Design Of The Controller And The Observer For The Concentration In Coagulation Bath Of Pan-Based Carbon Fiber

Since1960’s, the control problem of distributed parameter systems has been one of the main subjects concerned and studied in the control field. It has strong applied background. In theory, distributed parameter system is a more realistic model, the finite dimensional system simply replaces it, likely "close, narrow margin". In addition, almost all practical stochastic control systems are distributed parameter systems. Moreover, the theory has become increasingly mature and abundant. In recent50years, this theory has been rapid development. In particular, because of its obvious interdisciplinary nature, distributed parameter systems theory and modern mathematics and modern engineering technology have a very close contact and mutual influence. The control systems governed by diffusion parabolic equations are important parts of distributed parameter systems. To study them can not only pose more challenges to mathematical theories, but also deepen comprehension of control theory.A problem of stabilization of the concentration of spinning bath is considered using the method of backstepping in this paper. Firstly, the mass transfer mechanism during the reaction diffusion in spinning bath is analyzed and the one-dimensional distributed parameter diffusion mathematical model in spinning bath is constructed. Singularity pole in the mathematical model increases the difficulty of the problem, so there is few research on boundary feedback stabilization of reaction diffusion equations in polar coordinates. But polar coordinates can describe the periodic boundary of a large class, so it is significant to study the boundary control problem of polar coordinates. Second, this article for the issue, study boundary feedback stabilization of reaction diffusion equations in polar coordinates. A Volterra transformation is introduced to convert the reaction diffusion system into an exponentially stable system. Through backstepping technique, we can establish controller which achieve exponential stabilization of the closed-loop system. According to the system equivalence, we get a specific linear Klein-Gordon type hyperbolic PDE about the kernel in the solving process of this backstepping controller. We conduct a number of equivalent transformation of equations, transforming it into Bessel equation. We can get closed form kernel function. Thirdly, based on backstepping and design features of the system, we design the observer. By constructing suitable Lyapunov functions(energy function) to achieve stability or stabilization of closed-loop systems. Lastly, in order to test the performance of the controller and observer, we conducted a simulation experiment and illustrate that the design of the observer and the controller is feasible.