Estimation of multiply digital process control system extractive distillation stability

An approach to stability analysis of digital control systems associated non-stationary object on the example of the rectification process. Object modeling with cross-connections and the control scheme of the described system, discrete transfer functions in the shift operators. The equations of connection for each output of the closed-loop system. To solve this problem developed an algorithm for estimating the margin of stability of multivariable digital control systems based on the discrete root criterion, comprising the following main stages: obtaining of the characteristic polynomial of the closed-loop system for each output; computation of eigenvalues of the system matrix in the state space to determine roots of the characteristic equation and the stability of the system; determination of the stability and margin of stability by the deviation of maximum module of the root from the boundary of the high variability. To obtain the characteristic polynomial of a as discrete models of controllers and channels of IP object-use the transfer function of the first order with transport delay. The simulation was performed at different parameters of the control object, which is characterized by a stable and an unstable state of the system. VA-den analysis of the numerical values of the roots and character of their location on the complex plane, which to you-water that the system is stable or unstable. To confirm the obtained results were calculated and presented dynamic characteristics of the closed-loop system under different conditions, which confirm the initial assessment, the root criterion. To determine the factor stability of multivariable digital systems is proposed to use the deviation of the maximum root of the characteristic equation from the stability boundary. The obtained results apply to the class of symmetric multivariable control objects. The approach to assessing the sustainability of multivariable system regulation can be effectively used in automatic mode during the synthesis of robust control systems multidimensional technological objects.