On Sensitivity of Characteristic Transfer Functions of Multivariable Control Systems

In the paper, a systematic treatment of sensitivity analysis of multivariable control systems from a perspective 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 analysis and design of N SISO systems. The formulas are derived determining the sensitivity functions of the CTFs and sensitivity vectors of the canonical basis axes to small variations of parameters of general type MIMO systems. 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 not robust system with large degree of skewness of the canonical basis axes. In the second example, the sensitivity of the control system of a hexacopter (multirotor UAV with six rotors) to small degradations of the motors’ efficiency is analyzed.