Proportional-Integral-Derivative Control of Four-Variable Chaotic Oscillatory Circuit Based on DNA Strand Displacement

DNA molecular computing based on DNA strand displacement (DSD) technology is a potential computing model. Different functions can be realized by constructing DNA strand displacement analog circuit and analyzing its dynamic characteristics. In this paper, exploiting chemical reaction networks (CRNs) as the middle layer, a new chaotic oscillation circuit is constructed via DNA strand displacement and controlled by PID controller. The design of four-variable chaotic oscillatory circuit requires the combination and cascade by five DNA reaction modules. Based on the theory of stability and design principle of controller, the proportion terms, integration terms, and differentiation terms are added to chaotic oscillatory circuit for implementing PID controller. PID controller is implemented by five DNA reaction modules to stabilize the chaotic oscillation circuit. The validity of reaction modules circuit with their corresponding DSD reaction modules and controller is verified by visual DSD and Matlab. The PID controller may have better performance than PI controller, and it is an extension of PI controller.