# Transfer Function and Feedback Control System

An open loop transfer function of a certain unit feedback control system is described as below, where K is an adjustable gain (Proportional Controller) and G(s) is a process transfer function.

1. In the space provided (see attached), sketch a Root Locus plot of the closed loop system for positive Proportional Controller gains. Show all relevant coordinates (centroid, asymptotes, crossovers with Inn axis, if any, break-away/break-in coordinates, if any).

2. Find the value of the Proportional Gain such that the closed loop system exhibits a damping ratio of 0.707. For this value of the gain, briefly explain whether the closed loop dynamics can be adequately represented by a second order system model. If it can, find the appropriate parameters of the model.

3. For the same value of the gain, evaluate the following specifications of the closed loop step response: percent overshoot, settling time, and steady state error.

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#### Solution Preview

1. Transfer function

50

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s^3 + 15 s^2 + 50 s

There are three poles at -10, -5 and at origin.

There is a break-away point is -2.11.

The centroid will be (-10-5-0)/3= -5. The angles of ...

#### Solution Summary

Solution includes calculations and graphs for (1), (2) and (3).