[发明专利]一种焦化炉炉膛压力系统稳定切换控制器设计方法

摘要

本发明公开了一种焦化炉炉膛压力系统稳定切换控制器设计方法。本发明通过数据采集、模型建立、优化等手段，确立了一种焦化炉炉膛压力稳定切换控制器设计方法，利用该方法可以有效解决系统切换造成的不稳定性难题，保证系统稳定的前提下具有良好的控制效果。

主权项

一种焦化炉炉膛压力系统稳定切换控制器设计方法，其特征在于该方法包括以下步骤：步骤1、建立焦化炉炉膛压力的状态空间模型，具体是：步骤1.1首先采集焦化炉炉膛压力的输入输出数据，利用该数据建立焦化炉炉膛压力的状态空间模型，形式如下：$\stackrel{\&CenterDot;}{x}\left(t\right)=A_{\mathrm{\&sigma;}\left(t\right)}x\left(t\right)+B_{\mathrm{\&sigma;}\left(t\right)}{u}_{\mathrm{\&sigma;}\left(t\right)}\left(t\right)$y(t)＝C_σ(t)x(t)其中，x(t)为焦化炉系统状态，y(t)为焦化炉输出压力，u_σ(t)(t)为控制挡板开度，σ(t)为切换信号表示从[0,∞)到有限集S＝{1,2,…,N}的映射，A_σ(t)为Metzler矩阵，对于每个σ(t)∈S有，B_σ(t)≥0,C_σ(t)≥0；步骤2、设计焦化炉炉膛压力的状态反馈控制器，具体是：步骤2.1设计切换信号σ(t)且0≤t₁≤t₂，满足如下条件：N_σ(t₂,t₁)≤N₀+(t₂‑t₁)/τ^*其中，N_σ(t₂,t₁)为切换系统在(t₁,t₂)内的切换次数,τ^*>0为切换信号的平均驻留时间，N₀≥0；步骤2.2设计A_p+B_pK_pC_p,p∈SMetzler矩阵，K_p为增益，切换序列为0≤t₀<t₁<t₂<…，t∈[t_k,t_k+1),k∈N在t∈[t_k,t_k+1)设计李雅普诺夫函数和其导数为：V_i＝x^Tv⁽ⁱ⁾,i∈S${\stackrel{\&CenterDot;}{V}}_{\mathrm{\&sigma;}\left(t_k\right)}\left(x\right(t\left)\right)=x^T{A}_{\mathrm{\&sigma;}\left(t_k\right)}^T{v}^{\left(\mathrm{\&sigma;}\right(t_k\left)\right)}+u_{\mathrm{\&sigma;}\left(t_k\right)}^T{B}_{\mathrm{\&sigma;}\left(t_k\right)}^T{v}^{\left(\mathrm{\&sigma;}\right(t_k\left)\right)},t\&Element;\&lsqb;t_k,t_{k+1})$步骤2.3设计常数ρ>0，λ>1，和向量v^(p)∈Rⁿ，v^(q)∈Rⁿ，z^(p)∈R^s使其满足如下条件：$(A_p^T+{\mathrm{\&rho;I}}_n)v^{\left(p\right)}+z^{\left(p\right)}\&lt;0$v^(p)＞0v^(p)≤λv^(q)其中，是给定的非零向量，且在平均驻留时间满足步骤2.4设计加热炉炉膛压力系统的平衡点在适当切换信号σ(t)下是全局一致指数稳定，对任意初始状态x(t₀)，设计常数α和β使其系统状态响应满足如下条件：$\left|\right|x\left(t\right)\left|\right|\&le;{\mathrm{\&alpha;e}}^{-\mathrm{\&beta;}(t-t_0)}\left|\right|x\left(t_0\right)\left|\right|$$\mathrm{\&alpha;}=\frac{\sqrt{n}\stackrel{\&OverBar;}{\mathrm{\&mu;}}\left(v^{\left(\mathrm{\&sigma;}\right(t_0\left)\right)}\right)}{\underset{\&OverBar;}{\mathrm{\&mu;}}\left(v^{\left(\mathrm{\&sigma;}\right(t_k\left)\right)}\right)}{\mathrm{\&alpha;}}^{\&prime;}$其中，步骤2.5由步骤2.4可将上式转化为：$x^T\left(t\right)v^{\left(\mathrm{\&sigma;}\left(t_k\right)\right)}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i\left(t\right){v_i}^{\left(\mathrm{\&sigma;}\left(t_k\right)\right)}\&GreaterEqual;\underset{\&OverBar;}{\mathrm{\&mu;}}\left(v^{\left(\mathrm{\&sigma;}\left(t_k\right)\right)}\right)\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i\left(t\right)\&GreaterEqual;\underset{\&OverBar;}{\mathrm{\&mu;}}\left(v^{\left(\mathrm{\&sigma;}\left(t_k\right)\right)}\right)\left|\right|x\left(t\right)\left|\right|$$x^T\left(t_0\right)v^{\left(\mathrm{\&sigma;}\left(t_0\right)\right)}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i\left(t_0\right){v_i}^{\left(\mathrm{\&sigma;}\left(t_0\right)\right)}\&le;\stackrel{\&OverBar;}{\mathrm{\&mu;}}\left(v^{\left(\mathrm{\&sigma;}\left(t_0\right)\right)}\right)\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i\left(t_0\right)\&le;\stackrel{\&OverBar;}{\mathrm{\&mu;}}\left(v^{\left(\mathrm{\&sigma;}\left(t_0\right)\right)}\right)\left|\right|x\left(t\right)\left|\right|$步骤2.6依据步骤2.4和2.5可得如下不等式：$x^T\left(t\right)v^{\left(\mathrm{\&sigma;}\right(t_k\left)\right)}\&le;{\mathrm{\&alpha;}}^{\&prime;}{e}^{-\mathrm{\&beta;}(t-t_0)}{x}^T\left(t_0\right)v^{\left(\mathrm{\&sigma;}\right(t_0\left)\right)}$再结合步骤2.3，进一步可以转化为：$\begin{array}{c}{V}_{\mathrm{\&sigma;}\left(t_k\right)}\left(x\right(t\left)\right)\&le;e^{N_{\mathrm{\&sigma;}}ln\mathrm{\&lambda;}}{e}^{-\mathrm{\&rho;}\left(t-t_0\right)}{V}_{\mathrm{\&sigma;}\left(t_k\right)}\left(x\right(t_0\left)\right)\\ \&le;e^{\left(N_0+\frac{t-t}{{\mathrm{\&tau;}}^{*}}\right)ln\mathrm{\&lambda;}}{e}^{-\mathrm{\&rho;}\left(t-t_0\right)}{V}_{\mathrm{\&sigma;}\left(t_0\right)}\left(x\right(t_0\left)\right)\\ \&le;{\mathrm{\&alpha;}}^{\&prime;}{e}^{-\mathrm{\&beta;}\left(t-t_0\right)}{V}_{\mathrm{\&sigma;}\left(t_k\right)}\left(x\right(t_0\left)\right)\end{array}$步骤2.7依据步骤2.3最后一个不等式，可得如下形式：$V_{\mathrm{\&sigma;}\left(t_k\right)}\left(x\right(t\left)\right)\&le;{\mathrm{\&lambda;e}}^{-\mathrm{\&rho;}(t-t_k)}{V}_{\mathrm{\&sigma;}\left(t_{k-1}\right)}\left(x\right(t_k\left)\right)\&le;...\&le;{\mathrm{\&lambda;}}^k{e}^{-\mathrm{\&rho;}(t-t_0)}{V}_{\mathrm{\&sigma;}\left(t_0\right)}\left(x\right(t_0\left)\right)$进一步转化为：$V_{\mathrm{\&sigma;}\left(t_k\right)}\left(x\right(t\left)\right)\&le;{\mathrm{\&lambda;e}}^{-\mathrm{\&rho;}(t-t_k)}{V}_{\mathrm{\&sigma;}\left(t_{k-1}\right)}\left(x\right(t_k\left)\right)$$x^T\left(t_k\right)v^{\left(\mathrm{\&sigma;}\right(t_k\left)\right)}\&le;{\mathrm{\&lambda;x}}^T\left(t_k\right)v^{\left(\mathrm{\&sigma;}\right(t_{k-1}\left)\right)}$由2.3可得：$V_{\mathrm{\&sigma;}\left(t_k\right)}\left(x\right(t\left)\right)\&le;e^{-\mathrm{\&rho;}(t-t_k)}{V}_{\mathrm{\&sigma;}\left(t_k\right)}\left(x\right(t_k\left)\right),t\&Element;\&lsqb;t_k,t_{k+1})$对以上不等式求导得到：${\stackrel{\&CenterDot;}{V}}_{\mathrm{\&sigma;}\left(t_k\right)}\left(x\right(t\left)\right)\&le;-{\mathrm{\&rho;x}}^T{v}^{\left(\mathrm{\&sigma;}\right(t_k\left)\right)}\&le;-{\mathrm{\&rho;V}}_{\mathrm{\&sigma;}\left(t_k\right)}$再结合2.3可得：${\stackrel{\&CenterDot;}{V}}_{\mathrm{\&sigma;}\left(t_k\right)}\left(x\right(t\left)\right)=x^T(A_{\mathrm{\&sigma;}\left(t_k\right)}^T{v}^{\left(\mathrm{\&sigma;}\right(t_k\left)\right)}+z^{\left(\mathrm{\&sigma;}\right(t_k\left)\right)})$步骤2.8综合步骤2.2到步骤2.7可以得到的焦化炉炉膛压力状态反馈控制量，形式如下：$u_p\left(t\right)=K_{p}x\left(t\right)=\frac{1}{{\stackrel{\&OverBar;}{v}}^{\left(p\right)T}{B}_p^T{v}^{\left(p\right)}}{\stackrel{\&OverBar;}{v}}^{\left(p\right)}{z}^{\left(p\right)T}x\left(t\right).$