A survey of applications of second-order sliding mode control to mechanical systems.

*(English)*Zbl 1070.93011The second-order sliding mode control of mechanical systems (SMC) is very effective in the presence of uncertainties which take place in the real plant behavior. The main idea of SMC techniques is that of designing a sliding surface to which the controlled system trajectories must belong. The sliding behavior is insensitive to model uncertainties and disturbances and has the robustness property. But real-life SMC implementation technique presents a drawback due to finite switching frequency of real control devices. The high-frequency components of the control may excite parasitic resonant modes which may be either stable or unstable and can produce chattering phenomena which have high frequency and make the state trajectories rapidly oscillating about the sliding manifold. This leads to rapidly changing control actions and can induce fatigue in mechanical parts and the system could be damaged in a short time. To avoid chattering in a control system, filters are included at the input side so as to obtain a system in which the actual control and its derivatives appear explicitly. The suggested method is based on the well-known fact that in a complex mechanical system, as a rule, only one mode dominates. So the equivalent system of differential equations may be reduced to one equation of second order, i.e., the initial system may be greatly simplified. As examples, the authors consider overhead container cranes, the position control of a pantograph mechanical system in the presence of Coulomb friction, and a constrained manipulator. Simulations and/or experiments are given for each of the considered problems. In the solution of such underactuated problems the Lyapunov stability technique may be very effective.

Reviewer: Yuri N. Sankin (Ul’yanovsk)