set to zero, it is clear that the new control system is exactly the same as the traditional PID control system. It can obtain the optimal gain K through unidirectional search without drastic changes in the control response. f .

[0190] (8) The flow coefficient Gc involved in step 2 can be obtained based on experience or calculated from actual steady-state data. The specific calculation expression is as follows:

[0191]

[0192] Where V is the pulling speed (m / s), A is the cross-sectional area of ​​the crystallizer (m*m), and dr is the stopper opening (m).

[0193] Example

[0194] The following explanation can be understood in conjunction with... Figure 1 or Figure 5 The original PID crystallizer level control system includes: a PID controller C(s), a level actuator G1(s), a flow coefficient Gc, and a crystallizer model Gp(s), with structural parameters shown in Table 1. Under the control mode of this PID controller, the system exhibits robust stability.

[0195] Table 1. System Structure and Parameters

[0196] System architecture name Structural parameters <![CDATA[PID controller C(s) = K p + K i / s + K d * s]]> <![CDATA[K p =0.78373,K i =0.15878,K d =0.19256]]> Liquid level actuator G1(s) = 1 / (1+T*s) T＝0.1 Flow coefficient Gc Gc = 0.35 <![CDATA[Crystallizer model G p (s) = e -τ*s / (A * s)]]> τ = 0.24, A = 0.264

[0197] Since the flow coefficient Gc and time delay τ are variable in the actual continuous casting process, it is necessary to ensure that the system still possesses robust stability under PID control with a disturbance observer. The necessary and sufficient condition for the system model to possess robust stability is:

[0198]

[0199] Let T(s) be the weighting function and T(s) be the complementary sensitivity function.

[0200] according to Figure 5 The block diagram of the crystallizer level control system with a disturbance observer allows us to derive the general expression for the complementary sensitivity function:

[0201]

[0202] A. Weighting function Choice

[0203] The nominal object P (including the flow coefficient Gc = 0.35 and the crystallizer model Gp(s) = e(-0.24*s) / (0.264*s)) is different from the actual object. Uncertainty exists (Gc varies by ±30%, time delay τ varies by 0.12–0.36 s), according to robust H... ∞ According to control theory:

[0204]

[0205] The coefficient R varies in the range of [0.7, 1.3]; the coefficient L1 varies in the range of [-0.12, 0.12].

[0206] Weighting function as follows:

[0207]

[0208]

[0209] B. Design of the disturbance observer

[0210] 1. Determination of parameters for linear approximation process

[0211] Step 4: Approximate expression for the inverse of the pure time-delay element:

[0212]

[0213]

[0214] By performing discrete Fast Fourier Transform (FFT) on the actual liquid levels of multiple crystallizers over multiple days, the main periodic fluctuation frequency range of the liquid level is [0, 0.5Hz]. Therefore, the maximum disturbance frequency f is... max =0.5Hz. Maximum tolerable phase angle difference (ph) max =10°, the linear approximation element L(s) must satisfy:

[0215] |∠e jτω -∠L(jω)|≤10 / (2*pi*0.5)*ω

[0216] Where K1 = 1, the parameters of K2 and Tp are yet to be determined. Different K2 and Tp are used to approximate the inverse phase frequency characteristic of the pure time-delay element, and the phase frequency angle difference = ∠e jτω -∠L(jω) must satisfy the above constraints, and the simulation results are as follows: Figure 6 As shown, the left side represents the phase frequency characteristics of L(s) under different K2 and Tp, and the right side represents the corresponding phase frequency and phase angle difference.

[0217] Changing K2 has little impact on the phase-frequency characteristics of the linear approximation element L(s). Different Tp values ​​can be selected to obtain the phase angle corresponding to the compensation time delay within the target frequency band [0, 0.5Hz]. Figure 6 Simulation results show that K1=1, K2=0.1, and Tp=0.4 meet the requirements.

[0218] 2. Determination of Q(s) poles of the filter

[0219] According to condition 3) of the filter Q(s) pole selection in step 5, the target frequency band of the disturbance observer is known [0, 0.5Hz]. That is, the first corner frequency of the filter Q(s) is set near 0.5Hz, which allows the disturbance observer to accurately estimate the flow disturbance affecting the liquid level fluctuation. The first corner frequency of the filter Q(s) is related to the larger poles of Q(s) (let P1 > P2). The calculation of the first corner frequency is as follows:

[0220] P1≈-2*pi*f max = -3.14

[0221] Therefore, P1 = -3, and the pole P2 = P1 - 1 = -4.

[0222] 3. Determination of the gain coefficient Kf

[0223] In step 6, the gain coefficient Kf is determined. Kf is selected within the range [0, 1 / Gc], and must meet the system robustness requirements. Given the parameters of the linear approximation element (K1 = 1, K2 = 0.1, Tp = 0.4) and the filter poles (-3, -4) determined above, different gain coefficients Kf can be used to determine different complementary sensitivity functions T(s). The general expression for T(s) under different kf values ​​is:

[0224]

[0225] in:

[0226]

[0227] The weighting function has been determined in A above. To ensure the controller maintains robust stability even with uncertainties in the flow coefficient Gc and time delay τ, the sensitivity function T(s) needs to be less than 1 / 2 in all frequency bands.

[0228] In order to satisfy Furthermore, excessive compensation should be avoided, as it could cause oscillations in the crystallizer level control system. Simulation results are as follows... Figure 7 As shown, where Figure 7 The upper figure shows the amplitude-frequency characteristics of the complementary sensitivity function T(s) and 1 / W2 under different Kf values, while the lower figure shows the step disturbance response under different Kf values.

[0229] according to Figure 7 The simulation results show that neither Kf = 1 / Gc nor Kf = 0.7 / Gc meets the system robustness requirements. With a gain coefficient of Kf = 0.35 / Gc, the system disturbance observer can effectively suppress disturbances without causing system output oscillations. Moreover, even with uncertainties in the flow coefficient Gc and time delay τ, the system robustness and stability requirements are still met.

[0230] C. Simulation comparison of PID and PID+disturbance observer

[0231] The structural parameters of the control system are all known. A system model is built, and different types of disturbances are added to d(t) to perform actual anti-interference control. The results are shown in Figure 8. Figure 9 As shown. Under step disturbance conditions, the comparison between PID and this method is as follows: Figure 8 As shown. Under periodic disturbance conditions, the comparison between PID and this method is as follows. Figure 9 As shown.

[0232] Depend on Figure 8 and Figure 9It can be seen that, whether facing step disturbances or periodic disturbances, the control system and method proposed in this patent, based on conventional PID control, achieves better anti-interference ability and smaller level fluctuations than traditional PID crystallizer level control by adding a disturbance observer for compensation control.

[0233] This invention discloses a crystallizer level control system and method with a disturbance observer. The basic structure of this technical solution is based on the classic configuration of adding a disturbance observer to an existing PID feedback control system. On this basis, a gain control loop is used to achieve direct compensation based on disturbance observation within the system. Since the system is configured under classical robust control theory, the specific system settings can be completed using robust stability and Bode plots. In this classic two-degree-of-freedom controller structure composed of a disturbance observer (inverse nominal model) and a feedback controller, filter design is crucial. This technical solution completes the filter setting in two steps: first, under state-space observation, the transmission distance from the actual flow disturbance to its estimated flow disturbance is determined. The filter order is determined by a recursive function, and then the poles are configured under the constraint of robust stability. This process fully leverages the advantages of both methods, demonstrating the ingenuity of the configuration. Further pole confirmation focuses solely on the system's robust stability and mid-frequency band requirements. The weighting function is calculated on the Bode plot using an approximation method, combined with constraints consistent with engineering practice. The inverse nominal model is approximated using a notional approximation method. However, in the approximation process, a minor technical detail is made in the structural design of the high-gain low-pass component. Furthermore, specific constraints are imposed on the phase-frequency characteristics of the pure time-delay component in the inverse nominal model and the linear approximation expression during parameter determination. Overall, this technical solution is ingeniously designed, exhibiting strong anti-interference capabilities, low fluctuations, and high practicality.

Claims

1. A crystallizer level control system with disturbance observer, characterized in that: a disturbance observer based on inverse nominal model is set up, and direct compensation to the output of PID feedback controller is formed based on the observation result; the two-degree-of-freedom crystallizer level control system composed of PID controller and disturbance observer set up is completed under the constraint of system robust stability; the low-pass filter in the disturbance observer is determined according to the following steps: S1: establishing the estimated state matrix based on the Luenberger observer; S2: determining the transfer function from actual flow disturbance to its estimated flow disturbance based on the estimated state matrix and actual state matrix; S3: completing the determination of low-pass filter according to the determined transfer function; meanwhile, the "direct compensation to the output of PID feedback controller formed based on the observation result" is realized through the gain adjuster set between the output of low-pass filter in disturbance observer and the output of PID feedback controller; the uncertain crystallizer level control system with disturbance is set up through the determination of weight function, the approximation implementation of pure time delay part in inverse nominal model, the determination of filter pole and the determination of gain coefficient of gain adjuster respectively; in the above formula, T(S): complementary sensitivity function, indicating the closed-loop transfer function from system input to output.

2. The crystallizer level control system with disturbance observer according to claim 1, characterized in that: the specific structure of the gain adjuster is: wherein, Kp: proportional coefficient; Ki: integral coefficient; Kd: differential coefficient; Tp: to-be-determined parameter; s: Laplace differential operator.

3. The crystallizer level control system with disturbance observer according to claim 2, characterized in that: the to-be-determined parameter Tp is determined according to the following formula: wherein, Tp: to-be-determined parameter; s: Laplace differential operator.

4. The crystallizer level control system with disturbance observer according to claim 3, characterized in that: the to-be-determined parameter Tp is determined according to the following formula: wherein, Tp: to-be-determined parameter; s: Laplace differential operator.

5. The crystallizer level control system with disturbance observer according to claim 2, characterized in that: the flow coefficient Gc is determined according to experience or according to the following formula: wherein, Gc: flow coefficient; V: draw speed; unit: m / s; dr: stopper opening degree, unit: m.

6. The crystallizer level control system with disturbance observer according to claim 1, characterized in that: the approximation implementation of pure time delay part in inverse nominal model is completed through linear approximation method; the linear approximation approximation expression is realized by setting the following linear approximation expression and setting B(s) in it as a linear element with high-gain low-pass characteristic, L(s) = B(s) / (1 + Tp(s)) = K1 / (s + K2), wherein, L(s): linear approximation expression, used to form the approximation expression of pure time delay part in inverse nominal model in low-frequency range; B(s): linear element with high-gain low-pass characteristic; Tp: to-be-determined parameter; s: Laplace differential operator.

7. The crystallizer level control system with disturbance observer according to claim 6, characterized in that: B(s) in the formula is determined according to the following formula, B(s) = K1 / (s + K2), wherein, B(S): first-order inertia element; K1: to-be-determined parameter; K2: to-be-determined parameter; s: Laplace differential operator. The perturbation factors of the system are constituted by the flow coefficient Gc and the crystallizer object time delay τ, the multiplicative perturbation structure is used to represent the uncertain system, and the system robust stability constraint is 8. The crystallizer level control system with disturbance observer according to claim 7, characterized in that: ​ ​ The weight function is an upper bound of the multiplicative uncertainty of the system. ​ ​ ​ ​ d c : output of the gain adjuster K f : gain coefficient; G c : flow coefficient; Estimate traffic disturbances. ​ Gain coefficient K f ∈ [0, 1 / Gc]. ​ Gain coefficient K f ∈ [0, 0.35 / Gc]. ​ ​ ​ ​ ​ ​ A: cross-sectional area of crystallizer; unit: m 2 ; ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ The K2 and Tp are determined based on the Bode diagram of the inverse nominal model pure time delay part and the linear approximation expression under the condition that the phase frequency characteristic of the inverse nominal model pure time delay part and the linear approximation expression satisfy the following constraint, and the approximation expression of the inverse nominal model pure time delay part is completed according to the determined K1, K2 and Tp, In the formula, ∠e jτω : phase-frequency characteristic of the inverse nominal model; ∠L(jω): phase frequency characteristic of the linear approximation expression; ph max : maximum phase angle difference tolerable; f max : Maximum frequency of primary periodic disturbance, in Hz; ω: angular frequency, unit: rad / s.

9. The crystallizer liquid level control system with a disturbance observer according to claim 8, characterized in that: The determination of the fluctuation frequency range of the main period is completed by fast Fourier transform of the actual liquid levels of multiple groups of crystallizers in multiple days, and the determination of the maximum disturbance frequency and the maximum tolerable phase angle difference is completed accordingly.

10. The crystallizer liquid level control system with a disturbance observer according to claim 1, characterized in that: The determination of the weight function is based on the premise of satisfying the following condition, and the Bode diagram is used to determine, In the formula, R: change range of the flow coefficient Gc; L1: change range of the crystallizer object time delay τ; Frequency response of the weight function.

11. The crystallizer liquid level control system with a disturbance observer according to claim 1, characterized in that: The low-pass filter determined according to step S3 is a second-order low-pass filter, and the two corresponding poles are determined in the uncertainty system characterized by the multiplicative perturbation structure and by under the constraint of system robust stability, according to the following steps: S11: determining the larger one of the two poles according to the maximum disturbance frequency of the main period; S12: setting the difference between the two to 1, and determining the other accordingly.

12. The crystallizer liquid level control system with a disturbance observer according to claim 11, characterized in that: The determination of the fluctuation frequency range of the main period is completed by fast Fourier transform of the actual liquid levels of multiple groups of crystallizers in multiple days, and the determination of the maximum disturbance frequency is completed accordingly.

13. The crystallizer liquid level control system with a disturbance observer according to claim 11, characterized in that: The larger one of the two poles in step S11 is determined according to the following formula: In the formula, P i : the greater of the two poles; f max : maximum frequency of perturbation.

14. A control method of the crystallizer liquid level control system with a disturbance observer according to claim 1, characterized in that: At each sampling period of the system, the suppression type feedback of the uncertain disturbance of the system is completed by executing the following steps, SS1: obtaining the liquid level set value and the actual measured value, and calculating the difference between the two; SS2: calling the PID controller to calculate the stopper adjusting amount; SS3: calling the disturbance observer to calculate the estimated flow disturbance; SS4: calculating the disturbance control compensation amount according to the estimated flow disturbance; SS5: completing the adjusting control of the stopper position according to the stopper adjusting amount determined in step SS2 and the disturbance control compensation amount determined in step SS4.

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