Stability analysis root-locus

Do the root locus plots in Example 10-l(d). Confirm the stability analysis in Example 10-... 

Example 15.6 demonstrated that the root locus of a system not only provides information about the stability of a closed-loop system but also informs us about its general dynamic response characteristics as Kc changes. Therefore, the root locus analysis can be the basis of a feedback control loop design methodology, whereby the movement of the closed-loop poles (i.e., the roots of the characteristic equation) due to the change of the proportional controller gain can be clearly displayed. 

Representing the roots of the characteristic equation in the complex domain offers a simple way to perform a stability analysis. The system is stable if and only if all the poles are located in the open left-half-plane (LHP). If there is at least one pole in the right-half-plane (RHP), the system is unstable. The representation is similar wiA the well-known root-locus plot used to evaluate the stability of a closed-loop system. 

In Chapter 14 we define mathematically the sampling process, derive the z transforms of common functions (learn our German vocabulary), develop transfer functions in the z domain, and discuss stability. Design of digital controllers is studied in Chapter 15 using root locus and frequency response methods in the z plane. We use practically all the stability analysis and controller design techniques that we introduced in the Laplace and frequency domains, now applying them in the z domain for sampled-data systems. 

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