In this chapter we present experimental results on two experimental mechanical systems They illustrate the applicability of the methodologies exposed in the foregoing chapters. The first concerns flexible-joint manipulators, whose dynamics and control have been thoroughly explained. The second one focuses on an underactuated system, the inverted pendulum, which does not fall into the classes of mechanical systems presented so far. The state feedback control problem of flexible joint manipulators has constituted an interesting challenge in the Systems and Control and in the Robotics scientific communities. It was motivated by practical problems encountered for instance in industrial robots equipped with harmonic drives, that may decrease the tracking performances, or even sometimes destabilize the closed-loop system. Moreover as we pointed out in the previous chapter, it represented a pure academic problem, due to the particular structure of the model. From a historical point of view, the main directions that have been followed to solve the tracking and adaptive control problems have been: Singular Perturbation techniques (the stability results then require a high enough stiffness value at the joints so that the stability theoretical results make sense in practice)  , and nonlinear global tracking controllers derived from design tools such as the backstepping or the passivity-based techniques. We have described these last two families of schemes in the previous chapter, see sections 6.4, 6.4.2. In this section we aim at illustrating on two laboratory processes how these schemes work in practice and whether they bring significant performance improvement with respect to PD and the Slotine and Li controllers (which both can be cast into the passivity-based schemes, but do not a priori incorporate flexibility effects in their design).
KeywordsLyapunov Function Tracking Error Homoclinic Orbit Feedback Gain Inverted Pendulum
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