Abstract
This chapter investigates whether there exists an underactuated mechanical system for which one fails to control both the total mechanical energy and actuated variable(s) to some given desired values by studying a CWA (Counter-Weighted Acrobot), which is a modified DDA with its first link having a counterweight and only its second link being actuated. By analyzing globally the solution of the closed-loop system consisted of the CWA and the controller designed via the energy-based control approach, this chapter shows that unless the CWA is linearly controllable at the upright equilibrium point, where links 1 and 2 are in the upright position, the controller fails to achieve the goal of controlling the total mechanical energy to the potential energy at the equilibrium point and controlling the actuated joint variable to zero. This chapter presents numerical simulation results to validate the theoretical results.
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