Physics > QUESTIONS & ANSWERS > East Carolina University - CSDI 8104SampleMidtermSolutions CSDICSDI 8104e If the spaceship is flying (All)

East Carolina University - CSDI 8104SampleMidtermSolutions CSDICSDI 8104e If the spaceship is flying at a constant height what is the value on the ALL ANSWERS CORRECT

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5. Consider a rotating robot where you can control the angular velocity around a fixed axis. (a) Model this as a system where the input is angular velocity q˙ and the output is angle q. Give your m... odel as an equation relating the input and output as functions of time. Solution: 8 t 2 R; q(t) = q(0)+ tZ0 q˙(t)dt; where q(0) is the initial position. (b) Is this model BIBO stable? Solution: The model is not BIBO stable. For example, the input q˙(t) = u(t) is bounded but yields an unbounded output. (c) Design a proportional controller to set the robot onto a desired angle. That is, assume that the initial angle is q(0) = 0, and let the desired angle be y(t) = au(t), where u is the unit step function. Find the actual angle as a function of time and the proportional controller feedback gain K. What is your output at t = 0? What does it approach as t gets large? Solution: A proportional controller has the same structure as the helicopter controller: Just as with the helicopter controller, we can solve the integral equation to get q(t) = au(t)(1−e−Kt): The output at zero is q(0) = 0, as expected. As t gets large, the output approaches a [Show More]

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