rs) Consider again the industrial process requiring control of a flexible pointer from Assessment Quiz #3. The system has transfer function from torque t to angular position 10 G(s) = $(s) s2+2s+8 You were previously asked to design a discrete time controller C(z) to control the position in response to a step reference with less than 40% overshoot, but no specifications were included on the steady-state error, so most submissions concluded with steady-state error present. In this quiz problem, you will correct that omission in state space using integrator augmentation. Use the following steps to perform the design in state space likely continuous time, but you can explore discrete if you would like to) and test the performance in Simulink or in the Matlab command window. You can use any Matlab tools as long as you submit the required information for each step. Submit your answer as a single PDF file with all items 1-6 clearly marked, in order. 1. Given G(s), find a state space representation A, B, C, D. Submit your work (either Matlab code or hand calculation) and resulting A, B, C, D. 2. Find the augmented system matrices Aq, B qu, Bar, C4, D, for implementing integral augmentation, where q refers to the augmented state vector q Provide these matrices in your submission. 3. Select appropriate closed-loop poles to meet the %os requirement, plus a 3rd pole to be associated with the augmented state variable / e. Provide these desired closed-loop poles in your submission 4. Use Matlab's 'place' or another technique of your choice to design the state feedback gain K, , where the controller will be implemented as u = -K 9. (Note: this is the full state feedback option. If you prefer, you can use output feedback with the estimated state n in the feedback controller. See the lecture article for details.) Provide your final control vector or vectors in your submission 5. Test your controller either in Simulink or in the Matlab command window. Do you meet the %OS