Control Studies, Based On The Observation Cube System

The cube system is a simple experimental apparatus. But it is complicated as a controlled plant. It is multivariable, nonlinear, strong-coupling and structurally instable. So the cube can be stabilized only by adopting effective control method. This apparatus can be used to study the performance and control method of the systems, which are nonlinear, multivariable and strong-coupling. The cube used in this paper is provided by the company of Quanser in Canada.In this paper, the mathematical model of the cube is established with Lagrange equation, and then it is linearized. The cube is proved to be controllable and observable by analyzing the mathematical model. Then the LQR control law is obtained according to the linear model. Because one of the state variables can't be measured, a reduced-order observer is designed.In this paper, a control method combining RBF neural networks with genetic algorithms is adopted to control the cube system. Genetic algorithms are used to optimize the parameters of RBFNN controller. Then the weights of RBFNN are adjusted on line with RLS algorithm to enhance the robustness of the system. The RBFNN controller is constrained by the condition of the linear controller deisgn so that there are less parameters to be optimized.Both the LQR controller and the RBFNN controller are used to control the cube. The simulation is completed using MATLAB/Simulink. And the experiments are done on the cube with WinCon, which is a real-time control software developed by Quancer. The results show that the observers and the controllers have good performance.In this paper, the design of the Lipschitz nonlinear state observer is discussed, according to the characteristics of the cube. A reduced-order observer for Lipschitz nonlinear systems is studied in details. It is based on the linear matrix inequality. Then it is used to design the reduced-order observer for the cube system.