CN115616985B - Self-triggering state closed-loop control method of system based on data - Google Patents
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Abstract
The invention provides a closed-loop control method of a self-triggering state of a system based on data, which is divided into two parts of off-line sampling and on-line triggering. When offline sampling is performed, the control quantity of the system to be stabilized is not updated and only needs to be updated at the self-triggering time, so that the system to be stabilized and the controller communicate only at the self-triggering time, the communication times and time are reduced, and meanwhile, the system stability is not influenced. The controller solves an optimization problem based on the sampled data, generating an open-loop matrix parameter and a control gain matrix. When in on-line triggering, the open-loop matrix parameters and the control gain matrix are transmitted to the self-triggering module, the next self-triggering moment is calculated, and the next self-triggering moment is transmitted to the system to be stabilized and the controller. And the system to be stabilized transmits the state value to the controller at the next self-triggering moment, and the controller updates the control quantity. Therefore, the invention can carry out the self-triggering state closed-loop control on the system only by sampling data and calculating the self-triggering time without the prior system identification.
Description
Technical Field
The invention relates to the technical field of intelligent manufacturing, in particular to a data-based system self-triggering state closed-loop control method.
Background
In order to promote the traditional manufacturing industry to transform and upgrade to the intelligent manufacturing industry, the problems in the aspects of production line data acquisition, information processing, equipment management and control, operation scheduling, production plan management, decision making and the like are needed to be solved. The production line is a typical industrial internet system, and with the continuous development of communication level and network technology, the more modern engineering systems are used. In this system, information is transmitted over a wired or wireless network. In the research of industrial internet systems, the most fundamental problem is how to set the transmission time between different devices (e.g. sensors, controllers and actuators) so that the communication loss and the system performance in the system can reach a balanced state.
Many industrial internet systems use a periodic transmission mechanism to transmit data, which is simple but causes a great degree of transmission resource waste problem. For example, consider an open loop unstable system where the state of the system changes very much during initial operation like the time of a sample, but will change more slowly as the system gradually reaches steady state. In other words, sampling at adjacent times of the system at this time typically does not provide much useful information. The method of aperiodic sampling formally arises for this problem. Event triggering and self-triggering are two methods commonly used in aperiodic sampling. In addition, during self-triggering control, the measured value of the system only needs to be sampled at each triggering moment, so that the sensor and the output channel of the system can be completely closed at the non-triggering moment, the service life of the sensor can be prolonged to a great extent, and the resource use degree of the output channel can be reduced.
But the design of the self-triggering rules requires that the predicted values of the system state be obtained, which requires that the exact model of the system be known in advance. However, when the dimension of the system is large, the system identification often needs to consume more time and resources. In recent years, the development of computer technology has made data-driven methods realistic, and has provided end-to-end design methods, i.e., to obtain the control rules of the system directly from the data. This method is also called data-driven control, unlike the conventional method. Currently, no document considers the self-triggering rules of an unknown system directly through pre-collected data to perform self-triggering state control on the system.
Therefore, a method is needed to obtain the self-triggering rule of the system state based on the data of the system, and perform self-triggering state control on the system.
Disclosure of Invention
In view of this, the present invention provides a data-based system self-triggering state closed-loop control method, which can obtain a self-triggering rule of a system state based on data of a system, and does not need a pre-system identification to perform self-triggering state closed-loop control on the system.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
A closed-loop control method of a self-triggering state of a system based on data carries out closed-loop control on a system to be stabilized through a controller and a self-triggering module, and the method specifically comprises the following steps:
S1, performing offline data sampling on a system to be stabilized to obtain an average offline input matrix and an average offline state matrix; an input data matrix U, a future state data matrix X +, and a state data matrix X are constructed.
S2, substituting X + and X, and solving an LMI equation set to obtain a control gain matrix K=UG.
S3, substituting the average offline input matrix and the average offline state matrix, and solving the offline optimization problem to obtain the open-loop matrix parameters of the system to be stabilized.
S4, when the line is on, the self-triggering module judges whether the current moment is the self-triggering moment; the initial value of the self-triggering time is 0.
If not, the system to be stabilized does not communicate with the controller, and is controlled by using the control input quantity at the last self-triggering moment; the initial value of the control input quantity is preset.
The system to be stabilized communicates with the controller, the state matrix at the current moment is input into the controller through the network, and the controller updates the control input quantity and transmits the control input quantity to the system to be stabilized; the self-triggering module solves the online optimization problem to obtain an optimal solution of network noise and a predicted state, substitutes the optimal solution into a self-triggering condition to obtain the next self-triggering moment, and transmits the next self-triggering moment to the system to be stabilized.
Further, the specific method of S1 is as follows:
S1-1, initial value in q off-line state Next, presetting a group of offline input sequencesObtaining an offline state sequenceThe offline state sequence and the offline input sequence are collectively referred to as a system trajectory.
Wherein q is the sequence number of the track segment, q=0, 1,2,..q 0,q0 is the number of system track segments; n q is the data volume of the q-th section system track; n is the total data amount of one system track; t is time, t=0, 1,2,..n q -1; The off-line control value of the q-th segment system track at the t moment, And the off-line state value of the system track of the q-th section at the t moment.
S1-2, arranging the system tracks in a form of a Hank matrix to obtain an offline state matrix H L(us,q) of the q-th section system track and an offline control matrix H L(xs,q of the q-th section system track.
Splicing all the offline state matrixes according to the track sequence q to obtain a full track offline state matrixAll the offline control matrixes are spliced according to the track segment sequence to obtain a full track offline control matrix H j(xs); judgingAndIf the two are all the full order matrixes, executing S1-3; if not, returning to the step S1-1 to continue untilAndAre all full-line order matrices.
S1-3 collecting Q pairsAndRespectively calculating average matrixes to obtain average offline input matrixesAnd average offline state matrix
Wherein j=1, 2,., Q is the number of system tracks; l is a prediction time domain of a preset Hank matrix, and L is more than or equal to 2; u s is an offline state variable, x s is an offline control variable.
S1-4, selecting a group of system tracks to construct an input data matrixFuture state data matrixState data matrixWherein,For the set of offline control values at system trace 0 time,For the set of offline control values at system trace 1 time,Offline control values at the time of N-2 of the system track; for the offline state value at time 0 of the set of system traces, For the offline state value at time 1 of the set of system traces,The set of offline state values at time N-2 of the system trace,The set of system trace N-1 off-line state values at time.
Further, the specific method of S2 is as follows:
the formula of the LMI equation set is:
Wherein, the matrix G is a real matrix of N multiplied by N x, and the matrix P is an orthogonal real matrix of N x×nx.
The matrices Γ and Γ are defined as:
Wherein, I is an identity matrix and 0 is an all-zero matrix for the system noise boundary.
Substituting the matrix X + and the matrix X to obtain a matrix G and a matrix P, and further obtaining a control gain matrix K.
Further, the offline optimization problem is:
ρi＝maxx,α‖xi‖∞
s.t.‖x0‖∞≤1
Wherein the offline state vector Is an offline weight vector, the sign II- ∞ represents the infinite norm of the variable, and the matrixRepresenting an average offline input matrixFront (i+1) n u rows, matrixRepresenting an average offline state matrixRow (i+1) n x; ρ i is an open-loop matrix parameter, where i=1, 2, …, L-1; where n x is the dimension of the offline state quantity x t of the system trace at time t, n u is the dimension of the offline control quantity u t of the system trace at time t, x i is the offline state vector at time i, and x o is the offline state vector at time 0.
The online optimization problem is as follows:
s.t.
Wherein, Represent the firstThe time of the self-triggering is the same,Representing the current time to be predictedTo the point ofTime-of-day system state vector with optimal solution being predicted state optimal solution Indicating time of dayThe state value of the noise to which the system is subjected,From the current timeTo the point ofThe system control matrix of the moment in time,Indicating the current timeThe optimal solution of the network noise is the optimal solution of the network noiseRepresentation ofIs used for the loss function of (a),As a vector of weights, the weight values,Is a network noise boundary;
further, the self-triggering condition is:
Wherein the parameter sigma epsilon (0, 1) is a preset threshold parameter, t is a positive integer not less than 0, tau interval variable is a natural number, For the self-triggering interval, the next self-triggering time
Wherein the self-triggering functionThe formula of (2) is:
where ρ τ is the open-loop matrix parameter in the self-triggering interval, Is thatSystem state vector of time of day.
The beneficial effects are that:
1. The invention provides a closed-loop control method of a self-triggering state of a system based on data, which is divided into two parts of off-line sampling and on-line triggering. When offline sampling is performed, the state value of the system is transmitted to the controller through the network, an average offline input matrix and an average offline state matrix are finally obtained, meanwhile, the controller uses a feedback control mechanism of the system to control the system according to the received state value of the system, and the system always uses the control value until the self-triggering time update is reached. And the controller solves the optimization problem based on the sampling data according to the average offline input matrix and the average offline state matrix, and generates open-loop matrix parameters and a control benefit matrix. When in on-line triggering, the open-loop matrix parameters and the control gain matrix are transmitted to the self-triggering module, the next self-triggering moment is calculated, the calculated self-triggering moment is transmitted to the system to be stabilized and the controller through the transmission network, the state value of the moment is transmitted to the controller when the system to be stabilized is at the next self-triggering moment, the controller updates the control quantity, and the feedback control mechanism of the system is used for controlling the system. Therefore, the invention can carry out the self-triggering state closed-loop control on the system only by sampling data and calculating the self-triggering time without the prior system identification.
2. In the method, the control quantity of the system to be stabilized only needs to be updated at the self-triggering moment, so that the system to be stabilized and the controller only communicate at the self-triggering moment, and the communication times and time are reduced.
3. In the method, the system to be stabilized and the controller are communicated in a self-triggering mode, so that the stability of the system to be stabilized is not affected.
Drawings
Fig. 1 is a block diagram of a closed loop control system.
Fig. 2 is a flow chart of the method of the present invention.
Fig. 3 is a self-triggering effect diagram according to an embodiment of the present invention.
Fig. 4 is a self-triggering effect diagram of an inverted pendulum example of the present invention.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
As shown in fig. 1, the closed-loop control system designed for the system to be stabilized comprises a controller, a transmission network and a self-triggering module. The method is designed aiming at the closed-loop control system, so that the controller can communicate with the system to be stabilized only at the self-triggering time to update the control input quantity while the system to be stabilized is stabilized (the stability is not affected), and the communication time and the communication times are reduced.
The method of the invention is divided into two parts of off-line sampling and on-line triggering. When offline sampling is performed, the state value of the system is transmitted to the controller side through the network, network noise is generated when the state value passes through the network, the controller side uses a feedback control mechanism of the system to control the system according to the received state value of the system, and the system uses the control value until the next new state value is received. The controller side generates a series of estimated future states by solving a data-based optimization problem based on the received state values of the system.
And when the system is triggered online, the generated estimated states are transmitted to a self-triggering module to calculate the next self-triggering time, and are transmitted to the system to be stabilized and the controller through a transmission network, the system to be stabilized transmits the state value of the time to the controller when the next self-triggering time is reached, and the controller uses a feedback control mechanism of the system to control the system, updates the control quantity to be the next self-triggering time and transmits the updated control quantity to the self-triggering system.
The dynamic equation of the system to be stabilized is as follows:
xt+1＝Axt+But+wt,t∈N0,
Wherein x t,ut,wt is the state value of the self-ballasting system at time t, the control input value of the controller and the bounded disturbance to which the system is subjected. The system noise is randomly bounded, i.e. for any time t And desirably 0. A. B is a system matrix, unknown, but the system is ballastable, and multiple groups of system tracks can be collected through offline experiments. The matrix K is a matrix capable of stabilizing the matrix a+bk matrix sull, and K is to be designed. Variable(s)Representing bounded network noise via network transmission at time t l The state quantity of intrusion, wherein noise n t is noise caused by network transmission, is any bounded noise, and has any time tBased on a known quantity obtained from an unsteady system, network noise boundariesThe set N 0 = {0,1,2,3, … } represents a natural number set containing 0.
Based on the above ideas, as shown in fig. 2, the present invention provides a self-triggering state feedback control method based on data, which specifically comprises the following steps:
s1, performing offline data sampling on a system to be stabilized to obtain an average offline input matrix and an average offline state matrix; an input data matrix U, a future state data matrix X +, and a state data matrix X are constructed. The specific method comprises the following steps:
S1-1, initial value in q off-line state Next, presetting a group of offline input sequencesObtaining an offline state sequenceThe offline state sequence and the offline input sequence are collectively referred to as a system trajectory.
Wherein q is the sequence number of the track segment, q=0, 1,2,..q 0,q0 is the number of system track segments; n q is the data volume of the q-th section system track; n is the total data amount of one system track; t is time, t=0, 1,2,..n q -1; The off-line control value of the q-th segment system track at the t moment, And the off-line state value of the system track of the q-th section at the t moment.
S1-2, arranging the system tracks in a form of a Hank matrix to obtain an offline state matrix H L(us,q) of the q-th section system track and an offline control matrix H L(xs,q of the q-th section system track.
Splicing all the offline state matrixes according to the track sequence q to obtain a full track offline state matrixAll the offline control matrixes are spliced according to the track segment sequence to obtain a full track offline control matrix H j(xs); judgingAndIf the two are all the full order matrixes, executing S1-3; if not, returning to the step S1-1 to continue untilAndAre all full-line order matrices.
S1-3 collecting Q pairsAndRespectively calculating average matrixes to obtain average offline input matrixesAnd average offline state matrix
Wherein j=1, 2,., Q is the number of system tracks; l is a prediction time domain of a preset Hank matrix, and L is more than or equal to 2; u s is an offline state variable, x s is an offline control variable.
S1-4, selecting a group of system tracks to construct an input data matrixFuture state data matrixState data matrixWherein,For the set of offline control values at system trace 0 time,For the set of offline control values at system trace 1 time,Offline control values at the time of N-2 of the system track; for the offline state value at time 0 of the set of system traces, For the offline state value at time 1 of the set of system traces,The set of offline state values at time N-2 of the system trace,The set of system trace N-1 off-line state values at time.
S2, substituting the future state data matrix X + and the state data matrix X, solving an LMI equation set to obtain a control gain matrix K=UG, wherein the specific method comprises the following steps of:
the formula of the LMI equation set is:
wherein, the matrix G is a real matrix of N multiplied by N x, and the matrix P is an orthogonal real matrix of N x×nx. The matrices Γ and Γ are defined as:
Wherein, I is an identity matrix and 0 is an all-zero matrix for the system noise boundary.
Substituting the matrix X + and the matrix X to obtain a matrix G and a matrix P, and further obtaining a control gain matrix K.
S3, substituting the average offline input matrix and the average offline state matrix, and solving the offline optimization problem to obtain the open-loop matrix parameters of the system to be stabilized.
The offline optimization problem is:
ρi＝maxx,α‖xi‖∞
s.t.‖x0‖∞≤1
Wherein the offline state vector Is an offline weight vector, the sign II- ∞ represents the infinite norm of the variable, and the matrixRepresenting an average offline input matrixFront (i+1) n u rows, matrixRepresenting an average offline state matrixRow (i+1) n x; ρ i is an open-loop matrix parameter, where i=1, 2, …, L-1; where n x is the dimension of the offline state quantity x t of the system trace at time t, n u is the dimension of the offline control quantity u t of the system trace at time t, x i is the offline state vector at time i, and x o is the offline state vector at time 0.
S4, when the system to be stabilized is online, the self-triggering module judges whether the current moment is the self-triggering moment or not; the initial value of the self-triggering time is 0.
And if not, the system to be stabilized does not communicate with the controller, and the control is performed by using the control input quantity at the last self-triggering moment. The initial value of the control input quantity is preset by the self-triggering system according to the state value.
The system to be stabilized communicates with the controller, the state matrix at the current moment is input into the controller through the network, and the controller updates the control input quantity and transmits the control input quantity to the system to be stabilized; the self-triggering module solves the online optimization problem to obtain an optimal solution of network noise and an optimal solution of a predicted state, substitutes the optimal solution into the self-triggering condition according to the open-loop matrix coefficient to obtain the maximum value of the self-triggering interval meeting the self-triggering condition, and obtains the next self-triggering moment, and the self-triggering module transmits the next self-triggering moment to the system to be stabilized and the self-triggering module.
The online optimization problem is as follows:
s.t.
Wherein, Represent the firstThe time of the self-triggering is the same,Representing the current time to be predictedTo the point ofTime-of-day system state vector with optimal solution being predicted state optimal solution Indicating time of dayThe state value of the noise to which the system is subjected,From the current timeTo the point ofThe system control matrix of the moment in time,I.e. the current momentIs used for controlling the input quantity; indicating the current time The optimal solution of the network noise is the optimal solution of the network noise Representation ofIs used for the loss function of (a),As a vector of weights, the weight values,Is a network noise boundary.
The self-triggering conditions are:
Wherein the parameter sigma epsilon (0, 1) is a preset threshold parameter, t is a positive integer not less than 0, tau interval variable is a natural number, For the self-triggering interval, the next self-triggering time
Wherein the self-triggering functionThe formula of (2) is:
where ρ τ is the open-loop matrix parameter in the self-triggering interval, Is thatSystem state vector of time of day.
One embodiment as shown in fig. 3 runs an effect graph of 200 units of time. The continuous time equation for the system to be stabilized is expressed as:
discretizing the system according to the time of 0.1 second, and obtaining a state feedback gain which can enable the system to be stable by solving the LMI in the steps as follows:
K:＝[-0.4419 -5.6477]
The upper boundary of the process noise of the system is The parameter σ=0.27 is selected, and the system initial value is x 0＝[3,- 2]T. The abscissa in the simulation result represents the step length of time, the self-triggering sampling time is shown in fig. 3, and the simulation result proves the effectiveness of a data-based self-triggering state feedback control method.
As shown in fig. 4, the effect diagram of the second embodiment running 200 units of time on the inverted pendulum example is shown. The continuous time equation of the inverted pendulum is expressed as:
Where the parameter m 1 =1 is the weight of the inverted pendulum bob, m 2 =10 is the weight of the fixed inverted pendulum trolley, Is the length of the inverted pendulum rod, g=10 is the gravitational acceleration, and the upper limit of the process noise of the system is Discretizing the system according to the time of 0.15 seconds, and obtaining a state feedback gain which can enable the system to be stable by solving the LMI in the steps as follows:
K:＝[2,12,378,210]
the parameter σ=0.27 is selected, and the initial value of the system is x 0＝[0.98,0,0.2,0]T. The abscissa in the simulation result represents the step length of time, the self-triggering sampling time is shown in fig. 4, and the simulation result shows the effectiveness of the self-triggering state feedback control method based on data.
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. The closed-loop control method for the self-triggering state of the system based on the data is characterized by comprising the following specific steps of:
S1, performing offline data sampling on a system to be stabilized to obtain an average offline input matrix and an average offline state matrix; constructing an input data matrix U, a future state data matrix X + and a state data matrix X;
s2, substituting X + and X, and solving an LMI equation set to obtain a control gain matrix K=UG;
s3, substituting the average offline input matrix and the average offline state matrix, and solving an offline optimization problem to obtain open-loop matrix parameters of the system to be stabilized;
s4, when the line is on, the self-triggering module judges whether the current moment is the self-triggering moment; the initial value of the self-triggering moment is 0;
If not, the system to be stabilized does not communicate with the controller, and is controlled by using the control input quantity at the last self-triggering moment; the initial value of the control input quantity is preset;
the system to be stabilized communicates with the controller, the state matrix at the current moment is input into the controller through the network, and the controller updates the control input quantity and transmits the control input quantity to the system to be stabilized; the self-triggering module solves the online optimization problem to obtain an optimal solution of network noise and a predicted state, substitutes the optimal solution into a self-triggering condition to obtain the next self-triggering moment, and transmits the next self-triggering moment to the system to be stabilized.
2. The method of claim 1, wherein the specific method of S1 is:
S1-1, initial value in q off-line state Next, presetting a group of offline input sequencesObtaining an offline state sequenceThe offline state sequence and the offline input sequence are collectively called a system track;
Wherein q is the sequence number of the track segment, q=0, 1,2,..q 0,q0 is the number of system track segments; n q is the data volume of the q-th section system track; n is the total data amount of one system track; t is time, t=0, 1,2,..n q -1; The off-line control value of the q-th segment system track at the t moment, The off-line state value of the system track of the q-th section at the t moment;
S1-2, arranging the system tracks in a form of a Hank matrix to obtain an offline state matrix H L(us,q) of a q-th section system track and an offline control matrix H L(xs,q of the q-th section system track;
splicing all the offline state matrixes according to the track sequence q to obtain a full track offline state matrix All the offline control matrixes are spliced according to the track segment sequence to obtain a full track offline control matrix H j(xs); judgingAndIf the two are all the full order matrixes, executing S1-3; if not, returning to the step S1-1 to continue untilAndAre all full-line matrixes;
s1-3 collecting Q pairs AndRespectively calculating average matrixes to obtain average offline input matrixesAnd average offline state matrix
Wherein j=1, 2,., Q is the number of system tracks; l is a prediction time domain of a preset Hank matrix, and L is more than or equal to 2; u s is an offline state variable, x s is an offline control variable;
s1-4, selecting a group of system tracks to construct an input data matrix Future state data matrixState data matrixWherein,For the set of offline control values at system trace 0 time,For the set of offline control values at system trace 1 time,Offline control values at the time of N-2 of the system track; for the offline state value at time 0 of the set of system traces, For the offline state value at time 1 of the set of system traces,The set of offline state values at time N-2 of the system trace,The set of system trace N-1 off-line state values at time.
3. The method of claim 1, wherein the specific method of S2 is:
the formula of the LMI equation set is:
Wherein, the matrix G is a real matrix of N multiplied by N x, and the matrix P is an orthogonal real matrix of N x×nx;
The matrices Γ and Γ are defined as:
Wherein, The system noise boundary is formed by taking I as an identity matrix and 0 as an all-zero matrix;
Substituting the matrix X + and the matrix X to obtain a matrix G and a matrix P, and further obtaining a control gain matrix K.
4. The method of any of claims 1-2, wherein the off-line optimization problem is:
ρi＝maxx,α‖xi‖∞
s.t.‖x0‖∞≤1
Wherein the offline state vector Is an offline weight vector, the sign II- ∞ represents the infinite norm of the variable, and the matrixRepresenting an average offline input matrixFront (i+1) n u rows, matrixRepresenting an average offline state matrixRow (i+1) n x; ρ i is an open-loop matrix parameter, where i=1, 2, …, L-1; wherein n x is the dimension of the offline state quantity x t of the system track at the time t, n u is the dimension of the offline control quantity u t of the system track at the time t, x i is the offline state vector at the time i, and x o is the offline state vector at the time 0;
The online optimization problem is as follows:
Wherein t l represents the first self-triggering time, A system state vector representing the current time t l to t l +L-1 to be predicted, the optimal solution of which is the optimal solution of the predicted state A state value indicating that the system is subject to noise at time t l,Is a system control matrix from the current time t l to t l + L-1,The network noise at the current time t l is represented, and the optimal solution of the network noise is the optimal solution h *(tl of the network noise); Representation of G (t l) is a weight vector,Is a network noise boundary.
5. The method of claim 4, wherein the self-triggering condition is:
The parameter sigma epsilon (0, 1) is a preset threshold parameter, t is a positive integer not less than 0, tau interval variable is a natural number, tau l is a self-triggering interval, and the next self-triggering time t l+1:＝tl+τl;
Wherein the self-triggering function The formula of (2) is:
where ρ τ is the open-loop matrix parameter in the self-triggering interval, Is the system state vector at time t l + tau.
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