关于过程控制的外文翻译

毕业设计（论文）外文文献翻译

院系：电气与自动化学院

年级专业：2011级自动化2

姓名：

学号：

附件：System compensation

System compensation

1 Introduction

It was mentioned earlier that performance of a control system is measured by its stability, accucacy , and speed of response .in general these items are specified when a system is being designed to satisfy a specific task .Quite often the simultaneous satisfaction of all these requirements cannot be achieved by using the basic elements in the control system .Even after introducing controllers and feedback , we are limited as to the choice we may exercise in selecting a certain transient response while requiring a small steady state error. We will show how the desired transient as well as the steady state behavior of a system may be obtained by introducing compensatory elements (also called equalizer networks)into that control system loop .These compensation elements are designed so that they help achieve system performance , i. e .bandwidth, phase margin ,peak overshoot ,steady state error ,etc. without modifying the entire system in a major way .

Form our experience so far we recognize that any changes in system performance can be achieved only though varying the forward loop gain .Consider the third-order unity feedback system with the following forward loop transfer function,

()()()

K G s s s a s b =

++ From the Routh-Hurwitz criterion we know that stability requires ()K ab a b ≤+ We also know that the steady state error to a ramp input is

2

11lim [

]1()ss s ab e s s G s K

→=⋅=+ Obviously if it is necessary to minimize the steady state error, the gain K should be increased. Since K is constrained to a maximum value of a b （a +b ）,the minimum steady state error becomes

min 1

[]ss e a b

=

+ A further decrease in the error requires an increase in K which in turn has a destabilizing effect on the system ,It is therefore clear that the forward “gain game ”is rather limited .

2 the stabilization of unstable systems

Since the increasing of the forward loop gain K tends to destabilize a system, we must find ways it compensate it on such a way as to stabilize it again .It was established in Chapter 6 that the addition of

a pole in G(s)H(s) tends to have a destabilizing influence on system response .Can we the reverse the argument and say that the addition of a zero tends to have a stabilizing influence on system response? Let us answer this by considering an example .Consider the control system with its transfer function given in Example 6-5.

This system is unstable if K>c K

Now consider the same system but with the addition of a zero,

312(1)

()()(1)(1)

K s G s H s s s s τττ+=++

This is the type of function we obtain if we were to add derivative and proportional control to a third-order servomechanism .The characteristic equation becomes

321212312()(1)0(1)(1)

s s K s K

s s s τττττττ+++++=++

And the zeros of the characteristic equation are determined by

3212123()(1)0s s K s k τττττ+++++=

The Routh array becomes 3

s 12ττ (31K τ+)

2s 12ττ+ K 1b =

31212

12

(1)()K K τττττττ++-+

1s 1b 2b 2b =0 0s 1c ω 1c K =

For stability 10b ≥, and therefore

13231212()()0

K ττττττττ+-++>

Clearly ,with a proper selection of the time constants ,this may be satisfied .The Nyquist plot for this is shown in Fig.1