Theoretical and experimental investigation of a two-agent consensus dynamics with communication delays

Abstract

We utilize two DC motors with shaft-mounted encoders as agents of a coupled system, and both manipulate and measure the motors' velocities using Simulink graphical inter- face software and QuaRC data acquisition software. We create a mathematical model of the physical system using MATLAB's System Identification Toolbox, and design a con- trol scheme to drive the motors to a reference input. The control design calculations are facilitated by MATLAB's well-suited computational resources. We then introduce commu- nication delays into feedback pathways and show how the system stability and performance is affected as a function of the delay length. The system response is characterized through transient and steady-state regime inspection and frequency analysis. We demonstrate both that the system can be easily scaled to higher orders of complexity and that many scientific and industrial systems can be thus described and tailored with suitable control measures. Such an approach is suitable for control engineering curricula, as it gives concrete pres- ence to the abstractions of control theory and showcases practical, inexpensive methods for constructing control systems. Students can thus become familiarized with the hardware, software, wiring and physical connections which each contribute essential functionality, as well as the design of the control system itself.