Modern Control Systems

Dorf

Chapter 1 Introduction to Control Systems - all with Video Answers

Educators

Chapter Questions

Problem 1

Many luxury automobiles have thermostatically controlled air-conditioning systems for the comfort of the passengers. Sketch a block diagram of an airconditioning system where the driver sets the desired interior temperature on a dashboard panel. Identify the function of each element of the thermostatically controlled cooling system.

Manik Pulyani

Numerade Educator

04:02

Problem 2

Consider a steel vessel filled $10 \%$ of its capacity with water placed on a gas stove. The gas stove is switched on and a mercury thermometer is used to measure the temperature of the water in the vessel.
(a) If the gas stove is switched off when the temperature reached $75^{\circ} \mathrm{C}$, will the temperature of the water increase further?
(b) If no why?
(c) If yes, explain the difficulty of heating the water to a specified value.

Ronald Prasad

Numerade Educator

Problem 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 control feedback loop, and sketch a block diagram describing the operation of the control loop.

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00:52

Problem 4

The overflow of water from overhead tanks is a common sight in houses in towns and villages. If you know the current level of water in the tank, volume of water in the tank and flow of water into the tank, suggest an open loop control system to control the motor which drives the pump used to fill the tank.

Amrita Bhasin

Numerade Educator

12:22

Problem 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.
Figure can't copy

Mohammad Amin

Numerade Educator

03:18

Problem 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 used as the input to the process. A simple model of the price-wage inflationary spiral is shown in Figure P1.6. Add additional feedback loops, such as legislative control or control of the tax rate, to stabilize the system. It is assumed that an increase in workers' salaries, after some time delay, results in an increase in prices. Under what conditions could prices be stabilized by falsifying or delaying the availability of cost-of-living data? How would a national wage and price economic guideline program affect the feedback system?
Figure can't copy

Nick Johnson

Numerade Educator

02:46

Problem 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 set according to time signals from Arlington?" asked the sergeant.
"No," said the owner,"I set it by the five o'clock cannon fired from the fort each afternoon. Tell me, Sergeant, why do you stop every day and check your watch?"
The sergeant replied, "I'm the gunner at the fort!"
Is the feedback prevalent in this case positive or negative? The jeweler's chronometer loses two minutes each 24-hour period and the sergeant's watch loses three minutes during each eight hours. What is the net time error of the cannon at the fort after 12 days?

Charles Carter

Numerade Educator

00:35

Problem 8

The student-teacher learning process is inherently a feedback process intended to reduce the system error to a minimum. With the aid of Figure 1.3, construct a feedback model of the learning process and identify each block of the system.

Amrita Bhasin

Numerade Educator

01:23

Problem 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 $[23,24,51]$. This model includes the processing of the nerve signals by the brain. The heart-rate control system is, in fact, a multivariable system, and the variables $x, y, w, v, z$, and $u$ are vector variables. In other words, the variable $x$ represents many heart variables $x_1, x_2, \ldots, x_n$. Examine the model of the heart-rate control system and add or delete blocks, if necessary. Determine a control system model of one of the following physiological control systems:
1. Respiratory control system
2. Adrenaline control system
3. Human arm control system
4. Eye control system
5. Pancreas and the blood-sugar-level control system
6. Circulatory system

Asma Venkitta

Numerade Educator

02:40

Problem 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 [34,61]. GPS allows each aircraft to know its position in the airspace landing corridor very precisely. Sketch a block diagram depicting how an air traffic controller might use GPS for aircraft collision avoidance.

David Wellman

Numerade Educator

03:37

Problem 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 control that maintains the accuracy of the clock. Sketch a block diagram of the feedback system.
Figure can't copy

Chai Santi

Numerade Educator

03:30

Problem 12

An automatic turning gear for wind mills 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 to 1 . Discuss the operation of the windmill, and establish the feedback operation that maintains the main sails into the wind.
Figure can't copy

Chai Santi

Numerade Educator

Problem 13

A common example of a two-input control system is a home shower with separate valves for hot and cold water. The objective is to obtain (1) a desired temperature of the shower water and (2) a desired flow of water. Sketch a block diagram of the closed-loop control system.

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Problem 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 [44]. Smith suggests that (1) the available workers as a whole compare the various possible employments and enter that one offering the greatest rewards, and (2) in any employment the rewards diminish as the number of competing workers rises. Let $r=$ total of rewards averaged over all trades, $c=$ total of rewards in a particular trade, and $q=$ influx of workers into the specific trade. Sketch a feedback system to represent this system.

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02:46

Problem 15

(a) In the context of the solution of problem P1.4, what are the draw back of open loop system?
(b) Suggest a manual closed loop system for the same problem.

Nolan Smyth

Numerade Educator

01:03

Problem 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 $98^{\circ} \mathrm{F}$ in spite of external temperatures ranging from $0^{\circ}$ to $100^{\circ} \mathrm{F}$ or more. For a fever, the input, or desired, temperature is increased. Even to many scientists, it often comes as a surprise to learn that fever does not indicate something wrong with body temperature control but rather well-contrived regulation at an elevated level of desired input. Sketch a block diagram of the temperature control system and explain how aspirin will lower a fever.

Andrei Demkov

Numerade Educator

02:18

Problem 17

Consider an electric furnace whose temperature can increase from $30^{\circ} \mathrm{C}$ to $630^{\circ} \mathrm{C}$ in one hour. If the thermometer used in the control system takes one minute to reach the steady value, will the closed loop system work satisfactorily. Explain your answer.

Linda Hand

Numerade Educator

01:51

Problem 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 pressure that is to be controlled. Thus the motion of the diaphragm is an indication of the pressure difference between the desired and the actual pressures. It acts like a comparator. The valve is connected to the diaphragm and moves according to the pressure difference until it reaches a position in which the difference is zero. Sketch a block diagram showing the control system with the output pressure as the regulated variable.

Ranjeet Singh

Numerade Educator

00:24

Problem 19

In a car, to control speed, there is accelerator and break. Suppose break is not there, will you be able to decrease the speed when desired. Explain the need for two control signals (accelerator and break).

Donald Albin

Numerade Educator

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Problem 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?
Figure can't copy

Victor Salazar

Numerade Educator

02:30

Problem 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 [38]. Overall requirements can be satisfied more efficiently with a smaller aircraft by using multilift for infrequent peak demands. Hence the principal motivation for using multilift can be attributed to the promise of obtaining increased productivity without having to manufacture larger and more expensive helicopters. A specific case of a multilift arrangement where two helicopters jointly transport payloads has been named twin lift. Figure P1.21 shows a typical "two-point pendant" twin lift configuration in the lateral/vertical plane.

Develop the block diagram describing the pilots' action, the position of each helicopter, and the position of the load.

Eric Mockensturm

Numerade Educator

06:45

Problem 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 [50]. Develop a block diagram of a control system to reduce the effect of an earthquake force.

Harmender Singh Yadav

Numerade Educator

Problem 23

Engineers at the Science University of Tokyo are developing a robot with a humanlike face [56]. 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.

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02:45

Problem 24

An innovation for an intermittent automobile windshield wiper is the concept of adjusting its wiping cycle according to the intensity of the rain [60]. Sketch a block diagram of the wiper control system.

Uma Kumari

Numerade Educator

04:03

Problem 25

In the past 40 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. There are about 150,000 objects in Earth's orbit $1 \mathrm{~cm}$ or larger in size. About 10,000 of the space objects are currently tracked from groundstations on the Earth. Space traffic control [67] is becoming an important issue, especially for commercial satellite companies that plan to "fly" their satellites through orbit altitudes where other satellites are operating, and through areas where high concentrations of space debris may exist. Sketch a block diagram of a space traffic control system that commercial companies might use to keep their satellites safe from collisions while operating in space.

Mark J

Numerade Educator

11:26

Problem 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 down at the surface or straight up at the sky. Sketch a block diagram illustrating how the microrover can be positioned to point the camera in the desired direction. Assume that the pointing commands are relayed from the Earth to the microrover and that the position of the camera is measured and relayed back to Earth.

Donald Albin

Numerade Educator

00:17

Problem 27

A direct methanol fuel cell is an electrochemical device that converts a methanol water solution to electricity [84]. Like rechargeable batteries, fuel cells directly convert chemicals to energy; they are very often compared to batteries, specifically rechargeable batteries. However, one significant difference between rechargeable batteries and direct methanol fuel cells is that, by adding more methanol water solution, the fuel cells recharge instantly. Sketch a block diagram of the direct methanol fuel cell recharging system that uses feedback (refer to Figure 1.3) to continuously monitor and recharge the fuel cell.

David Collins

Numerade Educator