Nonlinear Time Series Model-Based Predictive Control Applied To Swing-up Of Inverted Pendulum

The Inverted pendulum is a common natural instability experimental device to verify control algorithms, which is a multivariable, nonlinear and strong-coupling natural instability system. The research of the inverted pendulum is not only an important way to test the effectiveness of various control algorithms, but also has a value in engineering. The main content is the research of the RBF-ARX nonlinear time series modeling and predictive control applied to the swing-up of one stage linear inverted pendulum.Traditional researches of inverted pendulum were most based on the physical model. The physical model needs the accurate analysis of the movement mechanism, so it has some defects. For example, some physical parameters are difficult to be precisely measured, and some simplifications are made in the process of modeling, so that the accuracy of the model would be degraded. To overcome these disadvantages of the physical method, the identification method is proposed and applied on the inverted pendulum.The full name of RBF-ARX model is the radial basis function neural network coefficient autoregressive model with exogenous variables, which uses RBF neural network to approximate the function coefficients of the ARX model. It has the excellent approximation performance of the RBF network. It can also control the complexity of the model using the ARX model’s autoregressive and moving average structure.On this basis, we design the data identification experiment and identify the RBF-ARX model using the collected data. In this paper, the initialization of model parameters was explained in detail. SNPOM(Structured Nonlinear Parameter Optimization Method) was used to the optimization of parameters. AIC criterion and other factors were used to estimate the model order. After this, two RBF-ARX SISO models were established, including swing-up and stabilization of inverted pendulum. Position control was added to the equilibrium state to create a SIMO model. Data validation proofs that the RBF-ARX model has good precision.Predictive controller could be designed on the basis of the identified model. At selected angle, switching SISO and SIMO model, system simulation achieved good results. At last, one stage linear inverted pendulum could swing up and keep the set angle in the real-time control experiment. The results prove that predictive control based on the RBF-ARX model is effective in nonlinear and fast system.