| In this paper, 1D mathematical model of billet heating process in Reheating Furnace is established by using heat exchanger theory. The model can describe process of billet heating satisfactory. Boundary formula of billet heating process is offered through predigestion in furnace heat exchange calculation based on considertion of total heating absorb rate, furnace temperature,billet surface temperature. A problem of stabilization and adaptive control of uncertain parameter about 1D heat mathematical model is considered.Based on the structure of 1D heat equation and Backstepping design idea, a kind of Backstepping boundary states feedback controller is designed to solve a problem of stabilization.The Backstepping controller can be designed by the way of finding a coordinate tranformation, the key problem is how to obtain kernel function. Kernel function is required to satisfy a Klein-Gordon-type hyperbolic PDE. Operator Riccati equation is avoided, instead, the boundary stabilization problem is converted to a problem of solving a specific Klein-Gordon-type hyperbolic PDE. Due to which, the numerical calculation effort is reduced enormously. Therefore boundary controller is constructed in closed form. For this model, the Backstepping boundary states feedback controller is designed in continuous closed form.Using Lyapunove theorem and the closed-loop solutions,the stabilizations of the control systems are approved. At the end, the simulation curves are posed, the curves show that the effect of the controller is perfect, the simulation system is stabilized.Base on the Backstepping boundary states feedback controller, an adaptive controller is designed to solve the problem of adaptive control of uncertain parameter.To deduce an error equation, fide a controlled law and the adjusted parameter is emphasis.In order to obtain the states of error equation approach to zero,Based on the simulation curves, the adjusted power of controlled system of uncertain parameter is obtained. |
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