Injection molding nozzle pressure finite frequency domain iterative learning control method and system

Abstract

The invention provides an injection molding nozzle pressure finite frequency domain iterative learning control method and system, and relates to the field of injection molding nozzle pressure control, and the specific scheme comprises the steps: building a discrete time state space model of an injection molding nozzle pressure system; estimating a system state through an observer, and constructing an iterative learning control law based on the observer; reconstructing the discrete time state space model by using an iterative learning control law; based on the reconstructed discrete time state space model, stability analysis is carried out by means of a repeated process stability theory and a generalized KYP lemma, so that the nozzle pressure tracks an expected reference trajectory; aiming at a discrete linear repetition system with multiple time delays, an iterative learning control law based on an observer is designed by means of a frequency domain method, and the tracking control problem of an injection molding nozzle pressure system with multiple time delays is solved.

Description

Technical Field

[0001] The invention belongs to the field of injection molding nozzle pressure control, and in particular relates to an injection molding nozzle pressure finite frequency domain iterative learning control method and system. Background Art

[0002] Injection molding is an important plastic processing technology. It processes plastic particles into various high-precision products. It has many advantages, such as high production efficiency, high molding accuracy, and automated operation. At present, injection molding technology has been widely used in textile equipment, medical equipment, cultural and educational supplies, automobile manufacturing, aerospace and other fields. The process has typical repetitive characteristics and mainly consists of three steps: filling, packaging and cooling. In the packaging step, additional material is "filled" into the mold cavity by pressure to compensate for the shrinkage associated with cooling and solidification. The packaging holding stage lasts until the material at the mold mouth is frozen and the material in the mold is no longer affected by the injection nozzle. In this process, the key process variable to be controlled is the nozzle pressure, so that the pressure tracks a desired reference trajectory to prevent material backflow and ultimately ensure the quality of the product.

[0003] Many advanced control techniques are used to achieve precise tracking control of various systems. Among these methods, iterative learning control (ILC) has become one of the most powerful methods in recent decades because it can effectively achieve high-precision tracking of systems that perform the same task multiple times; the concept of iterative learning control was first proposed by Ar imoto et al. in the study of robot repetitive control. As a typical control strategy that imitates the human learning process, its core idea is to continuously learn the repetitive factors inherent in the system operation process based on various data from completed batches, thereby gradually improving the tracking performance.

[0004] Research on the convergence of iterative learning control is mainly concentrated in the time domain. In contrast, although the convergence analysis in the frequency domain is important in both theory and application, it has been less studied. From the perspective of the frequency domain, the purpose of the iterative learning control law is to obtain a control input sequence to achieve the desired system performance (such as stability, noise suppression, etc.). In practical applications, different requirements need to be imposed on system performance within a limited frequency range, while stability theory imposes the same conditions on the entire spectrum, which may be conservative in some cases. In addition, time delays are inevitable in many industrial processes, for example, time delays caused by signal transmission between sensors, controllers or actuators. The existence of time delays will not only degrade system performance, but may even cause system instability.

[0005] It is well known that using the system state vector when designing iterative learning control laws can significantly improve control performance, convergence speed and tracking accuracy. However, many published results assume that the system state is directly measured, which is not practical in many cases. For example, the precise state information of the injection molding nozzle pressure system is usually not directly available.

[0006] Therefore, for the tracking control problem of discrete linear repetitive systems with multiple time delays, the existing technology has not been fully studied in the frequency domain; moreover, the design of iterative learning control laws with state feedback signals still has limitations and needs further study. Summary of the invention

[0007] In order to overcome the shortcomings of the above-mentioned prior art, the present invention provides a finite frequency domain iterative learning control method and system for injection molding nozzle pressure. For discrete linear repetitive systems with multiple time delays, an observer-based iterative learning control law is designed with the help of frequency domain method to solve the tracking control problem of injection molding nozzle pressure systems with multiple time delays.

[0008] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0009] A first aspect of the present invention provides a finite frequency domain iterative learning control method for injection molding nozzle pressure.

[0010] A finite frequency domain iterative learning control method for injection molding nozzle pressure, comprising:

[0011] Establish a discrete time state space model of the injection molding nozzle pressure system;

[0012] Estimate the system state through the observer and construct the observer-based iterative learning control law;

[0013] Reconstruct the discrete-time state-space model using iterative learning control laws;

[0014] Based on the reconstructed discrete-time state-space model, stability analysis is performed with the help of repeated process stability theory and generalized KYP lemma to make the nozzle pressure track the expected reference trajectory.

[0015] Furthermore, the discrete time state space model is expressed as follows:

[0016]

[0017] y m+1 (t) = Cx m+1 (t),

[0018] Where t is the time index, 0≤t≤T, T is the fixed iteration length, and m is the iteration index; xm (t)∈R n is the system status, y m (t)∈R m is the system output, u m (t)∈R p is the control input; d j is an unknown time delay, satisfying the condition and is the known upper bound; N is the number of time delays, A, B, and C are the system matrix, input matrix, and output matrix, respectively.

[0019] Furthermore, the observer is expressed as follows:

[0020]

[0021] Where L is the observer gain matrix, and are the observer state and observer output respectively.

[0022] Furthermore, the iterative learning control law is expressed as follows:

[0023] u m+1 (t) = u m (t)+Δu m+1 (t)

[0024]

[0025] in, is a time domain feedback controller, L2e m (t)+L3(e m (t+1)-e m (t)) is the iterative domain PD type feedforward controller, L1, L2, L3, is the controller gain matrix, Δu m+1 (t) is the correction term.

[0026] Furthermore, the reconstructed discrete-time state-space model is expressed as follows:

[0027]

[0028]

[0029]

[0030]

[0031] M=L2-L3,

[0032]

[0033]

[0034] Where t is the time index, 0≤t≤T, T is the fixed iteration length, and m is the iteration index; x m (t)∈R n is the system status, y m (t)∈R m is the system output, u m (t)∈R p is the control input; d j is an unknown time delay, satisfying the condition and is the known upper bound; N is the number of time delays, A, B, C are the system matrix, input matrix, and output matrix respectively; L1, L2, L3 are the controller gain matrices, and L is the observer gain.

[0035] Furthermore, the stability analysis is to ensure that the controlled system is stable within a limited frequency range, specifically:

[0036] Solve the controller gain matrix L1, L2, L3 and the observer gain L to ensure holds, where Ω is a finite frequency range, V(e iw ) is the tracking error from e m (t) to e m+1 (t) is the transfer function of

[0037] Furthermore, the generalized KYP lemma provides sufficient conditions to ensure the stability of the controlled system within a limited frequency range, specifically:

[0038] Sufficient conditions for ensuring the stability of the control system are given in the form of linear matrix inequalities;

[0039] The gain matrix of the observer-based iterative learning control law is given.

[0040] A second aspect of the present invention provides an injection molding nozzle pressure finite frequency domain iterative learning control system.

[0041] An injection molding nozzle pressure finite frequency domain iterative learning control system, comprising:

[0042] The model building module is configured to: build a discrete time state space model of the injection molding nozzle pressure system;

[0043] The control building module is configured to: estimate the system state through the observer and build an observer-based iterative learning control law;

[0044] The model reconstruction module is configured to: reconstruct the discrete time state space model using an iterative learning control law;

[0045] The stability analysis module is configured as follows: based on the reconstructed discrete time state space model, stability analysis is performed with the help of repeated process stability theory and generalized KYP lemma to make the nozzle pressure track the expected reference trajectory.

[0046] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of a finite frequency domain iterative learning control method for injection molding nozzle pressure as described in the first aspect of the present invention.

[0047] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in the finite frequency domain iterative learning control method for injection molding nozzle pressure as described in the first aspect of the present invention are implemented.

[0048] One or more of the above technical solutions have the following beneficial effects:

[0049] The present invention designs a new observer-based iterative learning control law for a discrete-time repetitive system with multiple time delays in a finite frequency domain, which is used to control the nozzle pressure so that it tracks the desired reference trajectory. The design consists of a time-domain feedback controller and an iterative-domain PD-type feedforward controller, which can improve the transient response in the time direction and increase the tracking error convergence speed of the learning process; using the repetitive process stability theory and the generalized Kalman-Yakubovich-Popov (KYP) lemma, sufficient conditions for ensuring system stability are given; in addition, based on the proposed iterative learning control strategy, control performance requirements can be imposed within a specific frequency range; at the same time, the control scheme has a simple structure and is easy to implement in industrial applications.

[0050] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0052] Figure 1 This is a flow chart of the method of the first embodiment.

[0053] Figure 2 It is a simplified schematic diagram of the injection molding machine of the first embodiment.

[0054] Figure 3 This is the spectrum diagram of the reference trajectory of the first embodiment.

[0055] Figure 4 This is the trajectory diagram output by the system of the first embodiment.

[0056] Figure 5 This is a root mean square error diagram of the first embodiment. DETAILED DESCRIPTION

[0057] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0058] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0059] Explanation of symbols: The superscript * represents the complex conjugate transpose of a matrix; the symbol ★ represents the block term in a symmetric matrix; Λ ⊥ Represents the orthogonal complement of the matrix Λ; sym(Λ)=Λ+Λ T ;ρ(A) represents the spectral radius of matrix A.

[0060] Embodiment 1

[0061] In one embodiment of the present disclosure, a finite frequency domain iterative learning control method for injection molding nozzle pressure is provided. Figure 1 As shown, the following steps are included:

[0062] Step S1: establishing a discrete time state space model of the injection molding nozzle pressure system;

[0063] Furthermore, the discrete time state space model is expressed as follows:

[0064]

[0065] y m+1 (t) = Cx m+1 (t),

[0066] Where t is the time index, 0≤t≤T, T is the fixed iteration length, and m is the iteration index; x m (t)∈R n is the system status, y m (t)∈R m is the system output, u m (t)∈Rp is the control input; d j is an unknown time delay, satisfying the condition and is the known upper bound; N is the number of time delays, A, B, and C are the system matrix, input matrix, and output matrix, respectively.

[0067] In this embodiment, N=2,

[0068] C=[1.239-0.9282].

[0069] Step S2: Estimate the system state through the observer and construct an observer-based iterative learning control law;

[0070] Furthermore, the observer is expressed as follows:

[0071]

[0072] Where L is the observer gain matrix, and are the observer state and observer output respectively.

[0073] Furthermore, the iterative learning control law is expressed as follows:

[0074] u m+1 (t) = u m (t)+Δu m+1 (t)

[0075]

[0076] in, is a time domain feedback controller, L2e m (t)+L3(e m (t+1)-e m (t)) is an iterative domain PD type feedforward controller, L1, L2, L3 are controller gain matrices, Δu m+1 (t) is the correction term.

[0077] Step S3: Reconstructing the discrete time state space model using iterative learning control law;

[0078] Furthermore, the reconstructed discrete-time state-space model is expressed as follows:

[0079]

[0080]

[0081]

[0082]

[0083] M=L2-L3,

[0084]

[0085] Where t is the time index, 0≤t≤T, T is the fixed iteration length, and m is the iteration index; x m (t)∈R n is the system status, y m (t)∈R m is the system output, u m (t)∈R p is the control input; d j is an unknown time delay, satisfying the condition and is the known upper bound; N is the number of time delays, A, B, C are the system matrix, input matrix, and output matrix respectively; L1, L2, L3 are the controller gain matrices, and L is the observer gain.

[0086] Step S4: Based on the reconstructed discrete-time state-space model, stability analysis is performed with the help of repeated process stability theory and generalized KYP lemma to make the nozzle pressure track the expected reference trajectory.

[0087] Furthermore, the stability analysis is to ensure the stability of the controlled system within a limited frequency range, specifically:

[0088] Solve the controller gain matrix L1, L2, L3 and the observer gain L to ensure holds, where Ω is a finite frequency range, V(e iw ) is the tracking error from e m (t) to e m+1 (t) is the transfer function of

[0089] Furthermore, the generalized KYP lemma provides sufficient conditions to ensure the stability of the controlled system within a limited frequency range, specifically:

[0090] Sufficient conditions for ensuring the stability of the control system are given in the form of linear matrix inequalities;

[0091] The gain matrix of the observer-based iterative learning control law is given.

[0092] The following describes in detail the implementation process of a finite frequency domain iterative learning control method for injection molding nozzle pressure in this embodiment from the aspects of problem description, design of iterative learning control law, stability analysis in finite frequency domain, and feasibility and effectiveness verification.

[0093] 1. Problem Description

[0094] Based on the open-loop test, in the injection molding nozzle pressure system, the response of the injection molding nozzle pressure to the opening of the hydraulic control valve is determined as the following autoregressive model:

[0095]

[0096] Among them, p represents the injection molding nozzle pressure, and z represents the hydraulic control valve opening.

[0097] Considering that the system is affected by multiple time delays, the model is restated as a discrete time state space expression, that is, the discrete time state space model of the injection molding nozzle pressure system:

[0098]

[0099] Where t is the time index, 0≤t≤T, T is the fixed iteration length, and m is the iteration index; x m (t)∈R n is the system status, y m (t)∈R m is the system output, u m (t)∈R p is the control input; d j is an unknown time delay, satisfying the condition and is a known upper bound.

[0100] 2. Design of Iterative Learning Control Law

[0101] For the subsequent convergence analysis, the following lemma is given:

[0102] Lemma 1:

[0103] Given matrices Λ, Σ and a symmetric matrix Γ, there exists a matrix W such that the following holds:

[0104] Γ+sym{Λ T WΣ}<0

[0105] If and only if the following two inequalities about W hold:

[0106] (Λ ⊥ ) T ΓΛ ⊥ <0,(Σ ⊥ ) T ΓΣ ⊥ <0

[0107] Lemma 2:

[0108] Consider the following with multiple time lags A discrete-time repetitive process:

[0109]

[0110] Then the system described by equation (2) is stable if and only if the following three conditions hold:

[0111] 1)

[0112] 2)

[0113] 3)ρ(G(e iw ))<1

[0114] Here G(e iw ) is the transfer function of system (2), which is specifically defined as:

[0115]

[0116] The tracking error at the mth iteration is defined as:

[0117] e m (t) = y d (t)-y m (t),

[0118] Among them, y d (t) is the reference signal, indicating the desired reference trajectory, y m (t)∈R m is the output signal.

[0119] The goal of this embodiment is to design an iterative learning controller so that the system output signal can track the desired reference trajectory as the number of iterations increases.

[0120] In many practical engineering applications, the state of a system or device is usually unmeasurable; therefore, in order to estimate the unmeasurable state, an observer is designed as shown below:

[0121]

[0122] Where L is the observer gain matrix to be designed, and are the observer state and observer output respectively.

[0123] Based on the observer, an iterative learning control law is established. The iterative learning control strategy adopted in this embodiment is to construct the input signal of the current iteration as the input signal of the previous iteration, and add the correction term to be designed, which is expressed by the formula:

[0124] u m+1 (t) = um (t)+Δu m+1 (t)

[0125] Here, the correction term Δu m+1 (t) Designed to:

[0126]

[0127] in, is a time domain feedback controller, L2e m (t)+L3(e m (t+1)-e m (t)) is an iterative domain PD type feedforward controller, that is, the PD term, L1, L2, L3, is the controller gain matrix to be designed; in particular, the PD term in the control law can improve the tracking error convergence speed of the learning process, and the state feedback control signal is used to improve the transient response in the time direction.

[0128] Bring the designed observer and iterative learning controller into the controlled system to obtain the reconstructed discrete-time state space model:

[0129]

[0130] in, M=L2-L3,

[0131]

[0132] Define the following standard shift operator z:

[0133] zx m+1 (t) = x m+1 (t+1)

[0134] From e m (t) to y m+1 The transfer function matrix of (t) is H(z):

[0135]

[0136] make And assuming that Q is reversible, we can then obtain:

[0137]

[0138] The tracking error at the mth iteration is:

[0139] E m (z) = Y d (z)-G(z)U m (z)

[0140] Among them, Y d is the Z transform of the reference signal, let V(z) = IH(z), the above tracking error can be restated as:

[0141] E m+1 (z)=V(z)E m (z)

[0142] Therefore, the necessary and sufficient condition for the tracking error to converge as m→∞ is:

[0143]

[0144] However, the iterative learning control scheme obtained based on this condition may show poor transient behavior during the convergence process; therefore, a stronger convergence criterion is usually required if the following holds:

[0145]

[0146] Then the tracking error converges monotonically, where Represents the largest singular value.

[0147] Lemma 3:

[0148] For the controlled system under consideration and a given reference trajectory, if

[0149]

[0150] Then the tracking error converges monotonically as the number of iterations m→∞.

[0151] Among them, the definition

[0152] The design problem of iterative learning control law is transformed into selecting appropriate control gain matrices L1, L2, L3 and observer gain L to ensure ||V(e iw )|| ∞ <1 holds; however, in the above lemma, V(e iw ) ∞ The goal of the norm calculation is to keep them below a specified level over the entire frequency range w∈[-π,π]; if e m If the spectrum belongs to a known limited range, there is no need to ensure that H ∞norm level, as this increases conservatism; therefore, attention must be focused on a limited frequency range; obviously, it is desirable to impose and verify frequency-domain norms within a specific frequency range, which may be most relevant for specific applications of iterative learning control; while stability theory imposes the same conditions on the entire frequency spectrum, which may be conservative in some cases; to address this issue, an alternative scheme based on the generalized KYP lemma is often adopted, assigning different norms to different frequency ranges; therefore, the above condition (4) can be replaced by:

[0153]

[0154] Here Ω is a finite frequency range.

[0155] Lemma 4:

[0156] The specific content of the generalized KYP lemma is explained below.

[0157] For the transfer function

[0158]

[0159] Delay d j satisfy If there exists a matrix P>0,Q>0,Z j >0 and a symmetric matrix X j , so that the following holds:

[0160]

[0161] Then, for a given real symmetric matrix Π, the transfer function G(e iw ) satisfies the inequality in a specific frequency domain range Ω

[0162]

[0163] in

[0164]

[0165] The above formula w c =(w1+w2) / 2,w m =(w2-w1) / 2.

[0166] Now, define

[0167] The low frequency range is:

[0168]

[0169] The intermediate frequency range is:

[0170]

[0171] The high - frequency range is:

[0172]

[0173] The above (3) can be re - expressed as the following two parallel repeated processes:

[0174]

[0175] and

[0176]

[0177] where

[0178]

[0179] Then, the transfer function described in the above equation from e m (t) to e m+1 (t) can be expressed as

[0180]

[0181] After the above derivation, we get

[0182] ||V(e iw )|| ∞ =||G1(e iw ) + G2(e iw )|| ∞ ≤||G1(e iw )|| ∞ +||G2(e iw )|| ∞

[0183] Therefore, if there exists a constant 0 < r < 1 such that

[0184] ||G1(e iw )|| ∞ < r, ||G2(e iw )|| ∞ < 1 - r,

[0185] then, the tracking error converges to 0 as the number of iterations increases.

[0186] III. Stability Analysis in the Finite - Frequency Domain

[0187] With the help of the generalized KYP lemma, two theorems are given to provide sufficient conditions for ensuring the stability of the controlled system in the finite - frequency range.

[0188] Theorem 1:

[0189] Given that the scalar \(r\) satisfies \(0 < r < 1\), if there exist positive definite matrices \(P>0\), \(Q>0\), \(Z\) j >0, matrix \(W\), symmetric matrix \(X\) j such that the following linear matrix inequalities hold

[0190]

[0191] where,

[0192]

[0193] Then, the system (5)-(6) operating in the finite frequency domain is stable.

[0194] Proof: Assume that for any time delay \(d\) j satisfying there exist matrices \(P>0\), \(Q>0\), \(Z\) j >0, symmetric matrix \(X\) j , matrix \(W\), scalar \(r\in(0,1)\) satisfying (7); according to (7), we have

[0195]

[0196] This means that condition 1) in Lemma 2 holds.

[0197] Next, inequality (7) can be restated as:

[0198]

[0199] where,

[0200] \(\Sigma\) i \(=[0\ I\ 0\ \cdots\ 0\ 0]\),

[0201]

[0202]

[0203] Choose and to be respectively:

[0204]

[0205] Based on Lemma 1, we have

[0206]

[0207] Further rewritten as

[0208]

[0209] where,

[0210]

[0211] Therefore, by Lemma 4, inequality (8) can be equivalent to

[0212] ||G1(e iw )|| ∞ <r, ||G2(e iw )|| ∞ <1 - r,

[0213] This shows that condition 3) in Lemma 2 holds; meanwhile, the inequalities P > 0, Q > 0 ensure that condition 2) in Lemma 2 holds; thus, the proof is complete.

[0214] However, there are couplings of unknown matrix variables in the above linear matrix inequalities, so they cannot be directly solved using the LMI toolbox of MATLAB. Next, efforts are made to derive a solvable sufficient condition.

[0215] Assume that matrix C is full - rank and its singular - value decomposition is:[[]]

[0216] C = U[R 0]V T ,

[0217] where U and V are both unitary matrices, and the diagonal elements of R are positive and decreasing; further, considering a special structure of matrix W, W = diag{W1, W1}, there exists a matrix D satisfying

[0218] CW1 = DC.

[0219] Let

[0220]

[0221] D = URW 11 R -1 U T ,

[0222] Obviously, it can make CW1 = DC hold.

[0223] Therefore, an equivalent representation of the above linear matrix inequality (7) can be given.

[0224] Theorem 2:

[0225] Given a scalar r satisfying 0 < r < 1, if there exist positive - definite matrices matrix W1, N = diag{N1, N2}, symmetric matrix such that the following linear matrix inequalities hold:

[0226]

[0227] in, S=diag{W1 -1 ,W1 -1},

[0228] Then the system (5)-(6) operating in the finite frequency domain is stable, and the gain matrix of the iterative learning controller and the observer gain are designed as:

[0229] L2=L3+M, L1=N1W1, L=N2D. (11)

[0230] Proof: With the help of Schur complement, inequality (7) is equivalent to:

[0231]

[0232] in,

[0233]

[0234]

[0235] Then, multiply the left and right sides of equation (12) by diag{S T ,S T ,…,S T ,I,I} and its transpose; let S = W -1 , Can get

[0236]

[0237] in,

[0238]

[0239] Furthermore, from (13), we can obtain the following two matrix inequalities:

[0240]

[0241] in,

[0242]

[0243]

[0244] make Since CW1=DC, we have and then

[0245] Then, by defining We can get (9) and (10).

[0246] Therefore, the design of observer-based iterative learning control law is completed.

[0247] 4. Feasibility and effectiveness verification

[0248] Through a specific application example, the feasibility and effectiveness of this solution are verified. Figure 2 It is a simplified schematic diagram of an injection molding machine. The pressure of the nozzle in the injection molding machine is controlled by an injection molding nozzle pressure system.

[0249] Based on the open-loop test, the response of the injection molding nozzle pressure to the hydraulic control valve opening was determined as the following autoregressive model:

[0250]

[0251] Where p represents the injection molding nozzle pressure and z represents the hydraulic control valve opening, which is converted into a discrete time state space expression with multiple time delays as shown below:

[0252]

[0253] y m+1 (t) = Cx m+1 (t),

[0254] Where N = 2,

[0255]

[0256] C=[1.239 -0.9282].

[0257] Assume that the reference trajectory to be tracked is:

[0258]

[0259] Figure 3 is the spectrum of the reference trajectory, from Figure 3 It can be seen that the important frequency range of the reference trajectory is 0-20Hz; therefore, the low-frequency limit parameter w of the proposed algorithm is l =125.6rad / s; In addition, in order to better evaluate the tracking performance during the iteration process, the following RMS formula is introduced:

[0260]

[0261] Select parameter r = 0.2, and then use MATLAB's LMI toolbox to solve the linear matrix inequality, and get the gain matrix of the iterative learning controller designed for this example:

[0262] L1=[-1.6393 1.1922], L2=0.8245, L3=0.7662.

[0263] The simulation results are as follows Figure 4-5 As shown, from Figure 4 It can be seen that under the action of the designed controller, the output signal gradually tracks the given reference signal as the number of iterations increases; Figure 5 The RMS of the tracking error in 20 iterations is depicted, from which it can be seen that the tracking error gradually decreases with the increase in the number of iterations; in particular, starting from the 5th iteration, the error is close to zero, indicating the effectiveness of the proposed iterative learning control scheme.

[0264] Embodiment 2

[0265] In one embodiment of the present disclosure, there is provided an injection molding nozzle pressure finite frequency domain iterative learning control system, comprising:

[0266] The model building module is configured to: build a discrete time state space model of the injection molding nozzle pressure system;

[0267] The control building module is configured to: estimate the system state through the observer and build an observer-based iterative learning control law;

[0268] The model reconstruction module is configured to: reconstruct the discrete time state space model using an iterative learning control law;

[0269] The stability analysis module is configured as follows: based on the reconstructed discrete time state space model, stability analysis is performed with the help of repeated process stability theory and generalized KYP lemma to make the nozzle pressure track the expected reference trajectory.

[0270] Embodiment 3

[0271] The purpose of this embodiment is to provide a computer-readable storage medium.

[0272] A computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the steps in a finite frequency domain iterative learning control method for injection molding nozzle pressure as described in the first embodiment of the present disclosure.

[0273] Embodiment 4

[0274] The purpose of this embodiment is to provide an electronic device.

[0275] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps in a finite frequency domain iterative learning control method for injection molding nozzle pressure as described in the first embodiment of the present disclosure are implemented.

[0276] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A finite frequency domain iterative learning control method for injection molding nozzle pressure, characterized in that: include: Establish a discrete time state space model of the injection molding nozzle pressure system; Estimate the system state through the observer and construct the observer-based iterative learning control law; Reconstruct the discrete-time state-space model using iterative learning control laws; Based on the reconstructed discrete-time state-space model, stability analysis is performed with the help of repeated process stability theory and generalized KYP lemma to make the nozzle pressure track the expected reference trajectory.

2. The injection molding nozzle pressure finite frequency domain iterative learning control method according to claim 1, characterized in that: The discrete time state space model is expressed by the formula: y m+1 (t)=Cx m+1 (t), Where t is the time index, 0≤t≤T, T is the fixed iteration length, and m is the iteration index; x m (t)∈R n is the system status, y m (t)∈R m is the system output, u m (t)∈R p is the control input; d j is an unknown time delay, satisfying the condition and is the known upper bound; N is the number of time delays, A, B, and C are the system matrix, input matrix, and output matrix respectively.

3. The injection molding nozzle pressure finite frequency domain iterative learning control method according to claim 1, characterized in that: The observer is expressed by the formula: Where L is the observer gain matrix, and are the observer state and observer output respectively.

4. The injection molding nozzle pressure finite frequency domain iterative learning control method according to claim 1, characterized in that: The iterative learning control law is expressed as follows: u m+1 (t)=u m (t)+Δu m+1 (t) in, is a time domain feedback controller, L2e m (t)+L3(e m (t+1)-e m (t)) is the iterative domain PD type feedforward controller, L1, L2, L3, is the controller gain matrix, Δu m+1 (t) is the correction term, and m is the iteration index.

5. The injection molding nozzle pressure finite frequency domain iterative learning control method according to claim 1, characterized in that: The reconstructed discrete time state space model is expressed by the formula: M=L2-L3, Where t is the time index, 0≤t≤T, T is the fixed iteration length, and m is the iteration index; x m (t)∈R n is the system status, y m (t)∈R m is the system output, u m (t)∈R p is the control input; d j is an unknown time delay, satisfying the condition and is a known upper bound; N is the number of time delays, A, B, C are the system matrix, input matrix, and output matrix respectively; L1, L2, L3 are the controller gain matrices, and L is the observer gain.

6. The injection molding nozzle pressure finite frequency domain iterative learning control method according to claim 1, characterized in that: The stability analysis is to ensure the stability of the controlled system within a limited frequency range, specifically: Solve the controller gain matrix L1, L2, L3 and the observer gain L to ensure holds, where Ω is a finite frequency range, V(e iw ) is the tracking error from e m (t) to e m+1 (t) is the transfer function of 7. The injection molding nozzle pressure finite frequency domain iterative learning control method according to claim 1, characterized in that: The generalized KYP lemma gives sufficient conditions to ensure the stability of the controlled system within a limited frequency range, specifically: Sufficient conditions for ensuring the stability of the control system are given in the form of linear matrix inequalities; The gain matrix of the observer-based iterative learning control law is given.

8. A finite frequency domain iterative learning control system for injection molding nozzle pressure, characterized in that: include: The model building module is configured to: build a discrete time state space model of the injection molding nozzle pressure system; The control building module is configured to: estimate the system state through the observer and build an observer-based iterative learning control law; The model reconstruction module is configured to: reconstruct the discrete time state space model using an iterative learning control law; The stability analysis module is configured as follows: based on the reconstructed discrete time state space model, stability analysis is performed with the help of repeated process stability theory and generalized KYP lemma to make the nozzle pressure track the expected reference trajectory.

9. An electronic device, comprising: a memory for non-transitory storage of computer readable instructions; a processor for executing the computer-readable instructions; Wherein, when the computer-readable instructions are executed by the processor, the method according to any one of claims 1 to 7 is executed.

10. A storage medium, characterized in that: The computer-readable instructions are non-transitorily stored, wherein when the computer-readable instructions are executed by a computer, the method of any one of claims 1 to 7 is performed.

Images