Parameterised controller synthesis for SISO-LTI uncertain plants using frequency domain information

Abstract

This paper extends the results of a new model-free approach which has been applied to guarantee nominal stability and performance. In this paper, using a particular controller structure, the robust stability (RS) and robust performance (RP) criteria for single input single output linear time invariant (SISO-LTI) plants with multiplicative uncertainty are transformed to affine functions in terms of controller parameters. It is shown that solving the feasibility problem of these new criteria will lead to controllers that guarantee the RS and performance. There is no need for a plant mathematical model. The required data for controller synthesis are just the frequency responses corresponding to limited samples of the uncertain plant. Also, there is no need for exact data at each frequency for the whole set of frequency responses. The approach is also applicable for designing both low- and high-order controllers. The effectiveness of the proposed technique is illustrated by simulation results.