Subspace identification method-based setpoints tracking control and its applications to the column cleaning process

As the last subprocess of copper flotation processes, the column cleaning process plays a decisive role in the tailing copper grade (TCG) and concentrate copper grade (CCG), which are the important factors in determining comprehensive economic indicators. Therefore, the problem of setpoints tracking control of TCG and CCG is particularly important. However, the unknown parameters in the column cleaning process bring great challenges to the problem of setpoints tracking. To overcome this problem, a state space model is constructed based on the two phase model of flotation. Due to the complexity of the column cleaning process, the state-space model matrices cannot be detected or calculated directly. Therefore, a deep autoencoder-based subspace identification method (SIM-DAE) is proposed to identify the state-space model matrices. Next, a Lyapunov-Krasovskii function is proposed to verify the stability and anti-interference performance of the identified system. Meanwhile, the state feedback controller is designed that the TCG and CCG can track with the setpoints. Finally, the effectiveness and feasibility of the proposed methods are verified by the data experiments and an industrial field platform.