Neuro-mechanical modelling and control of winding processes

This paper presents a novel modelling and control algorithm for systems which are governed by partial differential equations. Different from existing distributed parameter systems so far discussed in literature, the control input of the system considered in this paper appears only inside the boundary conditions. The purpose is to control the boundary condition so as to realize the total distribution control of the system output. For this purpose, an orthogonal B-spline neural network model is used to approximate the solution of the system. By substituting this B-spline model into the original partial differential equation and letting the residual orthogonal to all the selected basis functions, the dynamics of the weights of the B-spline model are obtained. Such a dynamics relates the input to the weights of the B-spline model through an ordinary differential equation, where the controller designed only needs to be focused on the control of the weights because all the basis functions are fixed. This leads to the design of an observer based controller which realizes the profile control of the system output with guaranteed stability. The control algorithm is applied to a winding process in the paper making industry, where the model of the winding process is developed and the corresponding controller is derived. Some simulations are provided to show the effectiveness of the control algorithm.