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1 Review Problems 1. Write a user-defined function with function call C=temp_conv(F) that converts the temperature from Farenheit Fto Celsius C. Execute the function for the case of F = 86. Solution function C = temp_conv(F) C = (F-32)*100/180; 2. […]

439 00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.2 0.6 0.8 1 1.2 1.4 Step Response Time (sec) Figure PS10-4 No5 Amplitude Closed-loop response 6. Consider the feedback control system shown in Figure 10.43. a. Find the values […]

419 Problem Set 10.1 1. Draw a block diagram for the feedback control of a liquid-level system, which consists of a valve with a control knob (0–100%) and a liquid-level sensor. Clearly label essential components and signals. Solution 2. Draw […]

459 c. The frequency response function is         2 jȦMȦ 255 22 jȦMȦ 12 12 25 2 0.01 1 jȦ MȦ  (jȦ jȦ  MȦ  144 2 0.01 1 G ªº […]

8. Consider Problem 7 in Problem Set 10.7. Using the full-state feedback controller obtained in Part (b), build a Simulink block diagram to simulate the resulting feedback control system. Find the closed-loop response if the initial conditions are x1(0) = […]

23 In Problems 19–24, (a) Find the inverse Laplace transform using the partial-fraction expansion method. (b) Repeat in MATLAB. 19. 34 (1) s ss   Solution (a) Expand as 34 34 ( ) 41 (1) 1 (1) AB A […]

11 Problem Set 2.1 In Problems 1–4, (a) Perform 12 /zz and express the result in rectangular form, (b) Verify that 12 1 2 //zz z z , (c) Repeat Part (a)in MATLAB. 1.3 2 j j  Solution (a) […]

35 Problem Set 3.1 In Problems 1–8 perform the indicated operations, if defined, for the vectors and matrices below. 0 30 2 1 0 1 , , , 1 12 15 4 2 3 ½  ªº ª º ½ […]

50 5. 110 220 001 ªº «» «» «» ¬¼ A Solution (a) Block diagonal matrix; () 0,1,3 O A . For 10 O we solve >@ 111 110 0 1 2 2 0 0 1 001 0 0  […]

120 2 12 12 (2 1) 3 (3 2) 0 ss X X F XsX   ° ®  ° ¯ Solve for 1 X : 2. A dynamic system with input f and output x is described by […]

65 Problem Set 4.1 In Problems 1–10 express the system model, assuming general initial conditions, in (a) Configuration form, (b) Standard, second-order matrix form. 1. 11 12 1 22 12 2 2( ) 10 2( ) 0 t xx xx […]

85 18. Electric charge qand electric current i are related via /idqdt . In Problem 17, find the transfer function if ()qt and ()vt are the system output and input, respectively. Solution Noting /idqdt , the governing equation can be […]

20. The block diagram representation of a system model is presented in Figure 4.33, where U, 1 X ,2 X , and Y denote the Laplace transforms of the input, the two state variables, and the output. (a) Derive the […]

208 Figure Review5 No3 b. Taking the Laplace transform of both sides of the preceding equation with zero initial conditions results in 2 eq () 1 () Xs Fs ms k  c. The state, the input, and the output […]

194 b. Using the differential equation obtained in Part (a), determine the state–VSDFHUHSUHVHQWDWLRQ8VHșa,ș1Ȧa, DQGȦ1as tKHVWDWHYDULDEOHVDQGXVHș2DQGȦ2as the output variables. Figure 5.99 Problem 4. Solution a. Assume that a1 șș!! . The free-body diagram is shown below. Applying the moment equation to […]

154 Rearranging the equations, we have 11 11 1 2 1 2 2 1 ()mx bx k k x k x f    22 21 2 3 2 2 ()mx kx k k x f  b. The […]

15. Consider the system shown in Figure 5.73, where a uniform sphere of mass mand radius rrolls along an inclined plane of 30°. A translational spring of stiffness kis attached to the sphere. Assuming that there is no slipping between […]

134 Problem Set 5.1 1. If the 50–kg block in Figure 5.12 is released from rest at A, determine its kinetic energy and velocity after it slides 5 m down the plane. Assume that the plane is smooth. Figure 5.12 […]

262 Figure 6.74 Problem 6. Solution The transfer function Vo(s)/Vi(s) is MATLAB Figures Problem 1 i(t) vC(t) V + – Voltage Sensor Switch f(x)=0 Solver Configuration Simulink–PS Converter Scope Re si st o r PS-Simulink Converter Electrical Reference DC Voltage […]

222 Problem Set 6.1 1. Determine the equivalent resistance Req for the circuit shown in Figure 6.8. Figure 6.8 Problem 1. Solution The equivalent resistance for the parallel-connected resistors R1and R3is eq1 1 3 111 RRR  or 13 eq1 […]

242 Figure 6.38 Problem 2. Solution Because the current drawn by the op-amp is very small, i.e., 0ii  || , we have at node 1, 12 ii o 1 12 vv vv RR    or 21 1o […]

274 which can be rearranged and gives the second equation 122 22 111 0vvv RRL   or 1222 0Lv Lv R v   b. Replacing the passive elements with their impedance representations gives the circuit in the sdomain […]

285 Problem Set 7.1 1. A car has an internal volume of 2.8 m3. If the sun heats the car from a temperature of 20°C to a temperature of 40°C, what will the pressure inside the car be? Assume the […]

298 Solution a. The characteristic length of the junction is 3 4 body 3 c2 surface ʌ1 0.001 4ʌ  Vr Lr Ar The Biot number of the junction is Thus, the junction can be treated as a lump-temperature system, […]

365 Figure PS8-5No11 12. A nonlinear dynamic system model is derived as 3 2 ( ) , (0) 0 , 0 3xxutx t dd  where ()ut is the unit-step function. (a) Build the Simulink model and use it to […]

351 In Problems 5 through 10 determine the state vector via the formal-solution approach. 5. 21 1 0 , unit-step function , (0) 42 2 1 uu  ªºªº ½  ®¾ «»«»  ¬¼¬¼ ¯¿ xx x  Solution […]

311 Problem Set 8.1 1. Consider a first-order system with time constant W and zero initial condition. Find the system’s unit-impulse response for 1 4 W and 1 2 W , plot the two curves versus 02tdd in the same […]

331 Figure PS8-2No21-1 Figure PS8-2No21-2 22. The equations of motion of a mechanical system are given below, where ()t G denotes the unit-impulse. Assuming zero initial conditions, plot the response 1()xt by (a) Simulating the Simulink model of the system. […]

379 Problem Set 9.1 1. A lightly damped single-degree-of-freedom system is subjected to free vibration. The response of the system is shown in Figure (VWLPDWHWKHYDOXHRIWKHYLVFRXVGDPSLQJUDWLRȗ. Figure 9.5 Problem 1. Solution Note that the first and fifth peak displacements are about […]

399 % modal response to external excitations f0 = [0.15 0 0]’; omega = 0.15; figure(1); 020 40 60 80 100 -5 020 40 60 80 100 -1 0 5x 10 1 0 1x 10 1 -5 q 020 40 […]