According to the nonlinear and parameters timevarying characteristics of stripper temperature control system, the PVC stripping process Generalized Predictive Control based on implicit algorithm is proposed. Firstly, supporting vector machine is adopted to dynamically modelize for the stripper temperature; Secondly, combining with realtime model linearized of nonlinear model, a predictive model is linearized for realtime online correction. Then, the implicit algorithm is used for optimal control law. Finally, the simulation results show that the algorithm has excellent validity and robustness of temperature control of the stripper.
Polyvinyl chloride (PVC) resin is a kind of bulk basis chemical raw material, one of the five common plastics. It is generated by the polymerization of vinyl chloride monomer PVC. Since vinyl chloride monomer has some toxicity, so the residual chloride in the PVC resin must be controlled within a certain range, which requires high precision of stripper temperature control. The removal of vinyl chloride monomer in PVC commonly uses stripping process, which is a typical complex industrial process with characteristics of highly nonlinear, timevarying and coupling. Domestic PVC stripper temperature control system usually uses cascade control scheme as common [
Generalized Predictive Control (GPC), a computer control method developed with the Adaptive Control, has been successfully used in industrial process control. In recent years, for nonlinear predictive control system, many foreign scholars have proposed model predictive control method based on piecewise linear [
The article puts forward the implicit algorithm PVC stripping process generalized predictive control based on high accuracy of PVC stripper temperature control. It builds models adopting support vector machine model as a predictive model after linearization, realtime online correction. And it adopts the implicit algorithm to solve for optimal control law. Simulation results show that the algorithm based on the implicit generalized predictive control for stripper temperature control with a good validity and robustness.
PVC stripping process is a complex industrial process with strong nonlinear characteristics. For nonlinear support vector regression, the basic idea is to map the data into a high dimensional feature space through a nonlinear mapping, and then linear regression in this space. Thus, linear regression of the high dimensional feature space corresponds to the low dimensional input space nonlinear regression. The specific method is implemented by the kernel function
Then substitute the obtained parameters
Regression function can be derived:
When
PVC stripping process has the characteristic of nonlinear, and the object model is difficult to be accurately established. First of all, to establish the procedure for support vector regression model, the following nonlinear system model is introduced:
Among them,
In the formula,
According to the site of the 106 group field data collection, to be normalized, of which 53 groups are used SVM training sample, with the other 53 group as the test samples. In the simulation, selecting the polynomial kernel function
In the formula,
The parameters of support vector machine model that supports vector coefficients is shown in Table
The parameter of SVM model.
Number of group 


1  −0.6541 
2  0.0000 
3  0.7959 
4  0.0000 
5  −0.6588 
6  0.3045 
7  0.9018 
8  −0.5018 
9  1.0000 
10  1.0001 
11  0.9666 
12  1.0001 
13  1.0000 
14  −0.4135 
15  −0.0000 
16  −0.0000 
17  −0.2612 
18  −0.0609 
19  −1.0118 
20  −0.6405 
21  1.0000 
22  −1.0000 
23  −1.0000 
24  1.0000 
25  −1.0000 
26  −1.0000 
27  1.0000 
28  −0.5313 
29  0.0000 
30  −0.0000 
31  −0.0000 
32  0.0000 
33  0.5482 
34  0.3102 
35  0.0000 
36  1.0000 
37  0.3309 
38  −1.0000 
39  −1.0000 
40  −0.0008 
41  0.0000 
42  0.0000 
43  0.0000 
44  0.2357 
45  0.5109 
46  −1.0000 
47  −0.0000 
48  0.6334 
49  1.0000 
50  1.0005 
51  1.0000 
52  −0.0725 
53  −0.0000 
The formula (
The simulation of modeling on SVR (Training sample).
The simulation of modeling on SVR (Testing sample).
Meanwhile, introducing the variance as the evaluation indexes:
Using a support vector machine method to create predictive models, it turns the nonlinear systems into linear timevarying systems, and thus adopts the generalized predictive algorithm based on linear model, and realizes the generalized predictive control of nonlinear systems [
Then linearize the following formula (
In the formula, parameters
The article begins with the stripping process of PVC for support vector machine modeling, with model online correction, and then linearized as Generalized Predictive Control prediction model and solves the optimal control law when using implicit algorithm, avoiding online solving Diophantine equations, thereby reducing the amount of computation.
PVC stripping process is a typical nonlinear system. When input is
Predict model is:
In the feedback correction, the use of SVM modeling can be corrected online, but in order to reduce the amount of computation repeated correction model, the following correction strategies can be used:
When the error
When the error
Reference trajectory chooses oneorder filter equations yields:
In the formula,
Performance index function select:
Written in vector form as follows:
Derivation of future control increment, that is
The optimal control law is:
Expand the above equation, the control increment sequence of the openloop control from time
While in actual practice, each time only the first component added to the system, while the control increment moments later recalculated each step, closedloop control measure is achieved, then we only need to calculate the first row
Now, the actual implementation is:
According to the actual input and output data of the Stripper, directly identify the matrix
The best predictive value can be drawn from projections theory:
The generalized predictive algorithm strikes the optimal control law algorithms with identification of the controller parameters directly from the input and output data. It avoids the online solving Diophantine equations and inverse matrix to improve the speed of operation and save computing time.
Algorithm Initialization: The length of time domain
Set square
According to formula (
According to the recursive least squares equation,
According to the vector
Calculate and reserve
In the control system of PVC stripping process, the support vector machine modeling and Generalized Predictive Control Implicit algorithm are combined with online correction of the model and error models feedback correction, and PVC stripping process is studied according to the actual situation to simulation. PVC stripping process according to the actual process, the stripper top temperature optimum temperature of 100°C, so the simulation signal is a given value 100°C.
Using support vector machine model obtained by the linearized expression:
Compare the Simulation curve of the normal algorithm GPC and implicit algorithm GPC. Simulation predicted length
(1) Good condition during operation, shown in Figure
The control result of PVC stripping process in proper operation.
Curve can be seen from Figure
(2) Set value temperature changes because of the different grades of polyvinyl chloride resin, or process requirements, the optimum temperature of the stripping column top is different. The simulation is given the first 15 minutes 100°C, in 15 minutes changing the resin grades; the optimum temperature was changed to 105°C, as the obtained control effect curve shows in Figure
The control result of PVC stripping process when set value changed.
As can be seen from Figure
(3) When the controlled object was disturbed, such as the uneven heating of the slurry and other factors led to sudden abrupt changes in temperature.
The simulation time of 15 minutes, adding the amplitude of a sudden disturbance 5°C, as control effect curve shown in Figure
The control result of PVC stripping process by a sudden noise.
(4) In simulation, during operation subject to the random disturbance of uncertainties factor is added, the value at −5~+5°C, for controlling the effect of the curve in Figure
The control result of PVC stripping process by random noise.
Above four cases can be seen from the simulation curve, using the implicit algorithm for GPC was better than general for GPC control effect.
The dynamic modeling is adopted based on the principle of support vector machines and the field data of PVC stripping process. Meanwhile, it combines the model online correction and error feedback correction with the realtime linear and nonlinear model. And the Generalized Predictive Control is adopted by using implicit algorithm with stripping process of PVC. Simulation results verify the validity of the model and the feasibility and robustness of the algorithm.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the Key Program of National Natural Science Foundation of China (61034005), the Postgraduate Scientific Research and Innovation Projects of Basic Scientific Research Operating Expenses of Ministry of Education (N100604001).