Consider the closed-loop system shown below: The loop has two proportional controllers. Kej and Ke2 (a) For what range of the controller gain Kei is the inner loop stable? (Hint: Use the characteristic equation only for the inner loop only and check the Routh's criteria for stability). (b) Let the controller gain Kej be 0.2. Calculate the closed-loop transfer function from D to Y. Assuming R= 0. (c) Calculate the range of the controller gain K2, that makes the overall closed loop system (Y/D) stable. Use Routh's test again. Y R+ 2 K2 (s – 1) (5s + 1)(8s + 1) 10 16

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KVL and KCL

KVL stands for Kirchhoff voltage law. KVL states that the total voltage drops around the loop in any closed electric circuit is equal to the sum of total voltage drop in the same closed loop.

Sign Convention

Science and technology incorporate some ideas and techniques of their own to understand a system skilfully and easily. These techniques are called conventions. For example: Sign conventions of mirrors are used to understand the phenomenon of reflection and refraction in an easier way.