The nonlinearity and non-separability of the antithetic PID (aPID) controller have provided greater flexibility in the design of biochemical reaction networks (BCRNs), resulting in significant impacts on biocontrol-systems. Nevertheless, the dilution of control species is disregarded in designs of aPID controllers, which would lead to the failure of inhibition mechanism in the controller and loss of robust perfect adaptation (RPA)—the biological counterpart of robust steady-state tracking. Here, the impact of dilution processes on the structure of aPID is investigated in this study. It is discovered that the proportional and low-pass filters are altered when the dilution processes is present in control species, which increases the coupling between the controller parameters. Moreover, additional integrations for the reference signal and control output generated by control species dilution further leads to the loss of RPA. Subsequently, a novel aPID controller represented by BCRNs, termed quasi-aPID, has been designed to eliminate the detrimental effects of the dilution processes. In an effort to ameliorate the interdependencies among controller parameters, a degradation inhibition mechanism is employed within this controller. Furthermore, this work establishes the limiting relationship between the controller’s reaction rates in order to guarantee RPA, while abstaining from the introduction of supplementary species and biochemical reactions. By using the quasi-aPID controller in both the Escherichia coli gene expression model and the whole-body cholesterol metabolism model, its effectiveness is confirmed. Simulation results demonstrate that, the quasi-aPID exhibits a smaller absolute steady-state error in both models and guarantees the RPA property.

中文翻译：

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物种稀释对立比例积分微分生物防治系统的分析与设计

对立 PID (aPID) 控制器的非线性和不可分离性为生化反应网络 (BCRN) 的设计提供了更大的灵活性，从而对生物控制系统产生重大影响。然而，aPID控制器的设计中忽略了控制物种的稀释，这将导致控制器中抑制机制的失败以及鲁棒完美适应（RPA）的丧失——鲁棒稳态跟踪的生物学对应物。本研究研究了稀释过程对 aPID 结构的影响。研究发现，当控制物质中存在稀释过程时，比例滤波器和低通滤波器会发生改变，这增加了控制器参数之间的耦合。此外，参考信号和控制物质稀释产生的控制输出的额外积分进一步导致 RPA 的损失。随后，一种以 BCRN 为代表的新型 aPID 控制器（称为准 aPID）被设计来消除稀释过程的有害影响。为了改善控制器参数之间的相互依赖性，在该控制器内采用了退化抑制机制。此外，这项工作建立了控制器反应速率之间的限制关系，以保证 RPA，同时避免引入补充物种和生化反应。通过在大肠杆菌基因表达模型和全身胆固醇代谢模型中使用准aPID控制器，证实了其有效性。仿真结果表明，准aPID在两个模型中都表现出较小的绝对稳态误差，并保证了RPA性能。