CN115576188A - Event trigger model prediction control method and system based on PID trigger condition - Google Patents
Event trigger model prediction control method and system based on PID trigger condition Download PDFInfo
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Abstract
The invention discloses an event trigger model predictive control method and system based on PID trigger conditions, which are realized by the following steps: step 1: obtaining a system t τ ＝t 0 State value x (t) at time τ |t s ) (ii) a Step 2: whether the state value obtained in the step 1 belongs to the robust terminal set region gamma (alpha epsilon) γ ) Judging; and 3, step 3: when the state value does not conform to the initially set robust terminal set region gamma (alpha epsilon) γ ) Then, after the trigger value delta is judged according to the state value, the state value is subjected to alternation calculation; when the state value belongs to the robust terminal set region gamma (alpha epsilon) γ ) And then, performing state value alternation calculation by using the feedback matrix. The control performance can be improved while more calculation amount and communication amount are reduced.
Description
Technical Field
The invention relates to the field of model predictive control, in particular to an event trigger model predictive control method and system based on PID trigger conditions.
Background
The modern control theory originated in the 60's of the last century has been widely applied in the fields of aerospace, guidance and the like because of the optimal performance indexes and the accurate system theoretical design method. However, because industrial process control has the characteristics of nonlinearity, time-varying property, strong coupling, uncertainty and the like, and an accurate mathematical model is difficult to obtain, the modern control theory does not achieve the expected control effect when being applied to the industrial process. In the face of the incoordination between theoretical development and practical application, people explore various methods which have low requirements on model precision and can also realize high-quality control from the characteristics and requirements of industrial process control.
Model Predictive Control (MPC) is just one of these new computer control algorithms, and its control concept is independent of the specific model, but the implementation of control is model dependent. As the model predictive control has the characteristics of being good at processing input and output coupling of a multivariable system, being capable of analytically considering system variable physical constraints and the like, the model predictive control is rapidly developed once coming out and is successfully applied to the industrial fields of petroleum, electric power, aviation and the like. The working principle of model predictive control is as follows: and solving a finite time domain optimal control problem on line at any sampling time. The optimal control problem takes a control input sequence as a decision variable, a cost function on a finite time domain as an optimization target, measurement information (such as a system state) obtained by current sampling as an initial condition, and constraints to be met by a controlled system model, the system state, control input and the like are considered. All the control quantities obtained by solving at the current moment are not used one by one, but only the control quantities required currently are adopted. The obtained measurement information is updated at the next sampling instant, and a new control input is obtained by re-solving the optimization problem. Therefore, model predictive control is essentially a solution to an open-loop optimal control problem. In addition, because the event-triggered model predictive control (ET-MPC) performs the solution of the optimal control problem and the transmission of control data only when the preset trigger condition is met, compared with the periodic model predictive control, the event-triggered model predictive control ensures the stable operation of the system and greatly reduces the energy consumption and the online calculation amount. Based on the analysis, the application prospect of the event-triggered model predictive control in the future industrial field is wider.
However, in the event-triggered model predictive control method designed based on the conventional triggering conditions, the energy consumption of the trigger is further reduced, and the online calculation amount is reduced.
Disclosure of Invention
Aiming at the problem that the number of triggering times needed for ensuring the stability of the system is large in general in the prior art, the invention provides the event triggering model predictive control method and the event triggering model predictive control system based on the PID triggering condition, so that the control performance can be improved while more calculated amount and communication amount are reduced.
The invention is realized by the following technical scheme: an event trigger model predictive control method based on PID trigger conditions is realized by the following steps:
step 1: obtaining a System t τ ＝t 0 State value x (t) at time τ |t s )；
And 2, step: whether the state value obtained in the step 1 belongs to the robust terminal set region gamma (alpha epsilon) γ ) Judging;
and step 3: when the state value does not conform to the initially set robust terminal set region gamma (alpha epsilon) γ ) Then, after the trigger value delta is judged according to the state value, the state value is subjected to alternation calculation; when the state value belongs to the robust terminal set region gamma (alpha epsilon) γ ) And then, performing state value alternation calculation by using the feedback matrix.
Further, when the state value does not belong to the robust terminal set area, in the cycle calculation, the calculated trigger value is compared with the set trigger threshold value, and when the trigger value is greater than or equal to the trigger threshold value, the optimization problem is updated
Using the first value of the optimal control sequence to iterate the real system state and the ideal system state; when the trigger value delta is less than the trigger threshold value delta 0 Then, if the last value of the optimal control sequence is used, the optimization problem is updated
Using the first value of the optimal control sequence to carry out iteration of the real system state and the ideal system state; and returning to the step 2;
Further, a trigger threshold δ 0 Is calculated by the formula
The formula for calculating the trigger value delta in the current state is as follows:
wherein ,KI Artificial adjustment parameters of the integral part; rho is the perturbation's supremum value, with | w (t) | ≦ rho; II E II 2 norm of perturbation matrix, representing the magnification of perturbation state action; II A II 2 norm of the system matrix, representing a magnification of the system status; γ: the adjustment parameter of the system for avoiding the Chino effect is a constant parameter, and gamma belongs to (0, 1); t is p Predicting a time domain; gamma T p Finger system avoids the minimum value that the sesame effect (the unreasonable phenomenon that a finger trigger triggers an unlimited number of times in a limited long time) should take; k D Artificial adjustment parameters of the differential part; k P Artificial adjustment parameters of the proportion part; x (t) τ |t s ): system t s A time state trajectory sequence; t is t τ : the current time; t is t s : the last trigger time from the current closest time; t is t x : an integral variable in the integral; x is a radical of a fluorine atom * : the optimal state of the system at the current time.
Further, if the trigger value is smaller than the trigger threshold value, the last value of the optimal control sequence is not used, the optimal control sequence is sequentially used until iterative computation is performed, and the number of triggers is not counted; and returning to the step 2;
further, the trigger threshold is calculated by inputting parameters in advance.
Further, when the state value belongs to the robust terminal set region, the current state is subjected to iterative optimization solution through the local feedback control rate in the step 3.
Further, in the calculation process, an inequality is required to satisfy the feasibility of the algorithm:
this is true. To satisfy the stability of the system, an inequality is required
Is formed in which
Wherein ρ is the supremum value of the perturbation, having | w (t) | ≦ ρ; iia iid is the 2-norm of the system matrix, representing the magnification of the system state; | E |: the 2-norm of the perturbation matrix, representing the multiple by which the perturbation state contribution is amplified; γ: the adjustment parameter of the system for avoiding the Chino effect is a constant parameter, and gamma belongs to (0, 1); epsilon γ : an invariant terminal domain; t is a unit of p Predicting a time domain;
the maximum eigenvalue of the matrix or vector;λ: minimum eigenvalues of the matrix or vector; q * ：
Wherein Q: a system state weighting matrix;
feedback matrix
The transpose matrix of (a) is,
feedback matrix, R: a weighting matrix controlling the input states; p: when the system enters a system state weighting matrix of a robust terminal domain; α: adjusting the reduction rate of a robust terminal set, wherein alpha belongs to (0, 1); χ: the parameters meeting the system state limiting conditions are as follows:
T p predicting a time domain; k is D Artificial adjustment parameters of the differential part; k I Artificial adjustment of parameters, K, of the integration part P The parameter is adjusted artificially in the proportion part.
A system of event trigger model predictive control method based on PID trigger condition, the state obtaining module: the state acquisition module collects a system state value in real time;
a state value judging module: judging whether the numerical value in the state acquisition module belongs to a robust terminal set region;
an alternation calculation module: by alternating the state values of the system;
a trigger value judgment module: comparing the trigger value with a trigger threshold value to further determine an optimization mode;
a feedback optimization module: and performing optimization control solution on the state through a feedback optimization module.
A terminal device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any of claims 1-7 when executing the computer program.
A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 7.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention proposes a method by which to consist of the proportional, integral and derivative of the error between the actual state and the optimal prediction. By optimizing the parameters, the method not only can reduce more calculation amount and communication amount, but also can improve the control performance, and has the following advantages: the trigger condition consists of three parts of proportion, integral and differentiation of errors between an actual state and an optimal state; and the invention realizes the further optimization of the ET-MPC algorithm based on PID by adjusting the parameters.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings used in the embodiments or technical descriptions will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flowchart of a method for event triggered model predictive control based on PID triggering conditions according to another embodiment of the present invention;
FIG. 2 shows states x of three MPCs in an embodiment of the present invention 1 (t) graph of the variation with time t
FIG. 3 shows three MPC states x in an embodiment of the present invention 2 (t) graph of the variation with time t
FIG. 4 shows the equation K in the embodiment of the present invention D Comparing the trigger effect of the ET-MPC based on PID with that of the traditional ET-MPC when the trigger effect is 0.5;
FIG. 5 shows the equation K in the embodiment of the present invention D Comparing the triggering effect of the ET-MPC based on PID with that of the traditional ET-MPC when the current time is = 10;
FIG. 6 shows the equation K in the embodiment of the present invention D And the triggering effect of the PID-based ET-MPC and the traditional ET-MPC is compared when the frequency is not less than 50.
Detailed Description
In the following, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as restrictive.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "transverse," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the invention and to simplify the description, but are not intended to indicate or imply that the device or element so referred to must have a particular orientation, be constructed and operated in a particular orientation, and are not to be construed as limiting the invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; the connection can be mechanical connection, electrical connection or communication; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless expressly stated or limited otherwise, the recitation of a first feature "on" or "under" a second feature may include the recitation of the first and second features being in direct contact, and may also include the recitation that the first and second features are not in direct contact, but are in contact via another feature between them. Also, the first feature being "on," "above" and "over" the second feature includes the first feature being directly on and obliquely above the second feature, or merely indicating that the first feature is at a higher level than the second feature. The first feature being "under," "beneath," and "under" the second feature includes the first feature being directly above and obliquely above the second feature, or simply meaning that the first feature is at a lesser level than the second feature.
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Example 1:
the method comprises the following specific steps:
step 1: obtain the result t s ＝t 0 Initial state x (t) of (1) τ |t s )；
Step 2: if it satisfies
Then solving the optimization problem to calculate the optimal control sequence
Otherwise, jumping to the step 5;
and step 3: if the trigger threshold is not met, then the most recently calculated optimal control sequence is used
And 4, step 4: when step 3 is not satisfied, s = s +1, and returns to step 2;
and 5: when step 2 is not satisfied, using the feedback matrix
The following is an explanation of the contents of the steps:
(0-1), an actual system state iterative formula:
(0-2) a nominal system state iterative formula:
(0-3) Using local feedback control Rate (i.e., feedback matrix)
) Then, the iterative formula of the system state:
wherein: a represents a system matrix, B represents a control matrix, and E represents a disturbance matrix.
(1-1) step 1, x (t) τ |t s )＝(x 1 x 2 … x n ) τ . In particular, when t τ ＝t 0 The initial value of the time system state is x (t) τ |t s )＝x(t 0 |t 0 )，t s Is the current last trigger time, t τ Is the current time.
(1-2) step 1, t τ ＝t s + i Δ T, where i Δ T is 0. Ltoreq.T p Δ T is the sampling period, T p To predict the time domain, i is the time interval between the current time and the last trigger time, and
(2-1) and in the step 2,
representative is centered at the origin with a radius of α ε γ Robust terminal set of
(2-2) in step 2, optimal sequence
(2-3) in step 2, optimal control sequence
The solution is performed by the optimization problem shown:
α∈(0,1),t τ ∈[t s ,t s +T p ].
wherein: s: recording the number of times of triggering time as a natural number; alpha epsilon γ : representing the size of the final robust terminal set region; x: the state variable of the system at the current moment; χ: the parameters meeting the system state limiting conditions are represented by the formula:
actual state variables of the system at the next moment;
the system predicts a state track sequence at the s-th triggering time;
at t s A predictive control sequence at the trigger time; t is p Predicting a time domain; α: adjusting the reduction rate of the robust terminal set, wherein alpha belongs to (0, 1); γ: the adjustment parameter for avoiding the Chino effect is a constant parameter, and gamma belongs to (0, 1); a: a system matrix; gamma (. Alpha. Epsilon.) γ ): the size of the robust terminal set area is symbolized, i.e.
αε γ : representing the size of the final robust terminal set region; epsilon γ : an invariant terminal domain;
the predicted state of the system at the current moment; b: a control matrix; u: prediction of control input U = (U) in time domain 1 (t τ |t s ),u 2 (t τ |t s ),u 3 (t τ |t s ),…,u m (t τ |t s )) T ；
With a state variable x 1 (t),x 2 (t),…,x n (t) an n-dimensional space formed by coordinate axes, which is called as an actual system state space; target function number
For a positive definite symmetric weighting matrix, the matrix P satisfies the inequality
wherein 
With t s On the basis of the time of triggering, at t τ Controlling the input optimal value at the moment;
a set of real numbers;
each element in the n-order matrix is a set of real numbers; arg: an inverse function;
the predicted state of the system at the next time;
system t s The next moment in time predicts the trajectory sequence of the states.
(3-1) in step 3, trigger threshold δ 0 Is calculated by the formula
(3-2) in the step 3, the calculation formula of the trigger value δ to be compared in the current state is as follows:
wherein ：δ0 : artificially setting a trigger threshold delta satisfying a condition 0 ‖x(t τ |t s )-x * (t τ |t s ) II is the 2-norm between the actual and nominal systems, representing the error between the two system states; | E |: the 2-norm of the perturbation matrix, representing the magnification by which the perturbation state is applied; II A II 2-norm of the system matrix, representing a multiple of amplifying the system status;
the optimal state of the system at the next moment; x is a radical of a fluorine atom * : the most optimal state of the system at the current moment; t: a generalized description of the time variable; t is t s : the last trigger time from the current closest time; t is t τ : the current time; t is t x : an integral variable in the integral; k I : artificial adjustment parameters of the integration part; k is D : artificial adjustment parameters of the micro-fraction; k P : artificial adjustment parameters of the proportional part; gamma T p : the finger system avoids the minimum value that the sesno effect (the unreasonable phenomenon that a finger trigger triggers an infinite number of times in a finite long time) should take; ρ: a perturbed supremum value, where | w (t) | ≦ ρ; iib: 2-norm of system matrix; II E II: 2-norm of perturbation matrix.
(4) And in step 4, the trigger value delta to be compared reaches a set trigger threshold value delta 0 When the trigger is triggered, the trigger triggering times t is recorded s Subscript s = s +1.
(5) Step 5, the feedback matrix used
When the actual system state satisfies x (t) τ |t s )∈γ(αε γ ) Applying local feedback control rate to system state
The aim is to stabilize the system as quickly as possible and to reduce the settling time of the system.
Example 2:
the detailed description of the steps is as follows:
(1) Obtaining when t s ＝t 0 Initial state x (t) of time τ |t s )，s＝0，i＝0。
(2-1) judging the current time x (t) τ |t s ) And gamma (. Alpha. Epsilon.) γ ) The relationship between them.
(2-1 a) if judged to obtain
Then jump to step (3-1) (the first run of the program jumps to step (3-c)).
(2-1 b) if judging to obtain x (t) τ |t s )∈γ(αε γ ) And jumping to the step (5).
(3-c) calculating a control input sequence
And (4) jumping to the step (4-c). (this step is only run during the first run of the program)
(3-1) comparing the actual state x (t) τ |t s ) And optimum state x * (t τ |t s ) Substituting into a trigger threshold value formula for judgment;
(3-2), iteration parameter i = i +1. If the trigger threshold is met, jumping to (3-3); and (5) if the trigger threshold value is not met, jumping to the step (3-4).
And (3-3) if the condition of triggering the threshold value is met, sequentially executing the steps (3-3 a) and (3-3 b).
(3-3 a) obtaining control inputs by computing an optimization control problem
(3-3 b) optimizing the first value u (t) of the control sequence s |t s ) By the formula
And
for the actual state x (t), respectively s +iΔt|t s ) And an optimal state x * (t s +iΔt|t s ) Updating, recording the trigger times of trigger, and changing the system state into x (t) s +(i+1)Δt|t s) and x* (t s +(i+1)Δt|t s ) Skipping to the step (4);
(3-4) if the trigger threshold is not satisfied, judging whether the last value u (t) of the control sequence is used s +T p |t s ) And updating the system state.
(3-4 a) the last value u (t) of the control sequence in (3-3 b) is not applied s +T p |t S ) The optimal control sequence to be finally calculated in time
Ith value u (t) s +iΔt|t s ) Substituting into the actual state iterative formula
And optimal state iterative formula
For the actual state x (t), respectively S +iΔt|t S ) And an optimal state x * (t S +iΔt|t S ) Updating to obtain x (t) S +(i+1)Δt|t S) and x* (t S +(i+1)Δt|t s ) And (4) returning to the step (2-1) without recording the trigger triggering times of the trigger.
(3-4 b) if the last value u (t) of the control sequence has been applied in the (3-4) judgment s +T p |t s ) Then steps (3-3 a) and (3) are performed in sequence-3b)。
(4) For state x (t) in (3-3 b) s +(i+1)Δt|t s) and x* (t s +(i+1)Δt|t s ) Is updated to x (t) s+1 +Δt|t s+1) and x* (t s+1 +Δt|t s+1 ) Note that the system state before update in (3-3 b) is x (t) s+1 |t s+1 )＝x(t s +iΔt|t s) and x* (t s+1 |t s+1 )＝x * (t s +iΔt|t s )
Example 3:
referring to the car-damper-spring model, the system can be described as:
between w (t) and rho, | | w (t) | | is less than or equal to rho. The input control is limited to be | | | u (t) | | | less than or equal to 2, and the initial state is set to be (0.5.75) T Setting the weighting matrix in the optimization problem to
R＝0.2, 
And
to satisfy the inequality
wherein 
In the simulation, the prediction time domain T is selected p =3.4s, sample time Δ t =0.2s, and total simulation time is 20 s. To satisfy the feasibility and stability of the algorithm, the passing meterCalculated to obtain rho less than or equal to 9.006 multiplied by 10 -4 ,γT p More than or equal to 0.1182 s and chi more than or equal to 1.5263, and selecting the robust terminal region as gamma (alpha epsilon) γ ) = x | x (t) | < 0.25}. In summary, we choose δ 0 ＝7.1708×10 -4 ,ρ＝5×10 -4 ,K I ＝0.1,K D ＝0.5,K P =1, α =0.95, γ =0.1, χ =4 to ensure the feasibility of the algorithm and the stability of the system.
(1) Acquiring an initial state value of the system: x (t) 0 |t 0 )＝(0.5 0.75) T Program initialization, parameters s =0, i =0;
(2-1) judging to obtain the system state
The step (3-c) is operated;
(3-c) calculating a control input sequence
Skipping to the step (4);
(4) Updating the system state to x (t) 1 |t 1) and x* (t 1 |t 1 ) Subscript s = s +1, parameter i =0, jump to step (2-1);
(2-1) judging the System State
Skipping to the step (3-1);
(3-1) determining that delta is less than or equal to delta 0 Skipping to the step (3-4);
(3-4) judging that u (t) is not used 1 +T p |t 1 ) Updating the system state, then u (t) 1 |t 1 ) By the formula
And
iterative solution is carried out to obtain a system state x (t) 1 +Δt|t 1) and x* (t 1 +Δt|t 1 ) And (4) returning to the step (2-1) for judgment.
(2-1) judging the System State
Skipping to the step (3-1);
(3-1) judging that delta is less than or equal to delta at the moment 0 ；
(3-2) parameter iteration: i = i +1, jumping to step (3-4);
(3-4) judging that u (t) is not used 1 +T p |t 1 ) Update the system state, then u (t) 1 +Δt|t 1 ) By the formula
And
iterative solution is carried out to obtain a system state x (t) 1 +2Δt|t 1) and x* (t 1 +2Δt|t 1 ) And (4) returning to the step (2-1) for judgment.
In summary, under the conditions
When the inequality delta is less than or equal to delta 0 And (3) when the step (2-1), (3-2) and (3-4) are completed, circularly executing.
If substituting δ satisfies δ in the system state>δ 0 The method comprises the following steps:
in this example, the system state after the update through step (3-3) is x (t) at the time of the second trigger 1 +3Δt|t 1 )。
(2-1) judging the System State
Skipping step (3-1);
(3-1) judging that delta is less than or equal to delta at the moment 0 ；
(3-2) parameter iteration: i = i +1, jumping to step (3-4);
(3-4) judging that u (t) is not used 1 +T p |t 1 ) Update the system state, then u (t) 1 +2Δt|t 1 ) By the formula
And
iterative solution is carried out to obtain a system state x (t) 1 +3Δt|t 1) and x* (t 1 +3Δt|t 1 ) And (4) returning to the step (2-1) for judgment.
(2-1) judging the System State
Skipping step (3-1);
(3-1) determining the delta at that time>δ 0 ；
(3-2) parameter iteration: i = i +1, jumping to step (3-3);
(3-3) obtaining a new control input sequence by solving an optimization problem
And will control the input value u (t) 2 |t 2 ) Acting on the system to obtain a new system state x (t) 1 +4Δt|t 1) and x* (t 1 +4Δt|t 1 ) Skipping to the step (4);
(4) Updating the system state x (t) 1 +4Δt|t 1) and x* (t 1 +4Δt|t 1 ) Is x (t) 2 +Δt|t 2) and x* (t 2 +Δt|t 2 ) And note x (t) 2 |t 2 )＝x(t 1 +3Δt|t 1) and x* (t 2 |t 2 )＝x * (t 1 +3Δt|t 1 ) Parameter s = s +1, i =0; and (4) skipping to the step (2-1).
In summary, in
When delta is>δ 0 Then, the steps (2-1), (3-2), (3-3) and (4) are performed.
When the system state satisfies x (t) τ |t s )∈γ(αε γ ) Then, the following steps are executed:
in this example, when the system state is x (t) 5 |t 5 ) Then, the terminal enters the terminal domain gamma (alpha epsilon) γ )：
(2-1) judging the system state x (t) 5 |t 5 )∈γ(αε γ ) Skipping to the step (5);
(5) Satisfies x (t) 5 |t 5 )∈γ(αε γ ) Using local feedback control rate
And carrying out optimization solution on the subsequent actual state.
The model established by the event triggered model predictive control algorithm based on the PID triggering condition is simulated, and the following results are obtained. FIGS. 2 and 3 are three MPC for state x, respectively 1(t) and x2 (t) trace comparison graph, fig. 4 is the change of input signal with time under three MPCs, and fig. 5 is the trigger phenomenon comparison of PID-based ET-MPC algorithm and traditional ET-MPC. Compared with a red line (a traditional ET-MPC algorithm), the blue line (the PID-based ET-MPC algorithm) is replaced by smaller triggering times at the cost of slightly increasing the adjusting time, so that the resources are saved, and the effectiveness of the algorithm is proved. In addition to this, by increasing the parameter K D The number of triggers can be further reduced (compare fig. 5 and fig. 6), and system resources are saved.
Note: to satisfy the feasibility of the algorithm, an inequality is required
This is true. To satisfy the stability of the system, an inequality is required
Is formed in which
s: recording the number of times of triggering time as a natural number; x: the state variable of the system at the current moment; χ: the parameters meeting the system state limiting conditions are expressed as follows:
actual state variables of the system at the next time;
with a state variable x 1 (t),x 2 (t),…,x n (t) an n-dimensional space formed by coordinate axes, which is called as an actual system state space;
the optimal state of the system at the next moment; x is a radical of a fluorine atom * : the optimal state of the system at the current moment; x is a radical of a fluorine atom * (t 1 |t 1 ): initial (most preferred) state of the system at the 1 st trigger time; x is the number of * (t s+1 |t s+1 ): initial (optimal) state of the system at the s +1 th trigger moment; x is a radical of a fluorine atom * (t s +iΔt|t s ): the system is triggered at the s th time, t th time s The optimal state track value of the system at the moment + i delta t; x is a radical of a fluorine atom * (t 1 +Δt|t 1 ): the system is triggered at the 1 st timeAt a time t 1 The optimal state track value of the system at the moment of + delta t; x is a radical of a fluorine atom * (t 1 +2Δt|t 1 ): the system is triggered at the 1 st time, the t 1 The track value of the optimal state of the system at the moment of +2 delta t;
the predicted state of the system at the current moment;
the system predicts a state track sequence at the triggering time s;
predicting the expression of the state locus in the integrand;
the predicted state of the system at the next time;
system t s Predicting a track sequence of a state at the next moment; x (t): with a state variable x 1 (t),x 2 (t),…,x n (t) is an n-dimensional space formed by coordinate axes, and is called as an actual system state space; x (t) τ |t s ): system t s A time state trajectory sequence; x (t) 0 |t 0 ): an initial state value of the system; x (t) 1 |t 1 ): the system is at trigger time t 1 An initial system state trajectory value of time; x (t) 1 +Δt|t 1 )：t 1 At time t 1 The system state trajectory value at + Δ t; x (t) 1 +2Δt|t 1 )：t 1 At time t 1 A system state trajectory value at +2 Δ t; (x) 1 x 2 … x n ) T : for describing the system state x (t) τ |t s ) A set of vector representations;
with a state variable x 1 (t),x 2 (t),…,x n (t) an n-dimensional space formed by coordinate axes, called as an actual system state space;
with state variables
An n-dimensional space formed by coordinate axes is called as an optimal system state space; u: control vector/input vector; u (t) s |t s ):t s An initial input vector at a moment; u (t) 1 |t 1 )：t 1 An initial input vector at a moment; u (t) s +Δt|t s )：t s At time t s An input vector at time + Δ t; u (t) s +2Δt|t s )： t s At time t s An input vector at time +2 Δ t; u (t) s +T p |t s )：t s At time t s +T p An input vector of a moment; u (t) 1 +T p |t 1 )：t 1 At time t 1 +T p An input vector of a time; u (t): inputting (or controlling) a vector; ii u (t) |: inputting a 2-norm of a control vector, representing the magnitude of the control vector;
a predicted control input vector;
at t s A predictive control sequence at the trigger time;
the representation in the integrated function;
an optimal control input vector;
with t s On the basis of the time of triggering, at t τ Controlling the input optimal value at the moment;
at an initial time t 0 On the basis of t τ Controlling the input optimal value at the moment; ax (t): multiplying the system matrix by the actual state of the system; ax * (t): multiplying the system matrix and the system optimal state; bu (t): multiplying the control matrix by the input vector; ew (t): multiplying the disturbance matrix by the disturbance state of the system; w: there should be no single occurrence of w in the patent; w (t): a system disturbance state vector; | w (t) |: 2-norm of disturbance state, representing the magnitude of disturbance quantity; γ: representing a set of robust terminal domains; a: a system matrix; α γ: multiplying the parameter alpha and gamma; alpha epsilon γ : representing the size of the final robust terminal set region; gamma (. Alpha. Epsilon.) γ ): the size of the robust terminal set area is symbolized, i.e.
t: a generalized description of the time variable; t is t s : the last trigger time from the current closest time; t is t s+1 : the next trigger time from the current closest time; t is t 0 : an initial time; t is t x : an integral variable in the integral; t is t τ : the current time; delta t is the sampling period; i, the time interval between the current time and the last trigger time, and
i +1: the time interval between the next moment of the current moment and the last triggering moment; i Δ t: the time interval between the current time and the last trigger time;
natural number set
A: a system matrix;
notation of the matrix:
ax (t): multiplying the system matrix by the actual system state; b: a control matrix;
multiplying a control matrix and a feedback matrix; bu (t): multiplying the control matrix by the input vector; e: disturbing the matrix; ew (t): multiplying the disturbance coefficient matrix and the disturbance state vector;
feedback matrix
Feedback matrix
The transposed matrix of (2); t: the document automatically converts the lower case T into the upper case T, and the original text does not have the parameter of T independently; t is p Predicting a time domain; α: adjusting the reduction rate of a robust terminal set, wherein alpha belongs to (0, 1); γ: the adjustment parameter for avoiding the Chino effect is a constant parameter, and gamma belongs to (0, 1); gamma T p The finger system avoids the minimum value which the sesame effect (the unreasonable phenomenon that a finger trigger triggers for an unlimited number of times in a limited long time) should obtain; gamma alpha epsilon γ : the parameters are multiplied by rules so that the adjustment of the parameters to avoid the sesame effect is a constant, and gamma belongs to (0, 1); adjusting the reduction rate of the robust terminal set, wherein alpha belongs to (0, 1),αε γ representing the size of the robust terminal set, ε γ An invariant terminal domain;
e represents the base of the natural logarithm, also known as the euler constant, which is an infinite acyclic decimal number with a value of 2.71828; epsilon γ : an invariant terminal domain; alpha epsilon γ : representing the size of the final robust terminal set region;
a set of real numbers;
each element in the n-order matrix is a set of real numbers; arg: an inverse function; u: prediction of control input U = (U) in time domain 1 (t τ |t s ),u 2 (t τ |t s ),u 3 (t τ |t s ),…,u m (t τ |t s )) T (ii) a J: a cost function; x: predicting the system state in the time domain, X = (X) 1 (t τ |t s ),x 2 (t τ |t s ),x 3 (t τ |t s ),…,x n (t τ |t s )) T (ii) a R: a weighting matrix controlling the input states; p: when the system enters a system state weighting matrix of a robust terminal domain; q: a system state weighting matrix; q * ：
δ 0 : artificially setting a trigger threshold delta satisfying a condition 0 (ii) a δ: a trigger value to be compared at the current time; rho is the perturbation's supremum value, with | w (t) | ≦ rho; | w (t) |: 2-norm of disturbance vector, representing the magnitude of external disturbance quantity; iia iid is the 2-norm of the system matrix, representing the system state as a magnification factor; | E |: the 2-norm of the perturbation matrix, representing the magnification by which the perturbation state is applied; k is I Artificial adjustment parameters of the integral part; k is D Artificial adjustment of differential partSaving parameters; k is P Artificial adjustment parameters of the proportion part; x is a radical of a fluorine atom 1 (t): the 1 st system state in the system state vector x (t); x is the number of 2 (t): the 2 nd system state in the system state vector x (t);
matrix of
The transposed matrix of (2);
the maximum eigenvalue of the matrix or vector;λ: minimum eigenvalues of the matrix or vector; v: to formula
Simplified symbolic representations of (a); α: adjusting the reduction rate of a robust terminal set, wherein alpha belongs to (0, 1);λ(Q): the minimum eigenvalue of the system state weighted matrix Q.
While there have been shown and described what are at present considered the fundamental principles and essential features of the invention and its advantages, it will be apparent to those skilled in the art that the invention is not limited to the details of the foregoing exemplary embodiments, but is capable of other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art. The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (10)
1. An event trigger model predictive control method based on PID trigger conditions is characterized by comprising the following steps:
step 1: obtaining a System t τ ＝t 0 State value x (t) at time τ |t s )；
Step 2: whether the state value obtained in step 1 belongs to the robust terminal set region γ (α ∈) γ ) Judging;
and 3, step 3: when the state value does not conform to the initially set robust terminal set region γ (α ∈) γ ) Then, after the trigger value delta is judged according to the state value, the state value is subjected to alternation calculation; when the state value belongs to the robust terminal region γ (α ∈) γ ) And then, performing state value alternation calculation by using the feedback matrix.
2. The event trigger model predictive control method based on the PID trigger condition as claimed in claim 1, wherein when the state value does not belong to the robust terminal set region, in the loop calculation, the calculated trigger value is compared with the set trigger threshold, and when the trigger value is greater than or equal to the trigger threshold, the optimization problem is updated
Using the first value of the optimal control sequence to iterate the real system state and the ideal system state; when the trigger value delta is smaller than the trigger threshold value delta 0 Then, if the last value of the optimal control sequence is used, the optimization problem is updated
Applying the first of the optimal control sequencesThe values are used for carrying out iteration of a real system state and iteration of an ideal system state; and returning to the step 2;
3. The event trigger model predictive control method based on the PID trigger condition as claimed in claim 1, characterized in that the trigger threshold δ 0 Is calculated by the formula
The trigger value delta under the current state is calculated by the formula:
wherein ,KI Artificial adjustment parameters of the integration part; rho is the infimum value of disturbance, and is less than or equal to rho in W (t); the 2 norm of the disturbance matrix represents the magnification of the disturbance state; the 2 norm of the system matrix represents the magnification factor of the system state; γ: the adjustment parameter of the system for avoiding the Chino effect is a constant parameter, and gamma belongs to (0, 1); t is a unit of p Predicting a time domain; gamma T P Finger system avoids the minimum value that the sesame effect (the unreasonable phenomenon that a finger trigger triggers an unlimited number of times in a limited long time) should take; k D Artificial adjustment parameters of the differential part; k is P Artificial adjustment parameters of the proportion part; x (t) τ |t S ): system t S A time state trajectory sequence; t is t τ : the current time; t is t S : the last trigger time from the current closest time; t is t x : an integral variable in the integral; x is a radical of a fluorine atom * : the optimal state of the system at the current time.
4. The event triggered model predictive control method based on the PID trigger condition according to claim 3, characterized in that if the trigger value is smaller than the trigger threshold value, the last value of the optimal control sequence is not used, and the optimal control sequence is used in turn to perform iterative computation, without counting the number of triggers; and returns to step 2.
5. The event triggered model predictive control method based on PID trigger condition as claimed in claim 3, characterized in that the trigger threshold is calculated from the advanced input parameters.
6. The event triggered model predictive control method based on the PID trigger condition as claimed in claim 1, wherein when the state value belongs to the robust terminal set region, the iterative optimization solution is performed on the current state through the local feedback control rate in the step 3.
7. The event trigger model predictive control method based on the PID trigger condition as claimed in claim 2, characterized in that, in the process of operation, in order to satisfy the inequality of feasibility requirement of the algorithm:
it holds that in order to satisfy the stability of the system, an inequality is required
Is formed in which
Wherein rho is the disturbed upper limit value, and is less than or equal to rho in | | w (t) |; the 2-norm of the system matrix represents the magnification factor of the system state action; the 2-norm of the disturbance matrix represents the magnification of the disturbance state; γ: the adjustment parameter for avoiding the Chino effect is a constant parameter, and gamma belongs to (0, 1); epsilon γ : an invariant terminal domain; t is a unit of p Predicting a time domain;
the maximum eigenvalue of the matrix or vector;λ: minimum eigenvalues of the matrix or vector; q * ：
Wherein Q: a system state weighting matrix;
feedback matrix
The transpose matrix of (a) is,
feedback matrix, R: a weighting matrix controlling the input states; p: when the system enters a system state weighting matrix of a robust terminal domain; α: adjusting the reduction rate of the robust terminal set, wherein alpha belongs to (0, 1); χ: the parameters meeting the system state limiting conditions are as follows:
T p predicting a time domain; k is D Artificial adjustment parameters of the differential part; k is I Product in a dayFractional artificial adjustment of parameter, K P The parameter is adjusted artificially in the proportion part.
8. A system of an event trigger model predictive control method based on PID trigger conditions is characterized in that a state acquisition module: the state acquisition module collects a system state value in real time;
a state value judging module: judging whether the numerical value in the state acquisition module belongs to a robust terminal set region;
an alternation calculation module: performing alternation calculation on the state value of the system;
a trigger value judgment module: comparing the trigger value with a trigger threshold value to further determine an optimization mode;
a feedback optimization module: and performing optimization control solution on the state through a feedback optimization module.
9. A terminal device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any of claims 1-7 when executing the computer program.
10. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 7.
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