On the Sensitivity of Characteristic Transfer Functions of Multivariable Control Systems

In the paper, a systematic treatment of sensitivity analysis of multivariable cont rol systems within the framework of the characteristic transfer functions (CTFs) method is given. The CTFs method (also called characteristic gain loci method) allows one to associate with an N-dimensional multi-input multi-output (MIMO) system a set of N independent single-input single-output (SISO) characteristic systems and thereby to reduce the analysis and design of a MIMO system to the analysis and design of N SISO systems. The formulas determining the sensitivity functions of the CTFs and the sensitivity vectors of the canonical basis axes to small variations of parameters of general type MIMO systems are derived. The relations between the sensitivity functions of the open-loop and closed-loop MIMO systems are established. Two illustrative examples are considered. The first of them concerns the sensitivity of a two-dimensional non-robust system with a large degree of skewness of the canonical basis axes. In the second example, the sensitivity of the control system of a hexacopter (a multirotor UAV with six rotors) to small degradations in motors efficiency is analyzed.