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1、p94The transfer function can be obtained in several ways.One method is purely mathematical and consists of taking the Laplace transform of the differential equations describing the components or system and then solving for the transfer function;nonzero initial conditions, when they occur, are treated as additional inputs.A second method is experimental.A known input(sinusoids and steps are commonly used)is apply to the system, the output is measured, and the transfer function is constructed from operating data and combination of the known transfer functions of the individual elements.This combination or reduction proce is termed block diagram algebra.2、p93 In Eq.(2-1B-2)the denominator D(s)of the transfer function is called the characteristic function since it contains all the physical characteristics of the system.The characteristic equation is formed by setting D(s)equal to zero.The roots of the characteristic equation determine the stability of the system and the general nature of the transient response to any input.The numerator polynomial N(s)is a function of how the input enters the system.Consequently, N(s)does,however, along with the specific input, determine the magnitude and sign of each transient mode and thus establishes the shape of the transient response as well as the steady-state value of the output.3、p94 The Laplace transformation comes from the area of operational mathematics and is extremely useful in the analysis and design of linear systems.Ordinary differential equations with constant coefficients transform into algebraic equations that can be used to implement the transfer function concept.Furthermore, the Laplace domain is a nice place in which to work, and transfer functions may be easily manipulated, modified, and analyzed.The designer quickly becomes adept in relating changes in the Laplace domain to behavior in the time domain without actually having to solve the system equations.When time domain solutions are required, the Laplace transform method is straightforward.The solution is complete, including both the homogeneous(transient)and particular(steady-state)solutions, and initial conditions are automatically included.Finally, it is easy to move from the Laplace domain into the frequency domain.4、p96 Analytical techniques require mathematical models.The transfer function is a convenient model form for the analysis and design of stationary linear systems with a limited number of differential equations and by block diagram algebra.From the deferential or intergro-differential equations describing the behavior of a particular plant, proce, or component, using the Laplace transformation and its properties can develop the transfer functions.5、p97 The stability of a continuous or discrete-time system is determined by its response to inputs or disturbance.Intuitively, a stable system is one that remains at rest(or in equilibrium)unle excited by an external source and returns to rest if all excitation are removed.The output will pa through a transient phase and settle down to a steady-state response that will be of the same form as, or bounded by, the input.If we apply the same input to an unstable system, the output will never settle down to a steady-state phase;it will increase in an unbounded manner, usually exponentially or with oscillations of increasing amplitude.6、p97 Stability can be precisely defined in terms of the impulse responsey(t)of a continuous system, or Kronecker delta responsey(k)of a discrete-time system, as follows:

A continuous(discrete-time)system is stable if its impulse responsey(t)(Kronecker delta responsey(k))approaches zero as time approaches infinity.An acceptable system must at minimum satisfy the three basic criteria of stability, accuracy, and a satisfactory transient response.These three criteria are implied in the statement that an acceptable system must have a satisfactory time response to specified inputs and disturbances.So, although we work in the Laplace and frequency domains for convenience, we must be able to relate these two domains, at least qualitatively, to the time domain.7、p99 The Routh Criterion: All the roots of the characteristic equation have real parts if and only if the elements of the first column of the Routh table have the same sign.Otherwise, the number of roots with positive real parts is equal to the number of changes of sign.The Hurwitz criterion is another method for determining whether all the roots

of the characteristic equation of a continuous system have negative real parts.It has the same principle with the Routh criterion in substantial although their forms or patterns are different, so they are commonly called Routh-Hurwitz criterion.8、The three basic performance criteria for a control system are stability, acceptable steady-state accuracy, and an acceptable transient response.With the system transfer function known, the Routh-Hurwitz criterion will tell us whether or not a system is stable.If it is stable, the steady-state accuracy can be determined for various types of inputs.To determine the nature of the transient response, we need to know the location in the s plane of the roots of the characteristic equation.Unfortunately, the characteristic equation is normally unfactored and of high order.9、The root locus technique is a graphical method of dertermining the location of the roots of the characteristic equation as any single parameter, such as a gain or time constant, is varied from zero to infinity.The root locus, therefore, provides information not only as to the absolute stability of a system but also as to its degree of stability, which is another way of describing the nature of the transient response.If the system is unstable or has an unacceptable transient response, the root locus indicates poible ways to improve the response and is a convenient method of depicting qualitatively the effects of any such changes.10、If the part of the real axis between two o.l.poles(o.l.zeros)belongs to the loci, there must be a point of breakaway from, or arrival at, the real axis.If no other poles and zeros are close by, the breakaway point will be halfway.In Fig.2-3A-2d, adding the polep3pushes the breakaway point away;a zero at the position ofp3would similarly attract the breakaway point.11、The frequency transfer function of a system or of its KZjPjfunction can be represented either by the single Nyquist diagram（a polar plot）or by plots of the amplitude ratio and the phase angle against the input（forcing）frequency.It is customary to plot the amplitude ratio in decibels and the phase angle in degrees against the common logarithm of the input frequency.In this form, the

two plots are known as Bode plots(after H.W.Bode).12、In Bode plots, the magnitude M in dB and the phase angle  in degrees are plotted against  on semilog paper.The development has shown the following：Bode magnitude and phase-angle plots of KZjPj are obtained by summing those of its elementary factors.These plot are much easier to make than polar plots or Nyquist diagrams, and can readily be interpreted in terms of different aspects of system performance.13、the plots are the mirror images of the corresponding integrator relative to the 0dB and 0axes.This is also true for the leads corresponding to the simple and quadratic lag below.The asymptotes meet at the break frequency or corner frequency given by1（or）on the normalized plot.14、Gain factor compensation: It is poible in some cases to satisfy all system specification by simple adjusting the open-loop gain factor K.Adjusting of the gain factor K does not affect the phase angle plot.It only shifts the magnitude plot up or down to correspond to the increase or decrease in K.15、Lead compensation: The addition of a cascade lead compensator to a system lowers the overall phase angle curve in the low-to-mid-frequency region.Lead compensation is normally used to increase the gain and/or phase margins of a system or increase its bandwidth.An additional modification of the Bode gain KB is usually required with lead networks.16、Lag compensation: The lag compensation is employed in some cases to decrease the bandwidth of the system, and it is also used to improve the relative stability for a given value of error constant, or to reject the noise of high-frequency.17、Lag-lead compensation: It is sometimes desirable to simultaneously employ both lead and lag compensation.Although one each of these two networks can be connected in series to achieve the desired effect, it is usually more

convenient to mechanize the combined lag-lead compensator.18、The transfer function can be obtained in several ways.One method is purely mathematical and consists of taking the Laplace transform of the differential equations describing the components or system and then solving for the transfer function;nonzero initial conditions, when they occur, are treated as additional inputs.A second method is experimental.A known input(sinusoids and steps are commonly used)is applied to the system, the output is measured, and the transfer function is constructed from operating data and curves.The transfer function for a subsystem or complete system is often obtained by proper combination of the known transfer functions of the individual elements.This combination or reduction proce is termed block diagram algebra.19、Design of a feedback control system using Bode techniques entails shaping and reshaping the Bode magnitude and phase angle plots until the system specifications are satisfied.These specifications are most convenient expreed in terms of frequency-domain figures of merit such as gain and phase margin for the transient performance and the error constants for the steady-state time-domain response.And shaping the asymptotic Bode plots of continuous-time systems by cascade or feedback compensation is a relatively simple procedure.