外文资料与翻译
PID Control
6.1 橄榄怎么腌制好吃Introduction
The PID controller is the most common form of feedback. It was an esntial element of early governors and it became the standard tool when process control emerged in the 1940s. In process control today, more than 95% of the control loops are of PID type, most loops are actually PI control. PID controllers are today found in all areas where control is ud. The controllers come in many different forms. There are standalone systems in boxes for one or a few loops, which are manufactured by the hundred thousands yearly. PID control is an important ingredient of a distributed control system. The controllers are also embedded in many special purpo control systems. PID control is often combined with logic, quential functions, lectors, and simple function blocks to build the complicated automation systems ud for energy production, transportation, and manufacturing. Many sophisticated control strategies, such as model predictive control, are also organized hierar
chically. PID control is ud at the lowest level; the multivariable controller gives the t points to the controllers at the lower level. The PID controller can thus be said to be the “bread and butter of control engineering. It is an important component in every control engineer’s tool box.
PID controllers have survived many changes in technology, from mechanics and pneumatics to microprocessors via electronic tubes, transistors, integrated circuits. The microprocessor has had a dramatic influence the PID controller. Practically all PID controllers made today are bad on microprocessors. This has given opportunities to provide additional features like automatic tuning, gain scheduling, and continuous adaptation.
6.2 Algorithm
We will start by summarizing the key features of the PID controller. The “textbook” version of the PID algorithm is described by:
6.1
where y is the measured process variable, r the reference variable, u is the control signal and e is the control error（e = − y）. The reference variable is often called the t point. The control signal is thus a sum of three terms: the P-term （which is proportional to the error）, the I-term （which is proportional to the integral of the error）, and the D-term （which is proportional to the derivative of the error）. The controller parameters are proportional gain K, integral time Ti, and derivative time Td. The integral, proportional and derivative part can be interpreted as control actions bad on the past, the prent and the future as is illustrated in Figure 2.2. The derivative part can also be interpreted as prediction by linear extrapolation as is illustrated in Figure 2.2. The action of the different terms can be illustrated by the following figures which show the respon to step changes in the reference value in a typical ca.
Effects of Proportional, Integral and Derivative Action
Proportional control is illustrated in Figure 6.1. The controller is given by D6.1E with Ti = and 咳嗽肺疼Td=0. The figure shows that there is always a steady state error in proportional control. The error will decrea with increasing gain, but the tendency towards oscillation will also increa.
Figure 6.2 illustrates the effects of adding integral. It follows from D6.1E that the strength of integral action increas with decreasing integral time Ti. The figure shows that the steady state error disappears when integral action is ud. Compare with the discussion of the “magic of integral action” in Section 2.2. The tendency for oscillation also increas with decreasing Ti. The properties of derivative action are illustrated in 神态描写片段Figure 6.3.
Figure 6.3 illustrates the effects of adding derivative action. The parameters K and Ti are chon so that the clod loop system is oscillatory. Damping increas with increasing derivative time, but decreas again when derivative time becomes too large. Recall that derivative action can be interpreted as providing prediction by linear extrapolation over the time Td. Using this interpretation it is easy to understand that derivative action does n
ot help if the prediction time T丝巾的各种围法d is too large. In Figure 6.3 the period of oscillation is about 6 s for the system without derivative Chapter 6. PID Control
什么是进程
Figure 6.1
Figure 6.2
Derivative actions cea to be effective when 数据上报Td is larger than a 1 s (one sixth of the period). Also notice that the period of oscillation increas when derivative time is incread.
A Perspective
There is much more to PID than is revealed by （6.1）. A faithful implementation of the equation will actually not result in a good controller. To obtain a good PID controller it is also necessary to consider。
Figure 6.3
∙Noi filtering and high frequency roll off
∙Set point weighting and 2 DOF
∙Windup
∙Tuning
∙Computer implementation
In the ca of the PID controller the issues emerged organically as the technology developed but they are actually important in the implementation of all controllers. Many of the questions are cloly related to fundamental properties of feedback, some of them have been discusd earlier in the book.
6.3 Filtering and Set Point Weighting
小孩哭闹Differentiation is always nsitive to noi. This is clearly en from the transfer function G(s) =s of a differentiator which goes to infinity for large s. The following example is also illuminating.
where the noi is sinusoidal noi with frequency w. The derivative of the signal is
The signal to noi ratio for the original signal is 1/an but the signal to noi ratio of the differentiated signal is w/an. This ratio can be arbitrarily high if w is large.
In a practical controller with derivative action it is there for necessary to limit the high frequency gain of the derivative term. This can be done by implementing the derivative term as
6.2
instead of D=sTdY. The approximation given by (6.2) can be interpreted as the ideal derivative sTd filtered by a first-order system with the time constant Td开题报告导师意见/N. The approximation acts as a derivative for low-frequency signal components. The gain, however, is limited to KN. This means that high-frequency measurement noi is amplified at most by a factor KN. Typical values of N are 8 to 20.
