Control Systems Engineering, Sixth Edition by Norman S. Nise Advanced Electronic Communications Systems Wayne Tomasi Sixth Edition Hanselman, _Stephen_Holiday,_Ryan_The_daily_stoi(zlibraryexau2g3p_onion).pdf The Daily. Download Control Systems Engineering By Norman S. Nise – Nise's Control Systems Engineering takes a practical approach, presenting clear and complete . Apago PDF Enhancer E1FFIRS 11/04/ Page 3 CONTROL SYSTEMS ENGINEERING Sixth Edition Norman S. Nise California.
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For the sixth edition of Control Systems Engineering, this suite offers professors . Please consult Appendix H at soundofheaven.info 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 SYSTEMS ENGINEERING. Sixth Edition. Norman S. Nise. California State Polytechnic University, Pomona. WILEY. John Wiley & Sons, Inc.
We assume that these mechanical effects are negligible and that the voltage across a potenti- ometer changes instantaneously as the potentiometer shaft turns. Analyze, design, and test to see that requirements and specifications are met. Please consult Appendix H at www. The author would like to thank John Wiley Sons, Inc. Control systems are also useful in remote or dangerous locations. Views Total views.
At the zeros of G s and the poles of H s 6. If any branch of the root locus is in the rhp, the system is unstable. If the branch of the root locus is vertical, the settling time remains constant for that range of gain on the vertical section. If the root locus is circular with origin at the center Determine if there are any break-in or breakaway points Number of branches, symmetry, starting and ending points The zeros of the open loop system help determine the root locus.
The root locus ends at the zeros. Thus, the zeros are the closed-loop poles for high gain. Not symmetric; On real axis to left of an even number of poles and zeros Chapter 8: On real axis to left of an even number of poles and zeros c.
On real axis to left of an even number of poles and zeros d. Yes e. 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. 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.
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. 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. Again, the system position will change with a disturbance, such as an additional force, and the system will not detect or correct for the disturbance. If the professor adds a fourth chapter—a disturbance—you are an open-loop system if you do not detect the disturbance and add study time to that previously calculated.
The result of this oversight would be a lower grade than you expected.
Closed-Loop Feedback Control Systems The disadvantages of open-loop systems, namely sensitivity to disturbances and inability to correct for these disturbances, may be overcome in closed-loop systems. The generic architecture of a closed-loop system is shown in Figure 1. The input transducer converts the form of the input to the form used by the controller. An output transducer, or sensor, measures the output response and converts it into the form used by the controller.
For example, if the controller uses electrical signals to operate the valves of a temperature control system, the input position and the output temperature are converted to electrical signals. The input position can be converted to a voltage by a potentiometer, a variable resistor, and the output temperature can be converted to a voltage by a thermistor, a device whose electrical resistance changes with temperature.
The first summing junction algebraically adds the signal from the input to the signal from the output, which arrives via the feedback path, the return path from the output to the summing junction. In Figure 1. The result is generally called the actuating signal. Under this condition, the actuating signal is called the error. The closed-loop system compensates for disturbances by measuring the output response, feeding that measurement back through a feedback path, and comparing that response to the input at the summing junction.
If there is any difference between the two responses, the system drives the plant, via the actuating signal, to make a correction.
Closed-loop systems, then, have the obvious advantage of greater accuracy than open-loop systems. They are less sensitive to noise, disturbances, and changes in the environment. Transient response and steady-state error can be controlled more conveniently and with greater flexibility in closed-loop systems, often by a simple adjustment of gain amplification in the loop and sometimes by redesigning the controller. We refer to the redesign as compensating the system and to the resulting hardware as a compensator.
On the other hand, closed-loop systems are more complex and expensive than open-loop systems. A standard, open-loop toaster serves as an example: It is simple and inexpensive. A closed-loop toaster oven is more complex and more expensive since it has to measure both color through light reflectivity and humidity inside the toaster oven. Thus, the control systems engineer must consider the trade-off between the simplicity and low cost of an open-loop system and the accuracy and higher cost of a closed-loop system.
In summary, systems that perform the previously described measurement and correction are called closed-loop, or feedback control, systems.
Systems that do not have this property of measurement and correction are called open-loop systems. Computer-Controlled Systems In many modern systems, the controller or compensator is a digital computer.
The advantage of using a computer is that many loops can be controlled or compensated by the same computer through time sharing. Furthermore, any adjustments of the 1. The computer can also perform supervi- sory functions, such as scheduling many required applications.
For example, the space shuttle main engine SSME controller, which contains two digital computers, alone controls numerous engine functions.
It monitors engine sensors that provide pressures, temperatures, flow rates, turbopump speed, valve positions, and engine servo valve actuator positions. The controller further provides closed-loop control of thrust and propellant mixture ratio, sensor excitation, valve actuators, spark igniters, as well as other functions Rockwell International, We now expand upon the topic of performance and place it in perspective as we define our analysis and design objectives.
For example, we evaluate its transient response and steady-state error to determine if they meet the desired specifications. A control system is dynamic: It responds to an input by undergoing a transient response before reaching a steady-state response that generally resembles the input.
We havealreadyidentified these two responses and cited a position control system an elevator as an example. In this section, we discuss three major objectives of systems analysis and design: We also address some other design concerns, such as cost and the sensitivity of system performance to changes in parameters.
Transient Response Transient response is important. In the case of an elevator, a slow transient response makes passengers impatient, whereas an excessively rapid response makes them uncomfortable. If the elevator oscillates about the arrival floor for more than a second, a disconcerting feeling can result.
Transient response is also important for structural reasons: Too fast a transient response could cause perma- nent physical damage. In this book, we establish quantitative definitions for transient response.
We then analyze the system for its existing transient response. Finally, we adjust parameters or design components to yield a desired transient response—our first analysis and design objective.
As we have seen, this response resembles the input and is usually what remains after the transients have decayed to zero. For example, this response may be an elevator stopped near the fourth floor or the head of a disk drive finally stopped at the correct track. We are concerned about the accuracy of the steady-state response. An antenna tracking a satellite must keep the satellite well within its beamwidth in order not to lose track.
Stability Discussion of transient response and steady-state error is moot if the system does not have stability. In order to explain stability, we start from the fact that the total response of a system is the sum of the natural response and the forced response. When you studied linear differential equations, you probably referred to these responses as the homogeneousandtheparticularsolutions,respectively.
Naturalresponsedescribesthe way the system dissipates or acquires energy. The form or nature of this response is dependent only on the system, not the input. On the other hand, the form or nature of the forced response is dependent on the input. In some systems, however, the natural response grows without bound rather than diminish to zero or oscillate.