Adaptive Control of nonlinear differential-algebraic systems in multibody dynamics
Our objective in the proposed project is to develop adaptive controller design techniques for tracking control of systems of nonlinear differential-algebraic equations with applications to underactuated mechanical multibody systems. While closed-loop tracking control of fully actuated multibody systems is well-established, systematic methods for underactuated systems are lacking. The latter type refers to multibody systems having more degrees of freedom than actuators, which results in diverse systems theoretic properties. Typical examples of practical relevance are systems with passive joints, cranes, cable robots or lightweight systems with flexible bodies. Especially for more complex systems with kinematic loops or flexible bodies, differential-algebraic equations are appropriate for modelling. In the proposed project, we first aim to conduct a structural analysis of multibody systems. Thereby it is intended to characterize important systems theoretic quantities and properties such as input-to-state stability, index, relative degree and internal dynamics on the basis of physically motivated considerations. Problems in controller design for multibody systems may arise when the index or relative degree of the differential-algebraic model exceed one or the system has unstable internal dynamics. To compensate a higher relative degree, the funnel observer, which has been developed by the applicants Berger and Reis, shall be applied. Unstable internal dynamics are aimed to be circumvented by an application of feedforward control strategies based on model inversion. Such a model inversion shall be based on so-called servo-constraints, which again lead to differential-algebraic equations. The performance and implementability of the developed methods is to be constantly verified by means of selected experiments.