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Introduction to Linear Control System
Introduction
Since the 1950 s, with the development of aerospace technology and control theory application scope expanding, increasingly obvious limitations of classical linear control theory, it can not meet the actual need, also can't solve the theory itself put forward some new problems. Promote research into linear system of this situation, after 1960 from the classical stage to the modern stage. American scholar R.E.kalman, first of all, the state space method is applied to the study of multivariable linear systems, put forward can controllability and observability of these two basic concepts, and corresponding criterion are put forward. In 1963, he concluded that reveal a linear system with e.g. Gilbert structure decomposition of important results, for the formation and development of the modern theory of the linear system has done pioneering work. After 1965, the modern theory of linear system theory and linear system theory and research methods such as multivariable frequency domain, new theory and new method of multivariable system. With the development of computer technology,in a linear system as an object of calculation method and computer aided design problem has also been widespread attention.
Main characteristics compared with the classical linear control theory, modern theory of linear system's main features are: (1) the object of study is usually multivariable linear systems, the classical theory mainly by the single input single output system as the research object. Therefore, the modern theory of linear system has a much larger scope. (2) in addition to the input variables and output variables, describing system state of internal state variables is considered, and the classical theory only considers external performance of the system (input and output relationship). Modern theory of linear system, therefore, consider a more comprehensive and more profound. (3) in the aspect of analysis and synthesis methods with time domain method is given priority to, and by using frequency domain method. The classical theory mainly using the method of frequency domain.Therefore, the modern theory of linear system can make full use of the two methods. And time domain method for dynamic description is more intuitive. (4) use more mathematical tools, in addition to the classic theory used in the Laplace transform, is widely used in modern linear system theory, matrix theory and the theory of differential equations, linear algebra for some problem is using the theory of functional analysis, group theory, ring, category theory and theory of complex functions such as advanced mathematics tool. Modern linear system theory, therefore, to explore a more general more complex problems.
Relation with other subjects of many practical systems (engineering systems, biological systems, economic systems, social systems, etc.) can be approximately describe linear system model, and linear system theory and method is more mature, therefore its application range is very wide. In aviation, aerospace, chemical, mechanical, electrical and other fields of technology, linear system theory are applied instance. In the field of science, control theory of linear system theory study not only for the other branch, provides a theoretical basis and has actual significance of mathematical research also puts forward some new problems.
The art of automatic control systems permeates life in all advanced societies today.Such systems art as a catalyst in promoting development. The automatic,the thermostat,the washer and dryer,the computer,the microprocessor,the space vehicles,and the control systems that have sped up the production and quality of manufactured goods all influence our way of life.Control systems are an integral component of any industrial society and are necessary for the production of goods required by an increasing world population.Technological developments have made it possible to travel to the moon and to explore outer space.The successful operation of space vehicles and the space shuttle depend on the proper functioning of the large number of control systems used in such ventures.
Assume that the toaster is set for the desired darkness of the toasted bread．The setting of the“darkness,”or timer,knob represents the input quantity,and the degree of darkness of the toast produced is the output quantity.If the degree of darkness is not satisfactory,because of the condition of the bread or some similar reason,this condition can in no way automatically alter the length of time heat is applied.Thus it can be said that the output quantity has no influence on the input quantity.The heater portion of the toaster,excluding the timer unit,represents the dynamic part of the overall system.
Another example is the dc shunt motor.For a given value of field current,a certain value of voltage is applied to the armature to produce the desired value of motor speed.In this case the motor is the dynamic part of the system,the applied armature voltage is the input quantity,and the speed of the shaft is the output quantity.A variation of the speed from the desired value,due to a change of mechanical load on the shaft,can in no way cause a change in the value of the applied armature voltage to maintain the desired speed.In this example it can also be said that the output quantity has n5 influence on the input quantity.
Systems in which the output quantity has no effect upon the input quantity are called open-loop control systems.The two examples just cited can be represented symbolically by a functional block diagram.The desired darkness of the toast or the desired speed of the motor is the command input;the selection of the value of time on the toaster timer or the value of voltage applied to the motor armature is represented by the reference-selector block;and the output of this block is identified as the reference input.The reference input is applied to the dynamic unit that performs the desired control function,and the output of this block i8 the desired output.
A person can be involved in the controlling actions of the systems above to sense the actual value of the output and compare it with the command input.If the output does not have the desired value,a person can alter the reference-selector position to achieve this value.Introducing the person provides a means through which the output is fed and the output is compared with the input.Any necessary change is then made in order to cause the output to equal the desired value.The feedback action therefore controls the input to the dynamic unit.Systems in which the output has an effect upon the input quantity are called closed-loop control systems.
To improve the performance of the closed-loop system so that the output quantity is maintained as close to the desired quantity as possible,the person can be replaced by a mechanical,electrical,or other form of comparison unit.The comparison between the reference input and the feedback signals results in an actuating signal that is the difference between these two quantities.The actuating signal acts to maintain the output at the desired value.
This system may now be properly called a closed-loop control system.The designation closed-loop implies the action resulting from the comparison between the output and input quantities in order to maintain the output at the desired value.Thus,the output is controlled in order to maintain the desired value.Examples of closed-loop control systems.A person selects and adjusts the desired room temperature(command input)and adjusts the temperature setting on the thermostat.A bimetallic coil in the thermostat is affected by the actual room temperature(output) and the reference-selector setting.If the room temperature is lower than the desired temperature,the coil strip alters its shape and causes a mercury switch closes. This activates the relay and in turn turns on the furnace．The furnace works and the room temperature gets higher. When the room temperature has reached the desired one,this deactivates the relay and in turn turns off the furnace.In this example,the bimetallic coil performs the function of comparator since the output(room temperature) is fed back directly to the comparator.The switch,relay,and furnace are the dynamic elements of this closed-loop control system.
A closed-loop control system of great importance to all multistory building is the automatic elevator.A person in the elevator presses the button corresponding to the desired floor.This produces an actuating signal which indicates the desired floor and activates the forward elements(control devices and elevator).As the elevator approaches the desired floor,the actuating signal decreases in value and,with the proper switching sequences,the elevator stops at the desired floor and the actuating signal is reset to zero.The closed-loop control system for the express elevator in the Sears Tower building in Chicago is designed so that it ascends or descends the 103 floors in just under 1minute with maximum passenger comfort.
The Air Force Materials Laboratory,Wright-Patterson Air Force Base,Ohio, has developed a robot under its Integrated Computer-Aided Manufacturing program for use on the production lines of aerospace manufacturing companies.The first"true" robot ,which is referred to as the 6cm Arm,looks like a gigantic artificial limb.This robot performs a number of production-line functions.Specifically,it performs drilling and routing operations on aircraft access panels ranging in size from12 in to 1 yd square.It can also do additional jobs like painting,welding,manipulating parts,assembly,and handling.The development of small,reliable and versatile minicomputers has permitted he practical development of robots which will have an increasingly important role in manufacturing.
The emphasis and urgency for practical large scale solar-energy systems has spurred the development of sun-following control systems.The movement of the sun in relation to the earth is nonuniform and often obscured by clouds.This sun follower has been designed to point at the sun within 1degree accuracy and to compensate for day-to-day changes in the sun's motion.This sun follower has essentially an open-loop drive actuated by a clock.There is a periodic sensing of the correct sun position,and corrections are made to reduce the sun-sensor error.The use of a microprocessor permits accurate sun following with trouble-free operation.This system can be used to control sun pointing of photovoltaic arrays,solar concentrators,or other devices that need to follow the sun in order to receive the maximum energy.
Desired performance can often be achieved.The design methods for control systems are covered in Chaps.6 to 9.Some systems require a precision in their performance that cannot be achieved by the some structure.Also,systems exist for which there are multiple inputs and/or multiple outputs.The design methods for such systems are often based on a representation of the system in terms of state variables.For example,position,velocity,and acceleration may represent the state variables of a position-control system.The definition of state-variable methods to achieve improved or sometimes optimal performance is presented in Chaps.12 to 18.The use of a digital computer to assist the engineer in the design process is emphasized throughput this book.
2. Definitions
From the preceding discussion the following definitions are evolved,based in part on the standards of the IEEE.
System:A combination of components that act together to perform a function not possible with any of the individual parts.The word system as used herein is interpreted to include physical,biological,organizational,and other entities,and combinations thereof,which can be represented through a common mathematical symbolism.The formal name systems engineering can also be assigned to this definition of the word system.Thus,the study of feedback control systems is essentially a study of an important aspect of systems engineering and its application.
Command input:The motivating input signal to the system,which is independent of the output of the system and exercises complete control over it(if the system is completely controllable).
Reference selector(reference input element)：73bhe unit that establishes the value of the reference input.The reference selector is calibrated in terms of the desired value of the system output.
Reference input:The reference signal produced by the reference selector,i.e.,the command expressed in a form directly usable by the system.It is the actual signal input to the control system.
Forward element(system dynamics):The unit that reacts to an actuating signal to produce a desired output.This unit does the work of controlling the output and thus may be a power amplifier. Output(controlled variable):The quantity that must be maintained at a prescribed value,i.e.,following the command input.
Open-loop control system:A system in which the output has no effect upon the input signal.
Feedback element:The unit that provides the means for feeding back the output quantity,or a function of the output,in order to compare it with the reference input.
Actuating signal:The signal that is the difference between the reference input and the feedback signal.It actuates the control unit in order to cause the output to have the desired value.
Closed-loop control system:A system in which the output has an effect upon the input quantity in such a manner as to maintain the desired output value.
Note that the fundamental difference between the open-and closed-loop systems is the feedback action,which may be continuous or discontinuous.Continuous control implies that the output is continuously fed back and compared with the reference input.In one form of discontinuous control the input and output quantities are periodically sampled and compared,i.e.,the control action is discontinuous in time.This type is commonly called a discrete-data or sampled-data feedback control system.A discrete-data control system may incorporate a digital computer which improves the performance achievable by the system.In another form of discontinuous control system the actuating signal must reach a prescribed value before the system dynamics reacts to it;i.e.,the control action is discontinuous in amplitude rather than in time.This type of discontinuous control system is commonly called an on-off or relay feedback control system.Both forms may be present in a system.In this text continuous control systems ale considered in detail since they lend themselves readily to a basic understanding of feedback control systems.Digital control systems are introduced in Chap.19.
With the above introductory material,it is proper to state a definition of a feedback control System:"A control system that operates to achieve prescribed relationships between selected system variables by comparing functions of these variables and using the comparison to effect control."In other books and papers on this subject the following terms may also be used.
Servomechanism(often abbreviated as servo):This term is often used to refer to a mechanical system in which the steady-state error is zero for a constant input signal.Sometimes by generalization it is used to refer to any feedback control system.
Regulator:This term is used to refer to systems in which there is a constant steady-state output for a constant signal.The name is derived from the early speed and voltage controls,called speed and voltage regulators.
The reader is cautioned to ascertain the meaning of a particular author. Throughout this text an attempt is made to conform to the IEEE definitions.
3.Engineering Control General Nature
In general,a control problem can be divided into the following steps:
1)A set of performance specifications is established.
2)As a result of the performance specifications a control problem exists.
3)A set of differential equations that describe the physical system is formulated.
4)Using the conventional contr01．theory approach aided by available or specially written computer programs:
A.The performance of the basic(or original)system is determined by application of one of the available methods of analysis(or a combination of them).
B.If the performance of the original system does not meet the required specifications,cascade or feedback compensation must be added to improve the response.
5)Using the modem control-theory approach,the designer specifies an optimal performance index for the system.With the help of computer programs,the design yields the necessary structure to minimize the specified performance index,thus producing an optimal system.
6)An alternate modern control-theory approach is the method of entire eigenstruture assignment.First the desired closed-loop eigenvalue spectrum is selected.Then the desired contribution of each mode to each state and output response is selected.The eigenvector spaces are identified,and the eigenvectors are assigned which best meet the selected modal composition of the states and outputs.
Design of the system to obtain the desired performance is the control problem.The necessary basic equipment is then assembled into a system to perform the desired control function.To a varying extent,most system are nonlinear.In many cases the nonlinearity is small enough to be neg1ected,or the limits of operation are small enough to allow a linear analysis to be made.In this textbook linear systems or those which can be approximated as linear systems are considered. Because of the relative simplicity and straightforwardness of this approach,the reader can obtain a thorough understanding of linear systems.After mastering the terminology,definitions,and methods of analysis for linear control systems,the engineer will find it easier to undertake a study of non1inear systems.A method of linearizing a nonlinear system is included in Chap.14.
A basic system has the minimum amount of equipment necessary to accomplish the control function.The differential equations that describe the physical system are derived,and an analysis of the basic system is made.If the analysis indicates that the desired performance has not been achieved with this basic system,additional equipment must be inserted into the system.Generally this analysis also indicates the characteristics for the additional equipment that are necessary to achieve the desired performance.After the system is synthesized to achieve the desired performance,based upon a linear analysis．final adjustments can be made on the actual system to take into account the nonlinearities that were neglected.It should be noted that a computer is generally used in the design depending upon the complexity of the system.
中文翻译：
线性系统导论
1.引言
20世纪50年代以后，随着航天等技术的发展和控制理论应用范围的扩大，经典线性控制理论的局限性日趋明显,它既不能满足实际需要,也不能解决理论本身提出的一些新问题。这种状况推动线性系统的研究，在1960年以后从经典阶段发展到现代阶段。美国学者R.E.卡尔曼首先把状态空间法应用于对多变量线性系统的研究，提出了能控性和能观测性这两个基本概念，并提出相应的判别准则。1963年他又和E.G.吉尔伯特一起得出揭示线性系统结构分解的重要结果，为现代线性系统理论的形成和发展作了开创性的工作。1965年以后，现代线性系统理论又有新发展。出现了线性系统几何理论、线性系统代数理论和多变量频域方法等研究多变量系统的新理论和新方法。随着计算机技术的发展，以线性系统为对象的计算方法和计算机辅助设计问题也受到普遍重视。
主要特点 与经典线性控制理论相比，现代线性系统理论的主要特点是：
①研究对象一般是多变量线性系统，而经典理论主要以单输入单输出系统为研究对象。因此，现代线性系统理论具有大得多的适用范围。
②除输入变量和输出变量外，还着重考虑描述系统内部状态的状态变量，而经典理论只考虑系统的外部性能（输入与输出的关系）。因此，现代线性系统理论所考虑的问题更为全面和更为深刻。
③在分析和综合方法方面以时域方法为主，兼而采用频域方法。而经典理论主要采用频域方法。因此，现代线性系统理论能充分利用这两种方法。而时域方法对动态描述要更为直观。
④使用更多的数学工具，除经典理论中使用的拉普拉斯变换外，现代线性系统理论大量使用线性代数、矩阵理论和微分方程理论，对某些问题还使用泛函分析、群论、环论、范畴论和复变函数论等较高深的数学工具。因此，现代线性系统理论能探讨更一般更复杂的问题。
与其他学科的关系 很多实际系统（工程系统、生物系统、经济系统、社会系统等）都可用线性系统模型近似地描述，而线性系统理论和方法又比较成熟，因此它的应用范围十分广泛。在航空、航天、化工、机械、电机等技术领域中，线性系统理论都有应用实例。在科学领域中，线性系统理论的研究不但为控制理论的其他分支提供了理论基础，而且对数学研究也提出了一些有实际意义的新问题。
今天，在所有发达的社会中，自动控制系统已渗入到人们的生活中。这些系统已成为推动社会进步与发展的催化剂。如自动烤箱、自动温度仪、自动洗衣机和干衣机、计算机、微处理器、航天器，以及那些提高生产率和产品质量的控制系统，都影响着我们的生活方式。控制系统对任何工业社会都是整体组成部分，是为日益增长的世界人口生产必需物质所必需的。技术的发展使人类有可能登上月球和探索外层空间。航天器和航天飞机的成功运行，就是依赖于在这些航天器和航天飞机中运用了大量的控制系统的独特功能。
假设已将烤箱设置到了人们所希望的面包的烤制色度。“色度”(也即定时)的旋钮就表示输入量，而烤制过程所产生的“色度”即为输出量。如果因为面包的因素或一些类似的原因，使色度不是令人满意的，而这些因素又不会自动改变加热时间，这种情况便称之为输出量不影响输入量。烤箱的加热部件(不含定时器单元)是整个系统的动态部分。
另一个例子是直流并励电动机。在某一给定的励磁电流下，在电枢上施加一定的电压便可产生所期望的电动机转速。在这种情况下，电动机是系统的动态部分，转子电压是输入量，转轴的转速是输出量。由于转轴上的机械负载发生变化而使转速偏离理想值而引起的转速变化，并不会引起施加于转子上的外加电压发生变化，因而并不会将转子的转速维持在理想值。这个例子也称为输出量不影响输入量。
这种输出量不影响输入量的系统，称之为开环控制系统。刚才所讲的这两个例子可以用功能方块图来描述。烤箱的期望色度或者电动机的转速为指令输入，而烤箱的定时器的时间选择，或者作用于电动机电枢上的电压用参考选择模块来代表，而该模块的输出便视为参考输入。参考输入作用于执行期望的控制功能动态单元上，而该模块的输出便是期望的输出。
人可以介入上述控制系统的控制行为，从而获取实际的输出值，并将其与控制的输入量进行比较。如果输出量没达到期望值，人可以通过调节参考选择位置来达到期望值。人的引入便提供了一种方式，通过这种方式将输出反馈回来，并将其与输入进行比较。然后进行必要的调整，以使输出达到期望值。这样反馈的控制作用使输入成了动态的量，这种输出能对输入量产生影响的系统，称为闭环控制系统。
为了提高闭环系统的性能，使输出尽可能达到期望值，可以采用机械装置、电子装置或者其他形式的比较单元来替代人的作用。参考输入与反馈信号进行比较，便得到一个这两个信号之差的实际信号。实际信号作用的结果是将输出信号维持在期望值。
确切地说，刚才所讲的这种系统便可称为闭环控制系统。闭环设计指的是一种行将产生结果的行为，其进行输出与输入量的比较，以将输出维持在期望值。因此，为将输出量维持在期望值，其本身是受控制的。下面给出闭环控制系统的几个例子。某人选择和调节房间的温度，使其达到某一期望值(指令输入)，因而便在恒温器上设置该温度。恒温器上的双金属片是受房间实际温度(输出)和参考选择器的设定影响的。如果房间的温度低于期望温度，双金属片就会产生变形导致水银开关闭合，致使继电器动作，电炉加热，房间升温。当房间温度达到期望温度，继电器断开，电炉关闭。在这个例子中，由于房间的温度(输出)直接反馈给了比较器，因此双金属片起到了比较器的作用。开关、继电器和电炉是这个闭环控制系统的动态元件。
对所有的多层建筑来说，自动电梯是非常重要的一个闭环控制系统。人们在电梯里按一下想要到的楼层按钮，就产生了一个激励信号，表明了其所期望达到的楼层，并且就此启动了前端元件(控制设备和电梯)。当电梯接近特定楼层时，激励信号就减小，相应的顺序开关动作，电梯便停在指定的楼层，且此时激励信号复位归零。芝加哥的SEARS．TOWER建筑内的快速电梯，其闭环控制系统的设计已做到了在楼内上升或者下降103层的过程可在1分钟之内完成，且乘客的感觉很舒适。
俄亥俄州WRIGHT-PATTERSON空军基地的空军材料实验室，开发了一种在集成计算机辅助制造程序环境下工作的机器人，并已应用于航空和航天器制造公司的生产线上。第一台“真”机器人，即6cm机器臂，看上去就像一个庞大的人造手臂。这个机器人能完成生产线上的许多工作，尤其是能在大小从12平方英寸到1平方码的飞机检修板上进行钻孔和切割操作。其还能干一些其他的事情，比如油漆、焊接、操控、装配、运作。小巧、可靠、多功能的微型计算机的开发，使得那些将在制造业中扮演越来越重要角色的机器人得到了实实在在的发展。
对开发大型实用的太阳能利用系统的重视程度和紧迫性，大大地刺激了阳光跟踪控制系统的发展。相对于地球来说，阳光的运动是无规律的，且时常因乌云密布而变得分辨不清。这种太阳跟随器能在精度范围内指示太阳的位置，并能对太阳在一天内的运动变化量进行补偿。实际上，其内部装有一个由时钟驱动的开环驱动器，其能对太阳的正确位置进行周期性的传感，并对其进行校正以减小太阳传感器的误差。微处理器的运用能实现对太阳进行无故障的精确跟踪。该系统可用来控制太阳能光电池阵列、日光采集器，以及其他需要跟踪太阳的设备的日照点，从而使其能从太阳获得最大的能量。
人们所期望的性能是常常可以获得的。控制系统的设计方法涵盖在第6章到第9章的内容之中。有一些系统在运行过程中所需要的精度是某些方法所达不到的。此外，需要有多个输入端和(或)多个输出端的系统是存在的。设计这类系统时常常要用状态变量来描述，例如，位置、速度、加速度都可以表示为位置控制系统中的状态变量。为提高性能，或者有时是为优化性能而采用的状态变量法的定义，在第12至18章中有所论述。本书一直都在强调应运用数字式计算机来帮助工程技术人员进行设计。
2．定义
在部分ⅡEEE标准的基础上，根据以上所述之内容可引出以下定义：
系统：一些共同作用，以实现任何单个元件无法独立完成的某一功能的所有元件的集合体。此处所说的“系统”，可理解为包括物理的、生物的、组织的和其他能用通用的数学符号表示的实体及其集合。其正式的名称“系统工程”也可用作表示“系统”的定义。因而，对反馈控制系统的研究，实际上就是对系统工程及其应用研究的一个重要方面。
指令输入：施加于系统的输入激励信号，与系统的输出无关，且受完整控制(如果系统是完全能控的话)。
参考调节器(参考输入元件)：为设立参考输入值的单元，因此也就是校验系统的理想输出值的元件。
参考输入：由参考调节器所产生的参考信号，也即以系统可直接使用的形式表示的给定指令，其为施加于控制系统的实际输入信号。
前端通道(系统的动态部分)：该单元对实际信号作出反应，从而产生理想的输出信号。其执行着控制输出的功能，因而可能是一个功率放大器。
输出(受控变量)：该值必须保持为某一规定值，即必须跟随给定的输入。
开环控制系统：输出对输入无任何影响的系统。
反馈通道：该单元为输出量的反馈提供通道(也即一种输出功能)，以便将其与参考输入信号相比较。
激励信号：该信号为参考信号与反馈信号值之差，其激励控制单元，以便产生输出，从而得到理想的输出。
闭环控制系统：一种输出对输入有影响的系统，通过这种影响，可确保获得理想的输出值。
要注意的是，开环系统与闭环系统的根本差别就在于反馈的作用，这种反馈可以是连续的，也可以是断续的。连续控制是指连续地进行反馈，并令其与参考输入进行比较。有一种断续控制的方式，其周期性地对输入和输出量进行采样并比较，即控制在时间上是不连续的。这种类型的控制方式，一般称之为离散数据或采样数据反馈控制系统。离散控制系统可与数字式计算机相结合，以提高系统的性能。在另一种断续的控制系统中，其激励信号必须达到某一设定值，系统对其动态响应才会出现，也就是说，控制作用在大小上而不是在时间上是断续的。这种断续控制系统，通常便称之为开关或后续反馈控制系统。这两种类型的控制可出现在同一个系统中。由于对连续控制系统的学习，可使读者对反馈控制系统有一个基本的认识，因此本文将对其进行详细的分析。而数字控制系统将在第19章中进行介绍。
根据以上介绍，可对反馈控制系统做出如下恰当定义： “反馈控制系统是这样一种系统，其通过对系统中的那些变量进行比较，并根据比较结果进行有效控制，从而使所选取的各系统变量之间实现指定的关系”。在有关这方面的书籍和论文中，还可能会用到以下术语：
随动系统(常缩写为servo)：该术语常用来表示这样一种系统，对应于恒定的输入信号来说，其稳态误差为零，有时可泛指任何一种反馈控制系统。
调节器：该术语是指对应于恒定的输入信号，具有恒定的稳态输出的系统。其名称来源于早期的转速和电压控制器，当时称作转速和电压调节器。
作者(对以上所述的定义表述)是很考究的，读者应该明了作者的这种意图。在整篇文章中，作者都始终在按照]EEE的定义进行表述。
3．控制工程的一般特征
一般说来，处理控制工程问题的步骤可分为以下几步：
1)确立全部技术性能要求。
2)根据技术性能要形成控制问题。
3)写出一组描述物理系统的微分方程表达式。
4)运用传统的控制理论方法，辅之以现成的或专门编制的计算机程序，并注意以下事项：
A．基本(或者说是初始)的系统性能，取决于所采用的几种分析方法中的某一种，或者这几种方法的结合；
B．如果初始系统的性能未达到技术性能的要求，就必须增加串联或反馈补偿环节，以提高响应效果。
5)运用现代控制理论方法，设计者给系统确定一个最优性能指标。在计算机程序的帮助下，将得出必要的设计框架，使给定的性能指标数尽可能地少，这样便产生了一个最优化系统。
6)运用现代系统控制理论的另一种方法，就是完全特征结构方式。首先选择一组所需的闭环特征值，然后再选定每种方式对每一个状态及输出响应的作用。这样便可得出特征向量空间，从而指定最能满足所选择的模型(其由状态量和输出量组成)．的特征向量。
为得到期望的性能指标而进行的系统设计就是一个控制问题。然后再将必需的基本设备装配到系统中去，以执行所要求的控制功能。大多数系统，在不同程度上都是非线性的。然而在多数情况下，其非线性程度是很小的，以至于可以忽略不计，或者是其对运行的限制程度是很小的，小到可以采用线性的分析方法对其进行分析。本书所讲的都是线性系统，或者是可近似看作线性的非线性系统。因为这种方式相对来说比较简单和直观，所以读者能够对线性系统得到一个很全面的了解。控制系统的工程师们在掌握了线性系统的术语、定义以及分析方法之后，将会发现进行非线性系统的研究就比较容易了。将非线性系统线性化的方法，在第14章有所阐述。
每一个基本系统，都有一个完成控制功能前提下的最小装置数量。描述物理系统的微分方程已推导得出，对基本系统进行分析的方法也已获取。如果分析结果表明，采用这种基本系统不能得到预期的性能，必须在系统中再安装一些附加的设备。通常情况下，这种分析还会指出为使系统达到期望性能所需附加装置的特性。在系统几经组合而达到了预期的性能之后，便进行线性分析。在线性分析的基础上进行实际系统的调整，调整过程中，再将那些被忽略的非线性因素考虑进去。应该指出的是，根据系统的复杂程度，通常可用计算机进行辅助设计。