Question

1. The unity feedback system has a transfer function \begin{equation} G(s) = \frac{C(s)}{E(s)} = \frac{K}{s(s + a)} \end{equation} and is to follow a ramp input, $r(t) = tu(t)$, so that the steady-state output position differs from the input position by 0.01 of the input velocity (e.g., $e(\infty) = 1/K_v = 0.01)$. The natural frequency of the closed-loop system will be $\omega_n = 5$ rad/s. Answer the following questions (a) The system type (b) The values of K and a (c) The closed-loop system's damping ratio ($\zeta$)

          1. The unity feedback system has a transfer function
\begin{equation} 
G(s) = \frac{C(s)}{E(s)} = \frac{K}{s(s + a)}
\end{equation}
and is to follow a ramp input, $r(t) = tu(t)$, so that the steady-state output position
differs from the input position by 0.01 of the input velocity (e.g., $e(\infty) = 1/K_v = 0.01)$.
The natural frequency of the closed-loop system will be $\omega_n = 5$ rad/s.
Answer the following questions
(a) The system type
(b) The values of K and a
(c) The closed-loop system's damping ratio ($\zeta$)

1. The unity feedback system has a transfer function

G(s) = (C(s))/(E(s)) = (K)/(s(s + a))

and is to follow a ramp input, r(t) = tu(t), so that the steady-state output position
differs from the input position by 0.01 of the input velocity (e.g., e(∞) = 1/Kv = 0.01).
The natural frequency of the closed-loop system will be = 5 rad/s.
Answer the following questions
(a) The system type
(b) The values of K and a
(c) The closed-loop system's damping ratio (ζ)

Added by Jose R.

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