PD-Based ADRC using time-varying gains: An Application to Microalgal-based bioprocess

Microalgae cultivation has gained significant attention in recent years due to its potential applications in various fields. However, achieving high productivity in these bioprocesses requires efficient process control. The dynamics of growth models typically comprise both known and unknown components due to mismatches between the nonlinear dynamics and their mathematical representations. Additionally, microalgal culture is subject to external disturbances. To address these issues, a classical proportional-derivative (PD) providing the feedback error, assisted by a time-varying gain extended state observer (ESO), maintaining the structure of an Active Disturbance Rejection Control (ADRC), was implemented. The formulation is aided by a time-varying gain extended state observer to avoid high-peaking estimation values. The optimal operating conditions were identified using the GEKKO Python package. The proposed controller was applied to the growth model of the microalga Isochrysis galbana, and numerical results demonstrated the effectiveness of the control strategy in eliminating steady-state error and ensuring asymptotic convergence to the optimal equilibrium despite unknown disturbances. A detailed analysis of the photobioreactor model, including stability under steady-state conditions, was also conducted. The results indicated that the model exhibits one, two, or no stable steady-state solutions when the dilution rate (D(t)) is manipulated.