Sliding mode rest-to-rest stabilization and trajectory tracking for a discretized flexible joint manipulator (Q1577521)

This paper considers a discretized model of the dynamics of a single-link flexible joint robotic manipulator in the form \[ \begin{cases} x_{1,k+1}= x_{1,k}+ ax_{2,k},\\ x_{2,k+1}= x_{2,k}+ b\sin x_{1,k}- c(x_{1,k}- x_{3,k}),\\ x_{3,k+1}= x_{3,k}+ ax_{4,k},\\ x_{4,k+1}= x_{4,k}+ d(x_{1,k}- x_{3,k})+ eu_k,\end{cases}\tag{\(*\)} \] where \(x_1\), \(x_2\), \(x_3\), \(x_4\) denote link and motor angular positions and velocities, \(u\) represents a control torque, \(a\)-\(e\) are parameters of the model. It is observed that the system \((*)\) is difference flat, and a corresponding trajectory tracking algorithm is derived. Alternatively, a sliding mode controller is proposed for the feedback linearized system \((*)\). The performance of the control algorithm has been illustrated with computer simulations. Since on one hand the model considered in the paper is very simple, and the much more general continuous-time case has been treated within the differential flatness paradigm, and on the other hand a sliding mode control following a feedback linearization clearly loses the inherent robustness of the sliding mode approach, the reviewer is unable to unveil a contribution in this publication.