Question

Phase ( \deg) Magnitude (dB) \omega = \frac{1}{\tau} A controlled system is arranged according to the block diagram below, where $G_{c}(s)$ is the controller, $G_{p}(s)$ the plant with a PT2-characteristic, $R(s)$ the reference, and $Y(s)$ the controlled variable. $R(s)$ $Y(s)$ $G_{c}(s)$ $G_{p}(s)$ The Bode-diagram of the plant has been determined according to the graph below. Bode Diagram Frequency (rad/s) Page 12 of 13 Page(s) Student No.: / Student Name: a) Determine the output amplitude of the plant $y$, when the plant is excited with a harmonic signal with the input amplitude $\delta = 5$ and an excitation frequency of $\omega = \frac{1}{\tau}$. In the following the plant is controlled by a P-controller with $G_{c}(s) = K_{p}$. b) Is the closed-loop system stable for any $K_{p}$? Please explain. c) Determine the phase margin $\phi$ for $K_{p} = 1$.

          Phase (
\deg)
Magnitude (dB)
\omega = \frac{1}{\tau}
A controlled system is arranged according to the block diagram below, where $G_{c}(s)$ is
the controller, $G_{p}(s)$ the plant with a PT2-characteristic, $R(s)$ the reference, and $Y(s)$
the controlled variable.
$R(s)$
$Y(s)$
$G_{c}(s)$
$G_{p}(s)$
The Bode-diagram of the plant has been determined according to the graph below.
Bode Diagram
Frequency (rad/s)
Page 12 of 13 Page(s)
Student No.:
/ Student Name:
a) Determine the output amplitude of the plant $y$, when the plant is excited with a
harmonic signal with the input amplitude $\delta = 5$ and an excitation frequency of
$\omega = \frac{1}{\tau}$.
In the following the plant is controlled by a P-controller with $G_{c}(s) = K_{p}$.
b) Is the closed-loop system stable for any $K_{p}$? Please explain.
c) Determine the phase margin $\phi$ for $K_{p} = 1$.

Phase (
)
Magnitude (dB)
ω= (1)/(τ)
A controlled system is arranged according to the block diagram below, where Gc(s) is
the controller, Gp(s) the plant with a PT2-characteristic, R(s) the reference, and Y(s)
the controlled variable.
R(s)
Y(s)
Gc(s)
Gp(s)
The Bode-diagram of the plant has been determined according to the graph below.
Bode Diagram
Frequency (rad/s)
Page 12 of 13 Page(s)
Student No.:
/ Student Name:
a) Determine the output amplitude of the plant y, when the plant is excited with a
harmonic signal with the input amplitude δ = 5 and an excitation frequency of
ω = (1)/(τ).
In the following the plant is controlled by a P-controller with Gc(s) = Kp.
b) Is the closed-loop system stable for any Kp? Please explain.
c) Determine the phase margin ϕ for Kp = 1.

Added by Austin D.

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