[Paper Review] Closed-loop control of active nematic flows

Katsu Nishiyama, John P. Berezney+6 more|arXiv (Cornell University)|Aug 26, 2024

Micro and Nano Robotics4 citations

TL;DR

This study demonstrates closed-loop proportional-integral (PI) feedback control of active nematic flows in a light-activated microtubule-based system, using real-time video microscopy and optical flow analysis to regulate spatially-averaged flow speed. The experimentally observed stabilization and induced oscillatory dynamics closely match predictions from a minimal coarse-grained model and nematohydrodynamic simulations, establishing PI control as a viable strategy for managing complex, non-equilibrium active matter despite intrinsic fluctuations and sample variability.

ABSTRACT

Living things enact control of non-equilibrium, dynamical structures through complex biochemical networks, accomplishing spatiotemporally-orchestrated physiological tasks such as cell division, motility, and embryogenesis. While the exact minimal mechanisms needed to replicate these behaviors using synthetic active materials are unknown, controlling the complex, often chaotic, dynamics of active materials is essential to their implementation as engineered life-like materials. Here, we demonstrate the use of external feedback control to regulate and control the spatially-averaged speed of a model active material with time-varying actuation through applied light. We systematically vary the controller parameters to analyze the steady-state flow speed and temporal fluctuations, finding the experimental results in excellent agreement with predictions from both a minimal coarse-grained model and full nematohydrodynamic simulations. Our findings demonstrate that proportional-integral control can effectively regulate the dynamics of active nematics in light of challenges posed by the constituents, such as sample aging, protein aggregation, and sample-to-sample variability. As in living things, deviations of active materials from their steady-state behavior can arise from internal processes and we quantify the important consequences of this coupling on the controlled behavior of the active nematic. Finally, the interaction between the controller and the intrinsic timescales of the active material can induce oscillatory behaviors in a regime of parameter space that qualitatively matches predictions from our model. This work underscores the potential of feedback control in manipulating the complex dynamics of active matter, paving the way for more sophisticated control strategies in the design of responsive, life-like materials.

Motivation & Objective

• To develop and implement real-time feedback control for regulating the spatially-averaged flow speed in active nematic materials.
• To investigate how controller parameters interact with intrinsic timescales of active nematics to produce stable or oscillatory dynamics.
• To assess the robustness of control under experimental challenges such as protein aggregation, sample aging, and inter-sample variability.
• To establish a quantitative link between experimental control outcomes and theoretical models of active nematic hydrodynamics.
• To explore the feasibility of using feedback control as a blueprint for future synthetic, life-like materials with embedded regulatory mechanisms.

Proposed method

• A proportional-integral (PI) control algorithm was implemented to adjust the intensity of uniform light based on real-time measurement of flow speed from video microscopy.
• Optical flow analysis extracted the vector field of flow, which was reduced to a scalar magnitude representing the spatially-averaged flow speed.
• The control law is defined as $ I = K_{\text{p}}(v_{\text{set}} - v) + K_{\text{i}} \int_0^t (v_{\text{set}} - v) dt' $, where $ I $ is the light intensity and $ K_{\text{p}}, K_{\text{i}} $ are tunable gains.
• A minimal coarse-grained model incorporating time-lagged motor dynamics was developed to predict system behavior and compare with experiments.
• Full nematohydrodynamic simulations were used to validate the model and explore the parameter space of controller-induced dynamics.
• The system's response was characterized via auto-correlation functions and power spectra to identify oscillatory behavior and transition boundaries.

Experimental results

Research questions

• RQ1 Can proportional-integral feedback control effectively regulate the average flow speed in a light-activated active nematic system despite intrinsic fluctuations and sample variability?
• RQ2 How do the controller's proportional and integral gains influence the stability and temporal dynamics of the active nematic flow?
• RQ3 What role do the intrinsic timescales of the active nematic—particularly motor dynamics—play in determining the emergence of oscillatory behavior under feedback control?
• RQ4 To what extent do experimental results match theoretical predictions from a minimal model and full hydrodynamic simulations?
• RQ5 Can feedback control induce non-trivial dynamics such as sustained oscillations in a system that is otherwise overdamped?

Key findings

• The experimental results show excellent agreement with predictions from both the minimal coarse-grained model and full nematohydrodynamic simulations, validating the theoretical framework.
• Proportional-integral control successfully stabilized the active nematic flow speed, even in the presence of sample aging, protein aggregation, and inter-sample variability.
• The system exhibited oscillatory behavior in a specific regime of controller parameters, with oscillation frequency increasing with $ K_{\text{p}}^{*} $ and $ K_{\text{i}}^{*} $, matching theoretical predictions.
• A tradeoff was observed between intrinsic fluctuations and controller penalty: low $ K_{\text{p}}^{*} $ reduced fluctuations, while high $ K_{\text{p}}^{*} $ increased them but also enhanced suppression via feedback.
• The model required inclusion of a time-lag in motor dynamics to accurately reproduce experimental behavior, especially when $ K_{\text{i}}^{*} = 0 $.
• The phase diagram of control-induced oscillations showed good qualitative agreement between experiment and theory, with the theoretical boundary between overdamped and oscillatory regimes closely matching experimental observations.