Dynamic control of the space tethered system

We discuss the problem of simultaneous dynamical stabilization and suppression of transverse and longitudinal vibrations of the space tethered system deployed along a certain trajectory. The dynamics of the system is described by a system of nonlinear partial differential equations for the longitudinal and transverse waves and we consider a non-classical version of the problem with one moving boundary. We formulate a mathematical model and perform the analytic and numerical analysis of the boundary control problem based on the Lyapunov method. A scheme of the deployment mechanism is suggested. It includes a control torque and transverse displacement of the boundary and ensures stable deployment of the whole system. •Boundary control of transverse and longitudinal vibrations.•Suppression of vibrations, asymptotic stability of the tethered system's deployment.•Efficient mechanism for stable deployment.•Dynamics of the tether is described by PDEs.•Numerical calculations prove asymptotic stability of the deployment process.