CN103605284B

CN103605284B - The cracking waste plastics stove hearth pressure control method that dynamic matrix control is optimized

Info

Publication number: CN103605284B
Application number: CN201310567638.9A
Authority: CN
Inventors: 薛安克; 张日东; 陈华杰; 郭云飞
Original assignee: Hangzhou Dianzi University
Current assignee: Hangzhou Dianzi University
Priority date: 2013-11-14
Filing date: 2013-11-14
Publication date: 2016-06-01
Anticipated expiration: 2033-11-14
Also published as: CN103605284A

Abstract

The present invention discloses the cracking waste plastics stove hearth pressure control method that dynamic matrix control is optimized. First the inventive method sets up the model of furnace pressure object based on the step response data of cracking waste plastics stove furnace pressure object, excavates basic plant characteristic; Then go according to the characteristic of dynamic matrix control to adjust the parameter of corresponding PI controller; Finally cracking waste plastics stove fire box temperature object is implemented PI control. The present invention proposes a kind of cracking waste plastics stove fire box temperature PI control method optimized based on dynamic matrix control, combine the good control performance of PI control and dynamic matrix control, effectively improve the deficiency of Traditional control method, also promote the development and apply of advanced control algorithm simultaneously.

Description

Furnace pressure control method of waste plastic pyrolysis furnace optimized by dynamic matrix control

技术领域technical field

本发明属于自动化技术领域，涉及一种基于动态矩阵控制(DMC)优化的废塑料裂解炉炉膛压力比例积分(PI)控制方法。The invention belongs to the technical field of automation, and relates to a dynamic matrix control (DMC) optimization-based proportional-integral (PI) control method for furnace pressure of a waste plastic pyrolysis furnace.

背景技术Background technique

随着现代工业过程的大型化和复杂化,一些传统的控制方法越来越难以满足工业的实际需求。一些先进过程控制技术虽然在理论上能够大大提高生产效率,但由于硬件、成本、实施难度等方面的原因，很难得到应用，所以目前占据主流的仍然是PID控制。目前废塑料裂解炉炉膛压力的控制通常采用比例积分(PI)控制。动态矩阵控制作为先进控制方法的一种，对模型要求低，计算量少，处理延时的方法简单易行，如果能将动态矩阵控制算法和PI技术结合，将动态矩阵控制的性能赋给PI控制，那将更加有利于生产效率的提高，同时也能够推动先进控制的发展。With the enlargement and complexity of the modern industrial process, some traditional control methods are more and more difficult to meet the actual needs of the industry. Although some advanced process control technologies can greatly improve production efficiency in theory, they are difficult to be applied due to reasons such as hardware, cost, and implementation difficulty. Therefore, PID control is still the mainstream at present. At present, the control of the furnace pressure of waste plastic pyrolysis furnace is usually controlled by proportional integral (PI). As one of the advanced control methods, dynamic matrix control has low requirements on the model, less calculation, and the method of processing delay is simple and easy. If the dynamic matrix control algorithm can be combined with PI technology, the performance of dynamic matrix control can be assigned to PI Control, it will be more conducive to the improvement of production efficiency, but also can promote the development of advanced control.

发明内容Contents of the invention

本发明的目的是针对现有先进控制方法的应用不足之处，提供一种基于动态矩阵控制优化的废塑料裂解炉炉膛压力PI控制方法，以获得更好的实际控制性能。该方法通过结合动态矩阵控制和PI控制，得到了一种带有动态矩阵控制性能的PI控制方法。该方法不仅继承了动态矩阵控制的优良性能，同时形式简单并能满足实际工业过程的需要。The purpose of the present invention is to provide a PI control method based on dynamic matrix control optimization for furnace pressure of waste plastic pyrolysis furnace in order to obtain better actual control performance. In this method, a PI control method with dynamic matrix control performance is obtained by combining dynamic matrix control and PI control. This method not only inherits the excellent performance of dynamic matrix control, but also has a simple form and can meet the needs of actual industrial processes.

本发明方法首先基于废塑料裂解炉炉膛压力对象的阶跃响应数据建立炉膛压力对象的模型，挖掘出基本的对象特性；然后依据动态矩阵控制的特性去整定相应PI控制器的参数；最后对废塑料裂解炉炉膛温度对象实施PI控制。The method of the present invention first establishes the model of the furnace pressure object based on the step response data of the furnace pressure object of the waste plastic cracking furnace, and digs out the basic object characteristics; then adjusts the parameters of the corresponding PI controller according to the characteristics of the dynamic matrix control; The furnace temperature object of the plastic cracking furnace implements PI control.

本发明的技术方案是通过数据采集、建立动态矩阵、建立预测模型、预测机理、优化等手段，确立了一种基于动态矩阵控制优化的PI控制方法，利用该方法可有效提高控制的精度与稳定性。The technical solution of the present invention is to establish a PI control method based on dynamic matrix control optimization through means such as data collection, establishment of dynamic matrix, establishment of prediction model, prediction mechanism, optimization, etc., and the accuracy and stability of control can be effectively improved by using this method sex.

本发明方法的步骤包括：The steps of the inventive method comprise:

步骤(1).通过过程对象的实时阶跃响应数据建立被控对象的模型，具体方法是：Step (1). Establish the model of the controlled object through the real-time step response data of the process object, the specific method is:

a.给被控对象一个阶跃输入信号，记录被控对象的阶跃响应曲线。a. Give the controlled object a step input signal, and record the step response curve of the controlled object.

b.将a步骤得到的阶跃响应曲线进行滤波处理，然后拟合成一条光滑曲线，记录光滑曲线上每个采样时刻对应的阶跃响应数据，第一个采样时刻为T_s，相邻两个采样时刻间隔的时间为T_s，采样时刻顺序为T_s、2T_s、3T_s……；被控对象的阶跃响应将在某一个时刻t_N＝NT后趋于平稳，当a_i(i＞N)与a_N的误差和测量误差有相同的数量级时，即可认为a_N近似等于阶跃响应的稳态值。建立对象的模型向量a：b. Filter the step response curve obtained in step a, then fit it into a smooth curve, and record the step response data corresponding to each sampling time on the smooth curve. The first sampling time is T _s , and two adjacent The time interval between each sampling moment is T _s , and the order of sampling moments is T _s , 2T _s , 3T _s ...; the step response of the controlled object will tend to be stable after a certain moment t _N = NT, when a _i ( When i>N) has the same order of magnitude as the error of a _N and the measurement error, it can be considered that a _N is approximately equal to the steady-state value of the step response. Build the model vector a of the object:

a＝[a₁,a₂,…a_N]^Τ a=[a ₁ ,a ₂ ,…a _N ] ^Τ

其中Τ为矩阵的转置符号，N为建模时域。where T is the transpose symbol of the matrix, and N is the modeling time domain.

步骤(2).设计被控对象的PI控制器，具体方法是：Step (2). Design the PI controller of the controlled object, the specific method is:

a.利用上面获得的模型向量a建立被控对象的动态矩阵，其形式如下：a. Use the model vector a obtained above to establish the dynamic matrix of the controlled object, the form of which is as follows:

$A A = = (\begin{matrix} {a a}_{11} & 00 & . . . . . . & 00 \\ {a a}_{22} & {a a}_{11} & . . . . . . & 00 \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ {a a}_{P P} & {a a}_{P P - - 11} & . . . . . . & {a a}_{P P - - M m + + 11} \end{matrix})$

其中，A是被控对象的P×M阶动态矩阵，a_i是阶跃响应的数据，P为动态矩阵控制算法的优化时域，M为动态矩阵控制算法的控制时域，M＜P＜N。Among them, A is the P×M order dynamic matrix of the controlled object, a _i is the data of the step response, P is the optimization time domain of the dynamic matrix control algorithm, M is the control time domain of the dynamic matrix control algorithm, M<P< N.

b.建立被控对象当前k时刻的模型预测初始响应值y_M(k)b. Establish the model to predict the initial response value y _M (k) of the controlled object at the current moment k

先得到k-1时刻加入控制增量Δu(k-1)后的模型预测值y_p(k-1)：First get the model prediction value y _p (k-1) after adding the control increment Δu(k-1) at time k-1:

y_P(k-1)＝y_M(k-1)+A₀Δu(k-1)y _P (k-1)=y _M (k-1)+A ₀ Δu(k-1)

其中，in,

${y the y}_{P P} ((k k - - 11)) = = [\begin{matrix} {y the y}_{11} ((k k | | k k - - 11)) \\ {y the y}_{11} ((k k + + 11 | | k k - - 11)) \\ . . \\ . . \\ . . \\ {y the y}_{11} ((k k + + N N - - 11 | | k k - - 11)) \end{matrix}],, {A A}_{00} = = [\begin{matrix} {a a}_{11} \\ {a a}_{22} \\ . . \\ . . \\ . . \\ {a a}_{N N} \end{matrix}],, {y the y}_{M m} ((k k)) = = [\begin{matrix} {y the y}_{00} ((k k | | k k - - 11)) \\ {y the y}_{00} ((k k + + 11 | | k k - - 11)) \\ . . \\ . . \\ . . \\ {y the y}_{00} ((k k + + N N - - 11 | | k k - - 11)) \end{matrix}]$

y₁(k|k-1),y₁(k+1|k-1),…,y₁(k+N-1|k-1)分别表示被控对象在k-1时刻对k,k+1,…,k+N-1时刻加入控制增量Δu(k-1)后的模型预测值，y₀(k|k-1),y₀(k|k-1),…y₀(k+N-1|k-1)表示k-1时刻对k,k+1,…,k+N-1时刻的初始预测值，A₀为阶跃响应数据建立的矩阵，Δu(k-1)为k-1时刻的输入控制增量。y ₁ (k|k-1), y ₁ (k+1|k-1),…, y ₁ (k+N-1|k-1) represent the controlled object’s response to k, k+1,...,k+N-1 time adding control increment Δu(k-1) model prediction value, y ₀ (k|k-1), y ₀ (k|k-1),...y ₀ (k+N-1|k-1) represents the initial prediction value of time k-1 for k, k+1,...,k+N-1 time, A ₀ is the matrix established by the step response data, Δu( k-1) is the input control increment at time k-1.

接着得到k时刻被控对象的模型预测误差值e(k)：Then get the model prediction error value e(k) of the controlled object at time k:

e(k)＝y(k)-y₁(k|k-1)e(k)=y(k)-y ₁ (k|k-1)

其中，y(k)表示k时刻测得的被控对象的实际输出值。Among them, y(k) represents the actual output value of the controlled object measured at time k.

进一步得到k时刻模型输出的修正值y_cor(k):Further obtain the corrected value y _cor (k) output by the model at time k:

y_cor(k)＝y_M(k-1)+h*e(k)y _cor (k)=y _M (k-1)+h*e(k)

其中，in,

${y the y}_{cor cor} ((k k)) = = [\begin{matrix} {y the y}_{cor cor} ((k k | | k k)) \\ {y the y}_{cor cor} ((k k + + 11 | | k k)) \\ . . \\ . . \\ . . \\ {y the y}_{cor cor} ((k k + + N N - - 11 | | k k)) \end{matrix}],, h h = = [\begin{matrix} 11 \\ α α \\ . . \\ . . \\ . . \\ α α \end{matrix}]$

y_cor(k|k),y_cor(k+1|k),…y_cor(k+N-1|k)分别表示被控对象在k时刻模型的修正值，h为误差补偿的权矩阵，α为误差校正系数。y _cor (k|k), y _cor (k+1|k),...y _cor (k+N-1|k) represent the correction value of the model of the controlled object at time k respectively, and h is the weight matrix of error compensation , α is the error correction coefficient.

最后的得到k时刻的模型预测的初始响应值y_M(k)：Finally, the initial response value y _M (k) predicted by the model at time k is obtained:

y_M(k)＝Sy_cor(k)y _M (k) = Sy _cor (k)

其中，S为N×N阶的状态转移矩阵，Among them, S is the state transition matrix of order N×N,

c.计算被控对象在M个连续的控制增量Δu(k),…,Δu(k+M-1)下的预测输出值y_PM，具体方法是：c. Calculate the predicted output value y _PM of the controlled object under M continuous control increments Δu(k),...,Δu(k+M-1), the specific method is:

y_PM(k)＝y_p0(k)+AΔu_M(k)y _PM (k) = y _p0 (k) + AΔu _M (k)

${y the y}_{PM PM} ((k k)) = = [\begin{matrix} {y the y}_{M m} ((k k + + 11 | | k k)) \\ {y the y}_{M m} ((k k + + 22 | | k k)) \\ . . \\ . . \\ . . \\ {y the y}_{M m} ((k k + + P P | | k k)) \end{matrix}],, {y the y}_{P P 00} ((k k)) = = [\begin{matrix} {y the y}_{00} ((k k + + 11 | | k k)) \\ {y the y}_{00} ((k k + + 22 | | k k)) \\ . . \\ . . \\ . . \\ {y the y}_{00} ((k k + + P P | | k k)) \end{matrix}],, Δ Δ {u u}_{M m} ((k k)) = = [\begin{matrix} Δu Δu ((k k)) \\ Δu Δu ((k k + + 11)) \\ . . \\ . . \\ . . \\ Δu Δu ((k k + + M m - - 11)) \end{matrix}]$

d.令被控对象的控制时域M=1，选取被控对象的目标函数J(k)，形式如下：d. Let the control time domain of the controlled object M=1, select the objective function J(k) of the controlled object, the form is as follows:

minJ(k)＝Q(ref(k)-y_PM(k))²+rΔu²(k)=Q(ref(k)-y_P0(k)-AΔu(k))²+rΔu²(k)minJ(k)=Q(ref(k)-y _PM (k)) ² +rΔu ² (k)=Q(ref(k)-y _P0 (k)-AΔu(k)) ² +rΔu ² (k )

ref(k)＝[ref₁(k),ref₂(k),…,ref_P(k)]^Τ ref(k)=[ref ₁ (k), ref ₂ (k),...,ref _P (k)] ^Τ

ref_i(k)＝βⁱy(k)+(1-βⁱ)c(k),Q＝diag(q₁,q₂,…,q_P)ref _i (k)=β ⁱ y(k)+(1-β ⁱ )c(k),Q=diag(q ₁ ,q ₂ ,…,q _P )

其中，Q为误差加权矩阵，q₁,q₂,…,q_P为加权矩阵的参数值；β为柔化系数，c(k)为设定值；r＝diag(r₁,r₂,…r_M)为控制加权矩阵，r₁,r₂,…r_M为控制加权矩阵的参数，ref(k)为系统的参考轨迹，ref_i(k)为参考轨迹中第i个参考点的值。Among them, Q is the error weighting matrix, q ₁ , q ₂ ,...,q _P is the parameter value of the weighting matrix; β is the softening coefficient, c(k) is the set value; r=diag(r ₁ ,r ₂ , …r _M ) is the control weighting matrix, r ₁ , r ₂ ,…r _M are the parameters of the control weighting matrix, ref(k) is the reference trajectory of the system, ref _i (k) is the i-th reference point in the reference trajectory value.

e.将控制量u(k)进行变换：e. Transform the control quantity u(k):

u(k)＝u(k-1)+K_p(k)(e₁(k)-e₁(k-1))+K_i(k)e₁(k)u(k)=u(k-1)+K _p (k)(e ₁ (k)-e ₁ (k-1))+K _i (k)e ₁ (k)

e(k)＝c(k)-y(k)e(k)=c(k)-y(k)

将u(k)代入到步骤d中的目标函数求解PI控制器中的参数得：Substituting u(k) into the objective function in step d to solve the parameters in the PI controller:

u(k)＝u(k-1)+w(k)^ΤE(k)u(k)=u(k-1)+w(k) ^Τ E(k)

w(k)＝[w₁(k),w₂(k)]^Τ w(k)=[w ₁ (k),w ₂ (k)] ^Τ

w₁(k)＝K_p(k)+K_i(k)，w₂(k)＝-K_p(k)w ₁ (k)=K _p (k)+K _i (k), w ₂ (k)=-K _p (k)

E(k)＝[e₁(k),e₁(k-1)]^Τ E(k)=[e ₁ (k), e ₁ (k-1)] ^Τ

其中，Kp(k)、K_i(k)分别为k时刻PI控制器的比例、微分参数，e₁(k)为k时刻参考轨迹值与实际输出值之间的误差，Τ为矩阵的转置符号。Among them, Kp(k) and K _i (k) are the proportional and differential parameters of the PI controller at time k respectively, e ₁ (k) is the error between the reference trajectory value and the actual output value at time k, and Τ is the transformation of the matrix set symbol.

综合上述式子，可得：Combining the above formulas, we can get:

$w w ((k k)) = = \frac{{((ref ref ((k k)) - - {y the y}_{P P 00} ((k k))))}^{T T} QAE QAE}{(({A A}^{T T} QA QA + + r r)) {E E.}^{T T} E E.}$

进一步可以得到：Further can get:

K_p(k)＝-w₂(k)K _p (k) = -w ₂ (k)

K_i(k)＝w₁(k)-K_P(k)K _i (k) = w ₁ (k) - K _P (k)

f.得到PI控制器的参数K_p(k)、K_i(k)以后构成控制量u(k)作用于被控对象，u(k)＝u(k-1)+K_p(k)(e₁(k)-e₁(k-1))+K_i(k)e₁(k)。f. After obtaining the parameters K _p (k) and K _i (k) of the PI controller, the control quantity u(k) is formed to act on the controlled object, u(k)=u(k-1)+K _p (k) (e ₁ (k)-e ₁ (k-1))+K _i (k)e ₁ (k).

h.在下一时刻，依照b到f中的步骤继续求解PI控制器新的参数k_P(k+1)、k_i(k+1)的值，依次循环。h. At the next moment, continue to solve the values of the new parameters k _P (k+1) and _ki (k+1) of the PI controller according to the steps in b to f, and cycle in turn.

本发明提出了一种基于动态矩阵控制优化的废塑料裂解炉炉膛温度PI控制方法,结合了PI控制和动态矩阵控制的良好的控制性能,有效地提高了传统控制方法的不足,同时也促进了先进控制算法的发展与应用。The present invention proposes a PI control method for the furnace temperature of waste plastic pyrolysis furnace based on dynamic matrix control optimization, which combines the good control performance of PI control and dynamic matrix control, effectively improves the shortcomings of traditional control methods, and also promotes Development and application of advanced control algorithms.

具体实施方式detailed description

以废塑料裂解炉炉膛压力过程控制为例：Take the furnace pressure process control of waste plastic pyrolysis furnace as an example:

废塑料裂解炉炉膛压力对象为带滞后的过程，调节手段采用调节烟道挡板的开度。The furnace pressure object of waste plastic cracking furnace is a process with hysteresis, and the adjustment means is to adjust the opening of the flue baffle.

步骤(1).通过废塑料裂解炉炉膛压力对象的实时阶跃响应数据建立被控对象的模型，具体方法是：Step (1). The model of the controlled object is established by the real-time step response data of the waste plastic cracking furnace furnace pressure object, and the specific method is:

a.给废塑料裂解炉炉膛一个阶跃输入信号，记录其阶跃响应曲线。a. Give a step input signal to the hearth of the waste plastic pyrolysis furnace, and record its step response curve.

b.将对应的阶跃响应曲线进行滤波处理，然后拟合成一条光滑曲线，记录光滑曲线上每个采样时刻对应的阶跃响应数据，第一个采样时刻为T_s，相邻两个采样时刻间隔的时间为T_s，采样时刻顺序为T_s、2T_s、3T_s……；挡板开度的响应值a_i将在某一个时刻t_N＝NT后趋于平稳，当a_i(i＞N)与a_N的误差和测量误差有相同的数量级时，即可认为a_N近似等于阶跃响应稳态值。建立对象的模型向量a：b. Filter the corresponding step response curve, then fit it into a smooth curve, and record the step response data corresponding to each sampling time on the smooth curve. The first sampling time is T _s , and two adjacent samples The time interval between moments is T _s , and the sequence of sampling _moments is T _s , 2T _s , _3T _s _. When i>N) has the same order of magnitude as the error of a _N and the measurement error, it can be considered that a _N is approximately equal to the steady-state value of the step response. Build the model vector a of the object:

a＝[a₁,a₂,…a_N]^Τ a=[a ₁ ,a ₂ ,…a _N ] ^Τ

其中Τ为矩阵的转置符号，N为建模时域，。where T is the transpose symbol of the matrix, N is the modeling time domain, .

步骤(2).设计废塑料裂解炉炉膛压力的PI控制器，具体方法是：Step (2). Design the PI controller of waste plastic cracking furnace hearth pressure, concrete method is:

a.利用上面获得的模型向量a建立废塑料裂解炉炉膛压力的动态矩阵，其形式如下：a. Use the model vector a obtained above to establish the dynamic matrix of the furnace pressure of the waste plastic cracking furnace, which has the following form:

其中，A是废塑料裂解炉炉膛压力的P×M阶动态矩阵，a_i是废塑料裂解炉炉膛压力的挡板开度的数据，P为动态矩阵控制算法的优化时域，M为动态矩阵控制算法的控制时域，M＜P＜N。Among them, A is the P×M order dynamic matrix of the furnace pressure of the waste plastics pyrolysis furnace, a _i is the data of the baffle opening of the waste plastics pyrolysis furnace pressure, P is the optimization time domain of the dynamic matrix control algorithm, and M is the dynamic matrix In the control time domain of the control algorithm, M<P<N.

b.建立废塑料裂解炉炉膛压力当前k时刻的初始预测值y_M(k)b. Establish the initial predicted value y _M (k) of the furnace pressure of the waste plastic cracking furnace at the current moment k

先得到k-1时刻挡板开度增加Δu(k-1)后的模型预测值y_p(k-1):First obtain the model prediction value y _p (k-1) after the baffle opening increases by Δu(k-1) at time k-1:

y_P(k-1)＝y_M(k-1)+A₀Δu(k-1)y _P (k-1)=y _M (k-1)+A ₀ Δu(k-1)

其中，in,

y₁(k|k-1),y₁(k+1|k-1),…,y₁(k+N-1|k-1)分别表示废塑料裂解炉炉膛压力在k-1时刻对k,k+1,…,k+N-1时刻加入Δu(k-1)后的模型预测值，y₀(k|k-1),y₀(k|k-1),…y₀(k+N-1|k-1)表示k-1时刻对k,k+1,…,k+N-1时刻的废塑料裂解炉炉膛压力的初始预测值，A₀为由废塑料裂解炉炉膛压力阶跃响应数据建立的矩阵，Δu(k-1)为k-1时刻的废塑料裂解炉压力的挡板开度控制增量。y ₁ (k|k-1), y ₁ (k+1|k-1),…, y ₁ (k+N-1|k-1) represent respectively that the furnace pressure of the waste plastic cracking furnace is at k-1 time The predicted value of the model after adding Δu(k-1) to k, k+1,...,k+N-1, y ₀ (k|k-1), y ₀ (k|k-1),...y ₀ (k+N-1|k-1) represents the initial prediction value of the furnace pressure of the waste plastic pyrolysis furnace at time k-1 to k, k+1,..., k+N-1 time, A ₀ is the waste plastic The matrix established by the furnace pressure step response data of the cracking furnace, Δu(k-1) is the baffle opening control increment of the waste plastic cracking furnace pressure at time k-1.

接着得到k时刻废塑料裂解炉压力的模型预测误差值e(k):Then obtain the model prediction error value e(k) of the waste plastics cracking furnace pressure at time k:

e(k)＝y(k)-y₁(k|k-1)e(k)=y(k)-y ₁ (k|k-1)

其中，y(k)表示k时刻测得的废塑料裂解炉压力的实际输出值。Among them, y(k) represents the actual output value of the waste plastic cracking furnace pressure measured at time k.

进一步得到k时刻废塑料裂解炉压力的模型输出的修正值y_cor(k):Further obtain the corrected value y _cor (k) of the model output of the waste plastic cracking furnace pressure at time k:

y_cor(k)＝y_M(k-1)+h*e(k)y _cor (k)=y _M (k-1)+h*e(k)

其中，in,

y_cor(k|k),y_cor(k+1|k),…y_cor(k+N-1|k)分别表示废塑料裂解炉炉膛压力在k时刻模型的修正值，h为误差补偿的权矩阵，α为误差校正系数。y _cor (k|k), y _cor (k+1|k), ... y _cor (k+N-1|k) respectively represent the correction value of the furnace pressure of the waste plastic cracking furnace at time k, and h is the error compensation The weight matrix of , α is the error correction coefficient.

最后的得到废塑料裂解炉炉膛压力在k时刻模型的初始预测值y_M(k)：Finally, the initial prediction value y _M (k) of the furnace pressure of the waste plastic cracking furnace at time k is obtained:

y_M(k)＝Sy_cor(k)y _M (k) = Sy _cor (k)

c.计算废塑料裂解炉炉膛压力在M个连续的控制增量Δu(k),…,Δu(k+M-1)下的预测输出值y_PM，具体方法是：c. Calculate the predicted output value y _PM of the furnace pressure of the waste plastic cracking furnace under M continuous control increments Δu(k),...,Δu(k+M-1), the specific method is:

y_PM(k)＝y_P0(k)+AΔu_M(k)y _PM (k) = y _P0 (k) + AΔu _M (k)

其中,in,

y_P0(k)是y_M(k)的前P项，y_M(k+1|k),y_M(k+2|k),…,y_M(k+P|k)为废塑料裂解炉炉膛压力在k时刻对k+1,k+2,…,k+P时刻的模型预测输出值。y _P0 (k) is the first P item of y _M (k), y _M (k+1|k), y _M (k+2|k),...,y _M (k+P|k) are waste plastics The furnace pressure of the cracking furnace at time k is the output value of the model prediction at time k+1, k+2,...,k+P.

d.令控制时域M＝1,并选取废塑料裂解炉炉膛压力的目标函数J(k)，形式如下：d. Let the control time domain M=1, and select the objective function J(k) of the furnace pressure of the waste plastic cracking furnace, the form is as follows:

其中，Q为误差加权矩阵，q₁,q₂,…,q_P为误差加权矩阵的参数值；β为柔化系数，c(k)为废塑料裂解炉炉膛压力的设定值；r＝diag(r₁,r₂,…r_M)为控制加权矩阵，r₁,r₂,…r_M为控制加权矩阵的参数，ref(k)为废塑料裂解炉炉膛压力的参考轨迹，ref_i(k)为参考轨迹中第i个参考点的值。Among them, Q is the error weighting matrix, q ₁ , q ₂ ,...,q _P is the parameter value of the error weighting matrix; β is the softening coefficient, c(k) is the set value of the furnace pressure of the waste plastic cracking furnace; r= diag(r ₁ ,r ₂ ,…r _M ) is the control weighting matrix, r ₁ ,r ₂ ,…r _M is the parameter of the control weighting matrix, ref(k) is the reference trajectory of the furnace pressure of the waste plastic cracking furnace, ref _i (k) is the value of the i-th reference point in the reference trajectory.

e.将废塑料裂解炉炉膛的烟道挡板开度控制量u(k)进行变换：e. Transform the opening control value u(k) of the flue baffle in the hearth of the waste plastic cracking furnace:

e(k)＝c(k)-y(k)e(k)=c(k)-y(k)

并将u(k)代入到步骤d中的目标函数，进一步求解废塑料裂解炉炉膛压力的PI控制器中的参数，可求得：Substituting u(k) into the objective function in step d, and further solving the parameters in the PI controller of the furnace pressure of the waste plastic pyrolysis furnace, can obtain:

u(k)＝u(k-1)+w(k)^ΤE(k)u(k)=u(k-1)+w(k) ^Τ E(k)

w(k)＝[w₁(k),w₂(k)]^Τ w(k)=[w ₁ (k),w ₂ (k)] ^Τ

w1(k)＝K_p(k)+K_i(k)，w₂(k)＝-K_p(k)w1(k) ₌ Kp( _k )+Ki(k), w2( _k )=-Kp( _k )

E(k)＝[e₁(k),e₁(k-1)]^Τ E(k)=[e ₁ (k), e ₁ (k-1)] ^Τ

其中，K_p(k)、K_i(k)分别为PI控制器的比例、微分参数，e₁(k)为k时刻参考轨迹值与实际输出值之间的误差，Τ为矩阵的转置符号。Among them, K _p (k) and K _i (k) are the proportional and differential parameters of the PI controller respectively, e ₁ (k) is the error between the reference trajectory value and the actual output value at time k, and Τ is the transposition of the matrix symbol.

综合上述式子，可得：Combining the above formulas, we can get:

进一步可以得到：Further can get:

K_p(k)＝-w₂(k)K _p (k) = -w ₂ (k)

K_i(k)＝w₁(k)-K_P(k)K _i (k) = w ₁ (k) - K _P (k)

f.得到PI控制器的参数K_p(k)、K_i(k)以后，构成烟道挡板开度的控制量u(k)＝u(k-1)+K_p(k)(e₁(k)-e₁(k-1))+K_i(k)e₁(k)，作用于废塑料裂解炉炉膛。f. After obtaining the parameters K _p (k) and K _i (k) of the PI controller, the control quantity u(k) that constitutes the opening of the flue damper = u(k-1)+K _p (k) (e ₁ (k)-e ₁ (k-1))+K _i (k)e ₁ (k), acting on the hearth of the waste plastic cracking furnace.

g.在下一时刻，依照b到f中的步骤继续求解PI控制器新的参数K_p(k+1)、K_i(k+1)并依次循环。g. At the next moment, continue to solve the new parameters K _p (k+1) and K _i (k+1) of the PI controller according to the steps in b to f and cycle in turn.

Claims

1. The waste plastics cracking furnace furnace pressure control method optimized by dynamic matrix control, is characterized in that the concrete steps of this method are:

Step (1). Establish the model of the controlled object through the real-time step response data of the process object, the specific method is:

1-a. Give the controlled object a step input signal, and record the step response curve of the controlled object;

1-b. Filter the step response curve obtained in step 1-a, then fit it into a smooth curve, and record the step response data corresponding to each sampling time on the smooth curve. The first sampling time is T _s , the interval between two adjacent sampling moments is T _s , and the sequence of sampling moments is T _s , 2T _s , 3T _s ...; the step response of the controlled object will tend to be stable after a certain moment t _N =NT _s , when a _i , i>N, and the error and measurement error of a _N have the same order of magnitude, it can be considered that a _N is approximately equal to the steady-state value of the step response; the model vector a of the object is established:

a＝[a ₁ ,a ₂ ,…a _N ] ^T

where T is the transpose symbol of the matrix, and N is the modeling time domain;

Step (2). Design the PI controller of the controlled object, the specific method is:

2-a. Utilize the model vector a obtained above to establish the dynamic matrix of the controlled object, its form is as follows:

A A = = (\begin{matrix} {a a}_{11} & 00 & ... ... & 00 \\ {a a}_{22} & {a a}_{11} & ... ... & 00 \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ {a a}_{P P} & {a a}_{P P - - 11} & ... ... & {a a}_{P P - - M m + + 11} \end{matrix})

Among them, A is the P×M order dynamic matrix of the controlled object, a _i is the data of the step response, P is the optimization time domain of the dynamic matrix control algorithm, M is the control time domain of the dynamic matrix control algorithm, M<P<N;

2-b. Establish the model to predict the initial response value y _M (k) of the controlled object at the current moment k

First get the model prediction value y _p (k-1) after adding the control increment Δu(k-1) at time k-1:

y _P (k-1)=y _M (k-1)+A ₀ Δu(k-1)

in,

{y the y}_{P P} ((k k - - 11)) = = [\begin{matrix} {y the y}_{11} ((k k | | k k - - 11)) \\ {y the y}_{11} ((k k + + 11 | | k k - - 11)) \\ . . \\ . . \\ . . \\ {y the y}_{11} ((k k + + N N - - 11 | | k k - - 11)) \end{matrix}],, {A A}_{00} = = [\begin{matrix} {a a}_{11} \\ {a a}_{22} \\ . . \\ . . \\ . . \\ {a a}_{N N} \end{matrix}],, {y the y}_{M m} ((k k)) = = [\begin{matrix} {y the y}_{00} ((k k | | k k - - 11)) \\ {y the y}_{00} ((k k + + 11 | | k k - - 11)) \\ . . \\ . . \\ . . \\ {y the y}_{00} ((k k + + N N - - 11 | | k k - - 11)) \end{matrix}]

y ₁ (k|k-1), y ₁ (k+1|k-1),…, y ₁ (k+N-1|k-1) represent the controlled object’s response to k, k+1,...,k+N-1 time adding control increment Δu(k-1) model prediction value, y ₀ (k|k-1), y ₀ (k|k-1),...y ₀ (k+N-1|k-1) represents the initial prediction value of time k-1 for k, k+1,...,k+N-1 time, A ₀ is the matrix established by the step response data, Δu( k-1) is the input control increment at time k-1;

Then get the model prediction error value e(k) of the controlled object at time k:

e(k)=y(k)-y ₁ (k|k-1)

Among them, y(k) represents the actual output value of the controlled object measured at k moment;

Further obtain the corrected value y _cor (k) of the model output at time k:

y _cor (k)=y _M (k-1)+h*e(k)

in,

{y the y}_{c c o o r r} ((r r)) = = [\begin{matrix} {y the y}_{c c o o r r} ((k k | | k k)) \\ {y the y}_{c c o o r r} ((k k + + 11 | | k k)) \\ . . \\ . . \\ . . \\ {y the y}_{c c o o r r} ((k k + + N N - - 11 | | k k)) \end{matrix}],, h h = = [\begin{matrix} 11 \\ α α \\ . . \\ . . \\ . . \\ α α \end{matrix}]

y _cor (k|k), y _cor (k+1|k),...y _cor (k+N-1|k) represent the correction value of the model of the controlled object at time k respectively, and h is the weight matrix of error compensation , α is the error correction coefficient;

Finally, the initial response value y _M (k) predicted by the model at time k is obtained:

y _M (k) = Sy _cor (k)

Among them, S is the state transition matrix of order N×N,

2-c. Calculate the predicted output value y _PM of the controlled object under M continuous control increments Δu(k),...,Δu(k+M-1), the specific method is:

y _PM (k) = y _p0 (k) + AΔu _M (k)

{y the y}_{P P M m} ((k k)) = = [\begin{matrix} {y the y}_{M m} ((k k + + 11 | | k k)) \\ {y the y}_{M m} ((k k + + 22 | | k k)) \\ . . \\ . . \\ . . \\ {y the y}_{M m} ((k k + + P P | | k k)) \end{matrix}],, {y the y}_{P P 00} ((k k)) = = [\begin{matrix} {y the y}_{00} ((k k + + 11 | | k k)) \\ {y the y}_{00} ((k k + + 22 | | k k)) \\ . . \\ . . \\ . . \\ {y the y}_{00} ((k k + + P P | | k k)) \end{matrix}],, {Δu Δu}_{M m} ((k k)) = = [\begin{matrix} Δ Δ u u ((k k)) \\ Δ Δ u u ((k k + + 11)) \\ . . \\ . . \\ . . \\ Δ Δ u u ((k k + + M m - - 11)) \end{matrix}]

Among them, y _P0 (k) is the first P item of y _M (k), y _M (k+1|k), y _M (k+2|k),...,y _M (k+P|k) are The output value of the model prediction at k time to k+1, k+2,..., k+P time;

2-d. Let the control time domain of the controlled object M=1, select the objective function J(k) of the controlled object, the form is as follows:

minJ(k)=Q(ref(k)-y _PM (k)) ² +rΔu ² (k)=Q(ref(k)-y _P0 (k)-AΔu(k)) ² +rΔu ² (k )

ref(k)=[ref ₁ (k), ref ₂ (k),...,ref _P (k)] ^T

ref _i (k)=β ⁱ y(k)+(1-β ⁱ )c(k),Q=diag(q ₁ ,q ₂ ,…,q _P )

Among them, Q is the error weighting matrix, q ₁ , q ₂ ,...,q _P is the parameter value of the weighting matrix; β is the softening coefficient, c(k) is the set value; r=diag(r ₁ ,r ₂ , …r _M ) is the control weighting matrix, r ₁ , r ₂ ,…r _M are the parameters of the control weighting matrix, ref(k) is the reference trajectory of the system, ref _i (k) is the i-th reference point in the reference trajectory value;

2-e. Transform the control variable u(k):

u(k)=u(k-1)+K _p (k)(e ₁ (k)-e ₁ (k-1))+K _i (k)e ₁ (k)

e(k)=c(k)-y(k)

Substituting u(k) into the objective function in step 2-d to solve the parameters in the PI controller:

u(k)=u(k-1)+w(k) ^T E(k)

w(k)=[w ₁ (k),w ₂ (k)] ^T

w ₁ (k)=K _p (k)+K _i (k), w ₂ (k)=-K _p (k)

E(k)＝[e ₁ (k),e ₁ (k-1)] ^T

Among them, Kp(k) and K _i (k) are the proportional and differential parameters of the PI controller at time k, e ₁ (k) is the error between the reference trajectory value and the actual output value at time k, and T is the rotation of the matrix set symbol;

Combining the above formulas, we can get:

w w ((k k)) = = \frac{{((r r e e f f ((k k)) - - {y the y}_{P P O o} ((k k))))}^{T T} Q Q A A E E. ((k k))}{(({A A}^{T T} Q Q A A + + r r)) {((E E. ((k k))))}^{T T} E E. ((k k))}

Further can get:

K _p (k) = -w ₂ (k)

K _i (k) = w ₁ (k) - K _P (k)

2-f. After obtaining the parameters K _p (k) and K _i (k) of the PI controller, the control quantity u(k) is formed to act on the controlled object, u(k)=u(k-1)+K _p (k )(e ₁ (k)-e ₁ (k-1))+K _i (k)e ₁ (k);

2-h. At the next moment, follow the steps in 2-b to 2-f to continue to solve the values of the new parameters k _P (k+1) and _ki (k+1) of the PI controller, and cycle in turn.