When a unit step is applied to a system at t= 0, its response is y(t)...
2. When a unit step is applied to a system at 0 its response is y(1) = | 4 +-e-3,-e-2,(2 cos 41 + 3 sin 41) | u(t) (a) What is the transfer function of the system? (b) What is the governing differential equation for this system?
Question three The figure below shows a unit step response of a second order system. From the graph of response find: 1- The rise timet, 2- The peak timet, 3- The maximum overshoot Mp 4- The damped natural frequency w 5. The transfer function. Hence find the damping ratio ζ and the natural frequency ah-Find also the transfer function of the system. r 4 02 15 25 35 45 Question Four For the control system shown in the figure below,...
3. Work the following problems: a. The transfer function of a system is: Y(s)/R(s) = 15(s+1)/(s2+9s+14). Determine y(t) when r(t) is a unit step input. b. Consider the following system: R(s)_ 0 G(s) i. Find the closed-loop transfer function Y(s)R(S) when G(s) = 10/(S2+2s+10) ii. Determine Y(s) when the input R(s) is a unit step. iii. Compute y(t).
5. (30) Find the unit step response of the system where its transfer function is defined as s + 10 G(s) = 20 (s2 + 165 + 100)(s + 1)(s + 2) Sketch the time response of this system roughly.
Y (s) R(s) 6460 (s 3) (s2 + 6s 64) G(s) Plot unit step response y(0) for on -10.6,E-0.707 Does the closed loop system T(s) G(S) behave like a pure 1 +G(s) second order system of the form H (s) = s2 +2ξω.s +
Y (s) R(s) 6460 (s 3) (s2 + 6s 64) G(s) Plot unit step response y(0) for on -10.6,E-0.707 Does the closed loop system T(s) G(S) behave like a pure 1 +G(s) second order system of...
3. (20 points) A system has an impulse response given by h (t) sin (2t) rt (a) Find the frequency response function of this system H (w). (b) Find the frequency domain output Y (w) if the input to the system is z (t) cos (3t).
4. The unit step response of a first order system is shown below: Step Response Amplitude 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Time (seconds) Please find the transfer function of this system. Please include detailed steps. Hint: Please find the time constant and the constant gain (the numerator)
4. The unit step response of a first order system is shown below: Step Response Amplitude 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Time (seconds) Please find the transfer function of this system. Please include detailed steps. Hint: Please find the time constant and the constant gain (the numerator)
Problem 1 Given the transfer function from input u(t) to output y(t), s2-4s +3 Y(s) U(s) (s2 + 6s + 8)(82 + 25) (a) Develop a state space model for this transfer function, in the standard form y=Cx + Du (b) Suppose that zero input is applied, such that u 0. Perform a modal analysis of the state response for this open-loop system. Your analysis should include the nature of the time response for each mode, as well as how...
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...