Silicon single crystal growth composite anti-jamming control method for suppressing multi-source multi-class jamming

Abstract

The application discloses a kind of silicon single crystal growth composite anti-interference control methods for inhibiting multi-source multi-class interference, and is specifically implemented according to the following steps: step 1, establish low-order linear system model in the process of silicon single crystal growth;Step 2, using state observer and two types of interference observer, design composite output feedback anti-interference controller;Step 3, the corresponding observer and controller gain matrix are obtained by silicon single crystal growth control system, and the composite anti-interference control strategy is obtained.The application solves the problem that the existing technology exists in the process of silicon single crystal growth is often mixed with a large number of measurement interference, so that some classic silicon single crystal growth control scheme cannot achieve the expected control effect in actual crystal pulling process.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor silicon single crystal growth process control technology, specifically relating to a composite anti-interference control method for silicon single crystal growth that suppresses multi-source and multi-type interference. Background Technology

[0002] Silicon is the most important basic material in the semiconductor industry, used to manufacture thyristors, solar photovoltaic cells, and various integrated circuits. With the rapid development of the solar photovoltaic industry and the scale of integrated circuits, there is an urgent need for the semiconductor materials industry to provide silicon single crystal wafers with larger diameters and higher quality to improve crystal utilization and reduce costs. Currently, the commonly used methods for preparing integrated circuit-grade silicon single crystals are the Czochralski method and the zone melting method. Among them, the Czochralski method is widely used for the preparation of integrated circuit-grade silicon single crystals because it can control crystal characteristics through doping and other means, making it easier to grow high-quality, large-diameter silicon single crystals compared to the zone melting method. However, the growth process of large-size, electronic-grade silicon single crystals involves complex physical changes, multi-field and multi-phase coupling, nonlinearity, and large hysteresis, which makes controlling the growth of high-quality crystals very difficult and challenging. Designing a better and more practical silicon single crystal growth control method is currently a key research focus.

[0003] Since many internal states within a single crystal furnace cannot be directly measured, output feedback control is a common method in silicon single crystal growth control systems. However, due to the influence of the internal environment of the silicon single crystal growth equipment and the characteristics of its various components, there are some non-negligible process disturbances in the silicon single crystal growth system. Furthermore, the measurement signals acquired using multiple sensors are often mixed with a large amount of measurement interference, causing some classic silicon single crystal growth control schemes to fail to achieve the expected control effect in actual crystal pulling processes. Summary of the Invention

[0004] The purpose of this invention is to provide a composite anti-interference control method for silicon single crystal growth that suppresses multi-source and multi-type interference. This method solves the problem that the silicon single crystal growth process in the prior art is often mixed with a large number of measurement interferences, so that some classic silicon single crystal growth control schemes cannot achieve the expected control effect in the actual crystal pulling process.

[0005] The technical solution adopted in this invention is a composite anti-interference control method for silicon single crystal growth that suppresses multi-source and multi-type interference, specifically implemented according to the following steps:

[0006] Step 1: Establish a low-order linear system model of the silicon single crystal growth process;

[0007] Step 2: Design a composite output feedback anti-interference controller using a state observer and two types of interference observers;

[0008] Step 3: The silicon single crystal growth control system obtains the corresponding observer and controller gain matrices to obtain the composite anti-interference control strategy.

[0009] The invention is further characterized in that,

[0010] Step 1 is implemented in the following steps:

[0011] Step 1.1: Establish a lifting speed v p With heater power P as input, crystal radius R c and silicon melt temperature T l The mechanism model for output

[0012]

[0013] in, This indicates the rate of change of temperature in the molten silicon. c represents the rate of change of crystal radius. l m l V represents the heat capacity of molten silicon. c α represents the crystal growth rate. c Indicates the tilt angle of the meniscus.

[0014] in,

[0015]

[0016]

[0017] Q c =Q hc -Q co -Q cl ,

[0018] Q h =PQ hc ,

[0019]

[0020] Q cl =k c A co G c ,

[0021] Q l =k l A ls G l ,

[0022]

[0023]

[0024] Among them, Qhc Q represents the amount of heat transferred from the heater to the crucible via thermal radiation. co Q represents the amount of heat lost by the crucible to the external environment through thermal radiation. cl Q represents the total heat transferred from the crucible to the melt through thermal conduction. lo Q represents the amount of heat lost from the surface of the molten silicon to the external environment through thermal radiation and convection. l Q represents the heat transferred from the silicon melt to the growth interface via thermal conduction. h Q represents the amount of heat absorbed by the heater. c The heat absorbed by the crucible is represented by Q, and the heat released during crystallization is represented by m. l The mass of the silicon melt is represented by x1 and x2, respectively, which represent the controlled output temperature T of the silicon melt. l The change increment and crystal radius R c The increment of change, P represents the heater power, σ represents the Boltzmann constant, and ε c ε represents the emissivity of the crucible. l A represents the emissivity of silicon melt. co A represents the surface area of ​​the silicon melt. ls T represents the surface area at the solid-liquid interface. c T represents the crucible temperature. o R represents the temperature of the external environment. cr H represents the radius of the crucible. cr H represents the height of the crucible. cl ρ represents the height of the melt in the crucible. s ρ represents the density of silicon crystals. l V represents the density of the silicon melt. p The pull-out speed is represented by k, where L represents the latent heat of crystallization, and k is the kinematic velocity. c k represents the thermal conductivity of the silicon melt. l G represents the thermal conductivity of a single silicon crystal. c G represents the temperature gradient of the quartz crucible. l The solid-liquid interface temperature gradient is represented by k, the crucible-to-liquid ratio is represented by t, and the crystal pulling time is represented by t.

[0025] Step 1.2: Linearize the silicon single crystal growth process mechanism model obtained in Step 1.1 to obtain a linear system model:

[0026] The nonlinear model is represented as

[0027]

[0028] Choose an equilibrium point (x0, u0) in the domain that satisfies

[0029] f(x0,u0)=0 (3)

[0030] By employing a small-perturbation linearization method and utilizing a first-order approximation through Taylor expansion, a low-order linear system model near the equilibrium point is obtained.

[0031]

[0032] in,

[0033]

[0034] in, Represents the rate of change of the system state. Indicates the system status. Let x0 and u0 represent the system state and the equilibrium point of the control input, respectively, and let A and B represent the known system parameters with appropriate dimensions.

[0035] Step 2 is implemented in the following steps:

[0036] Step 2.1: Establish a silicon single crystal growth control system:

[0037]

[0038] in, Let x(t) represent the rate of change of the system state, u(t) represent the system state, y(t) represent the control input, z(t) represent the measured output, and C, D1, D2, E, H3, H4 represent known system parameters of appropriate dimension, where the system state x(t) is unmeasurable and described by an external system. The structure is as follows:

[0039]

[0040] Where i represents the type of interference, i = 1, 2, d1(t) and d2(t) represent the system process interference and measurement interference, respectively, ω i (t) represents the internal state of the i-th type of disturbance system, δ j (t)∈L2[0,+∞),j=1,2,3,4 represents energy-bounded disturbance, W i M i H i Let represent the known parameters of the i-th type of system with appropriate dimension.

[0041] Step 2.2: Since the state of the silicon single crystal growth control system as shown in formula (5) is unmeasurable, a state observer is constructed to estimate the unmeasurable state based on the measurement output and the estimation of multi-source and multi-type disturbances. Then, a measurement disturbance observer is designed based on the measurement output and the estimated value of the process disturbance.

[0042] The state observer structure is as follows:

[0043]

[0044] in, Represents the rate of change of the system state estimate. This represents an estimate of the measured output y(t). Let L0 represent the estimate of the system state x(t), and L0 represent the gain of the state observer. and These represent estimates of process disturbances and measurement disturbances, respectively.

[0045] Step 2.3: Based on formulas (5) and (6), the process disturbance observer is constructed as follows:

[0046]

[0047] in, This represents the estimate of the internal state ω1(t) of the process disturbance. Let σ1(t) represent the derivative form of the intermediate auxiliary variable, L1 represent the gain of the process disturbance observer, and M1 and W1 represent the known system parameters with appropriate dimensions.

[0048] Step 2.4: From formula (6), the interference observer is constructed as follows.

[0049]

[0050] in, This represents an estimate of the internal state ω2(t) of the measurement disturbance. Let σ²(t) represent the derivative form of the intermediate auxiliary variable, L² represent the gain of the measurement interference observer, and M² and W² represent the known system parameters with appropriate dimensions.

[0051] Step 2.5: Define the system state estimation error as... The estimation error system is then...

[0052]

[0053] in, The derivative form of the system state estimation error, e ω1 (t) and e ω2 (t) represent the estimation errors of process disturbance and measurement disturbance, respectively, and are defined as follows: Therefore, based on formulas (6), (8), and (9), the process disturbance error system is as follows:

[0054]

[0055] in, H1 represents the derivative form of the process disturbance estimation error, and H1 represents the known system parameters with appropriate dimension.

[0056] Furthermore, the dynamic representation of the measurement interference error is as follows:

[0057]

[0058] in, The derivative form of the measurement disturbance estimation error is expressed as follows: The derivative form representing the internal state of the measurement disturbance. H2 represents the derivative form of the estimate of the internal state ω2(t) of the measurement disturbance, where H2 represents the known system parameters with appropriate dimension;

[0059] Step 2.6: Based on formula (5), and state estimation and process disturbance estimation, establish a composite output feedback anti-interference controller.

[0060]

[0061] Where K1 and K2 represent the gains of the feedback and feedforward controllers, respectively;

[0062] Step 2.7: Combining the above formulas, the composite closed-loop anti-interference control system is designed as follows:

[0063]

[0064] Where z(t) represents the control output;

[0065] For simplicity, the composite output feedback anti-interference closed-loop control system shown in formula (14) can be written as:

[0066]

[0067] in, Represents the rate of change of the system state. Indicates the system status. This indicates a bounded disturbance of energy. Represents the system matrix;

[0068] in,

[0069] Step 3 is implemented in the following steps:

[0070] Step 3.1: Select the Lyapunov function as...

[0071]

[0072] Where V(t) represents the Lyapunov function, Let P represent the system state, which is a Lyapunov matrix.

[0073]

[0074] Among them, P i >0, i={1,2,3,4};

[0075] According to the composite output feedback anti-interference controller shown in formula (15), the derivative of V(t) is:

[0076]

[0077] in,

[0078]

[0079] Π 11 =sym{P1A+P1BK1},

[0080] Π 22 =sym{P2A-P2L0C-P 23 L1L0C},

[0081]

[0082] Π 24 =-P2L0D2W2-P 23 L1L0D2W2,

[0083]

[0084]

[0085] Π 44 =sym{P4M2-P4L2D2W2M2},

[0086] Π 45 =-P4L2CD1W1H1,

[0087] Π 46 =P4H2-P4L2D2W2H2,

[0088] Π 47 =-P4L2CH3.

[0089] Step 3.2: Analyze the control performance of the composite output feedback anti-interference controller as shown in formula (15), and define the following index function to discuss H. ∞ Control performance:

[0090]

[0091] Where J(T) represents the index function, and γ>0 is H ∞ The control performance gain, δ(t) represents the energy-bounded disturbance, V(t)≥0 for any t>0, and V(0)=0 when x(0)=0. Therefore, from formula (18), we know that

[0092]

[0093] in,

[0094]

[0095] Π' 11 =sym{P1A+P1BK1}+E T E,

[0096]

[0097] From formula (19), when Ψ<0, J(T)<0;

[0098] To handle nonlinear terms in the matrix inequality Ψ<0, define X1 = K1Q1, X2 = P3L1, X3 = P4L2. Then, the matrix ψ in (19) is multiplied both on the right and left by diag(Q1,I,I,I,I,I,I,I,I), and the parameters α1>0 and α2>0 are defined. The additional conditions Q1>α1I, P3>α2I and Schur's complement lemma can be obtained.

[0099]

[0100] in,

[0101] Π″ 11 =sym{AQ1+BX1},

[0102] Π 19 =(BX1 Q1E T ),

[0103] Π' 22 =sym{P2A-P2L0C},

[0104]

[0105] Π′ 24 =-P2L0D2W2,

[0106]

[0107]

[0108] Π' 44=sym{P4M2-X3D2W2M2},

[0109] Π' 45 =-X3CH3,

[0110] Π′ 46 =P4H2-X3D2W2H2,

[0111] Π' 47 =-X3CH3,

[0112] Π 99 =diag{-α1I-I},

[0113] Π 10,10 =diag{-α1I -α2I -α2I -α2I}.

[0114] Based on the above discussion, Under the condition that J(T) < 0, T ∈ (0, +∞), we have: Therefore, as T → +∞, we have:

[0115] After determining the matrix inequality (20), This is necessarily true. At this point, there exists a parameter π > 0 such that... Therefore, according to stability theory, system (15) in The index below is stable.

[0116] In summary, system (15) in H ∞ The control performance exhibits exponential stability.

[0117] Step 3.3: For the silicon single crystal growth control system, the Linear Matrix Inequality (LMI) toolbox in MATLAB is used to numerically solve the above problem, and the corresponding observer and controller gain matrices are obtained respectively, thus obtaining the composite anti-interference control strategy.

[0118] The beneficial effect of this invention is that it provides a composite anti-interference control method for silicon single crystal growth that suppresses multi-source and multi-type interference, achieving effective control over the silicon single crystal growth process. Compared to most anti-interference control methods that ignore the influence of measurement interference in the measurement signal, the composite output feedback anti-interference control method designed in this invention considers both process interference and measurement interference in the silicon single crystal growth control system, and combines different anti-interference control schemes for suppression, ensuring that the closed-loop system of silicon single crystal growth has good control performance and improving the quality of silicon single crystals. Attached Figure Description

[0119] Figure 1 This is the overall flowchart of the method;

[0120] Figure 2This is a schematic diagram of the heat transfer method in a silicon single crystal growth equipment;

[0121] Figure 3 This is a schematic diagram of the heat transfer process in a silicon single crystal growth device;

[0122] Figure 4 This is a block diagram of the proposed anti-interference control scheme;

[0123] Figure 5 This is a control output diagram of a silicon single crystal growth system;

[0124] Figure 6 shows the system state, state estimation, and estimation error.

[0125] Figure 7 This is a measurement output diagram of a silicon single crystal growth system;

[0126] Figure 8 This is a control input diagram for a silicon single crystal growth system;

[0127] Figure 9 It is a plot of estimated errors for process and measurement disturbances;

[0128] Figure 10 It is a diagram of process disturbances and their estimation;

[0129] Figure 11 It is a diagram showing the measurement interference and its estimation. Detailed Implementation

[0130] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0131] This invention presents a composite anti-interference control method for silicon single crystal growth that suppresses multi-source and multi-type interference. First, a mechanism model of the silicon single crystal growth process is established by considering the heat transfer process, kinetics, and geometric relationships during the Czochralski method. Based on this model, a linear system model for silicon single crystal growth is obtained using a small-perturbation linearization method. To improve the anti-interference capability of the closed-loop control system for silicon single crystal growth, two different types of interference observers are used to estimate process interference and measurement interference, respectively. Then, a state observer is constructed based on the "purified" measurement output, and a composite output feedback anti-interference controller is designed based on the state observer. Subsequently, the stability of the composite closed-loop system is analyzed using linear matrix inequality techniques and Lyapunov stability theory. Simultaneously, the decoupling problem between the two types of interference observers, the state observer, and the output feedback controller is addressed. Finally, the designed composite output feedback anti-interference control strategy is applied to silicon single crystal growth equipment to verify the proposed control scheme.

[0132] The present invention provides a composite anti-interference control method for silicon single crystal growth that suppresses multi-source and multi-type interference. The flowchart is as follows: Figure 1 As shown, please follow these steps:

[0133] Step 1: Establish a low-order linear system model of the silicon single crystal growth process;

[0134] Step 1 is implemented in the following steps:

[0135] Step 1.1: Establish a mechanism model for silicon single crystal growth based on the heat transfer process, kinetics, and geometric relationships during the Czochralski method. During crystal pulling, the main control parameters in the Czochralski silicon single crystal growth process are the crystal pulling speed and the heater power. Therefore, this method establishes a model based on the pulling speed v... p With heater power P as input, crystal radius R c and silicon melt temperature T l The mechanism model for output

[0136]

[0137] in, This indicates the rate of change of temperature in the molten silicon. c represents the rate of change of crystal radius. l m l V represents the heat capacity of molten silicon. c α represents the crystal growth rate. c Indicates the tilt angle of the meniscus.

[0138] in,

[0139]

[0140]

[0141] Q c =Q hc -Q co -Q cl ,

[0142] Q h =PQ hc ,

[0143]

[0144] Q cl =k c A co G c ,

[0145] Q l =k l A ls G l ,

[0146]

[0147]

[0148] Among them, Q hc Q represents the heat transferred from the heater to the crucible via thermal radiation. co Q represents the amount of heat lost by the crucible to the external environment through thermal radiation. cl Q represents the total heat transferred from the crucible to the melt through thermal conduction. lo Q represents the amount of heat lost from the surface of the molten silicon to the external environment through thermal radiation and convection. l Q represents the heat transferred from the silicon melt to the growth interface via thermal conduction. h Q represents the amount of heat absorbed by the heater. c The value of m represents the heat absorbed by the crucible, Q represents the heat released during crystallization. l The mass of the silicon melt is represented by x1 and x2, respectively, which represent the controlled output temperature T of the silicon melt. l The change increment and crystal radius R c The increment of change, P represents the heater power, σ represents the Boltzmann constant, and ε c ε represents the emissivity of the crucible. l A represents the emissivity of silicon melt. co A represents the surface area of ​​the silicon melt. ls T represents the surface area at the solid-liquid interface. c T represents the crucible temperature. o R represents the temperature of the external environment. cr H represents the radius of the crucible. cr H represents the height of the crucible. cl ρ represents the height of the melt in the crucible. s ρ represents the density of silicon crystals. l V represents the density of the silicon melt. p The pull-out speed is represented by k, where L represents the latent heat of crystallization, and k is the kinematic velocity. c k represents the thermal conductivity of the silicon melt. l G represents the thermal conductivity of a single silicon crystal. c G represents the temperature gradient of the quartz crucible. l The solid-liquid interface temperature gradient is represented by k, the crucible-to-liquid ratio is represented by t, and the crystal pulling time is represented by t.

[0149] Step 1.2: Linearize the silicon single crystal growth process mechanism model obtained in Step 1.1 to obtain a linear system model:

[0150] The nonlinear model is represented as

[0151]

[0152] Choose an equilibrium point (x0, u0) in the domain that satisfies

[0153] f(x0,u0)=0 (3)

[0154] By employing a small-perturbation linearization method and utilizing a first-order approximation through Taylor expansion, a low-order linear system model near the equilibrium point is obtained.

[0155]

[0156] in,

[0157]

[0158] in, Represents the rate of change of the system state. Indicates the system status. Let x0 and u0 represent the system state and the equilibrium point of the control input, respectively, and let A and B represent the known system parameters with appropriate dimensions.

[0159] Step 2: Design a composite output feedback anti-interference controller using a state observer and two types of interference observers;

[0160] Step 2 is implemented in the following steps:

[0161] Step 2.1: Considering the multi-source and multi-type interference caused by the environment and equipment, establish a silicon single crystal growth control system:

[0162]

[0163] in, Let x(t) represent the rate of change of the system state, u(t) represent the system state, y(t) represent the control input, z(t) represent the measured output, and C, D1, D2, E, H3, H4 represent known system parameters of appropriate dimension, where the system state x(t) is unmeasurable and described by an external system. The structure is as follows:

[0164]

[0165] Where i represents the type of interference, i = 1, 2, d1(t) and d2(t) represent the system process interference and measurement interference, respectively, ω i (t) represents the internal state of the i-th type of disturbance system, δ j (t)∈L2[0,+∞),j=1,2,3,4 represents energy-bounded disturbance, W i M i H i Let represent the known parameters of the i-th type of system with appropriate dimension.

[0166] Step 2.2: Since the state of the silicon single crystal growth control system as shown in formula (5) is unmeasurable, a state observer is constructed to estimate the unmeasurable state based on the measurement output and the estimation of multi-source and multi-type disturbances. Then, a measurement disturbance observer is designed based on the measurement output and the estimated value of the process disturbance.

[0167] The state observer structure is as follows:

[0168]

[0169] in, Represents the rate of change of the system state estimate. This represents an estimate of the measured output y(t). Let L0 represent the estimate of the system state x(t), and L0 represent the gain of the state observer. and These represent estimates of process disturbances and measurement disturbances, respectively.

[0170] Step 2.3: Based on formulas (5) and (6), the process disturbance observer is constructed as follows:

[0171]

[0172] in, This represents the estimate of the internal state ω1(t) of the process disturbance. Let σ1(t) represent the derivative form of the intermediate auxiliary variable, L1 represent the gain of the process disturbance observer, and M1 and W1 represent the known system parameters with appropriate dimensions.

[0173] Step 2.4: From formula (6), the interference observer is constructed as follows.

[0174]

[0175] in, This represents an estimate of the internal state ω2(t) of the measurement disturbance. Let σ²(t) represent the derivative form of the intermediate auxiliary variable, L² represent the gain of the measurement interference observer, and M² and W² represent the known system parameters with appropriate dimensions.

[0176] Step 2.5: Define the system state estimation error as... The estimation error system is then...

[0177]

[0178] in, The derivative form of the system state estimation error, e ω1 (t) and e ω2(t) represent the estimation errors of process disturbance and measurement disturbance, respectively, and are defined as follows: Therefore, based on formulas (6), (8), and (9), the process disturbance error system is as follows:

[0179]

[0180] in, H1 represents the derivative form of the process disturbance estimation error, and H1 represents the known system parameters with appropriate dimension.

[0181] Furthermore, the dynamic representation of the measurement interference error is as follows:

[0182]

[0183] in, The derivative form of the measurement disturbance estimation error is expressed as follows: The derivative form representing the internal state of the measurement disturbance. H2 represents the derivative form of the estimate of the internal state ω2(t) of the measurement disturbance, where H2 represents the known system parameters with appropriate dimension;

[0184] Step 2.6: Based on formula (5), and state estimation and process disturbance estimation, establish a composite output feedback anti-interference controller.

[0185]

[0186] Where K1 and K2 represent the gains of the feedback and feedforward controllers, respectively;

[0187] Step 2.7: Combining the above formulas, the composite closed-loop anti-interference control system is designed as follows:

[0188]

[0189] Where z(t) represents the control output;

[0190] For simplicity, the composite output feedback anti-interference closed-loop control system shown in formula (14) can be written as:

[0191]

[0192] in, Represents the rate of change of the system state. Indicates the system status. This indicates a bounded disturbance of energy. Represents the system matrix;

[0193] in,

[0194] Step 3: Apply Lyapunov stability theory to ensure the stability of the composite closed-loop system, and use the linear matrix inequality (LMI) technique to handle the coupling problem between observers in the silicon single crystal growth control system, obtain the corresponding observer and controller gain matrices, and obtain the composite anti-interference control strategy.

[0195] Step 3 is implemented in the following steps:

[0196] Step 3.1: Select the Lyapunov function as...

[0197]

[0198] Where V(t) represents the Lyapunov function, Let P represent the system state, which is a Lyapunov matrix.

[0199]

[0200] Among them, P i >0, i={1,2,3,4};

[0201] According to the composite output feedback anti-interference controller shown in formula (15), the derivative of V(t) is:

[0202]

[0203] in,

[0204]

[0205] Π 11 =sym{P1A+P1BK1},

[0206] Π 22 =sym{P2A-P2L0C-P 23 L1L0C},

[0207]

[0208] Π 24 =-P2L0D2W2-P 23 L1L0D2W2,

[0209]

[0210]

[0211] Π 44 =sym{P4M2-P4L2D2W2M2},

[0212] Π 45=-P4L2CD1W1H1,

[0213] Π 46 =P4H2-P4L2D2W2H2,

[0214] Π 47 =-P4L2CH3.

[0215] Step 3.2: Analyze the control performance of the composite output feedback anti-interference controller as shown in formula (15), and define the following index function to discuss H. ∞ Control performance:

[0216]

[0217] Where J(T) represents the index function, and γ>0 is H ∞ The control performance gain, δ(t) represents the energy-bounded disturbance, and for any t>0, V(t)≥0. When V(0) = 0, therefore, according to formula (18),

[0218]

[0219] in,

[0220]

[0221] Π' 11 =sym{P1A+P1BK1}+E T E,

[0222]

[0223] From formula (19), when Ψ<0, J(T)<0;

[0224] To handle nonlinear terms in the matrix inequality Ψ<0, define X1 = K1Q1, X2 = P3L1, X3 = P4L2. Then, the matrix ψ in (19) is multiplied both on the right and left by diag(Q1,I,I,I,I,I,I,I,I), and the parameters α1>0 and α2>0 are defined. The additional conditions Q1>α1I, P3>α2I and Schur's complement lemma can be obtained.

[0225]

[0226] in,

[0227] Π″ 11 =sym{AQ1+BX1},

[0228] Π 19 =(BX1 Q1ET ),

[0229] Π' 22 =sym{P2A-P2L0C},

[0230]

[0231] Π′ 24 =-P2L0D2W2,

[0232]

[0233]

[0234] Π' 44 =sym{P4M2-X3D2W2M2},

[0235] Π' 45 =-X3CH3,

[0236] Π′ 46 =P4H2-X3D2W2H2,

[0237] Π' 47 =-X3CH3,

[0238] Π 99 =diag{-α1I-I},

[0239] Π 10,10 =diag{-α1I -α2I -α2I -α2I}.

[0240] Based on the above discussion, Under the condition that J(T) < 0, T ∈ (0, +∞), we have: Therefore, as T → +∞, we have:

[0241] After determining the matrix inequality (20), This is necessarily true. At this point, there exists a parameter π > 0 such that... Therefore, according to stability theory, system (15) in The index below is stable.

[0242] In summary, system (15) in H ∞ The control performance exhibits exponential stability.

[0243] Step 3.3: For the silicon single crystal growth control system, the Linear Matrix Inequality (LMI) toolbox in MATLAB is used to numerically solve the above problem, and the corresponding observer and controller gain matrices are obtained respectively, thus obtaining the composite anti-interference control strategy.

[0244] This invention applies a composite anti-interference control method to a silicon single crystal growth control system. The effectiveness of the proposed control method is verified by the actual parameters of the silicon single crystal growth control system. Under the influence of process and measurement interference, the constructed anti-interference output feedback controller can effectively suppress interference and ensure that the silicon single crystal growth control system has good control performance.

[0245] Because of the mechanical motion of many components during the operation of silicon single crystal growth equipment, these periodic movements generate numerous harmonic interferences. These interferences, mixed in with the control system through sensors, severely affect the control performance of the silicon single crystal growth system. Therefore, to eliminate the adverse effects of these interferences, this invention constructs different types of interference observers to observe process interference and measurement interference in the growth system, and based on this, designs a composite output feedback anti-interference controller to ensure that the closed-loop system of silicon single crystal growth has good control performance.

[0246] The invention will now be further described with reference to the accompanying drawings and a specific example.

[0247] This invention applies the proposed composite output feedback anti-interference control method to a silicon single crystal growth system. During crystal pulling, there are corresponding process and measurement interferences, mainly affecting the temperature of the silicon melt and the crystal diameter. Interference with the temperature signal primarily originates from the argon gas filling process, crystal rotation, crucible rotation, and heater power supply ripple. The interference caused by crucible rotation and heater power supply ripple is a periodic low-frequency interference. Furthermore, low-frequency periodic interference also exists in the crystal diameter measurement signal. This is because as the size of the single crystal furnace increases, the heating uniformity of the melt deteriorates, and the crystal is prone to wobbling during growth. The movement of the measuring aperture causes fluctuations in the diameter measurement signal. These interferences are always present during crystal growth, severely affecting the control performance of the silicon single crystal growth system. Since this part of the interference is mixed in with the sensor's measurement output, we consider it as measurement interference. Another part of the interference already exists during the modeling process. This interference is caused by the internal environment of the silicon single crystal growth equipment and the characteristics of various components, which can prevent the crystal pulling process from executing precisely according to the set steps. Therefore, we call this interference process interference and design a corresponding composite anti-interference controller to suppress the two types of interference, thereby improving the measurement and control accuracy and achieving the requirement of constant-speed equal-diameter growth control in the equal-diameter stage.

[0248] The linear system model for silicon single crystal growth is as follows:

[0249]

[0250] Where x = (x1 x2) T This refers to the system state, where x1 and x2 represent the control output silicon melt temperature T, respectively. lThe change increment and crystal radius R c The increment of change; u = (P v p ) T These are control inputs, P and v. p These represent the incremental changes in heater power and lifting speed, respectively.

[0251] Based on the actual crystal pulling process and the structure of the silicon single crystal growth equipment, the parameters of the silicon single crystal growth system are selected as follows:

[0252]

[0253] Using the LMI toolkit in MATLAB, the observer and controller gain matrices are obtained.

[0254]

[0255] In this case, the simulation conditions for applying the proposed composite output feedback anti-interference control strategy are as follows: the silicon melt temperature T is selected respectively. l Crystal diameter R c Heater power P and lifting speed v p The equilibrium point is T l =1693,R c =0.15, P=121119, v p =5×10 -6 .

[0256] Based on the above settings, the proposed composite output feedback anti-interference control method was applied to a silicon single crystal growth system, and the simulation results are as follows. Figures 5-11 As shown.

[0257] Figure 2 This diagram illustrates the heat transfer process in a silicon single crystal growth device. Dashed arrows represent heat conduction, solid arrows represent heat radiation, and hollow arrows represent heat convection. Figure 5 To control the output curve, the silicon melt temperature T, which cannot be used for designing the control law, is selected. l The change increment and crystal diameter R c The change increment is used as the control output. It can be seen that when a disturbance is added at 20 seconds, the curve fluctuates due to the disturbance. Compared to the method without a disturbance observer, the control output curve of the proposed control method quickly returns to near the equilibrium point, indicating that the controller designed in this invention can effectively suppress disturbances caused by measurement output interference. The system state, state estimation, and estimation error are shown in Figure 6. Combined with the state observer, the state of the unmeasured system can be estimated and used to design a feedback controller. The measurement output y(t) obtained through the sensor is shown in Figure 6. Figure 7 As shown, during the constant diameter stage of crystal growth, the crystal diameter R is affected by measurement interference. cThe increment of change is ±1.16, exceeding the theoretical value (theoretically, it should be stable within ±1mm). Control input heater power P and lifting speed v p like Figure 8 As shown, it consists of a feedback and a feedforward controller. The control input ensures that process disturbances are suppressed and that the closed-loop system has H... ∞ performance. Figure 9 Estimation error e of process and measurement disturbances d The fact that (t) approaches zero over time indicates that both types of interference observers can accurately estimate the interference. Figure 10 and Figure 11 The process and measurement interference curves and their estimates are presented, which were observed by different interference observers.

[0258] Based on the above simulation results, it can be confirmed that the control scheme proposed in this invention is feasible and reasonable, can eliminate the adverse effects of external interference, and ensure that the closed-loop system for silicon single crystal growth has good control performance.

Claims

1. A composite anti-interference control method for silicon single crystal growth to suppress multi-source and multi-type interference, characterized in that, The specific steps are as follows: Step 1: Establish a low-order linear system model of the silicon single crystal growth process; Step 1 is implemented in the following steps: Step 1.1: Establish a lifting speed With heater power P as input, crystal radius and silicon melt temperature The mechanism model for output （1） in, This indicates the rate of change of temperature in the molten silicon. Indicates the rate of change of crystal radius. This indicates the heat capacity of the silicon melt. Indicates the crystal growth rate. Indicates the tilt angle of the meniscus. in, in, This indicates the heat transferred from the heater to the crucible via thermal radiation. This indicates the heat lost by the crucible to the external environment through thermal radiation. This indicates the total heat transferred from the crucible to the melt through thermal conduction. This refers to the heat lost from the surface of the molten silicon to the external environment through thermal radiation and convection. This indicates that the silicon melt transfers heat to the growth interface through thermal conduction. This indicates the amount of heat absorbed by the heater. This indicates the amount of heat absorbed by the crucible. This indicates that crystallization releases heat. Indicates the mass of the silicon melt. and These represent the control output temperature of the molten silicon. Incremental change and crystal radius The increment of change, where P represents the heater power. Represents Boltzmann's constant. Indicates the emissivity of the crucible. Indicates the emissivity of silicon melt. This represents the surface area of ​​the silicon melt. This represents the surface area at the solid-liquid interface. Indicates the crucible temperature. Indicates the temperature of the external environment. Indicates the radius of the crucible. Indicates the height of the crucible. This indicates the height of the melt in the crucible. This indicates the density of silicon crystals. This indicates the density of the silicon melt. Indicates the lifting speed. Indicates the latent heat of crystallization. This indicates the thermal conductivity of the silicon melt. Indicates the thermal conductivity of silicon single crystal. This represents the temperature gradient of the quartz crucible. This represents the temperature gradient at the solid-liquid interface. Indicates the ratio of the cauldron to the pot. Indicates crystal pulling time; Step 1.2: Linearize the silicon single crystal growth process mechanism model obtained in Step 1.1 to obtain a linear system model: The nonlinear model is represented as （2） Choose an equilibrium point in the domain. ,satisfy （3） By employing a small-perturbation linearization method and utilizing a first-order approximation through Taylor expansion, a low-order linear system model near the equilibrium point is obtained. （4） in, ； in, Represents the rate of change of the system state. Indicates the system status. Indicates control input, and Let A and B represent the equilibrium points of the system state and control input, respectively, and let B and B represent the known system parameters with appropriate dimensions. Step 2: Design a composite output feedback anti-interference controller using a state observer and two types of interference observers; Step 2 is implemented in the following steps: Step 2.1: Establish a silicon single crystal growth control system: （5） in, Represents the rate of change of the system state. Indicates the system status. Indicates control input, Indicates the measurement output. Indicates control output. Represents known system parameters with appropriate dimensions and system state. It is unmeasurable, described by an external system, and its structure is as follows: （6） Where i represents the type of interference. , and These represent system process interference and measurement interference, respectively. This represents the internal state of the i-th type of interference system. This indicates a bounded disturbance of energy. This represents the known parameters of the i-th type of system with appropriate dimensions; Step 2.2: Since the state of the silicon single crystal growth control system as shown in formula (5) is unmeasurable, a state observer is constructed to estimate the unmeasurable state based on the measurement output and the estimation of multi-source and multi-type disturbances. Then, a measurement disturbance observer is designed based on the measurement output and the estimated value of the process disturbance. The state observer structure is as follows: （7） in, Represents the rate of change of the system state estimate. Indicates the measurement output The estimate, Indicates the system state The estimate, This represents the gain of the state observer. and These represent estimates of process disturbances and measurement disturbances, respectively. Step 2.3: Based on formulas (5) and (6), the process disturbance observer is constructed as follows: （8） in, Indicates the internal state of process disturbance The estimate, Represent the derivative form of the intermediate auxiliary variable. Indicates intermediate auxiliary variables. Indicates the observer gain for process disturbances. This represents known system parameters with appropriate dimensions; Step 2.4: Based on formula (6), the interference observer is constructed as follows. （9） in, Indicates the internal state of the measurement disturbance. The estimate, Represent the derivative form of the intermediate auxiliary variable. Indicates intermediate auxiliary variables. Indicates the gain of the measurement interference observer. This represents known system parameters with appropriate dimensions; Step 2.5: Define the system state estimation error as... Then the estimation error system is （10） in, The derivative form of the system state estimation error. and Representing the estimation errors of process disturbances and measurement disturbances respectively, defined as follows: , Therefore, based on formulas (6), (8), and (9), the process disturbance error system is as follows: （11） in, The derivative form of the process disturbance estimation error is expressed. This represents known system parameters with appropriate dimensions; Furthermore, the dynamic representation of the measurement interference error is as follows: （12） in, The derivative form of the measurement disturbance estimation error is expressed as follows: The derivative form representing the internal state of the measurement disturbance. Indicates the internal state of the measurement disturbance The estimated derivative form, This represents known system parameters with appropriate dimensions; Step 2.6: Based on formula (5), and state estimation and process disturbance estimation, establish a composite output feedback anti-interference controller. （13） in, and These represent the gains of the feedback and feedforward controllers, respectively. Step 2.7: Combining the above formulas, the composite closed-loop anti-interference control system is designed as follows: （14） in, Indicates control output; For simplicity, the composite output feedback anti-interference closed-loop control system shown in formula (14) can be written as: （15） in, Represents the rate of change of the system state. Indicates the system status. This indicates a bounded disturbance of energy. Represents the system matrix; in, Step 3: The silicon single crystal growth control system obtains the corresponding observer and controller gain matrices to obtain the composite anti-interference control strategy; Step 3 is implemented in the following steps: Step 3.1: Select the Lyapunov function as... （16） in, This represents a Lyapunov function. Let P represent the system state, which is a Lyapunov matrix. in, , ; According to the composite output feedback anti-interference controller shown in formula (15), The derivative is （17） in, Step 3.2: Analyze the control performance of the composite output feedback anti-interference controller as shown in formula (15), and define the following index function for discussion. Control performance: （18） in, Indicates the index function, yes Control performance gain, This represents a bounded disturbance of energy, for any have ,exist From time to time Therefore, according to formula (18), （19） in, From formula (19), when Sometimes, ; Step 3.3: For the silicon single crystal growth control system, the Linear Matrix Inequality (LMI) toolbox in MATLAB is used to numerically solve the above problem, and the corresponding observer and controller gain matrices are obtained respectively, thereby obtaining the composite anti-interference control strategy. Step 3 involves processing matrix inequalities. The nonlinear term in the definition Then, for the matrix in (19) Perform both right-side and left-side multiplication simultaneously. and define parameters and Additional conditions are introduced: And Schur's supplementary lemma （20） in, Based on the above discussion, Under what conditions are there , Therefore, when Sometimes, ; After determining the matrix inequality (20), This is necessarily true; at this point, there exists a parameter. Make Therefore, according to stability theory, system (15) in The index below is stable; In summary, system (15) in Its control performance exhibits exponential stability.

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