二阶控制系统 英汉双语.docx

part control theory 2.2 second-order systemsfrom the frequency-domain viewpoint, system order refers to the highest power of s in the denominator of the closed-loop transfer function of a system. in the time-domain, system order refers to the highest derivative of the controlled quantity in the equation describing the control systems dynamics. system order is very significant parameter for characterizing a system. 在频域里，系统的阶次指的是系统的闭环传递函数分母s的最高次。在时域里，系统的阶次指的是描述控制系统动力学方程的最高阶导数。系统的阶次是一个非常重要的参数对于描述一个系统的特征。second-order systems are very important to the control-system engineering. this type of system characterizes the dynamics of many control-system applications found in the fields of servomechanisms, space-vehicle control, chemical process control, bioengineering; aircraft control systems, hip controls, etc. it is interesting to note that most control system designs are based on second order system analysis. even if the system is of higher order, as it usually is, the systems may be approximated by a second-order system in order to obtain a first approximation for preliminary design purposes with reasonable accuracy. a more exact solution can then be obtained in terms of departures from the performance of a second-order system.二阶系统是一个非常重要的控制系统。这种系统描述了很多控制系统应用的动力学在一些自动控制，空间飞行器控制，化工过程控制，飞船控制，生物工程，飞行控制系统，飞船控制等方面。要注意的是大多数控制系统的设计都是基于二阶系统的分析。尽管平时常见的更高阶的系统，可能会近似的看做二阶的系统为了获得近似值在初步的设计带有合理的准确性。一个更高的准确性结果可以被获得依据脱离二阶系统性能。our choice of a system to study is the use of a dc electric motor to position an inertial load through a gearbox. such a system is very common and illustrates the combination of electrical and mechanical theory using a common mathematical description, the laplace transform. the system is shown in schematic form in fig.2.13. in operation, the set point is generated by means of a potentiometer. the angular position of the potentiometer generates a proportional bipolar voltage according to the potentiometers transfer function, in volts per radian. this voltage is compared to the achieved position of the load as measured by another potentiometer. the error voltage is usually passed through an amplifier since the motor may require greater power levels than those obtained directly from the summing junction. the amplifier may be considered a simple gain that is adjustable in most cases. this transfer function is shown in fig.2.14. the voltage output from the amplifier drives the motor. it will be remembered that dc motors rotate due to the interaction of two magnetic fields, one in the stator and one in the rotor, and the rotational speed may be varied by controlling the strength of one of these fields. the stationary magnetic field may be generated by passing a current through the field winding or by using permanent magnets for small motors. the rotating field is generated by passing a current through the armature winding. based on the kirchhoffs method and newtons second law, the transfer function of the motor may be expressed aswhere r is resistance of the field winding, l is inductance of the field winding, is the motor torque constant with units of newton meters per ampere, j is total inertia referred to the motor shaft and c is the total damping, also referred to the motor shaft.我们选择一个通过变速器用直流电机作为惯性负载的系统来研究。这样一个系统是很常见的，并且说明了机电理论使用的都是常见的数学方法拉普拉斯变换图2.13是该系统的示意图。在操作中，通过电位计来设定标定值，角度的电位计通过电位计的传递函数生成一个正比例的双极电压，单位是v/rad。这个电压被另一个电位计测量并比较是非达到额定负载。因为电机通常需要比连接处（summing junction）更大的功率，所以误差电压通常是通过一个放大器的。在大多数情况下，放大器可以被当做一个简单的增益。图2.14显示了这个传递函数。电机是由放大器输出的电压驱动的。我们知道，直流电机的转动是由于两个相互作用的磁场，一个在定子上一个在转子上，并且转速可以通过改变其中一个磁场的强度来改变。电流通过励磁绕组或使用永久磁铁可以产生供电机使用的恒定磁场。电流通过点数绕组产生旋转的磁场。基于基尔霍夫定理和牛顿第二定律，电机的传递函数可以表示为： (2 .22)其中，r是励磁绕组的电阻，l是励磁绕组的电感，是电动机的转矩常数，单位是nm/a，j是电机的转动惯量，c是总阻尼，也被称为电机轴。 fig. 2.13 motor-positioned loadfig. 2.14 position control system block diagramby taking the potentiometer block kp to the right of the summing junction fig 2 .14, the closed-loop transfer function may be written as (2 .23) from this it may be observed that the differential equation relating the input and output is of degree 2; hence the position control system is of second order. the usual notation of second-order systems takes the form (2 .24) where is the damping ratio and n is the undamped natural frequency . it may be shown that for the system just described . (2 .25)subsequent analysis of second-order systems will use the generalized notation above , shown in block diagram form in fig .2 .15 , through reference back to the motor-driven position control system will be made from time to time to give a physical basis for the results developed . r c fig. 2.15 generalized closed-loop transfer functionstep responsewe assume that the initial conditions to zero and the input is a unit step . therefore,r( s) = 1/ s , and the laplace transform of the output can be written as (2 .26)if it is assumed that the system is underdamped , that is , 1 ) is given by (2 .30)while the critically damped response (= 1 ) is (2 .31)fig .2 .16 shows the step response