# Closed Loop System Transfer Function

Consider a control system described by the attached state space model.

(1) For the system in question do the following:

- Find the system transfer function, {see attachment}

- Find the system eigenvalues

- Check the system controllability and observability

(2) Assume the state feedback of the form: {see attachment} and use pole placement by state feedback to place the compensated system eigenvalues at: -3, -4, -5 and -6. What are the gain values in the vector K?

(3) Write the closed loop transfer function of the system {see attachment}.

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#### Solution Summary

This solution goes through step by step identifying functions and solving for eigenvalues, observability, controllability, and gain values. Calculations and explanation are included. Solution can be found in the attached Word file.