The single degree of freedom system shown in the figure has mass 1 kg, length 1

Question

The single degree of freedom system shown in the figure has mass 1 kg, length 1 m, and k = 10000 N/m, c = 200 N.s/m, and a = 0.5m. Discuss the design of a control system that achieves the desired motion trajectory theta d = sin alpha t, where is an amplitude, alpha is the frequency, and t is the time. Use the inverse dynamics to determine the motor torque that produces the desired motion. Determine the complete solution that includes the effect of the transient solution. Note that in realty measurements are done online and therefore this complete solution may not be the same as theta a, Assume the complete solution which has the transient effect to be the actual solution theta a. Because of this step, the small angle assumption will need to be used in the project. Develop form of the control law for two different eases that have different values of the amplitude and frequency alpha. Select the appropriate control gains and actuator (motor) specifications. Compare the control law with the motor torque obtained using the solution of the inverse dynamics problem. Prepare a report that will document your design. The report should include error function plots that show the effectiveness of the controller design for different values of the velocity and position gains. In the report also show the block diagrams of the feedback control system used The report is due April 5, 2013 at the end of the class.

Explanation / Answer

shabana is a jerk

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