An interesting mechanical system with a challenging control problem is the ball and

Chapter 0, Problem P11.9

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An interesting mechanical system with a challenging control problem is the ball and beam, shown in Figure PI 1.9(a) [ 10]. It consists of a rigid beam that is free to rotate in the plane of the paper around a center pivot, with a solid ball rolling along a groove in the top of the beam. The control problem is to position the ball at a desired point on the beam using a torque applied to the beam as a control input at the pivot. A linear model of the system with a measured value of the angle 4> and its angular velocity dfy/dt = w is available. Select a feedback scheme so that the response of the closed-loop system has an overshoot of 4% and a settling time (with a 2% criterion) of 1 second for a step input.