Task 1 We considere the following parameters for the inverted pendulumsystem: • l = 1m • M = 100kg, m =10kg \text { - } g=9.81 \mathrm{~m} / \mathrm{s}^{2} 1. Let the output be y(t)u to the output y.0(t). Find the transfer function from the input 2. Find the stat-space equations for the system. 3. Determine the eigenvalues, poles, and zeros of the system. 4. Determine whether the system is controllable (reachable) and observable. 5. Use the transfer function model and close the loop with a negative feedback with a constant gain K, as shown in (e) on page above. Use Root-Locus method to see if the system can be stabilized by this feedback design.

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