Disturbance utilization control method based on discontinuous information

Abstract

The invention discloses a disturbance utilization control method based on discontinuous information in the technical field of automatic control. The disturbance utilization control method comprises the following steps: 1) establishing a discrete system model with input channel disturbance interference; 2) establishing an augmented system model which comprises an augmented state variable of an augmented system, an augmented system matrix and an augmented control matrix; 3) for packet loss possibly existing in network transmission, compensating lost information by applying a PD packet loss compensation measure; 4) establishing an interference observer based on the discontinuous information based on the discontinuous information and the information after PD packet loss compensation, and effectively estimating the interference existing in the system; 5) designing a disturbance utilization strategy, utilizing the disturbance, and accelerating the tracking of the system output to the expected output, and 6) proposing a condition for ensuring the consistent bounded property of the control system through a Lyapunov stability analysis method, the anti-interference performance can be ensured under the condition of packet loss, and the tracking speed of the system output to the expected output is improved by utilizing the disturbance.

Description

Technical Field

[0001] The present invention relates to the field of automatic control technology, and in particular to a disturbance utilization control method. Background Art

[0002] In actual industrial systems, the system will be subject to many internal and external disturbances, and different types of disturbances will affect the stability of the system. The Disturbance Observer-Based Control (DOBC) method has received more and more attention. In addition, with the update and iteration of Internet technology, network transmission has been increasingly cited in control systems. However, problems such as packet loss and delay in the network have greatly affected the control performance of the system. At present, although researchers have proposed some anti-interference control strategies under packet loss conditions, the packet loss condition, that is, the design of disturbance observers based on intermittent information, has not been solved. Finally, as a factor that affects the state of the system, interference is not always unfavorable. Inspired by this concept, some researchers have proposed the concept of disturbance utilization, but there is still a lot of room for optimization in the design of disturbance utilization conditions. Therefore, there are still many areas for in-depth research in interference estimation, diagnosis and utilization of interference under packet loss conditions. Summary of the invention

[0003] In view of the deficiencies in the prior art, the present invention provides a disturbance utilization control method based on intermittent information, which overcomes the deficiencies of the existing DOBC technology in the case of packet loss. While realizing disturbance estimation in the case of packet loss, it utilizes favorable disturbances to improve the control performance of the system under specific circumstances.

[0004] The object of the present invention is achieved in this way: a disturbance utilization control method based on discontinuous information comprises the following steps:

[0005] Step 1) establishing a discrete system model with input channel disturbance interference, including system state variables, control variables, and interference modeling;

[0006] Step 2) establishing an augmented system model, including augmented state variables of the augmented system and augmented system matrix and control matrix;

[0007] Step 3) For possible packet loss in network transmission, PD packet loss compensation measures are applied to compensate for the lost information and reduce the impact of packet loss on the system;

[0008] Step 4) Based on the intermittent information and the information after PD packet loss compensation, an interference observer based on intermittent information is established to effectively estimate the interference existing in the system;

[0009] Step 5) designing a disturbance utilization strategy based on the disturbance observer estimated based on the discontinuous information; accelerating the tracking of the system output to the desired output by utilizing the disturbance;

[0010] Step 6) Through the Lyapunov stability analysis method, under certain standard conditions, the ultimate consistent boundedness of the control system is guaranteed.

[0011] Further, step 1) is specifically as follows:

[0012] Model a discrete system with input channel disturbances:

[0013]

[0014] in, Indicates that the system state x(k) is contained in the n-dimensional real number set; Indicates that the control input is contained in the m-dimensional real number set; Indicates that the input channel perturbation d(k) is contained in the m-dimensional real number set; Indicates that the system output y(k) is contained in the j-dimensional real number set; A is the n×n-dimensional system matrix, B is the n×m-dimensional control matrix, and C is the j×n-dimensional output matrix;

[0015] The discrete system model d(k) is modeled as the following perturbation system:

[0016]

[0017] in, Represents the intermediate variables of the disturbance model, contained in a b-dimensional real number set; G is the system matrix of the b×b-dimensional disturbance system, and H is the m×b-dimensional amplitude matrix.

[0018] Further, step 2) is specifically as follows:

[0019] The system output tracking error is defined as follows:

[0020] θ(k+1)=θ(k)+Cx(k)-y d (3)

[0021] Where θ(k) represents the tracking error of the system output tracking the expected output, y d is the expected output of the system; by augmenting the tracking error θ(k) and the system state x(k), we can get the augmented state z(k) = [x(k); θ(k)]; based on the above augmented state z(k), the augmented system model is established:

[0022]

[0023] in, represents the system matrix of the augmented system, represents the control matrix of the augmented system, represents the output matrix of the augmented system; where I j×j represents the j-dimensional identity matrix.

[0024] Further, step 3) specifically includes:

[0025] A network transmission model of the augmented state z(k) in the presence of packet loss is established, and a design framework for the PD packet loss compensation strategy is given; in the presence of packet loss, the augmented state after transmission can be modeled as follows:

[0026]

[0027] in, is the augmented state after packet loss. Similarly, the augmented state after packet loss and packet loss compensation in the following text is also represented by To express; i k Indicates the number of consecutive packet loss steps in the augmented state at time k; is a variable that follows a Bernoulli distribution. When i k = m, is 1, otherwise it is 0; in addition, it is assumed that there is a maximum number of packet loss steps in the packet loss process and the maximum number of packet loss steps is U; when the maximum number of packet loss steps is known, the following PD packet loss compensation framework is designed:

[0028]

[0029] Among them, P m (m=1,2,…,U) and D m (m=0,1,2,…,U) are the proportional gain and differential gain of packet loss compensation respectively; the first line of formula (6) indicates the case where there is no packet loss at time k. At this time, the PD packet loss compensation framework will degenerate into the conventional proportional-differential control; the second line of formula (6) indicates the case where packet loss occurs at time k. The PD packet loss compensation framework will find the nearest known data packet. At the same time, based on finding the nearest known data packet, the algorithm will also search forward U steps; using the known nearest known data packet z k-m and known data z k-m 、z k-m-n-1 The changing trends between them.

[0030] Furthermore, the interference observer based on discontinuous information in step 4) is:

[0031]

[0032] in, is the intermediate variable w k The estimated value ofk It is the intermediate variable of the disturbance observer based on discontinuous information and has no practical significance; L 0 is the disturbance observation gain of the disturbance observer based on discontinuous information; L m (m=1,2,…,U) is the packet loss compensation proportional gain when the interference observer based on discontinuous information encounters packet loss; N m (m=1,2,…,U) is the packet loss compensation differential gain when the interference observer based on discontinuous information encounters packet loss.

[0033] Furthermore, the control law based on interference utilization in step 5) is:

[0034]

[0035] in, is the interference state d in the system k Estimator of K 0 and Y 0 is the proportional gain and differential gain of proportional-differential control, that is, when there is no packet loss in the system, the control law is equivalent to proportional-differential control; when packet loss occurs, K m (m=1,2,…,U) and Y m (m=1,2,…,U) are the proportional packet loss compensation gain and differential packet loss compensation gain of the controller respectively; in addition, is the judgment function of disturbance utilization:

[0036]

[0037] in, Using the corresponding element product ⊙ to determine the tracking error Cx k -y d The impact of disturbances on the output After the relationship To use the sigmoid function in formula (9) to obtain specific disturbance utilization parameters.

[0038] Further, the specific conditions of step 6) are as follows:

[0039] For a given parameter α 1 , α 2 , α 3 , α 4 , μ 1 , μ 2 and matrix κ, if there exists an n×n matrix Q 1 > 0, b×b matrix P 2 >0 and gain K m , Y m , L m 、N mSatisfies the following matrix inequality

[0040]

[0041] The proposed disturbance observer based on intermittent information and the control law based on disturbance utilization can ensure that the error between the disturbance estimation and the actual disturbance and the system state are ultimately uniformly bounded; in the matrix inequalities (10) and (11), I represents the unit matrix, and I b×b That is, the b×b-dimensional identity matrix. Similarly, diag{·} represents the identity matrix with · as the main diagonal element. In addition, given the parameter α 1 , α 2 , α 3 , α 4 , μ 1 , μ 2 , It can be arbitrarily selected in the design process, as long as the matrix inequalities (10) and (11) hold;

[0042]

[0043]

[0044] in, is the output matrix of the augmented system, and A symbol for an expression.

[0045] Compared with the prior art, the beneficial effects of the present invention are: first, there is currently no corresponding result proposing a disturbance observer design scheme under intermittent information; second, compared with the traditional disturbance complete compensation countermeasure, the disturbance utilization scheme of the present invention can utilize some beneficial disturbances, which can effectively reduce the energy consumption of control; third, the disturbance utilization scheme proposed by the present invention is also different from the existing disturbance utilization scheme, and pays more attention to ensuring the stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0047] Figure 1 Flow chart of the control method of the present invention.

[0048] Figure 2 It is a schematic diagram of the principle of the disturbance utilization control method based on discontinuous information of the present invention. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] like Figure 1 A disturbance utilization control method based on intermittent information is shown, comprising the following steps:

[0051] Step 1) Establish a discrete system model with input channel disturbance interference:

[0052]

[0053] in, Indicates that the system state x(k) is an n-dimensional column vector and is contained in the n-dimensional real number set; Indicates that the control input u(k) is an m-dimensional column vector and is contained in the m-dimensional real number set; Indicates that the input channel perturbation d(k) is an m-dimensional column vector and is contained in the m-dimensional real number set; It means that the system output y(k) is a j-dimensional column vector and is contained in the j-dimensional real number set. In addition, A is the n×n-dimensional system matrix, B is the n×m-dimensional control matrix, and C is the j×n-dimensional output matrix.

[0054] In addition, since the amplitude and frequency of some disturbances can be measured in advance, d(k) in the discrete system model is modeled as the following disturbance system form:

[0055]

[0056] in, The intermediate variable w(k) representing the disturbance model is a b-dimensional column vector and is contained in a b-dimensional real number set; G is a b×b-dimensional system matrix of the disturbance system, and H is an m×b-dimensional amplitude matrix.

[0057] Step 2) Establish an augmented system model; first, define the system output tracking error as follows:

[0058] θ(k+1)=θ(k)+Cx(k)-y d (3)

[0059] Where θ(k) represents the tracking error of the system output tracking the expected output, y dis the expected output of the system. By augmenting the tracking error θ(k) and the system state x(k), we can get the augmented state z(k) = [x(k); θ(k)]. Based on the above augmented state z(k), we modify formula (1) to get the following augmented discrete system model, which corresponds to the discrete system model in step 1), and is the augmented discrete system model, referred to as the augmented system:

[0060]

[0061] in, represents the system matrix of the augmented system, represents the control matrix of the augmented system, Represents the output matrix of the augmented system. j×j represents the j-dimensional identity matrix.

[0062] Step 3) Design a PD packet loss compensation framework. First, give the network transmission model of the augmented state z(k) in the presence of packet loss:

[0063]

[0064] in, is the augmented state after packet loss. Similarly, the augmented state after packet loss and packet loss compensation in the following text is also represented by To express. k Indicates the number of consecutive packet loss steps in the augmented state at time k. is a variable that follows a Bernoulli distribution. When i k = m, is 1, otherwise it is 0. For example, at time k, the augmented state z(k) has three consecutive packet losses. is 1, etc. are all 0. In addition, it is assumed that there is a maximum number of packet loss steps in the packet loss process and the maximum number of packet loss steps is U.

[0065] When the maximum number of packet loss steps is known, the following PD packet loss compensation framework is designed:

[0066]

[0067] Among them, P m (m=1,2,…,U) and D m(m=0,1,2,…,U) are the proportional gain and differential gain of packet loss compensation respectively. It should be noted here that in the design of subsequent steps, other symbols will be used to represent these two gains. The first line of formula (6) indicates the situation where there is no packet loss at time k. At this time, the PD packet loss compensation framework will degenerate into conventional proportional-differential control. The second line of formula (6) indicates the situation where packet loss occurs at time k. The PD packet loss compensation framework will find the nearest known data packet. At the same time, based on finding the nearest known data packet, the algorithm will also search forward U steps. Using the known nearest known data packet z k-m and known data z k-m 、z k-m-n-1 The changing trends between them.

[0068] In order to better explain the PD packet loss compensation framework, several examples are given here. If packet loss occurs at time k and k-1, the most recent available data packet is the data packet at time k-2, so the PD packet loss framework will use the trend of data changes between time k-2 and k-2, k-3 to compensate for packet loss. In addition, if there is a packet loss problem when using trend information, the available information at earlier times will be used. For example, if there is no packet loss at time k, but packet loss occurs at time k-1, the PD packet loss compensation framework will use the trend information between time k and k-2.

[0069] Step 4) Design of disturbance observer based on discontinuous information, the specific design is as follows:

[0070]

[0071] in, is the intermediate variable w k The estimated value of k It is the intermediate variable of the disturbance observer based on discontinuous information and has no practical significance; L 0 is the disturbance observation gain of the disturbance observer based on discontinuous information; L m (m=1,2,…,U) is the packet loss compensation proportional gain when the interference observer based on discontinuous information encounters packet loss; N m (m=1,2,…,U) is the differential gain of packet loss compensation when the interference observer based on discontinuous information encounters packet loss. When the interference observer faces packet loss, the proportional gain and differential gain of packet loss compensation will play a role to compensate for the lost information and ensure the performance of the interference observer.

[0072] In addition, to facilitate formula writing and understanding, the three packet loss sequences are: etc. have been redefined: z k-m =z k,m . Where m and n both represent the number of steps of packet loss. For example, δ 1,3Indicates i k The number of consecutive packet loss steps at the moment is 3, and the most recent available information is z k-3 , that is, z k,3 ; δ 3,3 Indicates i k-m-1 The number of consecutive packet loss steps at the moment is 3, and the most recent available information is z k,m+4 On this basis, a disturbance observer based on discontinuous information is proposed:

[0073] Step 5) Design disturbance utilization conditions and disturbance utilization control law. The control law based on disturbance utilization is expressed as:

[0074]

[0075] in, is the interference state d in the system k Estimator of K 0 and Y 0 is the proportional gain and differential gain of proportional-differential control, that is, when there is no packet loss in the system, the control law is equivalent to proportional-differential control. When packet loss occurs, K m (m=1,2,…,U) and Y m (m=1,2,…,U) are the proportional packet loss compensation gain and differential packet loss compensation gain of the controller respectively. In addition, is the judgment function of disturbance utilization, which can be expressed in the following form:

[0076]

[0077] in, Using the corresponding element product ⊙ to determine the tracking error Cx k -y d The impact of disturbances on the output After the relationship The sigmoid function in formula (9) will be used to obtain specific disturbance utilization parameters.

[0078] Step 6) Determine the control gain that guarantees the final consistent boundedness of the control system. The specific conditions are as follows:

[0079] For a given parameter α 1 , α 2 , α 3 , α 4 , μ 1 , μ 2 , If there exists an n×n matrix Q 1 > 0, b×b matrix P 2 >0 and gain K m , Y m , Lm 、N m Satisfies the following matrix inequality

[0080]

[0081] The proposed disturbance observer based on intermittent information and the control law based on disturbance utilization can ensure that the error between the disturbance estimation and the actual disturbance and the system state are ultimately bounded. The contents of matrix inequalities (10) and (11) are specifically expressed as follows. It should be noted that I represents the unit matrix, and I b×b That is, the b×b-dimensional identity matrix. Similarly, diag{·} represents the identity matrix with · as the main diagonal element. In addition, given the parameter α 1 , α 2 , α 3 , α 4 , μ 1 , μ 2 , It can be arbitrarily selected during the design process, as long as the matrix inequalities (10) and (11) hold.

[0082]

[0083]

[0084] Also note that and The writing is similar, but the actual meaning is different. The former is the output matrix of the augmented system, and the latter is a symbol used to represent an expression.

[0085] The above embodiments are only used to help understand the method and core idea of ​​the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A disturbance utilization control method based on intermittent information, characterized in that: The following steps are involved: Step 1) establishing a discrete system model with input channel disturbance interference, including system state variables, control variables, and interference modeling; Step 2) establishing an augmented system model, including augmented state variables of the augmented system and augmented system matrix and control matrix; Step 3) For possible packet loss in network transmission, PD packet loss compensation measures are applied to compensate for lost information and reduce the impact of packet loss on the system; Step 4) Based on the intermittent information and the information after PD packet loss compensation, an interference observer based on intermittent information is established to effectively estimate the interference existing in the system; Step 5) designing a disturbance utilization strategy based on the disturbance observer estimating the disturbance based on the discontinuous information; By utilizing interference, the system output can be accelerated to track the expected output; Step 6) Through the Lyapunov stability analysis method, under certain standard conditions, the ultimate consistent boundedness of the control system is guaranteed.

2. The disturbance utilization control method based on intermittent information according to claim 1 is characterized in that: Step 1) is specifically as follows: Model a discrete system with input channel disturbances: in, Indicates that the system state x(k) is contained in the n-dimensional real number set; Indicates that the control input is contained in the m-dimensional real number set; Indicates that the input channel perturbation d(k) is contained in the m-dimensional real number set; Indicates that the system output y(k) is contained in the j-dimensional real number set; A is the n×n-dimensional system matrix, B is the n×m-dimensional control matrix, and C is the j×n-dimensional output matrix; The d(k) in the discrete system model is modeled as the following perturbation system form: in, Represents the intermediate variables of the disturbance model, contained in a b-dimensional real number set; G is the system matrix of the b×b-dimensional disturbance system, and H is the m×b-dimensional amplitude matrix.

3. The disturbance utilization control method based on intermittent information according to claim 2 is characterized in that: Step 2) is specifically as follows: The system output tracking error is defined as follows: in, represents the tracking error of the system output tracking the expected output, y d is the expected output of the system; the tracking error By augmenting the system state x(k), we can get the augmented state Based on the above augmented state z(k), the augmented system model is established: in, represents the system matrix of the augmented system, represents the control matrix of the augmented system, represents the output matrix of the augmented system; where I j×j represents the j-dimensional identity matrix.

4. The disturbance utilization control method based on intermittent information according to claim 3 is characterized in that: Step 3) specifically includes: A network transmission model of the augmented state z(k) in the presence of packet loss is established, and a design framework for the PD packet loss compensation strategy is given; in the presence of packet loss, the augmented state after transmission can be modeled as follows: in, is the augmented state after packet loss. Similarly, the augmented state after packet loss and packet loss compensation in the following text is also represented by To express; i k Indicates the number of consecutive packet loss steps in the augmented state at time k; is a variable that follows a Bernoulli distribution. When i k = m, is 1, otherwise it is 0; in addition, it is assumed that there is a maximum number of packet loss steps in the packet loss process and the maximum number of packet loss steps is U; when the maximum number of packet loss steps is known, the following PD packet loss compensation framework is designed: Among them, P m (m=1,2,…,U) and D m (m=0,1,2,…,U) are the proportional gain and differential gain of packet loss compensation respectively; the first line of formula (6) indicates the case where there is no packet loss at time k. At this time, the PD packet loss compensation framework will degenerate into the conventional proportional-differential control; the second line of formula (6) indicates the case where packet loss occurs at time k. The PD packet loss compensation framework will find the nearest known data packet. At the same time, based on finding the nearest known data packet, the algorithm will also search forward U steps; using the known nearest known data packet z k-m and known data z k-m 、z k-m-n-1 The changing trends between them.

5. The disturbance utilization control method based on intermittent information according to claim 4 is characterized in that: The disturbance observer based on discontinuous information in step 4) is: in, is the intermediate variable w k The estimated value of k is the intermediate variable of the disturbance observer based on discontinuous information and has no practical significance; L0 is the disturbance observation gain of the disturbance observer based on discontinuous information; L m (m=1,2,…,U) is the packet loss compensation proportional gain when the interference observer based on discontinuous information encounters packet loss; N m (m=1,2,…,U) is the packet loss compensation differential gain when the interference observer based on discontinuous information encounters packet loss.

6. A disturbance utilization control method based on intermittent information according to claim 5, characterized in that: The control law based on interference utilization in step 5) is: in, is the interference state d in the system k K0 and Y0 are the proportional gain and differential gain of proportional-differential control, that is, when there is no packet loss in the system, the control law is equivalent to proportional-differential control; when packet loss occurs, K m (m=1,2,…,U) and Y m (m=1,2,…,U) are the proportional packet loss compensation gain and differential packet loss compensation gain of the controller respectively; in addition, is the judgment function of disturbance utilization: in, Using the corresponding element product ⊙ to determine the tracking error Cx k -y d The impact of disturbances on the output After the relationship To use the sigmoid function in formula (9) to obtain specific disturbance utilization parameters.

7. The disturbance utilization control method based on intermittent information according to claim 6 is characterized in that: The specific conditions of step 6) are as follows: For given parameters α1, α2, α3, α4, μ1, μ2 and matrix κ, if there exists an n×n matrix Q1>0, a b×b matrix P2>0 and a gain K m , Y m , L m 、N m Satisfies the following matrix inequality The proposed disturbance observer based on intermittent information and the control law based on disturbance utilization can ensure that the error between the disturbance estimation and the actual disturbance and the system state are ultimately uniformly bounded; in the matrix inequalities (10) and (11), I represents the unit matrix, and I b×b That is, the b×b-dimensional identity matrix. Similarly, diag{·} represents the identity matrix with · as the main diagonal element. In addition, given the parameters α1, α2, α3, α4, μ1, μ2, It can be arbitrarily selected in the design process, as long as the matrix inequalities (10) and (11) hold; in, is the output matrix of the augmented system, and A symbol for an expression.

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