Application Of RBF-ARX Model-based LQR Control On Quad-Rotor Helicopter Simulator

As a MIMO nonlinear coupling system, the quad-rotor is a hot research topic in recent days, and it is meaningful to have a study on it.In the past, most of the study of the quad-rotor was based on the traditional physical methods. The math models were established on the differential equations deduced by mechanism analysis. There are inevitable defects on such a method. The physical parameters are hard to be precisely measured, and some simplifications and linearizations are made in the process of modeling, and some other aspects, which in all has impacts on the accuracy of the model.In order to get away of these disadvantages of the physical method, the identification method is proposed and applied on the quad-rotor. The ARX model is a commonly used linear model, which has an excellent performance in approximation in a linear space. So as to represent the nonlinear object, the quad-rotor, a bunch of ARX models are adopted. The work space of the quad-rotor is linearly divided, and in each linear subspace there is an ARX model to represent its characteristics. Then a appropriate switching mechanism is applied to achieve the goal of global model. The RBF-ARX model is a nonlinear time-varying model whose structure resembles the ARX model. Its independent variables are groups of signals indicating the nonlinear status of the system, according to which its model parameters can be promptly adjusted to the best by taking the advantages of the RBF neural network. Owing to the self-adjusting parameters, the RBF-ARX model not only has an outstanding approximation in local linear space, but also has superior global performance.The LQR is a typical method in the optimal control theory, which depends on the state-space equations, and it achieves the desired goal by structuring an optimal state feedback control loop. Based on the mentioned 3 models, the design of the LQR controllers are presented in this paper, and the simulation and real-time control experiments have been carried out. The real-time control results show that systems based on all the 3 models have a satisfied performance. However, through the comparison analysis, the RBF-ARX model undoubtedly wins the best, which has a fast response, high precision and stable outputs.