4.1 Introduction A simple method for tracing the roots of the characteristic equation in the complex plane has been bound by r.W. Evans in 1948 and used extensively in control engineering. In this method. called the root locus method the roots of the characteristic equation are plotted for all values(usually from zero to infinity) of a particular system parameter(usually the gain)of our interest. The root locus method enables us to find the closed-loop poles from the open-loop poles and zeros as a parameter changes. Hence, by using the root locus method the designer can predict the effects on the location of the closed loop poles when varying the gain value or adding open-loop poles and/or open-loop zeros 2022-2-32022-2-3 2 4.1 Introduction A simple method for tracing the roots of the characteristic equation in the complex plane has been bound by R.W. Evans in 1948 and used extensively in control engineering. In this method, called the root locus method, the roots of the characteristic equation are plotted for all values (usually from zero to infinity) of a particular system parameter (usually the gain) of our interest. The root locus method enables us to find the closed-loop poles from the open-loop poles and zeros as a parameter changes. Hence, by using the root locus method the designer can predict the effects on the location of the closed￾loop poles when varying the gain value or adding open-loop poles and/or open-loop zeros