For the sixth edition of Control Systems Engineering, this suite offers professors . Please consult Appendix H at for a Apago PDF. SOLUTION MANUAL Apago PDF Enhancer Solutions to Problems Student companion website Founded in , John Wiley & Sons, Inc. has been a. Control System Engineering Norman S Nise 6th Edition. Control Sixth Edition ( PDF) Consumer Behavior Schiffman Kanuk 10th Edition.

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Baixe grátis o arquivo Control Systems Engineering - Nise, 6th enviado por Mitsui no curso de Engenharia Mecânica na UFMT. Sobre: Livro de . Control Systems Engineering, Sixth Edition by Norman S. Nise From Chapter 1 of Advanced Electronic Communications Systems, Sixth Hanselman, _Stephen_Holiday,_Ryan_The_daily_stoi(zlibraryexau2g3p_onion).pdf The Daily. Apago PDF Enhancer This page intentionally left blank Apago PDF For the sixth edition of Control Systems Engineering, this suite offers.

Return instructions and a free of charge return shipping label are available at www. Outside of the United States, please contact your local representative. Introduction, 4. Special Cases, 6. Additional Examples, 6. Bode Plots, The text emphasizes the practical application of the subject to the analysis and design of feedback systems. The study of control systems engineering is essential for students pursuing degrees in electrical, mechanical, aerospace, biomedical, or chemical engineering.

Control systems are found in a broad range of applications within these disciplines, from aircraft and spacecraft to robots and process control systems. Control Systems Engineering is suitable for upper-division college and univer- sity engineering students and for those who wish to master the subject matter through self-study.

The student using this text should have completed typical lower- division courses in physics and mathematics through differential equations. This review material can be omitted without loss of continuity if the student does not require it. Key Features The key features of this sixth edition are: Standardized Chapter Organization Each chapter begins with a list of chapter learning outcomes, followed by a list of case study learning outcomes that relate to specific student performance in solving a practical case study problem, such as an antenna azimuth position control system.

Topics are then divided into clearly numbered and labeled sections containing explanations, examples, and, where appropriate, skill-assessment exercises with answers. These numbered sections are followed by one or more case studies, as will be outlined in a few paragraphs.

Each chapter ends with a brief summary, several review questions requiring short answers, a set of homework problems, and experiments. Qualitative and Quantitative Explanations Explanations are clear and complete and, where appropriate, include a brief review of required background material. Topics build upon and support one another in a logical fashion. Groundwork for new concepts and terminology is carefully laid to avoid overwhelming the student and to facilitate self-study.

Although quantitative solutions are obviously important, a qualitative or intuitive understanding of problems and methods of solution is vital to producing the insight required to develop sound designs.

Therefore, whenever possible, new concepts are discussed from a qualitative perspective before quantitative analysis and design are addressed. For example, in Chapter 8 the student can simply look at the root locus and describe qualitatively the changes in transient response that will occur as a system parameter, such as gain, is varied.

This ability is developed with the help of a few simple equations from Chapter 4. Examples, Skill-Assessment Exercises, and Case Studies Explanations are clearly illustrated by means of numerous numbered and labeled Examples throughout the text. Where appropriate, sections conclude with Skill- Assessment Exercises. These are computation drills, most with answers that test comprehension and provide immediate feedback.

Complete solutions can be found at www. Broader examples in the form of Case Studies can be found after the last numbered section of every chapter, with the exception of Chapter 1. These case studies arc practical application problems that demonstrate the concepts introduced in the chapter.

One of the case studies, an antenna azimuth position control system, is carried throughout the book. The purpose is to illustrate the application of new material in each chapter to the same physical system, thus highlighting the continuity of the design process.

Another, more challenging case study, involving x Preface For the sixth edition of Control Systems Engineering, this suite offers professors who adopt the book with WileyPLUS the ability to create homework assignments based on algorithmic problems or multi-part questions, which guide the student through a problem.

Instructors also have the capability to integrate assets, such as the simulations, into their lecture presentations.

Students will find a Read, Study, and Practice zone to help them work through problems based on the ones offered in the text. You will find references to them in sidebar entries throughout the textbook. Visit www. The experiments allow the reader to verify the concepts covered in the chapter via simulation. Thus, the experiments may be used for a laboratory course that accompanies the class.

Cover sheets for these experiments are available at www. In addition, and new to this sixth edition, are Virtual Experiments. These experiments are more tightly focused than the Cyber Exploration Laboratory experiments and use LabVIEW and Quanser virtual hardware to illustrate immediate discussion and examples.

The experiments are referenced in sidebars throughout some chapters. Preface xi For this reason, approximately photos, diagrams, graphs, and tables appear throughout the book to illustrate the topics under discussion.

Control Systems Engineering, Sixth Edition

Numerous End-of-Chapter Problems Each chapter ends with a variety of homework problems that allow students to test their understanding of the material presented in the chapter. Also, the homework problems contain progressive analysis and design problems that use the same practical systems to demonstrate the concepts of each chapter.

Emphasis on Design This textbook places a heavy emphasis on design. Chapters 8, 9, 11, 12 and 13 focus primarily on design. Throughout the book, design examples involving physical systems are identi- fied by the icon shown in the margin. End-of-chapter problems that involve the design of physical systems are included under the separate heading Design Problems, and also in chapters covering design, under the heading Progressive Analysis and Design Problems.

In these examples and problems, a desired response is specified, and the student must evaluate certain system parameters, such as gain, or specify a system configuration along with parameter values. In addition, the text includes numerous design examples and problems not identified by an icon that involve purely mathematical systems.

Control Systems Engineering Nise, 6th Edition

Because visualization is so vital to understanding design, this text carefully relates indirect design specifications to more familiar ones. For example, the less familiar and indirect phase margin is carefully related to the more direct and familiar percent overshoot before being used as a design specification.

For each general type of design problem introduced in the text, a methodology for solving the problem is presented—in many cases in the form of a step-by-step procedure, beginning with a statement of design objectives. Example problems serve to demonstrate the methodology by following the procedure, making simplifying assumptions, and presenting the results of the design in tables or plots that compare the performance of the original system to that of the improved system.

This comparison also serves as a check on the simplifying assumptions. Transient response design topics are covered comprehensively in the text. They include: Design via gain adjustment using the root locus Design of compensation and controllers via the root locus Design via gain adjustment using sinusoidal frequency response methods Design of compensation via sinusoidal frequency response methods xii Preface Gain adjustment Design of compensation via the root locus Design of compensation via sinusoidal frequency response methods Design of integral control in state space Finally, the design of gain to yield stability is covered from the following perspectives: Routh-Hurwitz criterion Root locus Nyquist criterion Bode plots Flexible Coverage The material in this book can be adapted for a one-quarter or a one-semester course.

The organization is flexible, allowing the instructor to select the material that best suits the requirements and time constraints of the class.

Throughout the book, state-space methods are presented along with the classical approach. Chapters and sections as well as examples, exercises, review questions, and problems that cover state space are marked by the icon shown in the margin and can be omitted without any loss of continuity. Those wishing to add a basic introduction to state-space modeling can include Chapter 3 in the syllabus.

In a one-semester course, the discussions of slate-space analysis in Chapters 4, 5, 6 and 7, as well as state-space design in Chapter 12, can be covered along with the classical approach. Another option is to teach state space separately by gathering the appropriate chapters and sections marked with the State Space icon into a single unit that follows the classical approach.

Emphasis on Computer-Aided Analysis and Design Control systems problems, particularly analysis and design problems using the root locus, can be tedious, since their solution involves trial and error. To solve these problems, students should be given access to computers or programmable calcula- tors configured with appropriate software.

In addition, and new to this Preface xiii Many problems in this text can be solved with either a computer or a hand-held programmable calculator. For example, students can use the programmable calcu- lator to 1 determine whether a point on the s-plane is also on the root locus, 2 find magnitude and phase frequency response data for Nyquist and Bode diagrams, and 3 convert between the following representations of a second-order system: Pole location in polar coordinates Pole location in Cartesian coordinates Characteristic polynomial Natural frequency and damping ratio Settling time and percent overshoot Peak time and percent overshoot Settling time and peak time Handheld calculators have the advantage of easy accessibility for homework and exams.

Please consult Appendix H, located at www. Personal computers are better suited for more computation-intensive appli- cations, such as plotting time responses, root loci, and frequency response curves, as well as finding state-transition matrices. These computers also give the student a real-world environment in which to analyze and design control systems.

Please consult Appendix H at www. Without access to computers or programmable calculators, students cannot obtain meaningful analysis and design results and the learning experience will be limited.

Icons Identifying Major Topics Several icons identify coverage and optional material. The icons are summarized as follows: These problems, developed by JustAsk, are worked in detail and offer explanations of every facet of the solution. The Simulink icon identifies Simulink discussions, examples, exercises, and problems. Simulink coverage is provided as an enhancement and is not required to use the text. Symbolic Math Toolbox coverage is provided as an enhancement and is not required to use the text.

LabVIEWis provided as an enhancement and is not required to use the text. The State Space icon highlights state-space discussions, examples, exercises, and problems. State-space material is optional and can be omitted without loss of continuity.

The Design icon clearly identifies design problems involving physical systems. Also, an additional Progressive Analysis and Design Problem has been added at the end of the chapter problems. The new progressive problem analyzes and designs a hybrid electric vehicle.

Virtual Experiments are tightly focused and linked to a discussion or example. Cyber Exploration Laboratory experiments are general in focus and are envisioned to be used in an associated lab class. We also continue to use Simulink to demonstrate how to simulate digital systems. Finally, the Simulink tutorial has been updated to Simulink 7. A tutorial for this tool is included in Appendix D. This free resource can be accessed by going to www.

Professors also access their password-protected re- sources on the Instructor Companion Site available through this url. Instructors should contact their Wiley sales representative for access. Preface xv The following paragraphs hopefully shed light on this topic.

The primary goal of Chapter 1 is to motivate students. In this chapter, students learn about the many applications of control systems in everyday life and about the advantages of study and a career in this field.

Control systems engineering design objectives, such as transient response, steady-state error, and stability, are intro- duced, as is the path to obtaining these objectives. New and unfamiliar terms also are included in the Glossary. Many students have trouble with an early step in the analysis and design sequence: This step requires many simplifying assumptions based on experience the typical college student does not yet possess. Identifying some of these assumptions in Chapter 1 helps to fill the experience gap.

Chapters2and3 cover modeling of open-loop systems, using frequency response techniques and state- space techniques, respectively. Chapter 5 discusses the representation and reduction of systemsformedofinterconnectedopen-loopsubsystems. Onlyarepresentativesampleof physical systems can be covered in a textbook of this length. Electrical, mechanical both translational and rotational , and electromechanical systems are used as examples of physical systems that are modeled, analyzed, and designed.

Linearization of a nonlinear system—one technique used by the engineer to simplify a system in order to represent it mathematically—is also introduced. Chapter 4 provides an introduction to system analysis, that is, finding and describing the output response of a system. It may seem more logical to reverse the order of Chapters 4 and 5, to present the material in Chapter 4 along with other chapters covering analysis.

However, many years of teaching control systems have taught me that the sooner students see an application of the study of system representation, the higher their motivation levels remain. Chapters 6, 7, 8, and 9 return to control systems analysis and design with the study of stability Chapter 6 , steady-state errors Chapter 7 , and transient response of higher-order systems using root locus techniques Chapter 8.

Chapter 9 covers design of compensators and controllers using the root locus. Chapter 10, like Chapter 8, covers basic concepts for stability, transient response, and steady- state-error analysis.

However, Nyquist and Bode methods are used in place of root locus. Chapter 11, like Chapter 9, covers the design of compensators, but from the point of view of sinusoidal frequency techniques rather than root locus.

An introduction to state-space design and digital control systems analysis and design completes the text in Chapters 12 and 13, respectively. Although these chapters can be used as an introduction for students who will be continuing their study of control systems engineering, they are useful by themselves and as a supplement to the discussion of analysis and design in the previous chapters.

The subject matter cannot be given a comprehensive treatment in two chapters, but the emphasis is clearly outlined and logically linked to the rest of the book. Acknowledgments The author would like to acknowledge the contributions of faculty and students, both at California State Polytechnic University, Pomona, and across the country, whose suggestions through all editions have made a positive impact on the new edition.

I am deeply indebted to my colleagues, Elhami T. Ibrahim, Salomon Oldak, and Norali Pernalete at California State Polytechnic University, Pomona for author- ing the creative new problems you will find at the end of every chapter.

The new progressive problem, hybrid vehicle, that is at the end of every chapter is the creation of Dr Ibrahim. In addition to his busy schedule as Electrical and Computer Engineering Department Chairman and author of many of the new problems, Professor Oldak also error checked new additions to the book and prevented glitches from ever reaching you, the reader. I would like to express my appreciation to contributors to this sixth edition who participated in reviews, accuracy checking, surveys, or focus groups.

They are: The author would like to thank John Wiley Sons, Inc. Specifically, the following are due recognition for their contributions: Don Fowler, Vice President and Publisher, who gave full corporate support to the project; Daniel Sayre, Publisher, with whom I worked closely and who provided guidance and leadership throughout the development of the sixth edition; and Katie Singleton, Senior Editorial Assistant, who was always there to answer my questions and respond to my concerns in a professional manner.

There are many others who Preface xvii Rather than repeating their names and titles here, I refer the reader to the copyright page of this book where they are listed and credited.

Control Systems Engineering - Nise, 6th Edition

I am very thankful for their contributions. Specifically, kudos go out to Heather Johnson, Managing Editor, who, once again, was always there to address my concerns in a timely and professional manner. My sincere appreciation is extended to Erik Luther of National Instruments Corporation and Paul Gilbert and Michel Levis of Quanser for conceiving, coor- dinating, and developing the Virtual Experiments that I am sure will enhance your understanding of control systems.

Finally, last but certainly not least, I want to express my appreciation to my wife, Ellen, for her support in ways too numerous to mention during the writing of the past six editions. Specifically though, thanks to her proofing final pages for this sixth edition, you the reader hopefully will find comprehension rather than apprehension in the pages that follow. Norman S. Nise xviii Preface Numerous applications are all around us: The rockets fire, and the space shuttle lifts off to earth orbit; in splashing cooling water, a metallic part is automatically machined; a self-guided vehicle delivering material to workstations in an aerospace assembly plant glides along the floor seeking its destination.

These are just a few examples of the automatically controlled systems that we can create. We are not the only creators of automatically controlled systems; these systems also exist in nature. Within our own bodies are numerous control systems, such as the pancreas, which regulates our blood sugar. Our eyes follow a moving object to keep it in view; our hands grasp the object and place it precisely at a predetermined location. Even the nonphysical world appears to be automatically regulated.

Models have been suggested showing automatic control of student performance. The model can be used to predict the time required for the grade to rise if a sudden increase in study time is available. Using this model, you can determine whether increased study is worth the effort during the last week of the term. Figure 1. For example, consider an elevator. When the fourth-floor button is pressed on the first floor, the elevator rises to the fourth floor with a speed and floor-leveling accuracy designed for passenger comfort.

The push of the fourth-floor button is an input that represents our desired output, shown as a step function in Figure 1. The performance of the elevator can be seen from the elevator response curve in the figure. Two major measures of performance are apparent: In our example, passenger comfort and passenger patience are dependent upon the transient response.

If this response is too fast, passenger comfort is sacrificed; if too slow, passenger patience is sacrificed. The steady-state error is another important performance specification since passenger safety and convenience would be sacrificed if the elevator did not properly level.

We can point huge antennas toward the farthest reaches of the universe to pick up faint radio signals; controlling these antennas by hand would be impossible. Because of control systems, elevators carry us quickly to our destination, auto- matically stopping at the right floor Figure 1.

We alone could not provide the power required for the load and the speed; motors provide the power, and control systems regulate the position and speed. We build control systems for four primary reasons: Power amplification 2.

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Remote control 3. Convenience of input form 4. Compensation for disturbances For example, a radar antenna, positioned by the low-power rotation of a knob at the input, requires a large amount of power for its output rotation.

A control system can produce the needed power amplifica- tion, or power gain. Robots designed by control system principles can compensate for human disabilities. Control systems are also useful in remote or dangerous locations. For example, a remote-controlled robot arm can be used to pick up material in a radioactive environment. Control systems can also be used to provide convenience by changing the form of the input.

For example, in a temperature control system, the input is a position on a thermostat. The output is heat. Thus, a convenient position input yields a desired thermal output. Another advantage of a control system is the ability to compensate for disturbances. Early elevators were controlled by hand ropes or an elevator operator.

One of two modern Duo-liftelevatorsmakesitsway up the Grande Arche in Paris. Two elevators are driven by one motor, with each car acting as a counterbalance to the other. Today, elevators are fully auto- matic, using control systems to regulate position and velocity. The system must be able to yield the correct output even withadisturbance.

Forexample,consideranantenna systemthat points inacommanded direction. Conse- quently, the system itself must measure the amount that the disturbance has repositioned the antenna and then return the antenna to the position commanded by the input.

Numerous biological control systems were built into the earliest inhabitants of our planet. Let us now look at a brief history of human-designed control systems.

Awater clock invented by Ktesibios operated by having water trickle into a measuring container at a constant rate. The level of water in the measuring container could be used to tell time. For water to trickle at a constant rate, the supply tank had to be kept at a constant level. Soon after Ktesibios, the idea of liquid-level control was applied to an oil lamp by Philon of Byzantium.

The lamp consisted of two oil containers configured vertically. The lower pan was open at the top and was the fuel supply for the flame. The closed upper bowl was the fuel reservoir for the pan below. The containers were interconnected by two capillary tubes and another tube, called a vertical riser, which was inserted into the oil in the lower pan just below the surface.

As the oil burned, the base of the vertical riser was exposed to air, which forced oil in the reservoir above to flow through the capillary tubes and into the pan. The transfer of fuel from the upper reservoir to the pan stopped when the previous oil level in the pan was reestablished, thus blocking the air from entering the vertical riser. Hence, the system kept the liquid level in the lower container constant. The concept was further elaborated on by weighting the valve top.

If the upward pressure from the boiler exceeded the weight, steam was released, and the pressure decreased.

Ifitdidnotexceedtheweight,thevalvedidnotopen,andthepressureinsidethe boiler increased. Thus, the weight on the valve top set the internal pressure of the boiler. Also in the seventeenth century, Cornelis Drebbel in Holland invented a purely mechanical temperature control system for hatching eggs. The device used a vial of alcohol and mercury with a floater inserted in it. The floater was connected to a damper that controlled a flame.

A portion of the vial was inserted into the incubator to sense the heat generated by the fire. As the heat increased, the alcohol and mercury expanded, raising the floater, closing the damper, and reducing the flame. Lower temperature caused the float to descend, opening the damper and increasing the flame.

Speed Control In , speed control was applied to a windmill by Edmund Lee. Increasing winds pitched the blades farther back, so that less area was available. As the wind 1 See Bennett and Mayr for definitive works on the history of control systems.

William Cubitt improved on the idea in by dividing the windmill sail into movable louvers. Also in the eighteenth century, James Watt invented the flyball speed governor to control the speed of steam engines. In this device, two spinning flyballs rise as rotational speed increases. A steam valve connected to the flyball mechanism closes with the ascending flyballs and opens with the descending flyballs, thus regulating the speed.

Stability, Stabilization, and Steering Control systems theory as we know it today began to crystallize in the latter half of the nineteenth century. In , James Clerk Maxwell published the stability criterion for a third-order system based on the coefficients of the differential equation.

In , Edward John Routh, using a suggestion from William Kingdon Clifford that was ignored earlier by Maxwell, was able to extend the stability criterion to fifth-order systems.

This paper contains what is now known as the Routh-Hurwitz criterion for stability, which we will study in Chapter 6. A student of P. Chebyshev at the University of St. Petersburg in Russia, Lyapunov extended the work of Routh to nonlinear systems in his doctoral thesis, entitled The General Problem of Stability of Motion. During the second half of the s, the development of control systems focused on the steering and stabilizing of ships. Other efforts were made to stabilize platforms for guns as well as to stabilize entire ships, using pendulums to sense the motion.

Twentieth-Century Developments It was not until the early s that automatic steering of ships was achieved. In , the Sperry Gyroscope Company installed an automatic steering system that used the elements of compensation and adaptive control to improve performance. However, much of the general theory used today to improve the performance of automatic control systems is attributed to Nicholas Minorsky, a Russian born in It was his theoretical development applied to the automatic steering of ships that led to what we call today proportional-plus-integral-plus-derivative PID , or three-mode, con- trollers, which we will study in Chapters 9 and In the late s and early s, H.

Bode and H. Nyquist at Bell Telephone Laboratories developed the analysis of feedback amplifiers. These contributions evolved into sinusoidal frequency analysis and design techniques currently used for feedback control system, and are presented in Chapters 10 and In , Walter R. Evans, working in the aircraft industry, developed a graphical technique to plot the roots of a characteristic equation of a feedback system whose parameters changed over a particular range of values.

This technique, now known as the root locus, takes its place with the work of Bode and Nyquist in forming the foundation of linear control systems analysis and design theory. We will study root locus in Chapters 8, 9, and Contemporary Applications Today, control systems find widespread application in the guidance, navigation, and control of missiles and spacecraft, as well as planes and ships at sea.

For example, 1. The rudder commands, in turn, result in a rudder angle that steers the ship. We find control systems throughout the process control industry, regulating liquid levels in tanks, chemical concentrations in vats, as well as the thickness of fabricated material.

For example, consider a thickness control system for a steel plate finishing mill. Steel enters the finishing mill and passes through rollers. In the finishing mill, X-rays measure the actual thickness and compare it to the desired thickness. Any difference is adjusted by a screw-down position control that changes the roll gap at the rollers through which the steel passes. This change in roll gap regulates the thickness. Modern developments have seen widespread use of the digital computer as part of control systems.

For example, computers in control systems are for industrial robots, spacecraft, and the process control industry. It is hard to visualize a modern control system that does not use a digital computer. The space shuttle contains numerous control systems operated by an onboard computer on a time-shared basis. In space, the flight control system gimbals rotates the orbital maneuvering system OMS engines into a position that provides thrust in the commanded direction to steer the spacecraft. For example, the elevons require a control system to ensure that their position is indeed that which was commanded, since disturbances such as wind could rotate the elevons away from the commanded position.

Similarly, in space, the gimbaling of the orbital maneu- vering engines requires a similar control system to ensure that the rotating engine can accomplish its function with speed and accuracy. Control systems are also used to control and stabilize the vehicle during its descent from orbit. Numerous small jets that compose the reaction control system RCS are used initially in the exoatmo- sphere, where the aerosurfaces are ineffective. Control is passed to the aerosurfaces as the orbiter descends into the atmosphere.

Inside the shuttle, numerous control systems are required for power and life support. For example, the orbiter has three fuel-cell power plants that convert hydrogen and oxygen reactants into electricity and water for use by the crew.

The fuel cells involve the use of control systems to regulate temperature and pressure. The reactant tanks are kept at constant pressure as the quantity of reactant diminishes. Sensors in the tanks send signals to the control systems to turn heaters on or off to keep the tank pressure constant Rockwell Interna- tional, Control systems are not limited to science and industry.

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For example, a home heating system is a simple control system consisting of a thermostat containing a bimetallic material that expands or contracts with changing temperature. This expansion or contraction moves a vial of mercury that acts as a switch, turning the heater on or off. The amount of expansion or contraction required to move the mercury switch is determined by the temperature setting.

For example, in an optical disk recording system microscopic pits representing the information are burned into the disc by a laser during the recording process. During playback, a reflected laser beam focused on the pits changes intensity Figure 1. The light intensity changes are converted to an electrical signal and processed as sound or picture.

A control system keeps the laser beam positioned on the pits, which are cut as concentric circles. There are countless other examples of control systems, from the everyday to the extraordinary. As you begin your study of control systems engineering, you will become more aware of the wide variety of applications.

We can consider these configurations to be the internal architecture of the total system shown in Figure 1. It starts with a subsystem called an input transducer, which converts the form of the input to that used by the controller.

The controller drives a process or a plant. The input is sometimes called the reference, while the output can be called the controlled variable. Other signals, such as disturbances, are shown added to the controller and process outputs via summing junctions, which yield the algebraic sum of their input signals using associated signs. For example, the plant can be a furnace or air conditioning system, where the output variable is temperature.

The controller in a heating system consists of fuel valves and the electrical system that operates the valves. For example, if the controller is an electronic amplifier and Disturbance 1 is noise, then any additive amplifier noise at the first summing junction will also drive the process, corrupting the output with the effect of the noise.

The system cannot correct for these disturbances, either. Open-loop systems, then, do not correct for disturbances and are simply commanded by the input. For example, toasters are open-loop systems, as anyone with burnt toast can attest. The controlled variable output of a toaster is the color of the toast.

The device is designed with the assumption that the toast will be darker the longer it is subjected to heat. The toaster does not measure the color of the toast; it does not correct for the fact that the toast is rye, white, or sourdough, nor does it correct for the fact that toast comes in different thicknesses.

Other examples of open-loop systems are mechanical systems consisting of a mass, spring, and damper with a constant force positioning the mass.

The greater the force, the greater the displacement. This assumed positive direction of motion is similar to assuming a current direction in an electrical loop. Using our assumed direction of positive motion, we first draw a free-body diagram, placing on the body all forces that act on the body either in the direction of motion or opposite to it.

Finally, assuming zero initial conditions, we take the Laplace transform of the differential equation, separate the variables, and arrive at the transfer function. An example follows. Example 2. Begin the solution by drawing the free-body diagram shown in Figure 2. Place on the mass all forces felt by the mass. We assume the mass is traveling toward the right. Thus, only the applied force points to the right; all other forces impede the motion and act to oppose it.

Hence, the spring, viscous damper, and the force due to acceleration point to the left. Mass, spring, and damper system; b. Free-body diagram of mass, spring, and damper system; b. Now can we parallel our work with electrical networks by circumventing the writing of differential equations and by defining impedances for mechanical components?

If so, we can apply to mechanical systems the problem-solving techniques learned in the previous section.

Taking the Laplace transform of the force-displacement column in Table 2. From now on we use this approach. We chose Eq. The alternative, however, is available. Many mechanical systems are similar to multiple-loop and multiple-node electrical networks, where more than one simultaneous differential equation is required to describe the system. In mechanical systems, the number of equations of motion required is equal to the number of linearly independent motions.Upcoming SlideShare.

Industrial control systems are used in industrial production. For example, a remote-controlled robot arm can be used to pick up material in a radioactive environment. It responds to an input by undergoing a transient response before reaching a steady-state response that generally resembles the input.

Additional Poles, 4. Full Name Comment goes here. This condition, called instability, could lead to self-destruction of the physical device if limit stops are not part of the design. Donnelley Jefferson City. No notes for slide.

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