Comparison of Methods for Tracking Control of Nonlinear Uncertain Multi-Body Mechanical Systems

This paper presents a comparison of several alternative approaches to obtaining tracking control of a nonlinear uncertain system. A real-life multi-body system is in general highly nonlinear and is intrinsically error-prone due to uncertainties in the modeling system. The uncertainty which is time-varying, unknown but bounded, is therefore assumed in this paper, whereby it may arise from two general sources: uncertainty in the knowledge of the physical system and/or uncertainty in the ‘given force’ applied to the system. In this paper, the use of a new, generalized nonlinear controller is illustrated incorporating two control laws—generalized sliding surface control and generalized damping control. The generalized damping control law also provides two control approaches, one with an uncertainty bound and one without the bound on uncertainty. This leads to three sets of closed-form controllers that can guarantee, regardless of the uncertainty, a tracking signal of a desired reference trajectory of the nominal system, which we refer to as our best assessment of the actual real-life situation. A comparison of the use of the proposed three control designs is demonstrated using an example of a control problem in multi-body dynamics. Both the generalized sliding surface controller and the generalized bound damping controller require knowledge of the bound on uncertainty in order to guarantee a tracking signal of a desired reference trajectory within a desired error bound. In contrast, when using the generalized no-bound damping controller, tracking of the nominal system trajectory can be obtained regardless of the knowledge of the uncertainty’s bound. However, the tracking results from the generalized no-bound damping controller are the least optimal when compared with those obtained from the other two controllers. With simplicity and accuracy obtained, all three control approaches can be implemented for a wide range of complex multi-body mechanical systems.