ABSTRACT
This chapter focuses on the stability aspects of the closed-loop process and describes the methodologies for stability analysis. For a more precise analysis, one may use higher-order approximations for the delay or utilize techniques for stability analysis, which do not need approximations for the delay term such as the frequency response. Bode Stability Criterion states that the closed-loop process is stable if the amplitude ratio of the corresponding open-loop transfer function is smaller than 1 at the crossover frequency. Typically, a controller is designed based on a model, which is an approximation of the real system. In other words, controllers are designed based on an approximate model, but implemented on the real process. The governing equation of the dynamics of the closed-loop system was introduced and the closed-loop characteristic equation was defined to explore closed-loop stability through its roots. Two analysis methods, Routh's criterion and Root-Locus, were revisited to determine the stability characteristics of the closed-loop system.
