Question

PARTB 4. You are designing a system to enable a robot to stand on a trapeze. For small rotations, the robot can be assumed to obey the following differential equation d2 θ (t) dP--θ (t) = F(t) dt2 where θ(t) is the output angle (between the robot and a vertical reference) and F(1) is the input force exerted by a motor. a) Write the transfer function for the robot (ie a plant that converts the input to the output) b) Is the robot stable without a controller? c) An engineer suggests using a proportional controller as a cascade controller to improve the stability of the system. What is the transfer function of a proportional controller? d) What is the transfer function of a closed-loop transfer function in terms of the transfer function of a plant, G(s), and a controller, C(s)? e) What is the closed-loop transfer function for the robot with a proportional controller? Express your answer as a ratio of polynomials in s. f) Is the closed-loop system undamped, under-damped, critically damped or overdamped? What values of K will make the closed-loop system stable? g) h) What would be the steady-state error for the closed-loop system in response to a step input?

Answer 1

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