Subspace Based Data-Driven Minimum Variance Controller Design

As the fast developing of the aerospace technology, aircrafts become more complex and conventional control methods which need a precise mathematical model become much more difficult. Data-driven control, namely making direct use of large amounts of data generated by industrial processes to do a control, has brought new opportunities and challenges for the modern control methods. And the minimum variance control is widely used in the actual industrial control. In particular, it is useful in System performance evaluation. Thus, in this paper, the data-driven minimum variance controller design problem is presented.The research on the data-driven minimum variance control based on subspace identification is carried out in this paper. The main work of this thesis as follows:(1) Review the subspace identification theory. First introduce the principle of the matrix QR decomposition to achieve line orthogonal projection and oblique projection, and then analyzes the basic principles and procedures of the subspace identification algorithm.(2) Review the traditional minimum variance control and proposed the open-loop data minimum variance control. First we make use of the subspace identification method to construct the subspace equation of a direct relationship between the input data and output data, and then we use optimal prediction of the output got from the subspace equation to derived the minimum variance control, thus we achieve the open-loop data minimum variance control.(3) Propose the minimum variance control method for the closed-loop data. Taking into account the existence of closed-loop feedback, the direct identification of subspace equation will result in deviation. Thus we use innovation estimation method to get the innovation of the system, and then we use the subspace method to identify unbiased subspace matrix and to get the output optimal prediction equation. With that we can derive the minimum variance control, and thus we achieve the minimum variance control of the closed-loop data;(4) Propose the minimum variance control method for the dual-rate sampling system. First we use lifting technique to handle the original system, and use the lifted system to construct the subspace equation. As the right hand side of the subspace equation containing future output, we forward iteration the subspace equation and rearrange the right hand side of the iterationed equation, and thus we obtained optimal output prediction equation. With the output prediction equation we derive the minimum variance design, and finally we achieve the minimum variance control of the dual-rate system.