所屬科目：研究所、轉學考(插大)◆控制系統
(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.
(c) Suppose that Find the resonant frequencies of the systen in terms of r.
(d) Let f(t) =sin(ω0t) and ·. Find ω0, x2(0), and such that x1(t) = 0 for all t≥0.
(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%.
(c) Let Draw the root locus when k increases from 0 to ㆀo.If k = 1, what is the gain margin of the system?
(d) To stabilize the system, a control engineer chooses ) where p＞0. Show that the root locus contains a circle for K＞0.
(e) As in part (d), design the closed-loop poles at -1± j, design the controller
(b) Consider a system ruled by , find the representation of A, B, and C with Controllability Canonical Form.
(c) Without initial condition, what is the impulse response of the output by part (a)? Hint: the Laplace transform of Φ(t) is.Do NOT computed Φ(r)directly.
(d) Solve the impulse response,h(1),)with differential equation approach. What is your observation with the result in part (c)?
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as the state vector, where 
denotes the time derivative of 
for i = 1,2.
Find the resonant frequencies of the systen in terms of r.
. Find ω0, x2(0), and 
such that x1(t) = 0 for all t≥0.
order rational function.
Draw the root locus when k increases from 0 to ㆀo.If k = 1, what is the gain margin of the system?
) where p＞0. Show that the root locus contains a circle for K＞0.
, find the representation of A, B, and C with Controllability Canonical Form.
.Do NOT computed Φ(r)directly.
)with differential equation approach. What is your observation with the result in part (c)?