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Using MATLAB/ SIMULINK compute for the following questions.Show the results to your lecturer and document them in the assignment reports. PART 1: 1. Consider the problem of controlling an inverted pendulum on a moving base, as shown in Figure 1.The transfer function of the system is
−1 (𝑀𝑏𝐿)⁄ 𝑠2 −(𝑀𝑝 +𝑀𝑠)𝑔/(𝑀𝑏𝐿)
The design objective is to balance the pendulum (i.e., 𝜃(𝑡) ≈ 0 in the presence of disturbance inputs. A block diagram representation of the system is depicted in Figure 2. Let𝑀𝑠 = 10 𝑘𝑔,𝑀𝑏 = 100 𝑘𝑔,𝐿 = 1 𝑚,𝑔 = 9.81 𝑚/𝑠2,𝑎 = 5,𝑎𝑛𝑑 𝑏 = 10. The design specifications, based on a unit step disturbance, are as follows: i. Settling time (with a 2% criterion) less than 10 seconds, ii. Percent overshoot less than 40%, and iii. Steady-state tracking error less than 0.1° in the presence of the disturbance.