Of the gain to achieve the type of performance we desire. Since the root locus consists of the locations of all possible closed-loop poles, the root locus helps us choose the value The number of zeros at infinity is, the number of open-loop poles minus the number of open-loop zeros, and is the number of branches of the root locus that If has more poles than zeros (as is often the case), and we say that has zeros at infinity. The root locus then has branches, each branch starts at a pole of and approaches a zero of. No matter our choice of, the closed-loop system has poles, where is the number of poles of the open-loop transfer function. In the limit as, the poles of the closed-loop system are solutions of (zeros of ). In the limit as, the poles of the closed-loop system are solutions of (poles of ). Let be the order of and be the order of (the order of the polynomial corresponds to the highest power of ). If we write, then this equation can be rewritten as: The closed-loop transfer function in this case is:Īnd thus the poles of the closed-loop system are values of such that. , even if some elements of the open-loop transfer function are in the feedback path.
The figure below shows a unity-feedback architecture, but the procedure is identical for any open-loop transfer function The root locus of an (open-loop) transfer function is a plot of the locations (locus) of all possible closed-loop poles with some parameter, often a proportional gain, varied between 0 and. Using Control System Designer for Root Locus Design.Choosing a Value of K from the Root Locus.Plotting the Root Locus of a Transfer Function.
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