Mathematical modeling and partial feedback linearization control of a constrained and underactuated space tether

Abstract

This paper investigates the application of the nonlinear control technique called collocated partial feedback linearization to the position and stretching control of a planar underactuated mechanical system. This system is designed to emulate under certain conditions the behavior of a space tether connected to one mass (representing a satellite) at each of its extremities. The flexible cable is approximated by two rigid bodies (thin rods) with springs and dampers attached to represent the cable stiffness and structural damping. The control objective is to move both satellites to its desired positions and to guarantee that on the final configuration the tether is completely stretched. The stability of the closed-loop system is verified and it is proved that the system has global asymptotic stability. The performance of the proposed nonlinear control technique is analyzed via numerical simulations for two cases: one case considering three different values for the damping coefficients and one case considering three different values for the stiffness coefficients. The simulation results show that the collocated partial feedback linearization plus a proportional-derivative control is able to move the satellites to the desired positions and to keep the cable stretched.

A two‐level hybrid control strategy to augment transient stability and tracking accuracy of hybrid microgrid coupled with industrial loads

“…The second step deals with the transformation of non-linear co-ordination to form the partial feedback law whereas the last part makes the PFLC through the using of partial feedback law. The required definitions and details of these steps have been discussed in [37,38]. Now, applying the Lie derivative, we can derive the following inequality for the f j (x j ) and g j (x j ) with respect to the output DC bus voltage V d bus ,…”

“…The second step deals with the transformation of non‐linear co‐ordination to form the partial feedback law whereas the last part makes the PFLC through the using of partial feedback law. The required definitions and details of these steps have been discussed in [37, 38]. Now, applying the Lie derivative, we can derive the following inequality for the $$f_j(x_j)$$ and $$g_j(x_j)$$ with respect to the output DC bus voltage $$V_{d_{bus}}$$, $$$$\begin{equation} \def\eqcellsep{&}\begin{array}{cc}\dot{V}_{d_{bus}} = L _ { f } V_{d_{bus}} + L _ { g } V_{d_{bus}}K_m \end{array} .$$…”