Abstract:

For complex processes and unknown structures, it is an urgent problem to be solved to construct a simple model based on data information to simplify the solution of controllers for objects, while ensuring the effectiveness of the model. Taking the controlled autoregressive model as an example, a sparse identification method based on the modified minimum angle regression algorithm is proposed. Firstly, the system model is transformed into a hyperparameter high-dimensional sparse model. Then, the minimum angle regression algorithm is used for sparse system identification, and the absolute angle stopping criterion is proposed. The algorithm can obtain sparse parameter estimates of the model after a small number of iterations, and obtain effective time delay and order estimates at the same time. Combining the identified controlled autoregressive model, a proportional integral derivative （PID） controller based on specified phase point frequency and gain is introduced. Numerical simulation and attitude control simulation of the balancing robot show that the sparse identification algorithm has high identification accuracy under low data volume, the established model has good generalization performance, and the controller has good control effect.

Key words: least angle regression, sparse system identification, time-delay and order joint estimation, stopping criterion, optimal proportional integral derivative （PID） control