Question 1 An Inverted Pendulum System Is Shown In Fig 1 1 00 Permanent Magnet Dc Motor 01 Vi Figure 1 1 A Simple I 1 (48.04 KiB) Viewed 40 times
Question 1 An inverted pendulum system is shown in Fig. 1.1. 00) Permanent magnet DC motor 01) VI Figure 1.1: A simple inverted pendulum system This process is modeled by the following coupled differential equations: di W(t)=1+Ri(t)+Kot) dt do-Ki(t)+Mgl sin e(t), dt where M is the combined mass of the bob and the rod, I is the distance of the centre of gravity (of the combined bob and rod) from the axis of rotation, and Jis the combined moment of inertia about the axis of rotation. The angular position of the pendulum is sensed using a potentiometer with gain Ko{V/rad) – the output of this sensor is volt) volts. i) Draw a Simulink diagram for this process. (5 marks] ii) Show that the voltage required for an equilibrium angle of 6. (rad) is vo (V), where, VO RMgi -sin(e) [3 marks] ii) Derive a linear state-space representation of this process about the equilibrium pendulum angle of Co(rad). [5 marks] Page 2 of 6
for this process V,(s) iv) Determine a third-order transfer function model, G(5) = V(s) about the equilibrium pendulum angle (rad). Show that if L'R is small, that this could be approximated by the second order transfer function model, G(s) JRs +K-s-Mgicos [7 marks]
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!