Modern Control Systems 14th Global Edition Richard Dorf, Robert Bishop - Solutions

E5.11 A system with unity feedback is shown in Figure E5.11. Determine the steady-state error for a step and a ramp input when R(s) G(s)= 10(s+5) s(s+2)(s+4)(s+6) G(s) Y(s) FIGURE E5.11 Unity feedback system.
E5.10 A second-order control system has the closedloop transfer function T s( ) = / Y s( ) R s( ). The system specifications for a step input follow:1. Percent overshoot P O. . ≤ 5%.2. Settling time Ts < 4 s.3. Peak time Tp < 1 s.Show the desired region for the poles of T s( ) in order to
E5.9 A unity negative feedback control system has the loop transfer function L(s) =G(s)G(s) = K s(s+ K) (a) Determine the percent overshoot and settling time (using a 2% settling criterion) due to a unit step input. (b) For what range of K is the settling time is approx- imately T, 1s?
E5.8 A control system for positioning the head of a floppy disk drive has the closed-loop transfer function T(s) = 0.313(s +0.8) (s+0.6)(s2+48 +5) Plot the poles and zeros of this system, and discuss the dominance of the third pole. What percent overshoot for a step input do you expect?
E5.7 Effective control of insulin injections can result in better lives for diabetic persons. Automatically controlled insulin injection by means of a pump and a sensor that measures blood sugar can be very effective. A pump and injection system has a feedback control as shown in Figure E5.7.
E5.6 Consider the block diagram shown in Figure E5.6[16]. (a) Calculate the steady-state error for a ramp input. (b) Select a value of K that will result in zero percent overshoot to a step input. Provide rapid response.Plot the poles and zeros of this system and discuss the dominance of the
E5.5 Consider the feedback system in Figure E5.5. FindK such that the closed-loop system minimizes the ITAE performance criterion for a step input.
E5.4 A feedback system with negative unity feedback has a loop transfer function L(s) = G(s)G(s) = 2(s+8) s(s+4) (a) Determine the closed-loop transfer function T(s) Y(s)/R(s). (b) Find the time response, y(t), for a step input r(t)= A for t>0. (c) Determine the percent overshoot of the response.
E5.3 New passenger rail systems that could profitably compete with air travel are under development. Two of these systems, the French TGV and the Japanese Shinkansen, reach speeds of 160 mph [17]. The Trans-rapid, a magnetic levitation train, is shown in Figure E5.3(a).The use of magnetic
E5.2 The engine, body, and tires of a racing vehicle affect the acceleration and speed attainable [9]. The speed control of the car is represented by the model shown in Figure E5.2. (a) Calculate the steady-state error of the car to a step command in speed. (b) Calculate overshoot of the speed to a
E5.1 A laser cutter is used to cut a parabolic path on sheet metal. We want to have a finite steady-state error for the laser beam positioning control system. (a) Which type of number system is required? (How many integrations?)(b) If we want to achieve a zero steady-state error, which type of
15. Using the second-order system approximation (see Problem 14), estimate the gain K so that the percent overshoot is approximately P O. . ≈ 15%.a. K = 10b. K = 300c. K = 1000d. None of the above
14. A second-order approximate model of the loop transfer function is: a. (s)(s) = b. (s)(s) = c. (s)(s) = d. (s)(s) = (3/25) K s2+7s+10 (1/25) K $27s+10 (3/25)K s+7s+500 6K s+7s+10
13. A plant has the transfer function given by 1 G(s) = (1+s)(1 +0.5s) and is controlled by a proportional controller Ge(s) = K, as shown in the block diagram in Figure 5.42. The value of K that yields a steady-state error E(s) = Y(s)- R(s) with a magnitude equal to 0.01 for a unit step input is:
12. Consider the feedback control system in Figure 5.43 whereThe nominal value of K = 10. Using a 2% criterion, compute the settling time, Ts, for a unit step disturbance, T s d ( ) = /1 ,s R when 0. ( )s =a. Ts = 0.02 sb. Ts = 0.2 sc. Ts = 1.03 sd. Ts = 4.83 s G(s)= K s+10
11. Consider the unity feedback control system in Figure 5.42 where K L(s) = G(s)G(s) = s(s+5) The design specifications are: i. Peak time Tp
10. A system has the closed-loop transfer function T s( ) given by Y(s) T(s) = R(s) 2500 (s+20)(s + 10s+125)* Using the notion of dominant poles, estimate the expected percent overshoot. a. P.O.5% b. P.O.20% c. P.O. 50% d. No overshoot expected
9. Compute the expected percent overshoot to a unit step input for the value of Kin Problem 8.a. P O. . = 1.4%b. P O. . = 4.6%c. P O. . = 10.8%d. No overshoot expected
8. Find the value of K so that the system provides an optimum ITAE response for a step input.a. K = 1.10b. K = 12.56c. K = 51.02d. K = 104.7
7. The percent overshoot of the output to a unit step input is:a. P O. . = 9%b. P O. . = 1%c. P O. . = 20%d. No overshoot
6. The steady-state error to a unit step input R s( ) = /1 s is: a. eslim e(t) = 0 1400 b. elim e(t) = 1/2 1-x c. lss= lim e(t)=1/6 1400 d. esslim e(t) = 00 1400
5. A type-1 system has a zero steady-state tracking error to a ramp input.True or False
4. For a second-order system with no zeros, the percent overshoot to a unit step is a function of the damping ratio only.True or False
3. The rise time is defined as the time required for the system to settle within a certain percentage of the input amplitude.True or False
2. The number of zeros of the forward path transfer function at the origin is called the type number.True or False
1. In general, a third-order system can be approximated by a second-order system’s dominant roots if the real part of the dominant roots is less than 1/10 of the real part of the third root.True or False
DP1.10 In addition to maintaining automobile speed, many vehicles can also maintain a prescribed distance to an automobile in front, as illustrated in Figure DP1.10. Design a feedback control sysytem that can maintain cruise speed at a prescribed distance to the vehicle in front. What happens if
DP1.9 Consider the human transportation vehicle(HTV) depicted in Figure DP1.9. The self-balancing HTV is actively controlled to allow safe and easy transportation of a single person [97]. Describe a closed-loop feedback control system to assist the rider of the HTV in balancing and maneuvering the
DP1.8 A challenging application of control design is the use of nanorobots in medicine. Nanorobots will require onboard computing capability, and very tiny sensors and actuators. Fortunately, advances in biomolecular computing, bio-sensors, and actuators are promising to enable medical nanorobots
DP1.7 The Hubble space telescope was repaired and modified in space on several occasions [44, 46, 49]. One challenging problem with controlling the Hubble is damping the jitter that vibrates the spacecraft each time it passes into or out of the Earth’s shadow. The worst vibration has a period of
DP1.6 Vehicle traction control, which includes antiskid braking and antispin acceleration, can enhance vehicle performance and handling. The objective of this control is to maximize tire traction by preventing locked brakes as well as tire spinning during acceleration. Wheel slip, the difference
DP1.5 A large, braced robot arm for welding large structures is shown in Figure DP1.5. Sketch the block diagram of a closed-loop feedback control system for accurately controlling the location of the weld tip.
DP1.4 As part of the automation of a dairy farm, the automation of cow milking is under study [36]. Design a milking machine that can milk cows four or five times a day at the cow’s demand. Sketch a block diagram and indicate the devices in each block.
DP1.3 Describe a feedback control system in which a user utilizes a smart phone to remotely monitor and control a washing machine as illustrated in Figure DP1.3. The control system should be able to start and stop the wash cycle, control the amount of detergent and the water temperature, and
DP1.2 Aircraft are fitted with autopilot control that, at the press of a button, automatically controls the flight path of an aircraft, without manual control by a pilot.In this way, the pilot can focus on monitoring the flight path, weather, and onboard systems. Design a feedback control in block
DP1.1 Background noise affects the audio output quality of a headphone. Noise-cancelling headphones use active noise control to reduce this unwanted ambient noise. Sketch a block diagram of an “active noise control” feedback system that will reduce the effect of unwanted noise. Indicate the
AP1.7 Space X has developed a very important system to allow for recovery of the first stage of their Falcon rocket at sea, as depicted in Figure AP1.7. The landing ship is an autonomous drone ship. Sketch a block diagram describing a control system that would control the pitch and roll of the
AP1.6 The robotic vacuum cleaner depicted in Figure AP1.6 is an example of a mechatronic system that aids humans in maintaining their homes. A dirt detection control system would enable the robotic vacuum cleaner to vacuum the same area more than once if the dirt level is unsatisfactory, since a
AP1.5 The Burj Dubai is the tallest building in the world[94]. The building, shown in Figure AP1.5, stands at over 800 m with more than 160 stories. There are 57 elevators servicing this tallest free-standing structure in the world. Traveling at up to 10 m/s, the elevators have the world’s
AP1.4 Adaptive optics has applications to a wide variety of key control problems, including imaging of the human retina and large-scale, ground-based astronomical observations [98]. In both cases, the approach is to use a wavefront sensor to measure distortions in the incoming light and to
AP1.3 Many modern luxury automobiles have an advanced driver-assistance systems (ADAS) option.The collision avoidance feature of an ADAS system uses radars to detect nearby obstacles to notify drivers of potential collisions. Figure AP1.3 illustrates the collision avoidance feature of an ADAS
AP1.2 Advanced wind energy systems are being installed in many locations throughout the world as a way for nations to deal with rising fuel prices and energy shortages, and to reduce the negative effects of fossil fuel utilization on the quality of the air. The modern windmill can be viewed as a
AP1.1 The development of robotic microsurgery devices will have major implications on delicate eye and brain surgical procedures. One such device is shown in Figure AP1.1. Haptic (force and tactile) feedback can greatly help a surgeon by mimicking the physical interaction that takes place between
P1.27 A direct methanol fuel cell is an electrochemical device that converts a methanol water solution to electricity [75]. Like rechargeable batteries, fuel cells directly convert chemicals to energy; they are very often compared to batteries, specifically rechargeable batteries. However, one
P1.26 NASA is developing a compact rover designed to transmit data from the surface of an asteroid back to Earth, as illustrated in Figure P1.26. The rover will use a camera to take panoramic shots of the asteroid surface. The rover can position itself so that the camera can be pointed straight
P1.25 In the past 50 years, over 20,000 metric tons of hardware have been placed in Earth’s orbit. During the same time span, over 15,000 metric tons of hardware returned to Earth. The objects remaining in Earth’s orbit range in size from large operational spacecraft to tiny flecks of paint.
P1.24 An innovation for an intermittent automobile windshield wiper is the concept of adjusting its wiping cycle according to the intensity of the rain[54]. Sketch a block diagram of the wiper control system.
P1.23 Engineers at the Science University of Tokyo are developing a robot with a humanlike face [52]. The robot can display facial expressions, so that it can work cooperatively with human workers. Sketch a block diagram for a facial expression control system of your own design.
P1.22 Engineers want to design a control system that will allow a building or other structure to react to the force of an earthquake much as a human would.The structure would yield to the force, but only so much, before developing strength to push back [47].Develop a block diagram of a control
P1.21 The potential of employing two or more helicopters for transporting payloads that are too heavy for a single helicopter is a well-addressed issue in the civil and military rotorcraft design arenas [37].Overall requirements can be satisfied more efficiently with a smaller aircraft by using
P1.20 A high-performance race car with an adjustable wing (airfoil) is shown in Figure P1.20. Develop a block diagram describing the ability of the airfoil to keep a constant road adhesion between the car’s tires and the race track surface. Why is it important to maintain good road adhesion?
P1.19 Ichiro Masaki of General Motors has patented a system that automatically adjusts a car’s speed to keep a safe distance from vehicles in front. Using a video camera, the system detects and stores a reference image of the car in front. It then compares this image with a stream of incoming
P1.18 A cutaway view of a commonly used pressure regulator is shown in Figure P1.18. The desired pressure is set by turning a calibrated screw. This compresses the spring and sets up a force that opposes the upward motion of the diaphragm.The bottom side of the diaphragm is exposed to the water
P1.17 Baseball players use feedback to judge a fly ball and to hit a pitch [35]. Describe a method used by a batter to judge the location of a pitch so that he can have the bat in the proper position to hit the ball.
P1.16 All humans have experienced a fever associated with an illness. A fever is related to the changing of the control input in the body’s thermostat. This thermostat, within the brain, normally regulates temperature near 98°F in spite of external temperatures ranging from 0°F to 100°F or
P1.15 Small computers are used as part of a start-stop system in automobiles to control emissions and obtain improved gas mileage. A computer-controlled start-stop system that automatically stops and restarts an engine to reduce the time the engine idles could improve gas mileage and reduce
P1.14 Adam Smith (1723–1790) discussed the issue of free competition between the participants of an economy in his book Wealth of Nations. It may be said that Smith employed social feedback mechanisms to explain his theories [41]. Smith suggests that (1)the available workers as a whole compare
P1.13 A common example of a two-input control system is an automobile power transmission system, with a gear shifter and an accelerator pedal. The objective is to obtain (1) a desired speed and (2) a desired torque.Sketch a block diagram of the closed-loop control system.
P1.12 An automatic turning gear for windmills was invented by Meikle in about 1750 [1, 11]. The fantail gear shown in Figure P1.12 automatically turns the windmill into the wind. The fantail windmill at right angle to the mainsail is used to turn the turret.The gear ratio is of the order of 3000
P1.11 Automatic control of water level using a float level was used in the Middle East for a water clock[1, 11]. The water clock (Figure P1.11) was used from sometime before Christ until the 17th century.Discuss the operation of the water clock, and establish how the float provides a feedback
P1.10 The role of air traffic control systems is increasing as airplane traffic increases at busy airports.Engineers are developing air traffic control systems and collision avoidance systems using the Global Positioning System (GPS) navigation satellites [34, 55]. GPS allows each aircraft to know
P1.9 Models of physiological control systems are valuable aids to the medical profession. A model of the heart-rate control system is shown in Figure P1.9 [23, 48]. This model includes the processing of the nerve signals by the brain. The heart-rate control system is, in fact, a multivariable
P1.8 In a public address system, when the microphone is placed too close to the loudspeaker, a positive feedback system is inadvertently created. The audio input from the microphone is amplified, which comes out through the loudspeaker. This audio output is received by the microphone again, which
P1.7 The story is told about the sergeant who stopped at the jewelry store every morning at nine o’clock and compared and reset his watch with the chronometer in the window. Finally, one day the sergeant went into the store and complimented the owner on the accuracy of the chronometer.“Is it
P1.6 Feedback systems do not always involve negative feedback. Economic inflation, which is evidenced by continually rising prices, is a positive feedback system.A positive feedback control system, as shown in Figure P1.6, adds the feedback signal to the input signal, and the resulting signal is
P1.5 A light-seeking control system, used to track the sun, is shown in Figure P1.5. The output shaft, driven by the motor through a worm reduction gear, has a bracket attached on which are mounted two photocells. Complete the closed-loop system so that the system follows the light source.
P1.4 The accurate control of a nuclear reactor is important for power system generators. Assuming the number of neutrons present is proportional to the power level, an ionization chamber is used to measure the power level. The current io is proportional to the power level. The position of the
P1.3 In a chemical process control system, it is valuable to control the chemical composition of the product.To do so, a measurement of the composition can be obtained by using an infrared stream analyzer, as shown in Figure P1.3. The valve on the additive stream may be controlled. Complete the
P1.2 Control systems can use a human operator as part of a closed-loop control system. Sketch the block diagram of the valve control system shown in Figure P1.2.
P1.1 Automobiles have variable windshield wiper speed settings for different rain intensity. Sketch a block diagram of a wiper system where the driver sets the wiper speed. Identify the function of each element of the variable speed control of the wiper system.
E1.15 For people with diabetes, keeping track of and maintaining blood glucose at safe levels is very important. Continuous blood glucose monitors and readers are available that enable a measurement of blood glucose with a painless scan rather than a fingerprick, as illustrated in Figure E1.15.
E1.14 Sketch a block diagram of a person playing a video game. Suppose that the input device is a joystick and the game is being played on a desktop computer.
E1.13 Consider the inverted pendulum shown in Figure E1.13. Sketch the block diagram of a feedback control system. Identify the process, sensor, actuator, and controller. The objective is keep the pendulum in the upright position, that is to keep u=0, in the presence of disturbances. Optical
E1.12 Unmanned aerial vehicles (UAVs) are being developed to operate in the air autonomously for long periods of time. By autonomous, we mean that there is no interaction with human ground controllers.Sketch a block diagram of an autonomous UAV that is tasked for crop monitoring using aerial
E1.11 Future advanced commercial aircraft will be E-enabled. This will allow the aircraft to take advantage of continuing improvements in computer power and network growth. Aircraft can continuously communicate their location, speed, and critical health parameters to ground controllers, and
E1.10 Describe the process of human biofeedback used to regulate factors such as pain or body temperature.Biofeedback is a technique whereby a human can, with some success, consciously regulate pulse, reaction to pain, and body temperature.
E1.9 Describe the block diagram of the control system of a skateboard with a human rider.
E1.8 An autonomous self-driving vehicle can sense its environment and navigate without human input.Describe a simplified feedback control system for a guidance system that ensures the vehicle navigates its surroundings safely.
E1.7 Because a sailboat cannot sail directly into the wind,and traveling straight downwind is usually slow, the shortest sailing distance is rarely a straight line. Thus sailboats tack upwind—the familiar zigzag course—and jibe downwind. A tactician’s decision of when to tack and where to go
E1.6 An autofocus camera will adjust the distance of the lens from the film by using a beam of infrared or ultrasound to determine the distance to the subject[42]. Sketch a block diagram of this control system, and briefly explain its operation.
E1.5 Fly-fishing is a sport that challenges the person to cast a small feathery fly using a light rod and line.The goal is to place the fly accurately and lightly on the distant surface of the stream [59]. Describe the fly-casting process and a model of this process.
E1.4 A surgeon uses a control system, that is a robot surgical system, to perform surgery remotely. Sketch a block diagram to illustrate this feedback system.
E1.3 A CD player laser beam focusing system has an array of photodiodes that is used to determine if the laser beam is in focus. The laser beam focus is controlled by an input current to a lens focusing motor. A microprocessor controls the input current to the motor by comparing the output from the
E1.2 Describe typical actuators that can convert the following [93]:a. Mechanical energy to fluidic energyb. Mechanical energy to electrical energyc. Electrical energy to mechanical energyd. Kinetic energy to electrical energye. Electrical energy to heat
E1.1 Describe typical sensors that can measure each of the following [93]:a. Linear positionb. Velocity (or speed)c. Nongravitational accelerationd. Rotational position (or angle)e. Rotational velocityf. Temperatureg. Pressureh. Liquid (or gas) flow ratei. Torquej. Forcek. Earth’s
15. Closed-loop control systems should have which of the following properties:a. Good regulation against disturbancesb. Desirable responses to commandsc. Low sensitivity to changes in the plant parametersd. All of the above
14. Control engineering is applicable to which fields of engineering?a. Mechanical and aerospaceb. Electrical and biomedicalc. Chemical and environmentald. All of the above
13. A system with more than one input variable or more than one output variable is known by what name?a. Closed-loop feedback systemb. Open-loop feedback systemc. Multivariable control systemd. Robust control system
12. Complete the following sentence:An open-loop control system utilizes an actuating device to control a process . a. without using feedbackb. using feedbackc. in engineering designd. in engineering synthesis
11. Early pioneers in the development of systems and control theory include:a. H. Nyquistb. H. W. Bodec. H. S. Blackd. All of the above
10. Complete the following sentence:Control engineers are concerned with understanding and controlling segments of their environments, often called . a. systemsb. design synthesisc. trade-offsd. risk
9. Complete the following sentence: are intrinsic in the progression from an initial concept to the final product. a. Closed-loop feedback systemsb. Flyball governorsc. Design gapsd. Open-loop control systems
8. Complete the following sentence:Control of an industrial process by automatic rather than manual means is often called . a. negative feedbackb. automationc. a design gapd. a specification
7. Important modern applications of control systems include which of the following?a. Safe automobilesb. Autonomous robotsc. Automated manufacturingd. All of the above
6. Early applications of feedback control include which of the following?a. Water clock of Ktesibiosb. Watt’s flyball governorc. Drebbel’s temperature regulatord. All of the above
5. A multivariable system is a system with more than one input and/or more than one output.True or False
4. The block diagram in Figure 1.30 is an example of a closed-loop feedback system.True or False
3. Engineering synthesis and engineering analysis are the same.True or False
2. A closed-loop control system uses a measurement of the output and feedback of the signal to compare it with the desired input.True or False
1. The flyball governor is generally agreed to be the first automatic feedback controller used in an industrial process.True or False

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Modern Control Systems 14th Global Edition Richard Dorf, Robert Bishop - Solutions

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