Research Projects

The problem of finding a control input that steers a dynamical system (such as a crane or a continuum robot or an antenna) from a given initial position to a desired final position, while satisfying certain constraints during the motion, is called a trajectory control problem. This is a difficult problem to solve for flexible structures, since flexibility renders them highly susceptible to undesirable vibrations when moved. Nevertheless, it is important to solve trajectory control problems for many engineering systems such as flexible robots and tower cranes which consist of 1D flexible structures. Development of algorithms which solve trajectory control problems, with time and speed constraints, for 1D flexible structures is the focus of this proposal. In addition, we will also perform experimental validation of the proposed algorithms. For flexible structures, the first principles based mathematical models which capture their complex dynamics accurately are partial differential equations (PDEs). Approximating the PDEs with ODEs for controller design can lead to a loss of performance and even large errors due to the spillover effect. Hence the theoretical developments in this proposal are based on the PDE models of flexible structures. We have formulated three objectives, all of which propose to develop algorithms for solving trajectory control problems for 1D flexible structures. But they differ in the complexity of the flexible structure models they consider: the first objective considers linear PDE models, the second objective considers linear PDE models coupled to finite-dimensional systems and the third objective considers nonlinear PDE models coupled to finite-dimensional systems. The models in each of the objectives cater to different applications. The objectives are ordered such that ideas developed for addressing an objective, will facilitate addressing the subsequent one. Few works in the literature have addressed trajectory control problems for 1D flexible structures using PDE models and even their techniques and results are quite restrictive. We will use the flatness technique (with generating functions approach and semi-discretization approach) for solving the trajectory control problems considered in this proposal. The algorithms we plan to develop in this project will lead to novel theoretical advancements in the field of flatness-based trajectory control. Owing to our extensive experience working with the flatness technique, we are well-equipped for developing the necessary algorithms. We will establish the practical value of the trajectory control algorithms developed in this project by validating them in experiments. For this purpose we will design and fabricate novel laboratory setups. This will facilitate the transitioning of these algorithms to industrial applications. The experimental activities envisioned will lead to the establishment of a facility for testing algorithms developed for 1D flexible structures.