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110年 - 110台灣聯合大學系統_碩士班招生考試_電機類:控制系統#104974
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題組內容
3. Consider the following feedback system with plant
and controller
(a) (6%) Plot the root locus for K＞0 and K＜0, respectively.
相關申論題
(a) Choose x1 as the output of the system. Write down the state space representation using as the state vector, where denotes the time derivative of for i = 1,2.
#445227
(b) Find the transfer function from f to x1.
#445228
(c) Suppose that Find the resonant frequencies of the systen in terms of r.
#445229
(d) Let f(t) =sin(ω0t) and ·. Find ω0, x2(0), and such that x1(t) = 0 for all t≥0.
#445230
(a) Find the conditions on k and a such that the closed-loop system is stable.
#445231
(b) Find k and a to satisfy the following requirements simultaneously:i. The closed-loop transfer function from r to y is a stable, order rational function.ji. The steady-state error with respect to the unit-ramp input r(t) = t, t ≥0, is less than 0.2.iii. The percent maximum overshoot with respect to the unit-step input r(t) = 1, t≥0, isless than 10%.
#445232
(c) Let Draw the root locus when k increases from 0 to ㆀo.If k = 1, what is the gain margin of the system?
#445233
(b) Sketch the Nyquist plot for K＞0.
#445235
(c) Analyze the stability from Nyquist plot for all K.
#445236
(d) To stabilize the system, a control engineer chooses ) where p＞0. Show that the root locus contains a circle for K＞0.
#445237
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110年 · #100776
and controller
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and controller