Disturbance decoupling for biological fermentation systems with single input single output

The biological fermentation process has the characteristics of nonlinearity and multivariable coupling. To improve the performance of decoupling control in the fermentation process, a disturbance decoupling control based on the Lie symmetry method is proposed to obtain the analytical feedback control for a class of biological fermentation systems with single input single output (SISO). Firstly, the state-space equations and the disturbance decoupling model for a class of SISO biological fermentation systems are defined; Secondly, the key technologies and algorithm approaches of Lie symmetry theory for differential equations are introduced, and the conditions and the properties of Lie symmetry for nonlinear control systems under group action are given in detail; Finally, the derived distribution of Lie symmetric infinitesimal generators is used to prove the sufficient conditions for local disturbance decoupling in the system, and the closed-loop state feedback analytical law of the system is constructed. The proposed control method is applied to the disturbance decoupling control of mycelium concentration and substrate concentration in the biological fermentation process. Numerical simulation results show that the proposed control method can effectively improve the system decoupling control performance. Meanwhile, using Lie symmetry, the cascade decoupling standard form and the static state feedback law of biological fermentation systems can be constructed.