A new tension control law for deployment of tethered satellites

Space Tether Deployment Control with Explicit Tension Constraint and Saturation Function

“…Under the preceding assumptions, the dynamic equation for the system reads [8,9] lθ 0 0 2l 0 θ 0 Ω 3lΩ 2 sin θ cos θ 0…”

“…The performance of the proposed controller is demonstrated through some case studies on a benchmark system with the same orbital and system parameters as used in [8,9] for comparison purposes. All the case studies are performed in MATLAB (version R2013a) using the numerical integrator ode45 with default settings.…”

“…(14) inspires one to study the stability of the proposed control law on a basis of general nonlinear theory, unlike the linearization procedures followed by [8,9]. To this end, define the scalar function Vx Ex U 1 ξ U 2 ξ with…”

“…Although effective, the heavy computational loads for numerical optimization may give rise to a great challenge for practical implementation in spacecraft due to the limited onboard computing power. The second type of approach accounts implicitly for the positive tension constraint by carefully tuning controller parameters so that the resulting tether tension is always positive [8,9]. Unfortunately, the tuning of parameters is not an easy task and is usually on a case-by-case basis for initial conditions.…”

Libration control of bare electrodynamic tether for three-dimensional deployment

“…Sun and Zhu have developed a new tension control law for the in-plane deployment on the basis of the fractional-order method and analyzed its stability [18]. As indicated from the aforementioned studies and other related research [19][20][21], pure tension control has been shown to be effective in controlling in-plane motions. However, the control problem of three-dimensional deployment is not the same case, and requires augmenting the tension control with other types of actuation, such as Lorentz force and thrust.…”