Design of multivariable tracking systems via engineering performance indices based on $H_{\infty }$-approach

This paper proposes an algorithm for designing a measured output-feedback controller with given or achievable engineering performance indices for linear multivariable systems. The control plant is subjected to bounded external disturbances from the class of polyharmonic functions with an infinite number of harmonics and a bounded sum of their amplitudes for each disturbance component. As a result, additional tracking errors appear in controlled variables. The problem is to design a multivariable output-feedback controller ensuring given or achievable tracking errors, the settling time determined by a given or achievable degree of stability of the closed loop system, and a set of the oscillation indices $M_i$ for the $i$th closed loop relating the $i$th reference signal to the $i$th controlled variable $z_i$. In addition, the controller should ensure the conditions $M_i\leqslant\gamma$, where $\gamma$ is a given value or the minimand. As shown below, $H_{\infty }$ control methods are quite convenient for solving such problems. An illustrative example of designing an interconnected electric drive is presented.