μ -Synthesis FO-PID for Twin Rotor Aerodynamic System

μ -synthesis is a NP-hard optimization problem based on the generalized Robust Control framework which manages to find a controller which fulfills both robust stability and robust performance. In order to solve such problems, nonsmooth optimization techniques are employed to find nearly-optimal parameters values. However, the free parameters available for tuning must be involved only in classical arithmetic operations, which leads to a problem for the fractional-order operator or for its integer-order approximation, exponential operations being involved. The main goal of the current article consists of presenting a possibility to integrate a fixed-structure multiple-input-multiple-output (MIMO) fractional-order proportional-integral-derivative (FO-PID) controller in the μ -synthesis optimization problem. The solution consists in a possibility to find a set of tunable parameters isomorphic with the fractional-order such that the coefficients involved in the approximation of the fractional element, along with the formulation of a fixed-structure mixed-sensitivity loop shaping μ -synthesis control problem. The proposed design procedure is applied to a twin rotor aerodynamic system (TRAS) using both MATLAB numerical simulation and practical experiments on laboratory scale equipment. Moreover, a comparison with the unstructured μ -synthesis is performed, highlighting the advantages of the proposed solution: simpler form and guaranteed robust stability and performance.