Low Order Structured Weight Optimization for H∞ loop shaping design procedure

A low order structured weight optimization algorithm for H_∞ loop shaping design procedure is proposed, which can be used for single input single output plant H_∞ controller design. This work is build on the method proposed by Shu Katayama^[15], the improvements are given as below: the first one is that special structured decision variables are defined according to structure of weight, and additional linear matrix inequalities are given to guarantee the weight is a stable minimal phase one. The second one is that parameters of weight are derived directly by solving corresponding LMIs, instead of fitting transfer function which is needed by algorithm given in Ref. [15], so the proposed algorithm is faster and resulting parameters of weight is more accurate. The whole design procedure is rigorous and systematic, robust stability and desired performance of control system are guaranteed by the constraints defined by corresponding LMIs and singular value bounds. Numerical example shows that lower computational cost is spent and desired control performance is obtained using the proposed approach.