Analysis of the simultaneous control of energy and actuated variable of TORA with pendulum

In this paper, as a new example of mechanical systems with underacutation degree two, we present a system called P-TORA, which is a pendulum mounted on a TORA. We study the simultaneous control of its total mechanical energy and actuated variable of such a system. We design a controller by using the energy-based control approach and we provide a global motion analysis of the system under the proposed controller. We prove that the control objective can be achieved for almost all initial conditions of the system. We validate the presented theoretical results by numerical simulation, and show that the simultaneous control can be applied to solve the swing-up and stabilizing control for the system.