Assignment_1.pdf - Mechatronics Assignment 1 \u2022 Problem 1 \u2013 Consider a closed-loop rotary speed-control system with a proportional controller Kp as

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Mechatronics Assignment # 1 K. Craig 1 Mechatronics Assignment # 1 Problem # 1 Consider a closed-loop, rotary, speed-control system with a proportional controller K p , as shown below. The inertia of the rotor is J. The damping coefficient B in mechanical systems is usually difficult to estimate accurately. Because the computed gain value depends on the estimate of B, the actual system performance can be quite different than the predicted value if our estimate of B is very inaccurate. + - S K p T d (s) Σ + + 1 Js B + ( 29 d s ( 29 s Mechatronics Assignment # 1 K. Craig 2 Suppose the nominal value of B = 1. Discuss the sensitivity of the steady-state response to uncertainties in B, for a step command input. Specifically, compare the sensitivity for K p =1 and for K p = 9. Discuss the sensitivity of the closed-loop transfer function to uncertainties in B (whose nominal value is B = 1). Assume J = 1. Here, the sensitivity is a function of the Laplace variable s. Use the magnitude frequency response plot to compare the sensitivities for K p = 1 and K p = 9. Consider now the position control system shown below with K p = 0.05, J = 20, and B = 1. + - S K p T d (s) Σ + + ( 29 1 s Js B + R(s) C(s) 