Question 1 An inverted pendulum system is shown in Fig. 1.1. 001). Permanent magnet DC motor (1) oo(t) Fig. 1.1 Inverted

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Question 1 An Inverted Pendulum System Is Shown In Fig 1 1 001 Permanent Magnet Dc Motor 1 Oo T Fig 1 1 Inverted 1 (38.39 KiB) Viewed 62 times

Question 1 An inverted pendulum system is shown in Fig. 1.1. 001). Permanent magnet DC motor (1) oo(t) Fig. 1.1 Inverted Pendulum This process is modeled by the following coupled differential equations: di di 1 (VE) - Ri(1) - K 4t)) L doo dt 1 J (Ky (1) + Mg/ sin 0(0) Here M is the mass of the pendulum, / the distance of the centre of gravity of the pendulum from the axis of rotation, and Jis the moment of inertia of the pendulum about the axis of rotation. The armature current is iO), the rotational speed of the motor is act) and the angle that the pendulum makes to the vertical is e(t). (0) Give a Simulink representation of this process based on three integrators. [5 Marks] The operating point is the fully upright position; the angle (1) is assumed to be small (ii) Derive a linear state space representation of this process. [5 Marks) (III) Determine a third-order transfer function model, G(s) = 0() for this process. V(8) [5 Marks) Page 2 of 16