4. (20 pts) Assume the rotational velocity of certain system is given by 2s +8 AS...
Time (s) Problem 4 (16 pts) A sailing ship of mass, m, is initially at rest, i.e. V(O) strong wind arises of magnitude and keep push the ship. 0. At time Vo = 40m/s Assume that the force of the wind on the sails in the direction of travel is given by Fw(t) = Bw [V - v(t)] Assume that the viscous drag of the water on the ship is given by a. (4 pts) Formulate a differential equation that...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input torque is supplied by an electric motor Specifically, T(t) T(t) -Kamp Vin(t) where 1) "Vin is the input voltage supplied to the motor N-m 2) "Kamp" is the motor gain (this constant has units of Volt) So, the transfer function for this system is (s)Kamp The moment of inertia is known...
Q5. (20 pts] Given i (0)=0 and Vc(0)=0, find the following for the circuit of Fig. 5 using time domain techniques a) W., alpha, S1, and s2. b) vc(-) = vc(final) = vc(steady-state). c) vc(t) for t20. t=0 / 0.11 1812 | + 0.4uF + V(t) 48V = Fig. 5
Ks+8-0. For this system. 6. A negative feedback system has characteristic equation 1+ s2 +2s +2 (a) Sketch the root-locus, marking all important points, numerical values, incl. the angle of departure (possibly in terms of tan(x (b) Find the gain when the roots are both equal and find these 2 equal roots. 6 pts) 4 pts) Ks+8-0. For this system. 6. A negative feedback system has characteristic equation 1+ s2 +2s +2 (a) Sketch the root-locus, marking all important points,...
The velocity in a certain two-dimensional flow field is given by the equation: ✓ = 2xti – 2 yı where the velocity is in ft/s when x, y, and t are in feet and seconds, respectively. (a) Is flow steady or unsteady (b) Determine the expression of acceleration (c) Check if the flow is compressible or incompressible (d) Check if the flow is rotational or irrotational (e) Sketch the streamlines of t= ls on a x-y plane W
Please solve as a MATLAB code. A unity feedback closed loop control system is displayed in Figure 4. (a) Assume that the controller is given by G (s) 2. Based on the lsim function of MATLAB, calculate and obtain the graph of the response for (t) at. Here a 0.5°/s. Find the height error after 10 seconds, (b) In order to reduce the steady-state error, substitute G (s) with the following controller This is a Proportional-Integral (PI) controller. Repeat part...
Problem 7. (15 pts] Given the system below, find the following: a. The steady-state error for 15u(t) b. The steady state error for 20tu(t) R(s) 255 +1 10
20. a. Find the system function given the following difference equation: = x (n b. Find the steady-state response to x(n)-cos(π n). C. Find the magnitude and phase of the frequency response for π. ω d. Obtain b from c 20. a. Find the system function given the following difference equation: = x (n b. Find the steady-state response to x(n)-cos(π n). C. Find the magnitude and phase of the frequency response for π. ω d. Obtain b from c
Question #1 (60 pts): A closed-loop digital control system having a proportional controller is given in the following figure\(G_{1}(s)=\frac{1-\exp (-T s)}{s(s+1)}, G_{2}(s)=\frac{1}{s}, G_{3}(s)=\frac{1-\exp (-T s)}{s(s+2)}\)where \(\exp (\cdot)\) denotes the standard exponential function.a) Obtain the overall transfer function of the closed-loop system.b)Obtain the range of proportional gain (i.e., \(\mathrm{K}\) ) that guarantees the system stability via Jury'sStability Test.c) Assume that the input of the system is a unit step input (i.e., \(r(t)=u_{s}(t)\) ), obtain the gain value from the range obtained in...
Problem 4: (65 points) Let a system be given by the state space representation 8 8 10 * = X+ u(t), y = [1 -1]x – u(t) 1 1 -1 0 Y(S) d) (7) Find the transfer function US) e) (5) Is the system BIBO stable? 3 f) (9) Let the initial state x(0) -3 u(t) = 0) for all t > 0. = Find the zero input response (i.e., with the input