Given a closed-loop single-input single-output system x(t) Ax(t) cTx(t) y(t) The system is controlled by a PID controller given by = = + bu(t) u(t) = − kpe(t) – kvė(t) — kï | e(t)dt Je(t) where e(t) = r(t) − y(t) and r(t) is a reference input. Give a state representation of the closed-loop system where r(t) is the input and y(t) is the output.

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Given a closed-loop single-input single-output system
=
X(t)
Ax(t) + bu(t)
y(t) = c¹x(t)
The system is controlled by a PID controller given by
u(t) = −kpe(t) — kvė(t) – kī | e(t)dt
felt
where e(t) = r(t) − y(t) and r(t) is a reference input.
Give a state representation of the closed-loop system where r(t) is the input and y(t) is the output.
Transcribed Image Text:Given a closed-loop single-input single-output system = X(t) Ax(t) + bu(t) y(t) = c¹x(t) The system is controlled by a PID controller given by u(t) = −kpe(t) — kvė(t) – kī | e(t)dt felt where e(t) = r(t) − y(t) and r(t) is a reference input. Give a state representation of the closed-loop system where r(t) is the input and y(t) is the output.
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