Closed-loop control of active nematic flows

TL;DR

This paper tackles the challenge of steering chaotic, non-equilibrium dynamics in active matter by implementing a real-time feedback loop that modulates light intensity to control a 2D active nematic powered by light-sensitive kinesin motors. A minimal linear model incorporating motor-binding dynamics and a PI control law links input light to spatially averaged speed through $v = \langle |\mathbf{v}(\mathbf{x},t)| \rangle_{\mathbf{x}}$, enabling quantitative agreement with full nematohydrodynamic simulations. Key findings show that proportional control can cause droop and, at higher gains, induce oscillations due to intrinsic motor timescales, while adding integral action eliminates droop and stabilizes the mean speed; fluctuations exhibit controlled-resolution PSD features consistent with theory. The results establish feedback control as a viable route for robust, programmable active matter and point to future advances in designing responsive, life-like materials with adaptive dynamics.

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.

Figures (5)

• Figure 1: Integration of hardware, wetware and software into control system (A.) We introduce control through the time-varying application of uniform light to a microtubule-based active nematic which is driven by light-sensitive kinesin motors. (B.) The system state is measured through video microscopy. Optical flow analysis generates a vector field of the flow, which is reduced to a scalar magnitude. (C.) A standard proportional-integral control algorithm is applied to adjust the applied light.
• Figure 2: Feedback control dynamics adjusts the applied light to regulate active nematic speed (A.) Trajectory of PI controlled nematic (black circles) and uncontrolled nematic (red circles) with target speed of 1.04µms. (B.) Time series demonstrating speed oscillations in PI controlled nematic (C.) Histogram of the active nematic speed for PI controlled (black) and uncontrolled nematic (red). Mean speed $\pm$ standard distribution are 1.04 ± 0.05µms for PI controlled nematic and 0.97 ± 0.23µms for uncontrolled nematic. (D.) Applied light over time for controlled (gray) and uncontrolled (blue) systems. The controller algorithmically determines the appropriate applied light to follow the desired speed profile (solid line, black)
• Figure 3: Varying PI control parameters exhibits expected behavior (A.) Response of system with varied $K_{P}$ with a set speed of 1.3µms. (B.) Steady state droop as a function of proportional gain matches theoretical predictions. (C.) Response of system at set speed of 1.3µms with varied integral gain terms. (D.) Steady state droop disappears when the integral term is used.
• Figure 4: Changing control gains impacts the power spectra of fluctuations in the mean speed $v$. Top row are experimental observations and bottom row are theoretical predictions from Eqn. \ref{['eq:PSD']}. (A,D) shows the emergence of oscillatory fluctuations for proportional-only control at large gains in both experimenta and model, (B,E) Introduces a small amount of integral gain, which results in non-monontic behavior as $K_{\text{p}}^*$ is varied, and (C,F)
• Figure 5: Comparison between experimental and theoretically-predicted phase diagram (using $\tau_m=10$s and $\tau_v=250$s) as a function of scaled gains $K_{\text{p}}^*,K_{\text{i}}^*$. Data point symbols indicate oscillatory (magenta circles) or purely exponentially decaying auto-correlation functions (cyan squares), see supplementary information for details ESI. The cyan line demarcates the theoretical boundary between underdamped and overdamped regimes with contours indicating the frequency of oscillations.