a) The equations of motion of the inverted pendulum model were derived in Example 3.5.6 in Chapter
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b) Obtain the linearized equations for the following values: M = 10 kg, m = 50 kg, L = 1 m, I = 0, and g = 9.81 m/s2.
c) Use the linearized model developed in part (b) to design a PID controller to stabilize the pendulum angle near ( = 0. It is required that the 2% settling time be no greater that 4 s and that the response be nonoscillatory. This means that the dominant root should be real and no greater than - 1. No restriction is placed on the motion of the base. Assume that only ( and ( can be measured.
Figure P11.20Figure P11.20
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