# 1 the system the actual roll angle is

1 Executive Summary: There are two main types of control systems, an open loop and a closed loop system. (Gene F Franklin 2015) . As the output signal, which in this experiment is being adjusted as well as being used in the control computation it is known as a closed loop or fee dback control system, where the output is the command roll angle. There are six main components in a feedback control system; the desired value, the controller, the compactor, a final control element, the measurement inducer and the communication paths. (Gene F Franklin 2015) . These components are used to ensure that the actual value in the system is attuned to the desired value. This system is a rocket attitude -control system, where the set point is the command roll angle.

Where the actual command roll angle is compared with th e desired roll angle and through the system the actual roll angle is adjusted to match the desired command roll angle. The root locus diagram was invented by Evans and it can be used as a guide to understand the design’s system (Gene F Franklin 2015) . To start, a tra nsfer function must be written for the closed loop and the characteristic equation is written where the roots are the poles of the transfer function. (Gene F Franklin 2015) To be able to study the roots, the equation must be written in polynomial form with a K value. The root lo cus is the plot of all the root values where the k values range from zero to infinity (Gene F Franklin 2015) . The main objective of control design is system stability. In order to achieve this, it is necessary to ensure that the poles lie in the left half of the s -plane. In t he rocket attitude control system in our problem, the open loop poles are located at 0, -2 and -5 and since one pole is located at 0 the system marginally stable.

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To address this marginal stability, the closed loop poles were relocated by increasing the controller gain K. The gain was adjusted to make the relative damping ratio of the closed loop system equal to 0.45. This moved the location of all three poles to the left half plane thereby stabilising the system.

The gain margin of this system is 31.2 d B and the phase margin 82.3 °. These values suggest that the system designed is robust . If the gain is increased further, the gain and phase margins would reduce, increasing the risk of instability in an operating environment.

When K = 35.2 dB, there is no damping and any oscillations would continue indefinitely.2 Contents Executive Summary: ….

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