CONTROL SYSTEMS LABORATORY STABILITY ANALYSIS EXPERIMENT REPORT

CONTROL SYSTEMS LABORATORY EXPERIMENT 6 STABILITY ANALYSIS 151220102038 Hakan Kahraman Introduction The main purpose of experiment is how to analyse stability of a control system using Routh’s Algorithm. We have discussed stable, marginal stable and unstable control systems in this experiment.

Definitions and Theory Asymptotically Stable System All the roots of the characteristic polynomial lie in the left half plane (Re(s) < 0 Marginally Stable System No solution grows unbounded but some do not decay (Re(s) ≤ 0) Unstable System At least one root of the characteristic polynomial lies in the right half plane (Re(s)> 0) Figure 1

Stages of Experiment First Part In the first part of experiment we have obtained the step responses of the inner loop of considered system given in Figure 1 for three different 𝐾1 values as 5, 10,15 respectively. We have determined the range of 𝐾1 using Routh’s Algorithm as 𝐾1 - 0.78 for 𝐾1 is equal to 2.2. The transfer function of inner loop for 𝐾1 is equal to 2.2 𝑌(𝑠) 20𝐾2 𝑠 = 3 2 𝑅(𝑠) 𝑠 + 10𝑠 + 20(𝐾2 + 1)𝑠 + 44 𝑌(𝑠)

Finally we have observed stability of 𝑅(𝑠) for 𝐾2 = 5

Figure 6

As you seen there are three pole on the left hand plane for 𝐾2 =5 > - 0.78 so this system is a stable system.

Conclusion We have discussed stability of control systems in this experiment. We have observed step responses and pole-zero diagrams of different systems to determine the stability of different systems and we have used Routh’s Algorithms to determined stability.