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1、1.2. Explain how the rudder positioning system discussed in problem 1.1 can be modified to become a closed-loop control system.1.3. An electric hot-water heater is illustrated in Figure P1.3. The heating element is turned on and off by a thermostatic switch in order to maintain a desired temperature
2、. Any demand for hot water results in hot water leaving the tank and cold water entering. Draw the simple functional block diagram for this closed-loop control system and qualitatively explains how it operates if the desired temperature of the thermostat is changed.1.4. Explain how the system discus
3、sed in problem 1.3 operates if the ambient temperature surrounding the tank suddenly changes .Refer to the block diagram.1.6. Devise a system that can control the speed of an internal-combustion engine in accordance with a command in the form of a voltage. Explain the operation of your system.1.7. D
4、evise a system that can control the position, rate, and acceleration of an elevator used in an apartment house. What specifications or limits would you place on the position, velocity, and acceleration capabilities of the system?1.8. For the control system devised in Problem 1.7, describe what happe
5、ns when a man weighing 200 lb enters the elevator that has stopped at one of the floors of the apartment building. Utilize a functional block diagram.1.9. The economic model illustrated in Figure Pl.9 illustrates the relationship between wages, prices, and cost of living. Note that an automatic cost
6、 of living increase results in a positive feedback loop. Indicate how additional feedback loops in the form of legislative control can stabilize the economic system.1.10. Explain what happens to the automatic position control system illustrated in Figure 1.20 if the speed-measuring device fails. Can
7、 the system still operate?1.11 Determine what happens in the autopilot system illustrated in Figure 1.23 if the aircraft suddenly enters a turbulent atmosphere.1.12 Modify the block diagram of the attitude-control system of the space vehicle illustrated in Figure 1.16, to allow for sudden failure of
8、 the computer and manual control of the vehicle.2.1. Determine the poles and zeros of2.2. Determine the Lap lace transform of f(t) which is given by, ,2.3. Determine the Laplace transforms F(s) for the function /(r) illustrated:Figure 12.3From Table2.1, item2, and the time-shifting theorem, we obtai
9、n 2.5. Determine the 1inal value of c(r) when the Laplace transform of c(s) is given by2.6. Determine the final value of r(r) when the Laplace transform of C(s) is given by2.7. Determine the Laplace transform of: From knowledge of the Laplace transform of a sine wave (see Table 2.1, item7) and the t
10、ime-shifting theorem.2.9. Determine the Laplace transform of the function f(t) where2.10 determine the residues of F(s) wherewhich has single poles at s=-2 and s-42.15. Determine the value of c(t) for the following differential equation using the Laplace transform. Where 2.19. We wish to determine t
11、he transfer function of an element in a control system. To determine its transfer function, a unit ramp is applied to the input r(t). The output of this element is recorded, and is modeled according to the following equation: Determine the transfer function, ,of this element.2.22. The signal-flow gr
12、aph of a control system is represented by the following, where D(s) represents an external disturbance input into the control system:(a) Determine the transfer function (b) Determine the transfer function2.25. Determine the state transition matrix as a sum of an infinite series using E.q (2.323) for
13、 a system whose P matrix is given by:Carry out the computation in E.q (2.323) from k=0 through k=2.4. 1 A control system whose two closed-loop poles and one closed-loop zero are located in the s-plane is illustrated:(a) Determine the closed-loop transfer function in its simplest form.(b) Determine t
14、he impulse response of this system using the table of Laplace transforms in Appendix A.4.2 A control-system engineer is trying to reduce costs in his development project to produce a positioning system using a two-phase ac servomotor. The engineer finds a discarded two-phase ac servomotor on a shelf
15、 in the parts room, and wants to know its characters so that he can determine its usefulness for the project. It is decided to observe the response of this motor in a unit gain feedback loop to a unit step input as illustrated:From the observed characteristics, determine:(a) The undamped natural res
16、onant frequency of this system.wn(b) The motor time constant, tm.(c) The motor constant. Km.4.3 The two phase ac servomotor and load, in conjunction with the gear train specified in Problem3 .19,i s used in a simple positioning system as shown in Figure P4.1. Assume that a difference amplifier, whos
17、e gain is 20, is used as the error detector and also supplies power to the control field.(a) What are the undamped natural frequency and damping ratio (b) What are the percent overshoot and time to peak resulting from the application of a unit step input(c) Plot the error as a function of time on th
18、e application of a unit step input.4.4 repeat Problem 4.3 with the gain of the difference amplifier increased to 40.What conclusions can you draw from your results?4.5Repeat Problem 4.3 with the gain of the difference amplifier decreased to 10.What conclusions can you draw from your result?4.9. A tw
19、o-phase ac induction motor is used to position a device in a feedback configuration represented by Figure P4.I. The time constant of the motor and load, Tm.is 0.5 sec.(a) Determine the combined amplifier and motor constant gain Km which will result in a damping ratio of 0.5.(b) What is the resulting
20、 undamped natural frequency for the value of gain determined in part (a)?4.13. For Figure p4.13 determine the following:(a) Undamped natural frequency, wn.(b) Damping ratio .(c) Maximum percent overshoot.(d) Time to peak, tp.5.1. Assume that the system shown in Figure p5.r has the following characte
21、ristics:5.11. A control system is used to position the rudder of an aircraft. Its block diagramed an be adequately represented shown in Figure p5.l l.(a) Determine the sensitivity of the systems transfer function with respect to G(s) .(b) Determine the sensitivity of the systems transfer function wi
22、th respect to Ka.(c) Determine the absolute value of the sensitivities determined in parts (a) and (b) to wind gusts that can be approximated to primarily exist at l rad/sec. which element is more sensitive at this frequency, the amplifieror servo motor?(d) How much will the systems transfer functio
23、n vary at I rad/sec if Ka changes by 50%5.14. Figure P5.14 illustrates an electronic pacemaker used to regulate the speed of the human heart. Assume that the transfer function of the pacemaker is given by and assume that the heart acts as a pure integrator. (a) For optimum response, a closed-loop da
24、mping ratio of 0.5 is desired. Determine the required gain K of the pacemaker in order to achieve this.(b) What is the sensitivity of the system transfer function? C(s)/R(s), to small changes in K?(c) Determine this sensitivity at dc.(d) Find the magnitude of this sensitivity at the normal heart rat
25、e of 60 beats/minute5.15 A control system used to position a load is shown in Figure p5.15.(a) Determine the steady-state error for a step input of l0 units(b)How should G(s) be modified in order to reduce this steady-state error to zero?5.20. A control system containing a reference in put, R(s) and
26、 a disturbance input.D(s), is illustrated:.(a) Determine the steady-state error, ess, for a unit-step disturbance at D(s) in terms of the unknown transfer function G(s).(b) Select the simplest value of G (s) which will result in zero steady-state error for E(s) when D(s) is a unit step input.6.1. Th
27、e stability of the feedback control system of Figure p6.1 is to be determined.(a)Determine the systems P matrix from its state equations.(b)Find the systems characteristic equation from knowledge of the P matrix.(c)Using the Routh- Hurwitz criterion, determine whether this feedback control system is
28、 stable.6.6. A control system used to position a load is illustrated in Figure P6.6.(a) Determine the characteristic equitation of this control system.(b) Determine the maximum value of K which can be used before the system becomes unstable using the Routh-Hurwitz criterion.6.8. Using the Routh Hurw
29、itz stability criterion, determine if the feedback control system shown in Figure P.68 is stable for the following transfer functions:6.31. A feedback control system has the configuration shown in Figure P6.31.where U(s) represents an extraneous signal appearing at the input to the plant7.11 It is d
30、esired that the system considered in problem 6.28 have a phase margin of 45at the crossoverfrequency. Determine the stabilizing element required to achieve this.8.2. A control system containing a controller and a process are illustrated in the block diagram in Figure P8.2(i).(a)Determine the state e
31、quations of this control system.(b)Determine the characteristic equation from knowledge of P8.5. Repeat Problem 84 for the following specifications:8.22. The optimum sensitivity for the control system illustrated in Figure P8.22 is to be determined in the H sense. The process G(s) has a transfer function given byThe weighting function. W(s), is given by