posted 1 years ago

\ddot{y}(t)+7 \dot{y}(t)+10 y(t)=4

y(0)=\dot{y}(t)=0

\text { Note: } \mathcal{L}(1)=\frac{1}{s} \text { and } \mathcal{L}\left(e^{-a t}\right)=\frac{1}{s+a} \text {. }

posted 1 years ago

Find the departure angles at pi and p2, and the arrival angle at 21.

\text { Departure angle: } \phi_{d e p}=\sum_{j=1}^{m} \psi_{j}-\sum_{i \neq d e p}^{n} \phi_{i}-180(2 k+1)

\text { Arrival angle: } \psi_{a r r}=\sum_{i=1} \dot{\phi}_{i}-\sum_{j \neq a r r}^{m} \psi_{j}+180(2 k+1)

(2) (2.5 points) Find the range of K for closed-loop stability using the Routh stability criterion.

posted 1 years ago

(2) (2.5 points) Determine K, and K2 such that wn = 4 rad/sec, and t, = 1 sec. Note:uhere u and t are the natural freguency and damning ratio respectivel:

Consider the closed-loop control system shown below:

Derive the closed-loop sensitivity function: S(s) = E(s)/R(e).

t_{s}=\frac{4}{\omega_{n}} \text {, where } \omega_{n} \text { and } \zeta \text { are the natural frequency and damping ratio, respectively. }

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posted 1 years ago

a. Compute the controller gain Kp so that the undamped natural frequency of the closed-loop system is w, = 4 rad/s.

b. Compute the controller gain Kp so that the damping ratio of the closed-loop system is = 0.7.

Compute the steady-state output for a step reference input r(t)=4u(t) and controller gain kr=2

posted 1 years ago

a. Determine whether the closed-loop system is stable for control gain K, 2.

b. Compute the controller gain Kp so that step response shows 25% overshoot.

c. Estimate the settling time for a step reference input if the control gain is K, 0.5.

G_{p}(s)=\frac{1}{s^{2}+6 s+8}

posted 1 years ago

G(s)=\frac{I(s)}{E_{\text {in }}(s)}=\frac{1}{L s+R}

where the output is current /() and the input is source voltage e (). If the system parameters are L 0.02Hand R = 1.5 2, determine the bandwidth (in hertz, Hz) of the RL circuit.

posted 1 years ago