Non-periodic intermittent control of an engine group under a disturbance state

Abstract

The present invention discloses a non-periodic intermittent control for an engine group under a perturbed state. An event-dependent intermittent controller is designed. In addition, the perturbation of its input channel is estimated by using a perturbation observer and compensated in the controller, and the external perturbation is processed by using the H∞ control method. The controller only acts when the trajectory of the Lyapunov-Krasovskii functional runs into a preset working region. Under the proposed intermittent control framework, by using the Lyapunov theory and matrix inequalities, a simple sufficient condition for ensuring system synchronization is given. It is ensured that the error system is ultimately uniformly bounded to achieve the synchronization of the error system.

Description

Technical Field

[0001] The present invention relates to a non-periodic intermittent control method, and particularly to a non-periodic intermittent control of an engine group under a disturbance state. Background Art

[0002] The intermittent control method of an engine group can effectively reduce fuel consumption and improve its performance; compared with the traditional time-dependent method, the non-periodic intermittent control method realized through event dependence has higher control efficiency and faster response. Considering various disturbances existing in the actual production process and the mutual influence between engine groups, complex networks, control theory, mathematics and other related disciplines can be used to model the engine group to analyze its working state.

[0003] Therefore, the discussion on the non-periodic intermittent control strategy of the engine group is crucial for the use of the engine group. Based on this idea, researchers have carried out a large number of studies on the synchronization of the non-periodic intermittent control strategy of continuous-time engines and achieved a series of results. Summary of the Invention

[0004] The object of the present invention is to propose a non-periodic intermittent control of an engine group under a disturbance state, which can effectively improve the performance of the engine group control system.

[0005] A non-periodic intermittent control of an engine group under a disturbance state is characterized in that a non-periodic intermittent control of the engine group is realized depending on events. In the present invention, the following steps are included:

[0006] Considering the interference existing in the actual environment, a system dynamics model of the engine group with external disturbance is established;

[0007] For the unknown but bounded output channel disturbance, a disturbance observer is designed to observe the disturbance in real time and output it.

[0008] For the external non-matching disturbance, the H∞ control method is adopted for processing.

[0009] A piecewise controller is designed to act on the Lyapunov-Krasovskii functional and wherein in the R1 region, the controller includes synchronous error feedback and observed disturbance state compensation, in the R2 region, the controller is 0, and in the R3 region, the controller maintains the state of the previous moment.

[0010] Combining the previous steps, with the help of the Lyapunov stability theorem, matrix inequalities, etc., a non-periodic intermittent control synchronization criterion of the engine group under a disturbance state is obtained, and then a synchronous state is achieved;

[0011] Under external disturbances, for the engine group system model in Reference [1], the following dynamic model is established:

[0012]

[0013] g(x) = 1.5tanh(x).

[0014]

[0015]

[0016] where x i (t) is the state variable of the i-th subsystem, f(x) represents the activation function, u_i(t) represents the control input, L ij , Γ represents the coupling matrix and the inner coupling matrix, d i (t) represents the disturbance in the i-th input channel, ω i (t) represents the additional disturbance and is assumed to be a square-integrable function, A, B g , B, B w are known parameter matrices.

[0017] The disturbance in the control channel is generated by the exogenous system, and the model of the exogenous system is as follows:

[0018]

[0019]

[0020] w 4 (t) = 0.1sin(0.2t).

[0021] η 1 (t) = 3e -0.5t sin(3t), ω 4 (t) = sin(t).

[0022] where δ i (t) is the state variable of the i-th system, η i (t) represents the disturbance caused by the exogenous signal on the i-th system and is assumed to be a square-integrable function, A d , B d , C d are known parameter matrices.

[0023] Define the synchronization error e xi (t) = x i (t) - y(t), and the state equation of the synchronization error system can be obtained:

[0024]

[0025] where \(g(e xi (t)) = g(x_i(t)) - g(y(t)).

[0026] Design a disturbance observer for the disturbances in its input channels. The structure of the disturbance observer is as follows:

[0027]

[0028] where \(\lambda i (t)\) is an intermediate variable, the observed value of, the observed value of;

[0029] Define the disturbance error The state equation of the disturbance error system can be obtained;

[0030]

[0031] For its synchronization error and disturbance error, with the help of the Kronecker product, it can be further written as:

[0032]

[0033] where \(E x (t)=\text{col}\{e x1 (t), e x2 (t), \cdots, e xN (t)\}, E δ (t)=\text{col}\{e δ1 (t), e δ2 (t), \cdots, e δN (t)\}, G(E x (t))=\text{col}\{g(e x1 (t)), g ( ex2 (t)), \cdots, g(e xN (t))\}, Z i (t) represents the measured output.

[0034] Design a piecewise controller

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Among them and

[0041] Design a control scheme to ensure the synchronization of the system. The proof process is as follows:

[0042] C001: For V(t) ∈ R 1 In the interval of (t), its controller is Construct an energy function in the following form:

[0043]

[0044] C002: Among them, P 1 , P 2 is an arbitrary positive definite matrix;

[0045] C003: Calculate the first derivative of V(t):

[0046]

[0047] C004: Using the Lipschitz condition and matrix inequality method, it can be further obtained that:

[0048] C005:

[0049] C006: This control scheme can ensure the uniform bounded stability of the system. The proof process is as follows:

[0050] C007: Use the H ∞ performance to handle the unmatched disturbances w(t) and η(t), that is Among them Z(t) is the measured output. It can be obtained that:

[0051] C008∶

[0052]

[0053] C009: Among them,

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] Ω 1，2 = Δ 1，2 , Ω 1，3 = Δ 1，3 , Ω 2，2 = Δ 2，2 , Ω 2，3 = Δ 2，3 , Ω 2，4 = Δ 2，4

[0061]

[0062] C010: Based on the Lyapunov stability theory, when Δ ≤ 0, there is That is . Then in the interval V(t) ∈ R 1 (t), the system can finally achieve exponential synchronization and the perturbation can be estimated.

[0063] C011: For the interval V(t) ∈ R 2 (t) ∪ R 3 (t), as can be seen from Claim 4. In this region, it satisfies When t → ∞, V(t) → 0, so synchronization can also be achieved in this interval.

[0064] C012: Next, consider the initial state, which is considered in two cases: y(t 0 ) ∈ R 1 (t) and V(t 0 ) ∈ R 2 (t) ∪ R 3 (t).

[0065] C013: When V(t 0 ) ∈ R 1 (t), The controller functions normally. As can be seen from B007 where α 1 > α 2 , λ > β 2 > β 1 , so the exponential decay rate when V(t) ∈ R 1 (y) is greater than B 1 (t), making V(t) contact with B 1 (t) and enter the region R 2 (t) ∪ R 3 (t). Let this moment be t 1 .

[0066] C014: It can be concluded that:

[0067]

[0068] C015: When t → ∞, V(t) → 0, and synchronization can be achieved.

[0069] C016: When V(t 0 ) ∈ R 2 (t) ∪ R 3 (t), u i (t) = 0. When the controller is not in operation, the energy function will rebound upward. After contacting the boundary of B 1 (t), the controller is updated, causing the energy function to decrease. This process repeats until V(t) → 0. Therefore, the energy function only fluctuates in the interval R 2 (t) ∪ R 3 (t), and there is:

[0070] C017:

[0071] C018: When t → ∞, V(t) → 0, and synchronization can be achieved.

[0072] C019: Proven. Therefore, under the designed non-periodic intermittent control strategy of the system, synchronization can be achieved. Description of the Drawings

[0073] Figure 1 is the system block diagram;

[0074] Figure 2 is the system topology diagram;

[0075] Figures 3 - 4 is the disturbance estimation error diagram of the system;

[0076] Figures 5 - 6 is the synchronization error diagram of the system;

[0077] Figure 7 is the disturbance and estimated disturbance diagram of the system;

[0078] Figure 8 is the energy function diagram; Detailed Implementation Manner

[0079] The following further clarifies the present invention in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art to the present invention fall within the scope defined by the appended claims of this application.

[0080] A non-periodic intermittent control of an engine group under a disturbance state includes the following steps:

[0081] Step 1: Set various system parameters;

[0082] Step 2: Set up a disturbance observer;

[0083] Step 3: Set up an estimation error system;

[0084] Step 4: Design a segmented controller:

[0085] Step 5: Verify whether synchronization is achieved in the estimation error system;

[0086] Step 6: Verify whether synchronization is achieved in the error system at the working moment, rest moment, and holding moment respectively.

[0087] The following introduces an embodiment of the present invention:

[0088] Consider an engine group system under a disturbance state, and its corresponding dynamic model is:

[0089]

[0090]

[0091] g(x) = 1.5tanh(x).

[0092]

[0093]

[0094] Its interference is generated by an exogenous system, and the exogenous system model is:

[0095]

[0096]

[0097]

[0098] η 1 (t) = 3e -0.5t sin(3t), ω 4 (t) = sin(t).

[0099] Design a disturbance observer system, and its model is:

[0100]

[0101] According to the LMI toolbox, it can be solved that:

[0102]

[0103] The system structure block diagram is as Figure One shown, Figure Two which is the coupling topology diagram of the system,Figure Three and Figure Four is the observed error graph of the perturbation, Figure Five and Figure Six is the synchronization error graph of the system, Figure Seven is the actual perturbation and estimated perturbation graph, Figure Eight is the energy function graph,

[0104] References

[0105] [1]G.Zong, D.Yang, J.Lam, X.Song.Fault-Tolerant Control of Switched LPVSystems: A Bumpless Transfer Approach.IEEE / ASME Transactions on Mechatronics2022; 27∶1436-1446

Claims

1. A non-periodic intermittent control of a generator set under a disturbance state, comprising the following steps: Step 1: Considering the interference in the actual environment, the engine group system dynamics model with external disturbance is established as follows: g(x)=1.5tanh(x), where x i (t) is the state variable of the ith subsystem, i = 1, 2, 3, 4, f(x) represents the activation function, u i (t) represents the control input, L ij and Γ represent the external coupling matrix and the internal coupling matrix respectively, d i (t) represents the disturbance in the i-th input channel, ω i (t) represents the additional disturbance and is assumed to be a square integrable function, A, B g , B, B w is the known parameter matrix; The disturbance in the control channel is generated by the exogenous system, and the model of the exogenous system is as follows: ω4(t)=0.1sin(0.2t),η1(t)=3e - 0.5t sin(3t), η4(t)=sin(t), where δ i (t) is the i-th system state variable, η i (t) represents the disturbance caused by the exogenous signal on the ith system and is assumed to be a square integrable function. d , B d , C d is the known parameter matrix; Definition of synchronization error e xi (t) = x i (t)-y(t), we get the state equation of the synchronization error system: where g(e xi (t)) = g(x i (t)) - g(y(t)); Step 2: Design a disturbance observer for unknown but bounded output channel disturbances, as follows; where λ i (t) is the intermediate variable, is δ i The observed value of (t), is d i The observed value of (t); Defining disturbance error The state equation of the disturbance error system is obtained: With the help of Kronecker product, the synchronization error system and the disturbance error system can be further written as follows: Where E x (t) = col{e x1 (t), e x2 (t),…,e xN (t)},W δ (t) = col(e δ1 (t), e δ2 (t),…,e δN (t)},G(E x (t)) = col{g(e x1 (t)), g(e x2 (t)),…,g(e xN (t))}, Z(t) is the measurement output; Step 3: Design a segmented controller u i (t) are as follows: Among them, V(t) is the energy function; R1(t), R2(t) and R3(t) are three non-intersecting intervals, as follows: satisfy g( i≠j, α1>α2, β1<β2<λ; in the R1 region, the controller includes synchronous error feedback and observed disturbance state compensation, the controller in the R2 region is 0, and the controller in the R3 region maintains the state of the previous moment; for its external non-matching disturbance, the H∞ control method is used to deal with it, as follows: Using H ∞ The performance handles the mismatched disturbances w(t) and η(t), that is, in Z(t) is the measurement output; Step 4: With the help of Lyapunov stability theorem, matrix inequality, etc., the non-periodic intermittent control synchronization criterion of the engine group under disturbance state is obtained, and then the synchronization state is achieved. The proof is as follows: B001: For the interval V(t)∈R1(t), the controller Construct an energy function of the following form: Where P1 and P2 are positive definite matrices; B002: Calculate the first-order derivative of V(t): B003: Using the Lipschitz condition and matrix inequality method, we can get: B004: Using H ∞ The performance handles the mismatched disturbances w(t) and η(t), that is, in We can get: in, D 3，3 =-γ 2 I N ,D 4，4 =-γ 2 I N , Oh 1，2 =D 1，2 ,Oh 1，3 =D 1，3 ,Oh 2，2 =D 2，2 ,Oh 2，3 =D 2，3 ,Oh 2，4 =D 2，4 , B005: Based on Lyapunov stability theory, when Δ≤0, we have Right now Then in the interval V(t)∈R1(t), the system can eventually achieve exponential synchronization and the disturbance can be estimated; B006: For the interval V(t)∈R2(t)∪R3(t), it satisfies When t→∞, V(t)→0, so synchronization can also be achieved in this interval; B007: Now consider the initial state, divided into two cases: V(t0)∈R1(t) and V(t0)∈R2(t)∪R3(t); B008: When V(t0)∈R1(t), The controller works normally, as can be seen from B005 Among them, α1>α2, λ>β2>β1, so the exponential decay rate when V(t)∈R1(t) is greater than B1(t), so that V(t) will contact B1(t) and enter the R2(t)∪R3(t) region, and let this time be t1; B009: Combining the conclusions of B005 and B008, we can conclude that: When t→∞, V(t)→0, synchronization can be achieved; B0010: When V(t0)∈R2(t)∪R3(t), u i (t) = 0. When the controller is not in effect, the energy function will rebound upward. After contacting the boundary of B1(t), the controller is updated to make the energy function decrease. This cycle repeats until V(t) → 0. Therefore, the energy function fluctuates only in the interval R2(t) ∪ R3(t). We have: When t→∞, V(t)→0, synchronization can be achieved; B0011: The proof is complete, so the system can achieve synchronization under the designed non-periodic intermittent control strategy.

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