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engineering
modern control systems
Modern Control Systems 14th Global Edition Richard Dorf, Robert Bishop - Solutions
P10.6 Repeat Problem P10.5 by using a phase-lead compensator and compare the results.DAta from in P10.5 tachometer and a DC direct-drive torque motor, as A stabilized precision rate table uses a precision shown in Figure P10.5. We want to maintain a high steady-state accuracy for the speed
P10.5 tachometer and a DC direct-drive torque motor, as A stabilized precision rate table uses a precision shown in Figure P10.5. We want to maintain a high steady-state accuracy for the speed control. To obtain a zero steady-state error for a step command design, select a proportional plus
P10.4 Magnetic particle clutches are useful actuator devices for high power requirements because they can typically provide a 200-W mechanical power output.The particle clutches provide a high torque-to-inertia ratio and fast time-constant response. A particle clutch positioning system for nuclear
P10.3 A simplified version of the attitude rate control for a supersonic aircraft is shown in Figure P10.3. When the vehicle is flying at four times the speed of sound (Mach 4) at an altitude of 100,000 ft, the parameters are [26]Design a compensator G s c( ) so that the response to a step input
P10.2 A magnetic tape recorder transport for modern computers requires a high-accuracy, rapid-response control system. The requirements for a specific transport are as follows: (1) The tape must stop or start in 10 ms, and (2) it must be possible to read 45,000 characters per second. This system is
P10.1 The design of a lunar excursion module is an interesting control problem. The attitude control system for the lunar vehicle is shown in Figure P10.1. The vehicle damping is negligible, and the attitude is controlled by gas jets. The torque, as a first approximation, will be considered to be
E10.21 Consider the unity feedback system shown in Figure E10.21. Design the controller gain, K, such that the maximum value of the output y(t) in response to a unit step disturbance T s d ( ) = 1 s is less than 0.1. FIGURE E10.21 Closed-loop feedback system with a disturbance input. Controller
E10.20 Consider the system shown in Figure E10.20.Design the proportional-derivative controllerG s c ( ) such that the system has a phase margin of 40° . ≤ ≤ P M. 60°. FIGURE E10.20 Unity feedback system with PD controller. R(s) + Controller Process E(s) 1 Kp+ KD Y(s) s(s-2)
E10.19 A unity feedback control system has the plant transfer function 1 G(s)= s(s-2) Design a PID controller of the form Ge(s) = Kp + Kps+KI S so that the closed-loop system has a settling time of T,
E10.18 The nonunity feedback control system shown in Figure E10.18 has the transfer functions 1 G(s) = and H(s) = 10. s-20 Design a compensator G. (s) and prefilter Gp (s) so that the closed-loop system is stable and meets the following specifications: (i) a percent overshoot to a unit step input
E10.17 Consider again the system of Exercise 10.9. SelectKP and KI so that the step response is deadbeat and the settling time (with a 2% criterion) is Ts ≤ 2 s.
E10.16 Consider again the system and specifications of Exercise E10.15 when the required crossover frequency is ωc = 3 rad s.Data from in E10.15 A unity feedback control system has a plant transfer function 100 G(s) = s(s+8) We desire to attain a steady-state error to a ramp r(t) = At of less
E10.15 A unity feedback control system has a plant transfer function 100 G(s) = s(s+8) We desire to attain a steady-state error to a ramp r(t) = At of less than 0.16A and a phase margin of P.M. = 35. We desire to have a crossover frequency we 20 rad/s. Determine whether a phase-lead or a phase-lag
E10.14 A robot will be operated by NASA to build a permanent lunar station. The unity feedback position control system for the gripper tool has the process transfer function 6 G(s) == s(1+0.5s)(1+0.166s) Determine a phase-lag compensator G(s) that will provide a phase margin of P.M. = 40.
E10.13 The design of Example 10.3 determined a lead network in order to obtain desirable dominant root locations using a cascade compensator G s c ( ) in the system configuration shown in Figure 10.1(a). The same lead network would be obtained if we used the feedback compensation configuration of
E10.12 The control of an automobile ignition system has unity feedback and a loop transfer functionL s( ) = G s c( )G s( ), whereLet K K I P = 1 and determine KKP so that the complex roots have a damping ratio of ζ = 1 2 . K G(s)= = and G(s) Kp + K/s. $($+6)
E10.11 A unity feedback system has G(s)= 1350 s(s+1)(s +25) A lead network is selected so that G(s) 1+0.5s = 1+0.05s Determine the peak magnitude, Mp, and the band- width, w, of the closed-loop frequency response. From Mp estimate the percent overshoot, P.O., to a unit step. Compare with the actual
E10.10 A control system with a controller is shown in Figure E10.10. Select KI = 2 in order to provide a reasonable steady-state error to a step [8]. Find KP to obtain a phase margin of P M. . = 60°. Find the peak time and percent overshoot of this system.
E10.9 A control system with a controller is shown in Figure E10.9. Select KP and KI so that the percent overshoot to a step input is P O. . = 4%, and the velocity constant Kυ is equal to 10. Verify the results of your design.
E10.8 A unity feedback system has a plant 2257 G(s)= S(TS+1)' where 2.8 ms. Select a compensator Ge(s) = Kp + K1/s, so that the dominant roots of the characteristic equa- tion have damping ratio equal to
E10.7 NASA astronauts retrieved a satellite and brought it into the cargo bay of the space shuttle, as shown in Figure E10.7(a). A model of the feedback control system is shown in Figure E10.7(b). Determine the value of K that will result in a phase margin of P M. . = 40°when T = 0.6 s. FIGURE
E10.6 Consider the system with the loop transfer functionsWhen K = 10, find T s( ) and estimate the expected percent overshoot and settling time (with a 2% criterion).Compare your estimates with the actual percent overshoot of P O. . = 47.5% and a settling time of Ts = 32.1 s. K(s+4) L(s) =
E10.5 Consider a unity feedback system with the transfer function G(s)= K s(s+3)(s+5) We desire to obtain the dominant roots with 0.55. The compensator is wn 2 and G(s)= $+7 s+13 Determine the value of K that should be selected.
E10.4 Consider a unity feedback system with K G(s) = s(s+5)(s+10)' where K is set equal to 100 in order to achieve a spec- ified K,, = 2. We wish to add a lead-lag compensator Ge(s) = (s+ 0.15)(s+ 0.7) (s +0.015)(s+7) Show that the gain margin of the compensated sys- tem is G.M.=28.6 dB and that
E10.3 A unity feedback control system in a manufacturing system has a process transfer function G(s)= s+1' and it is proposed to use a compensator to achieve a percent overshoot P.O.
E10.2 A control system with negative unity feedback has a process 400 G(s)= s(s+40) and we select a proportional plus integral compensa- tion, where G(s) = Kp +1 Note that the steady-state error of this system for a ramp input is zero. (a) Set K = 1 and find a suit- able value of Kp so the step
E10.1 A negative feedback control system has a transfer function Ge(s)G(s) = We select a compensator G(s) = K 5+5 s+a S in order to achieve zero steady-state error for a step input. Select a and K to target a percent overshoot to a step of P.O.
15. Using a Nichols chart, determine the gain and phase margin of the system in Figure 10.38 with loop gain transfer function 8s +1 L(s) = G(s)G(s) = s(s+2s+4)* a. G.M. = 20.4 dB, P.M. = 58.1 == b. G.M. = 0 dB, P.M. = 47 c. G.M. = 6 dB, P.M. = 45 d. G.M.= dB, P.M. = 23
14. Consider the feedback system depicted in Figure 10.38, where 1 G(s) = s(s+4) A suitable compensator for G. (s) this system that satisfies the specifications: (i) P.O. 20%, and (ii) velocity error constant K, 10, is which of the following: a. G(s)= S+4 (s+1) 160 (10s+1) b. G(s)= 200s+1 c. Ge(s)
13. A viable phase-lag compensator for a unity negative feedback system with plant transfer function 1000 G(s) (s+8)(s+14)(s+20) that satisfies the design specifications: (i) no percent overshoot; (ii) rise time T, < 5s, and (iii) position error constant Kp > 6, is which of the following: s+1 a.
12. Consider the feedback system in Figure 10.38, where 1 G(s)= s(s +10)(s+15)
11. Consider a feedback system in which a phase-lead compensator 500 G(s)= (s+1)(s+5)(s+10) The feedback system is a negative unity feedback control system shown in Figure 10.38. Compute the gain and phase margin. a. G.M. dB, P.M. = 60 b. G.M. = 20.5 dB, P.M. = 47.8 c. G.M. = 8.6 dB, P.M. = 33.7 d.
10. Consider the feedback system in Figure 10.38, where 1 G(s) = = s(1+s/8)(1+s/20) The design specifications are: K, 100, G.M. 10 dB, P.M. 45, and the crossover frequency, we 10 rad/s. Which of the following controllers meets these specifications? (1+s)(1 + 20s) a. G(s) = b. G(s)= (1+s/0.01)(1 +
9. Consider the feedback system in Figure 10.38, where the plant model is 500 G(s) = s(s +50) and the controller is a proportional-plus-integral (PI) controller given by G(s) = Kp + KI S Selecting Ky = 1, determine a suitable value of Kp for a percent overshoot of P.O=20%. 2. Kp =0.5 b. Kp = 1.5 c.
8. Consider a unity feedback system in Figure 10.38, where G(s) = 1450 s(s+3)(s +25) A phase-lead compensator is introduced into the feedback loop, where 1+0.3s Ge(s) = 1+0.03s The peak magnitude and the bandwidth of the closed-loop frequency response are: a. Mp b. Mp = 1.9 dB; wb = 12.1 rad/s =
7. A position control system can be analyzed using the feedback system in Figure 10.38,where the process transfer function is 5 G(s): = s(s+1)(0.4s+1) A phase-lag compensator that provides a phase margin of P.M. 30 is: 1+s a. G(s)= 1+106s b. G(s) = 1+26s 1+115s 1+106s c. G(s) = 1+118s d. None of
6. Consider the feedback system in Figure 10.38, where G(s) = 1000 s(s + 400)(s +20) A phase-lag compensator is designed for the system: 1+0.25s Ge(s) = 1+2s When compared with the uncompensated system (that is, G(s) = 1), the compensated system utilizing the phase-lag compensator: a. Increases the
5. A phase-lead compensator can be used to increase the system bandwidth. True or False
4. A deadbeat response of a system is a rapid response with minimal percent overshoot and zero steady-state error to a step input.True or False
3. The arrangement of the system and the selection of suitable components and parameters is part of the process of control system design.True or False
2. Generally, a phase-lag compensator speeds up the transient response.True or False
1. A cascade compensator is a compensator that is placed in parallel with the system process.True or False
CP9.10 A closed-loop feedback system is shown in Figure CP9.10. (a) Obtain the Nyquist plot, and determine the phase margin. Assume that the time delay T = 0 s.(b) Compute the phase margin when T = 0.05 s.(c) Determine the minimum time delay that destabilizes the closed-loop system. Time delay
CP9.9 For the system in CP9.8, use the nichols function to obtain the Nichols chart and determine the phase margin and gain margin.Data from in CP9.8 Consider the system represented in state variable 2 *0-0+00 ( = -1-18 20 y(t) = [ 6 0 ] x(t) +[0]u(t). Using the nyquist function, obtain the
CP9.8 Consider the system represented in state variable 2 *0-0+00 ( = -1-18 20 y(t) = [ 6 0 ] x(t) +[0]u(t). Using the nyquist function, obtain the Nyquist plot.
CP9.7 An engineering laboratory has presented a plan to operate an Earth-orbiting satellite that is to be controlled from a ground station. A block diagram of the proposed system is shown in Figure CP9.7. It takes T seconds for a signal to reach the spacecraft from the ground station and the
CP9.6 A block diagram of the yaw acceleration control system for a bank-to-turn missile is shown in Figure CP9.6. The input is yaw acceleration command (in g’s), and the output is missile yaw acceleration (in g’s). The controller is specified to be a proportional, integral(PI) controller. The
CP9.5 Consider a unity feedlach system with the loop transfer function L(s) = G(s)G(s) = K(s+25) s(s+ 10)(s+20) Develop an m-file to plot the bandwidth of the closed- loop system as K varies in the interval 1 < K < 80.
CP9.4 A negative feedback control system has the loop transfer function Ke-Tx L(s) =G(s)G(s)= s+15 (a) When T=0.05 s, find K such that the phase margin is P.M. 55 using the margin function. (b) Obtain a plot of phase margin versus T for K as in part (a), with 0
CP9.3 Using the nichols function, obtain the Nichols chart with a grid for the following transfer functions: (a) G(s)= (b) G(s) = (c) G(s)= 1 s+ 0.2 1 2+2s+1' 12 3+682 +11s+6' Determine the approximate phase and gain margins from the Nichols charts and label the charts accordingly.
CP9.2 Using the nyquist function, obtain the Nyquist plot for the following transfer functions: (a) G(s) = (b) G(s): ==== (c) G(s) = 15 s+20 40 2+6s+25 12 3+4s+48 +1
CP9.1 Consider a unity negative feedback control system withVerify that the gain margin is ∞ and that the phase margin is 10°. L(s) G(s)G(s) = = 141 s+2s+12
DP9.11 The primary control loop of a nuclear power plant includes a time delay due to the need to transport the fluid from the reactor to the measurement point as shown in Figure DP9.11. The transfer function of the controller is Ge(s) = Kp + KI The transfer function of the reactor and time delay
DP9.10 Consider the system is described in state variable form by(b) Design the gain matrix K to meet the following specifications: (i) the closed-loop system is stable; (ii) the system bandwidth ωb ≥ 1 rad s; and(iii) the steady-state error to a unit step inputR s( ) = 1 s is zero. x(t) =
DP9.9 A two-tank system containing a heated liquid has the model shown in Figure DP9.9(a), where T0 is the temperature of the fluid flowing into the first tank and T2 is the temperature of the liquid flowing out of the second tank. The block diagram model is shown in Figure DP9.9(b). The system of
DP9.8 The control of a high-speed steel-rolling mill is a challenging problem. The goal is to keep the strip thickness accurate and readily adjustable. The model of the control system is shown in Figure DP9.8. Design a control system by selecting K so that the step response of the system is as fast
DP9.7 Vehicles for lunar construction and exploration work will face conditions unlike anything found on Earth. Furthermore, they will be controlled via remote control. A block diagram of such a vehicle and the control are shown in Figure DP9.7. Select the gain K to have a percent overshoot of P O.
DP9.6 The physical representation of a steel strip-rolling mill is a damped-spring system [8]. The output thickness sensor is located a negligible distance from the output of the mill, and the objective is to keep the thickness as close to a reference value as possible. Any change of the input
DP9.5 An electrohydraulic actuator is used to actuate large loads for a robot manipulator, as shown in Figure DP9.5 [17]. The system is subjected to a step input, and we desire the steady-state error to be minimized.However, we wish to keep the percent overshootP O. . ≤ 10%. Let T = 0.8 s.(a)
DP9.4 A robot tennis player is shown in Figure DP9.4(a),and a simplified control system for θ2 ( )t is shown in Figure DP9.4(b). The goal of the control system is to attain the best step response while attaining a high Kv for the system. Select Kv1 = 0.35 and Kv2 = 0.65, and determine the phase
DP9.3 An automatic drug delivery system is used in the regulation of critical care patients suffering from cardiac failure [24]. The goal is to maintain stable patient status within narrow bounds. Consider the use of a drug delivery system for the regulation of blood pressure by the infusion of a
DP9.2 Flexible-joint robotic arms are constructed of lightweight materials and exhibit lightly damped open-loop dynamics [15]. A feedback control system for a flexible arm is shown in Figure DP9.2. Select K so that the system has maximum phase margin. Predict the percent overshoot for a step input
DP9.1 A mobile robot for toxic waste cleanup is shown in Figure DP9.1(a) [23]. The closed-loop speed control is a unity feedback system. The Nichols chart in Figure DP9.1(b) shows the plot of G j c( ) ω ω G j ( ) K versus ω.The value of the frequency at the points indicated is recorded in the
CDP9.1 The system of Figure CDP4.1 uses a controllerG s c a ( ) = K . Determine the value of Ka so that the phase margin is P M. . = 70°. Plot the response of this system to a step input.
AP9.11 Patients with a cardiological illness and less than normal heart muscle strength can benefit from an assistance device. An electric ventricular assist device(EVAD) converts electric power into blood flow by moving a pusher plate against a flexible blood sac. The pusher plate reciprocates to
AP9.10 A multiloop block diagram is shown in Figure AP9.10.(a) Compute the transfer function T s( ) = Y s( ) R s( ). (b) Determine K such that the steady-state tracking error to a unit step input R s( ) = 1 s is zero. Plot the unit step response.(c) Using K from part (b), compute the system
AP9.9 Consider a unity feedback system with and G(s) 1 s($ + 6s+12) G&(s) = Kp +1 Let Kp = 0.3. K S and determine the gain Kp that provides the maximum phase margin.
AP9.8 A control system is shown in Figure AP9.8. The gain K is greater than 500 and less than 4000. Select a gain that will cause the system step response to have a percent overshoot of P O. . ≤ 20%. Plot the Nichols chart and calculate the phase margin. FIGURE AP9.8 Gain selection. R(s) K(s+
AP9.7 Building elevators are limited to about 800 meters.Above that height, elevator cables become too thick and too heavy for practical use. One solution is to eliminate the cable. The key to the cordless elevator is the linear motor technology now being applied to the development of magnetically
AP9.6 The acidity of water draining from a coal mine is often controlled by adding lime to the water. A valve controls the lime addition and a sensor is downstream.For the model of the system shown in Figure AP9.6, determine K and the distance D to maintain stability.We require D > 2 meters in
AP9.5 A unity feedback control system given by L(s) = G(s)H(s)= Se-sT s(s+3)(s+4) Determine the (a) phase margin for T = 0 and (b) limiting value of T for stability.
AP9.4 The loop transfer function of a system is described K L(s) G(s)H(s)= $($+2.45) Find the value of K for marginal stability. Find the gain margin and the phase margin for K = 22 and K = 42.
AP9.3 Figure AP9.3 shows an automatic water treatment plant. It is typically a mechanical–chemical arrangement that uses reagent to purify water. The plant comprises an input pipeline embedded with a flow meter and sensors. The temperature and the flow rate of the boiler and the cooling water are
AP9.2 Anesthesia is used in surgery to induce unconsciousness. One problem with drug-induced unconsciousness is differences in patient responsiveness.Furthermore, the patient response changes during an operation. A model of drug-induced anesthesia control is shown in Figure AP9.2. The proxy for
AP9.1 For positive constants of K, T1, and T2, a control system is described by its loop transfer function as L(s) G(s)H(s)= K(1+Ts) s (1+Ts) Considering gain K = 0.06, compute the phase margin and gain margin for (a) T = 5 and T = 2. (b) T =2 and T2=5. (c) Comment on the stability.
P9.28 Consider the feedback system shown in Figure P9.28.(a) Determine the value of KP such that the phase margin is P M. . = 60°.(b) Using the P.M. obtained, predict the percent overshoot of the closed-loop system to a unit step input.(c) Plot the step response, and compare the actual percent
P9.27 Consider the system shown in Figure P9.27.Determine the maximum value of K K = max for which the closed-loop system is stable. Plot the phase margin as a function of the gain 1 . ≤ ≤ K Kmax Explain what happens to the phase margin as K approaches Kmax. FIGURE P9.27 Nonunity feedback
P9.26 A specialty machine shop is improving the efficiency of its surface-grinding process [21]. The existing machine is mechanically sound, but manually operated. Automating the machine will free the operator for other tasks and thus increase overall throughput of the machine shop. The grinding
P9.25 A closed-loop system has the loop transfer function Ke-sT L(s) = Ge(s)G(s) = (s+1) (a) Determine the gain K so that the phase margin is P.M.=60 when T = 0.15. (b) Plot the phase mar- gin versus the time delay T for K as in part (a).
P9.24 A closed-loop system with unity feedback has a loop transfer function K(s+30) L(s) = G(s)G(s) = $2 (a) Determine the gain K so that the phase margin is P.M. 35. (b) For the gain K selected in part (a) determine the gain margin of the system. (c) Predict the bandwidth of the closed-loop system.
P9.23 A closed-loop system has a loop transfer function K L(s) =G(s)G(s)= s(s+3)(s+10) (a) Determine the gain K so that the phase margin is P.M. 40. (b) For the gain K selected in part (a), determine the gain margin of the system.
P9.22 The Nichols chart for G j c( ) ω ω G j ( ) of a closed-loop system is shown in Figure P9.22. The frequency for each point on the graph is given in the following table: Point 1 2 3 4 5 6 7 8 9 1 2.0 2.6 3.4 4.2 5.2 6.0 7.0 8.0 Determine (a) the resonant frequency, (b) the band- width, (c)
P9.21 Consider a unity feedback system with the loop transfer function(a) Sketch the Bode plot for K = 1. Determine(b) the gain margin, (c) the value of K required to provide a gain margin equal to 20 dB, and (d) the value ofK to yield a steady-state error of 10% of the magnitude A for the ramp
P9.20 The Bell-Boeing V-22 Osprey Tiltrotor is both an airplane and a helicopter. Its advantage is the ability to rotate its engines to a vertical position, as shown in Figure P7.33(a), for takeoffs and landings and then switch the engines to a horizontal position for cruising as an airplane. The
P9.19 In the United States, billions of dollars are spent annually for solid waste collection and disposal. One system, which uses a remote-control pick-up arm for collecting waste bags, is shown in Figure P9.19. The loop transfer function of the remote pick-up arm is(a) Plot Nichols chart, and
P9.18 A model of an automobile driver attempting to steer a course is shown in Figure P9.18, whereK = 2.0. (a) Find the frequency response and the gain and phase margins when the reaction timeT = 0. (b) Find the phase margin when the reaction time is T = 0.3 s. (c) Find the reaction time that
P9.17 The primary objective of many control systems is to maintain the output variable at the desired or reference condition when the system is subjected to a disturbance [22]. A typical chemical reactor control scheme is shown in Figure P9.17. The disturbance is represented by U s( ), and the
P9.16 An electric carrier that automatically follows a tape track laid out on a factory floor is shown in Figure P9.16(a) [15]. Closed-loop feedback systems are used to control the guidance and speed of the vehicle. The cart senses the tape path by means of an array of 16 phototransistors. The
P9.15 Consider the automatic ship-steering system transfer function. G(s) = -0.164(s+ 0.2)(s-0.32) s2 (s+ 0.25)(s-0.009) The deviation of the tanker from the straight track is measured by radar and is used to generate the error signal, as shown in Figure P9.15. This error signal is used to control
P9.14 Electronics and computers are being used to control automobiles. Figure P9.14 is an example of an automobile control system, the steering control for a research automobile. The control stick is used for steering. A typical driver has a reaction time ofT = 0.2 s.(a) Using the Nichols chart,
P9.13 A controller is used to regulate the temperature of a mold for plastic part fabrication, as shown in Figure P9.13. The value of the delay time is estimated as 1.2 s.(a) Using the Nyquist criterion, determine the stability of the system for K K a = = 1. (b) Determine a suitable value for Ka
P9.12 A simplified model of the control system for regulating the pupillary aperture in the human eye is shown in Figure P9.12 [20]. The gain K represents the pupillary gain, and τ is the pupil time constant, which is 0.75 s. The time delay T is equal to 0.6 s. The pupillary gain is K = 2.5.(a)
P9.11 A control system for a chemical concentration control system is shown in Figure P9.11. The system receives a granular feed of varying composition, and we want to maintain a constant composition of the output mixture by adjusting the feed-flow valve.The transport of the feed along the conveyor
P9.10 Machine tools are often automatically controlled as shown in Figure P9.10. These automatic systems are often called numerical machine controls [9]. On each axis, the desired position of the machine tool is compared with the actual position and is used to actuate a solenoid coil and the shaft
P9.9 The space shuttle, shown in Figure P9.9(a), carried large payloads into space and returned them to Earth for reuse [19]. The shuttle used elevons at the trailing edge of the wing and a brake on the tail to control the flight during entry. The block diagram of a pitch rate control system is
P9.8 Electrohydraulic servomechanisms are used in control systems requiring a rapid response for a large mass. An electrohydraulic servomechanism can provide an output of 100 kW or greater [17]. An illustration of a servovalve and actuator is shown in Figure P9.8(a). The output sensor yields a
P9.7 A vertical takeoff (VTOL) aircraft is an inherently unstable vehicle and requires an automatic stabilization system. An attitude stabilization system for the K-16B U.S. Army VTOL aircraft has been designed and is shown in block diagram form in Figure P9.7 [16].(a) Obtain the Bode plot of the
P9.6 A direct-drive arm is an innovative mechanical arm in which no reducers are used between motors and their loads. Because the motor rotors are directly coupled to the loads, the drive systems have no backlash, small friction, and high mechanical stiffness, which are all important features for
P9.5 A speed control for a gasoline engine is shown in Figure P9.5. Because of the restriction at the carburetor intake and the capacitance of the reduction manifold, the lag τt occurs and is equal to 1.5 seconds.The engine time constant τe is equal to J b = 4 s.The speed measurement time
P9.4 The Nyquist plot of a conditionally stable system is shown in Figure P9.4 for a specific gain K. (a) Determine whether the system is stable, and find the number of roots (if any) in the right-hand s-plane. The system has no poles of G s c( )G s( ) in the right half-plane. (b) Determine
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