The Design of 2DOF IMC-PID Controller in Biochemical Reaction Networks

Abstract

DNA molecules can be adopted to design biomolecular control circuits that can effectively control biochemical reaction processes. However, the leak reaction in actual biochemical reactions causes a significant uncertainty for reactions. In this paper, the first-order time-delay system is selected as the controlled object. A two-degree-of-freedom internal model PID controller (2DOF IMC-PID) is constructed for the first time within the framework of chemical reaction networks (CRNs). Under this control strategy, the set-point tracking and disturbance suppression are tuned with individual controllers, respectively. The controller parameters are determined by two filtering parameters that affect the controller’s performance, so the parameter tuning is simpler and more targeted. Then, the 2DOF IMC-PID controller is implemented in DSD reaction networks, with less overshoot in the 2DOF IMC-PID control system than the traditional PID control system and the 2DOF PID control system. Finally, a 2DOF IMC-PID division gate control system is established to effectively inhibit the impacts of leak reactions on the computation results. Although the leak reaction occurs at the division gate, the ideal output can be produced by the 2DOF IMC-PID division gate control system.

Disturbance Observer-Based PID Control System Using DNA Strand Displacement and Its Application in Exponential Gate

“…The integral element 𝑥 = 𝑘 𝛿 and the integral element 𝑥̇ = 𝑘 𝛿 are expressed in ( 26)- (27). The summing process of 𝑥 and 𝑥 is expressed by (28). The integral element 𝑥 = 𝑘 𝑒 and the integral element 𝑥̇ = −𝑘 𝑥 +𝑘 𝑦 are expressed in ( 29)- (30).…”

“…The data in detail are displayed in Table X. For the purpose of proving the superiority of the FDOB-PID control system even more, the PID [16] , the 2DOF-PID [17] , and the IMC-PID [28] are selected as the comparison objects. The controlled objects are 𝐺 (𝑠) of (41) listed in Table V.…”

“…Yuan et al [26] proposed a CRNs-based state feedback control and Romberg observer, then completed the transformation of the space state equation into a molecular controller. Li Y et al [28] built a 2DOF-IMC through CRNs, which solved the time-delay problem in the controlled object.…”

Cascade PID Control Systems Based on DNA Strand Displacement With Application in Polarization of Tumor-Associated Macrophages

“…DNA strand displacement (DSD) reactions [12,13] with programmability are taken into account for realizing the CRNbased control systems. In recent years, an increasing number of control systems based on DNA strand displacement have been developed, such as PI [8], PID [10], [11], state feedback [10], [14], static pre-filters [14], and two-degree-of-freedom (2-DOF) PID control systems [15], [16]. First, Oishi et al [8] proposed the DSD design strategies for three fundamental chemical reactions (i.e., catalytic, degradation, and annihilation reactions) that make up the CRN of PI control systems.…”

A Theoretical Framework for Implementable Nucleic Acids Feedback Systems

“…By making such an abstraction, this approach enables the representation of gains and negative signals using positive quantities that are essential for error computation in a negative feedback control system. The dual-rail representation and implementations for elementary catalysis, degradation and annihilation reactions provide a systematic framework to convert control theory into biochemistry, which can be implemented with synthetic DNA oligonucleotides, where the representation of transfer functions [ 11 ], linear feedback systems [ 12 , 13 , 14 , 15 , 16 , 17 ], and nonlinear controllers [ 18 , 19 , 20 ] can be realised through the assembly of DSD networks.…”