Question

An inverted pendulum system is shown in Figure 1. It is assumed that the pendulum is a mass on a massless rod of length l-0.5 m and the mass on the tip of the rod, m1 kg. The mass of the cart M-5 kg. Assume also that there is no friction in the system The displacement of the cart is indicated by x and the displacement of the pendulum is shown as θ Figure 1. Inverted Pendulum on a cart The dvnamic equation of the svstem can be derived as: You are required to work in groups of two students each (you can choose your group member) to complete the following tasks 0 (s) F(s) 1. Obtain the system models of both the cart and the pendulum in transfer functions G,(s) X(s) and G2(s)=F(S ,at equilibrium posiion of 0 around zero (0) -_ (2 marks) 2. Use root-locus to design a PID controller (see hints on the last page) such that the pendulum displacement θ can be controlled to respond to a step input with settling time 4-1.25 seconds (2% criterion) and a maximum percentage overshoot ofMp-1.52%.

Answer 1

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