Design And Simulation Study Of Backstepping And Optimal Controller For Temperature Of Quenching Furnace

A problem of stabilization of the temperature of the large quenching furnace is considered using the method of Backstepping and the method of optimization in this paper.Firstly, the heat transfer mechanism during the procedure of heating metal workpiece in the quenching furnace is analyzed and the one-dimensional distributed-parameter temperature mathematical model of the heated metal workpiece in the quenching furnace is constructed.Second, based on the structure transformation method with integrator Backstepping design idea, a new Backstepping boundary states feedback controller is designed Operator Riccati equation is avoided, instead, the boundary stabilization problem is converted to a problem of solving a specific linear Klein-Gordon-type hyperbolic PDE in the solving process of this Backstepping controller. It doesn't involve much deep and complicated mathematical knowledge in this method. So the numerical calculation effort is reduced enormously and the analytical solution of the kernel can be achieved by the simple method. For the mathematical models in this paper, moreover, the closed-loop solutions are found in closed form, and the control design problem can be solved in closed form, an explicit expression for the gain kernel of the boundary control law is obtained. The closed-loop solutions explicitly are further obtained. The closed-loop solutions explicitly are further obtained. The simulation curves of the dynamic model of the quenching furnace in this paper are posed by adopted the Backstepping controller, the curves show that the effect of the controller is perfect, the simulation system is stabilized.Finally, based on the explicit solution of the transformed kernel, an inverse optimal contro(?)ler is designed. Unlike LQR controller for PDE, the operator Riccati equation is avoided, instead, the optimality problem is converted to a problem of solving a linear hyperbolic PDE. The system is stabilized and cost functions that penalize both the control and the state is minimized by this inverse optimal controller. The simulation curves of the mathematical model of the quenching furnace are posed, the curves show that ths effect of the controller is perfect, the simulation system is stabilized and the cost function is minimized.