# Stable Control Systems

1. a. Draw the Bode diagram for the attached system.

b. Is the system stable?

2. Robots can be used in manufacturing and assembly operations where accurate, fast and versatile manipulation is required. The open-loop transfer function of a direct-drive arm may be approximated by:

G H (s) = K(s+2) / s(s+5)(s^2+2s+5)

a. Determine the value of gain K when the system oscillates.

b. Calculate the roots of the closed-loop system for the K determined in part a)..

3. For the system attached, determine the range of K for which the system is stable.

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#### Solution Preview

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1. a. To derive the Bode plots for amplitude and phase we need to find the poles and zero's of the closed loop transfer function.

b. In order to check the stability of the system we need to examine the characteristic equation of the denominator of the closed loop transfer function, ...

#### Solution Summary

This solution provides steps to determine each of the problems involving stable control systems.