Using MATLAB/ SIMULINK compute for the following questions

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 isΒ 
𝐺(𝑠) =
βˆ’1 (𝑀𝑏𝐿)⁄ 𝑠2 βˆ’(𝑀𝑝 +𝑀𝑠)𝑔/(𝑀𝑏𝐿) Β 
The design objective is to balance the pendulum (i.e., πœƒ(𝑑) β‰ˆ 0 in the presence of disturbance inputs. A block diagram representation of the system is depicted in Figure 2. Let𝑀𝑠 = 10 π‘˜π‘”,𝑀𝑏 = 100 π‘˜π‘”,𝐿 = 1 π‘š,𝑔 = 9.81 π‘š/𝑠2,π‘Ž = 5,π‘Žπ‘›π‘‘ 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 0.1Β° in the presence of the disturbance.


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