Integrated minimum-time trajectory generation, fault detection, and reconfiguration for a double-tank system using flatness and B-splines

The main contribution of this paper is to provide a unified treatment to the problems of constrained minimum-time trajectory generation, fault detection and identification, and (after a fault has been detected and identified) trajectory reconfiguration, in an integrated scheme using a differential flatness and B-splines parameterisation. Using the flatness/B-splines parameterisation the problem of minimum-time constrained trajectory planning is cast into a feasibility-search problem in the splines control-points space, in which the constraint region is characterised by a polytope. A close approximation of the minimum-time trajectory is obtained by systematically searching the end-time that makes the constraint polytope to be minimally feasible. Fault detection is carried out by using B-splines in an FIR filter implementation. Thus, the three - traditionally dealt with separately - problems (namely, trajectory generation, fault detection, and trajectory reconfiguration) are solved in a unified manner, using the same mathematical/computational tools. This, not only offers an elegant solution, but also has the potential to simplify the coding of the algorithms for the real-time application of the strategy. All through the paper, a case-study consisting in an input-constrained double-tank system is analysed in order to illustrate the techniques in an intuitive manner.