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Q1:EXERCISE 4.17.29: (Chapter 4, Problem 29 in the 8th Edition). EXERCISE 4.17.54: (Chapter 4, Problem 54 in the 8th Edition). (a) Consider the translational mechanical system shown below. A I-pound force, f(t), is applied at t = 0. If f = 1, find K and M such that the response is characterized by a 4-second settling time and a 1-second peak time. Also, what is the resulting percent overshoot? [Section: 4.6] GSee Answer
Q2:(a) Find the damping ratio and natural frequency for each second-order system of Problem 4.17.6 and show that the value of the damping ratio conforms to the type of response (underdamped, overdamped, and so on) predicted in that problem. [Section: 4.5]See Answer
Q3:EXERCISE 4.17.16: (Chapter 4, Problem 16 in the 8th Edition). Find the location of the poles of second-order systems with the following specifications: [Section: 4.61 (a) %OS = 15; T₂ = 0.5 second (b) %OS = 8; T₂ = 10 seconds (c) Ts = 1 second; Tp = 1.1 secondsSee Answer
Q4: 2. (19 pts.) (Chapter 3) Given the dc servomotor and load shown, represent the system in state space, where the state variables are the armature current, ia, load displacement, OL, and load angular velocity, wL. Assume that the output is the angular displacement of the armature. Do not neglect armature inductance. See Answer
Q5: For the following G(s), find analytical expressions for the magnitude and phase response. G(s)=\frac{10}{s(s+1)}See Answer
Q6: Given the following open-loop plant: G(s)=\frac{20(s+2)}{s(s+5)(s+7)} design a controller to yield a 10% overshoot and a settling time of 2 seconds. Place the third pole 10 times as far from the imaginary axis as the dominant pole pair. Use the phase variables for state-variable feedback.See Answer
Q7: Use MATLAB to plot the Bode diagram for the 1-DOF mechanical system in Problem 9.11 (Fig. P9.11).Estimate the frequency response for the position input xin(r) = 0.04 sin 50r m by reading the Bode diagram(indicate the frequency response parameters on the plot of the Bode diagram). Obtain a more accurate answer by using MATLAB's bode command with left-hand-side arguments for computing magnitude and phase angle.See Answer
Q8: Make a plot of the log magnitude and the phase, using log-frequency in rad/s as the coordinate.USE asymptotic approximations (Do not use bode function in Matlab).See Answer
Q9:Consider the closed-loop system shown below: Find the sensitivity functionSee Answer
Q10: Consider again the simple RL circuit shown in Fig. 9.5 (Example 9.1). The transfer function of the RLcircuit is G(s)=\frac{I(s)}{E_{\mathrm{in}}(s)}=\frac{1}{L s+R} where the output is current /(1) and the input is source voltage e(t). If the system parameters are L = 0.02 Hand R = 1.5 ohms determine the bandwidth (in hertz, Hz) of the RL circuit.See Answer
Q11: 2. (19 pts.) (Chapter 3) Given the dc servomotor and load shown, represent the system in state space, where the state variables are the armature current, ia, load displacement, OL, and load angular velocity, WL. Assume that the output is the angular displacement of the armature. Do not neglect armature inductance. See Answer
Q12: Given the transfer function G(s)=\frac{3 s+1}{2 s^{2}+6 s+40} determine the sinusoidal transfer function.See Answer
Q13: 1. A) Find and plot closed-loop pole locations of the system below for K=0, 10, 25, 40, 50 B) Calculate the angles and magnitude of the closed-loop transfer function for each of the poles depending on the K above. C) Plot closed loop time response for each closed loop transfer function for K = 0, 10, 25, 40, 50. D) Discuss the transient response: pole locations and time response. E) Discuss the steady-state response. See Answer
Q14: Given the I/O equation 2 y+10 y=3 u \text { compute the frequency response } y_{\mathrm{ss}}(t) \text { for the input } u(t)=18 \sin 4 t \text {. }See Answer
Q15: Figure P10.4 shows a closed-loop control system. a. Compute the controller gain Kp so that the undamped natural frequency of the closed-loop system is0, =4 rad/s. Compute the controller gain Kp so that the damping ratio of the closed-loop system is 30.7.Compu c. Compute the steady-state output for a step reference input r(t)Kp = 2.4U( and controller gainSee Answer
Q16: Consider the closed-loop system shown below: T > 0. Determine stability of the closed-loop system using where K, > 0, K; > 0 and Routh's stability criterion.See Answer
Q17: Figure P9.11 shows a 1-DOF mechanical system driven by the displacement of the left end, x(t), which could be supplied by a rotating cam and follower (see Problem 2.2). When displacements x,(1) 0 and x= 0 the spring k is neither compressed nor stretched. The system parameters are m 2 kg, k = 500 N/m,and h = 20 N-s/m. Determine the frequency response if the position input is x(t) = 0.04 sin 50f m. See Answer
Q18: A typical liquid storage process is shown in the figure, qi and q are volumetric flow rates, assuming thatthe liquid density is constant and the tank is cylindrical with cross sectional area A, and the tank has avalve at the outlet which has a flow head equation of \boldsymbol{q}=\frac{1}{\boldsymbol{R}_{\mathrm{r}}} \boldsymbol{h} Then the differential equation which describes this process will be A \frac{d h}{d t}=q_{i}-\frac{1}{R_{v}} hSee Answer
Q19: Problem 5. In the Problem 4, calculate the steady-state errors with the unit step (r(t) = 1)(5 points) and the unit ramp (r(t) = t) (5 points) references.See Answer
Q20: .Consider the closed-loop system shown below: Find the sensitivity function (i.e. S(s) = E(s)/R(s)) (5 points) and calculate the steady-state error with the unit ramp reference (i.c. r(t) = t) (5 points) using final value theorem.See Answer

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