# me351_hw4 - the Routh’s criterion to determine the...

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ME 351 Modeling and Control of Dynamic Systems Homework # 4 Due: Weds 15.04.2009 [1]. For the control system shown below, find the value of K and K t so that the maximum overshoot of the output is approximately 4.3% and the rise time t r is approximately 0.2 s. Verify your design in MATLAB/Simulink. [2]. For the control system shown above, find the values of K and Kt so that the damping ratio of the system is 0.6 and the settling time of the unit-step response is 0.1 s. Verify your design in MATLAB/Simulink. [3]. Using the Routh’s criterion, determine the stability of the closed-loop system that has the following characteristic equations. Determine the number of roots in the right-half s-plane. (a) s s s 3 2 25 10 450 0 + + + = (b) s s s 3 2 25 250 10 0 + + + = [4]. Given the forward-path (open-loop) transfer function of unity-feedback (closed-loop) control systems, apply
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Unformatted text preview: the Routh’s criterion to determine the stability of the closed-loop system as a function of K. Determine the value of K that will cause pure oscillations in the system. Determine the frequency of oscillations. (a) 3 K(s 4)(s 20) s (s 100)(s 500) + + + + (b) 2 K(s 10)(s 20) s (s 2) + + + [5]. For the electric circuit shown, find the following: (a) The time-domain equation relating i(t) and v1(t); (b) The time-domain equation relating i(t) and v2(t); (c) Assuming all initial conditions are zero, the transfer function V2(s)/V1(s) and the damping ratio ξ and undamped natural frequency ω n of the system; (d) The values of R that will result in v2(t) having an overshoot of no more than 25%, assuming v1(t) is a unit step, L = 10 mH, and C = 4 μ F....
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