New approach to the mixed H2-norm sensitivity minimization

The robust controller design based on the minimization of the H²-norm of a mixed sensitivity function is considered. Two weighting functions and a weighting factor are introduced in the control design to trade off between feedback properties in different frequency ranges. By working in the discrete Fourier transform (DFT) domain, we convert the original H²-norm minimization problem into a problem of solving a vector minimization in the l² space. The advantage of using this approach is that its solution can be analytically expressed and numerically calculated via existing algorithms. The optimal estimate can be efficiently computed due to the particular block structure of the matrices involved. The approximation can be made arbitrarily close to the original H² minimization problem if the number of the DFT points is large. By changing the Bode plots of the weights W₁, W₂ and the weighting factor lambda , we can adjust the design to achieve the desirable performance of the control systems. Two examples are also given to demonstrate the effectiveness of our approach.