Stability And Control Of A Tethered Mass System

Cables are widely used in various engineering fields, such as civil engineering, electric communication engineering and space engineering. The objective of this study is to develop LQR controllers for a tethered mass system.A dynamical model is derived, which makes three kinds of motion (translation, load hoisting or lowering, rotation) simultaneously. A set of non-linear differential equation of this model is formulated based on Lagrange's Equation. The tension of the cable, the control force of translation and the control torque of rotation are obtained by the method of Newton's Laws in vector space.The tethered mass system is modeled as a spherical pendulum. The motion of in-plane and out-plane are coupled each other. The existence of nonlinearities and symmetry between the dynamics of the in-plane and out-plane directions produce energy exchange between the two modes. The frequencies of translational actuation influence the stability of the tethered mass system. When the frequencies approach the natural frequency of the system, the period of energy exchange decreases and the amplitude of the pendulum increase. When the frequencies equal to the natural frequency of the system, resonance appears. The cable been lowered leads to asymptotic stability of the system. Oppositely, the system is unstable if the cable been hoisted. It is interesting when the system slew uniformly, chaotic motion presents. The equation of motion is linearized near the equilibrium position of the tethered mass system. Then the LQR controllers are developed to control translation and rotation of the system separately. These controllers demonstrate effective performances by numerical simulations. The simulations also indicate that the system track the reference trajectories well under the control of trajectory track control laws. In the end, an experimental apparatus for tethered mass system is utilized to...