CN111694279A - Multi-variable nonlinear system self-adaptive balanced multi-model decomposition and control method - Google Patents

Multi-variable nonlinear system self-adaptive balanced multi-model decomposition and control method Download PDF

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CN111694279A
CN111694279A CN202010619020.2A CN202010619020A CN111694279A CN 111694279 A CN111694279 A CN 111694279A CN 202010619020 A CN202010619020 A CN 202010619020A CN 111694279 A CN111694279 A CN 111694279A
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CN111694279B (en
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杜静静
陈俊风
李建
姜学平
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Changzhou Campus of Hohai University
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Abstract

The invention discloses a multivariable nonlinear system self-adaptive balanced multi-model decomposition and control method. Aiming at the complexity of a nonlinear multivariable system, firstly, gridding the multivariable nonlinear system by utilizing a gridding algorithm based on gap measurement; secondly, decomposing the multivariable nonlinear system by using a multi-model decomposition algorithm based on gap measurement; and designing a predictive controller by using a predictive control algorithm based on each obtained sub-model, finally performing weighted synthesis by using a trapezoidal weighting mode, and performing global control on the system to obtain the self-adaptive balanced multi-model decomposition and multi-model predictive controller of the multivariable nonlinear system. The invention greatly simplifies the steps of decomposing and controlling the system and improves the efficiency.

Description

Multi-variable nonlinear system self-adaptive balanced multi-model decomposition and control method
Technical Field
The invention discloses a multivariable nonlinear system self-adaptive balanced multi-model decomposition and control method.
Background
All process control systems in reality are non-linear, and linear controllers can meet the requirements when the system is operating near an operating point. However, linear controllers are not satisfactory for process control nonlinear systems that have a wide operating range. Especially for multivariable nonlinear process control systems, the control difficulty is greater. The multi-model control method based on the decomposition-synthesis principle can effectively convert a complex nonlinear control problem into a combination of a plurality of simple linear control problems through decomposition; solving these linear control problems enables the solution of the nonlinear control problem. The multi-model control method has the characteristic of simplicity, so that the multi-model control method has wide application in the field of nonlinear control. The predictive control is directly faced with a multivariable system and software and hardware constraints of the system, so that the method has great advantages for processing the control problem of the multivariable nonlinear system by combining a multi-model method and a predictive control method.
However, the existing multi-model decomposition algorithm is complex in price ratio and depends on prior knowledge too much. And the method is better for a single-input single-output system. When the system is a multivariable system, the variables are coupled to each other, making the system much more complex. Regardless of the selection of scheduling variables, system decomposition, and design, scheduling, etc. of the controller are much more complex than single-input single-output systems.
Disclosure of Invention
In order to solve the problems existing in the multi-model decomposition and control of the multivariable process control system, the invention provides a multivariable nonlinear system self-adaptive balanced multi-model decomposition and control method.
The technical scheme of the invention is as follows:
a multivariable nonlinear system self-adaptive equalization multi-model decomposition and control method comprises the following steps:
(1) gridding the multivariable nonlinear system by using a gridding algorithm based on gap measurement
(1-1), assuming that the scheduling variable of the nonlinear multivariable system is [ a, b ]';
(1-2) firstly gridding the component a and then gridding the component b by using a dichotomy gridding algorithm based on gap measurement;
(1-3) repeating the step (1-2) until the dimensionality of a and b is unchanged, and assuming that the finally obtained gridding result is that a is [ a ]1,a2,…,am],b＝[b1,b2,…,bn]At each combination point of a, b (a)i,bj) And (5) linearizing the original multivariable nonlinear system to obtain a series of linearized models P (i, j).
(2) And decomposing the multivariable nonlinear system by utilizing a multi-model decomposition algorithm based on the gap measurement
(2-1), selecting an initial threshold value lambda which is lambda 0 and a step length xi;
(2-2) classifying the gridding result from the first grid point by using a multivariate system decomposition algorithm based on gap measurement based on the gridding result obtained in the step (1);
(2-3) assuming that m is obtainedkSubspace corresponds to mkThe sub-models calculate the nonlinear metric value of each subspace by utilizing the maximum-minimum principle based on the gap metric;
(2-4), reducing the threshold by a step size, namely lambda-lambda;
(2-5) jumping to the step (2-2);
(2-6) assuming that m is obtainedk+1A subspace;
(2-7) if mk+1Is equal to mkI.e. mk+1＝＝mkThen jumping to step (2-4);
on the contrary, if mk+1Greater than mkI.e. mk+1>mkThen, stop;
(2-8)、mkand recording the result as the final decomposition result, wherein the final threshold is the current threshold plus the step size, and λ ═ λ + ξ, so far, the multi-model decomposition of the multivariate system is finished, and the nonlinear metric values of each subspace are relatively close and approximate to the final threshold, so that the decomposition results are balanced in the sense of nonlinear metric.
(3) And designing a predictive controller by using a predictive control algorithm based on each obtained sub-model, finally performing weighted synthesis by using a trapezoidal weighting mode, and performing global control on the system to obtain the self-adaptive balanced multi-model decomposition and multi-model predictive controller of the multivariable nonlinear system.
The invention has the beneficial effects that:
the invention provides a multivariable nonlinear system-oriented adaptive equalization multi-model decomposition algorithm, which can obtain an optimal decomposition threshold value through adaptive equalization and decompose the system by only one rough threshold value and step length to obtain an equalized decomposition result in the nonlinear measurement sense. And then, a multi-model predictive control algorithm is provided based on the obtained decomposition result to carry out optimization control on the system, so that the workload involved in multi-model decomposition can be greatly reduced, and the decomposition efficiency and quality are improved. This is of great benefit to simplifying the steps of the decomposition algorithm, improving the decomposition efficiency, simplifying the controller structure, and improving the closed-loop performance of the multimode controller.
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FIG. 1 is a schematic diagram of the structure of embodiment 1;
FIG. 2 is a reference input r of embodiment 1 under the multi-mode controller according to the present invention1，r2And outputting tracking response curves of h and T in a closed loop;
FIG. 3 is a control input F of the multi-mode controller proposed according to the present invention in the embodiment 11,qcThe tracking response curve of (1);
FIG. 4 shows the tracking effect of example 1 under the multi-model predictive controller designed by the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Example 1
Consider a multivariable nonlinear system as an inverted conical tank system, as shown in FIG. 1, where the two input flows are each FiAnd FjAll initial temperatures being Ti350K. The flow rate of the coolant is qcTemperature is TciOutput temperature TcoBetween 289 and 313K. The dynamic equation of the system is as follows:
Figure BDA0002562364450000031
where R and H are the radius and the height of the cone, respectively. The parameters are respectively R0.798 m, H1 m, K50 m5/ 2min-1，Fj＝10cm3min-1，Tci＝289K，Tco313K. The control of the system is aimed at by operation FiAnd q iscSo that the liquid level h and the temperature T can meet the control requirements. It is obvious from equation (1) that the system nonlinearity is very strong, and a single linear controller cannot meet the requirement.
By adopting the self-adaptive balanced multi-model decomposition algorithm of the multivariable system, the initial threshold value is 0.7, the step length is 0.01, and the final decomposition result is as follows: the threshold was 0.53, T was gridded to 8 points, and h was gridded to 30 points. The whole system is divided into two subsystems, as shown in fig. 2, the operating point for the first subsystem is OP1The operating point for the second subsystem is OP2。
The first region's non-linearity measure is 0.5229 and the second is 0.5132, both being less than and near the threshold, and thus being the result of an equalized decomposition. And a multi-model predictive controller is designed based on the obtained two subsystems, and the obtained closed-loop control effect is very good. As shown in fig. 3 and 4, the system output can track the change of the set value signal in the whole operation space, and the response speed is fast, accurate and stable.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (1)

1. A multivariable nonlinear system self-adaptive equalization multi-model decomposition and control method is characterized by comprising the following steps:
(1) gridding the multivariable nonlinear system by using a gridding algorithm based on gap measurement
(1-1), assuming that the scheduling variable of the nonlinear multivariable system is [ a, b ]';
(1-2) firstly gridding the component a and then gridding the component b by using a dichotomy gridding algorithm based on gap measurement;
(1-3) repeating the steps (1-2) until the dimensionality of a and b is unchanged, and linearizing the original multivariable nonlinear system at each combination point (ai, bj) of a and b to obtain a series of linearized models P (i, j) under the assumption that the finally obtained gridding result is a ═ a1, a2, …, am ], b ═ b1, b2, …, bn;
(2) and decomposing the multivariable nonlinear system by utilizing a multi-model decomposition algorithm based on the gap measurement
(2-1), selecting an initial threshold value lambda which is lambda 0 and a step length xi;
(2-2) classifying the gridding result by using a multivariate system decomposition algorithm based on gap measurement based on the gridding result obtained in the step (1);
(2-3) supposing to obtain mk submodels corresponding to the mk subspace, and calculating the nonlinear metric value of each subspace by using a maximum-minimum principle based on the gap metric;
(2-4), reducing the threshold by a step size, namely lambda-lambda;
(2-5) jumping to the step (2-2);
(2-6), assuming that mk +1 subspaces are obtained;
(2-7), if mk +1 is equal to mk, i.e., mk +1 ═ mk, then jumping to step (2-4);
conversely, if mk +1 is greater than mk, i.e., mk +1> mk, then stop.
(2-8) and mk are recorded as a final decomposition result, the final threshold is the current threshold plus the step length, and lambda is lambda + xi, so far, the multi-model decomposition of the multivariable system is finished;
(3) and designing a predictive controller by using a predictive control algorithm based on each obtained sub-model, finally performing weighted synthesis by using a trapezoidal weighting mode, and performing global control on the system to obtain the self-adaptive balanced multi-model decomposition and multi-model predictive controller of the multivariable nonlinear system.
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107450325A (en) * 2017-09-06 2017-12-08 东南大学 CO after one kind burning2The Multi model Predictive Controllers of trapping system
CN109100940A (en) * 2018-09-28 2018-12-28 河海大学常州校区 A kind of Multi model Predictive Controllers based on gap metric weighting function
CN110442027A (en) * 2019-08-16 2019-11-12 河海大学常州校区 A kind of gap multi-model weighting function methods of self-tuning
CN110658722A (en) * 2019-10-18 2020-01-07 河海大学常州校区 Self-equalization multi-model decomposition method and system based on gap
CN110825051A (en) * 2019-11-14 2020-02-21 河海大学常州校区 Multi-model control method of uncertainty system based on gap metric

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107450325A (en) * 2017-09-06 2017-12-08 东南大学 CO after one kind burning2The Multi model Predictive Controllers of trapping system
CN109100940A (en) * 2018-09-28 2018-12-28 河海大学常州校区 A kind of Multi model Predictive Controllers based on gap metric weighting function
CN110442027A (en) * 2019-08-16 2019-11-12 河海大学常州校区 A kind of gap multi-model weighting function methods of self-tuning
CN110658722A (en) * 2019-10-18 2020-01-07 河海大学常州校区 Self-equalization multi-model decomposition method and system based on gap
CN110825051A (en) * 2019-11-14 2020-02-21 河海大学常州校区 Multi-model control method of uncertainty system based on gap metric

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