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Sequential quadratic programming for the control of an architectural cable net geometry

In order to efficiently construct anticlastic concrete shell structures in architecture, flexible formwork can be used, whose main component is a cable net under tension. To cope with the fabrication tolerances of the cable net and thus to reduce the deviations between the nominal digital design model and the as-built one, which is needed to guarantee the properties of the shell, we propose a control algorithm which iteratively steers the geometry of the cable net to the desired one. Our contribution in this paper is twofold. We formulate an optimal control problem and provide two different formulations of the nonlinear equality and inequality constraints. Whereas one of the formulations is a set of implicit nonlinear equations, the other one is the solution to a second-order cone program, which can efficiently be solved. We use both formulations and combine them into a control algorithm, which is based on Sequential Quadratic Programming (SQP), and where the solution in each iteration is feasible for the nonlinear constraints. A simulation example is presented to demonstrate the performance of the developed control algorithm.