# Application of maximum fire predictive function co

2022-07-23
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The application of predictive functional control in the combustion system of industrial boilers; Automatic data processing has three characteristics of general predictive control: predictive model, rolling optimization and feedback correction. The biggest difference between it and other predictive control algorithms is that it pays attention to the structural form of the control quantity, and considers that the control quantity is related to a group of functions corresponding to the process characteristics and tracking the set value. Therefore, the control quantity calculated at each time is equal to a group of the same conditions, which can be seen in the linear combination of the previously selected functions in the farmers' market. These functions are called basis functions, and the known process responses of these basis functions are used, By optimizing the objective function, the weight coefficients of each basis function are obtained and the corresponding control quantities are obtained

for the convenience of algorithm implementation, the PFC prediction process model adopts a parameter model in the form of discrete state equation, which is described as:

the optimization objective function of predictive function control is to minimize the sum of squares of the difference between the prediction process output and the reference trajectory value on the selected fitting points (s) of prediction time domain H

among them, the fitting points are some discrete points between 0 and T, which need to be determined in advance, and their number should be greater than or equal to the number of basis functions

for the above formula, the linear calculation equation of control quantity at n time can be obtained:

coefficient, NC is the order of polynomial; The calculation formula of each coefficient is:

as can be seen from the above expression, the coefficient β n. VX can be used in the off-line furnace combustion control system, and the method is proved to be effective by simulating the establishment of a new industrial demonstration base

2 predictive functional control of pure delay process

for the following large delay system:

the output value of the process is determined by the predictive model and the control quantity before a delay time. If

is treated according to formula (2-3), although predictive control can be used to deal with the process with large pure delay, there is a lag time in the model, which reduces the reaction rate of the control, and the real PFC control can only be realized after the pure lag time, so as to minimize the deviation between the predicted value and the trajectory

referring to the idea of Smith predictive control, the actual measured value is modified by the process model without time delay, and the control quantity of the improved PFC algorithm is given:

this control quantity can be applied to the process with large pure delay after some time-domain changes. Specifically, the start time domain of the iteration process should be set at step L. the first step L is regarded as the lag time, and its control quantity is zero. The control quantity U (k) calculated in formula (2-4) should be applied at the current time. After that, recursive iterative calculation is carried out continuously, which can not only speed up the control speed, but also obtain satisfactory control effect

3 realization of predictive function controller

the combustion control is divided into three loops, and each loop is described by a pure lag model. The material industry is the foundation of various industrial fields. Taking the measurable disturbance as a feedforward can not only eliminate the influence of the measurable disturbance on the controlled quantity, but also reduce the interaction between loops

3.1 parameter identification - real time algorithm of time-varying forgetting factor

gives the prediction model:

the order of polynomials a, B and C in the model is determined according to the actual situation. In this paper, it is order 2. Their coefficients are obtained through parameter identification. The identification method adopts the variable forgetting factor least square method. The formula is as follows:

where n (k) is the memory length. In this paper, it is selected as 1000, which is σ (k) Variance of, α 2 is the initial covariance matrix P0 = α The value in 2 · I is taken as 10, and trace [QK] is the trace of matrix QK

3.2 implementation of predictive function control

using recursive time-varying forgetting factor λ (k) The least square method and recursive identification parameters can ensure that the identification parameters can adapt to the slow change of the system without outbreak. The recursive parameter identification is completed once at each sampling interval to obtain the estimation model formula (3-1). According to the estimation model, the predictive function controller formula (2-4) can be obtained. The control action is directly calculated, and the calculated control quantity is used as the input of the controlled process, It must produce the corresponding output, and then sample the input and output data to identify the parameters

4 continuous system simulation of boiler combustion system

simulation uses the method of CSS (continuous systemsimulation) , which is a system simulation method based on signal flow graph. It incorporates the idea of simulating the modular programming structure of computer into

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